/
Автор: Raymer D.P.
Теги: modeling construction aircraft modeling design for homebuilders simplified aircraft design
ISBN: 0-9722397-0-7
Год: 2003
Текст
Dan Raymer's SIMPLIFIED AIRCRAFT DESIGN FOR HOMEBUILDERS By Danie! P. Raymer, Ph.D. President, Conceptual Research Corporation
Dan Raymer's SIMPLIFIED AIRCRAFT DESIGN FOR HOMEBUILDERS ISBN 0-9722397-0-7 Library of Congress Control Number: 2002094899 First Edition 2003 Copyright @ 2003 by Daniel P. Raymer. Printed and bound in the United States of America. All Rights Reserved including translation into foreign languages and conversion to electronic media. No part of this book may be reproduced or transmitted in any form or by any means without written permission from the publisher, except by a reviewer who may quote brief passages in a review. For information please contact Design Dimension Press. The author and publisher have endeavored to ensure the accuracy and completeness of information contained in this book, but assume no responsibility for errors, inaccuracies, omissions, or any inconsistency herein. All information herein is used at readers' own risk and no liability shall be assumed by the author or publisher for the use of any information herein. ATTENTION CORPORATIONS, UNIVERSITIES, HIGH SCHOOLS, AND AVIATION CLUBS AND ORGANIZATIONS: Quantity discounts are available on bulk purchases of this book. For information please contact Design Dimension Press. Pubtished by Design Dimension Press, Los Angeies, CA, USA (a subsidiary of Conceptual Research Corporation) PO Box 923156, Syimar, CA 91392 ddp@aircraftdesign.com 11
DEDICATION This book is dedicated to my technical heroes - Wilbur and Orville Wright. Not only did they solve the flight control questions that stumped their contemporaries; they also essentially invented analytical propeller design, parametric wind tunnel testing, and the whole process of scientific aircraft conceptual design. Another contribution - they correctly perceived that flying an aircraft would be a trained skill, and they taught themselves that skill over a careful three-year period prior to the first powered flight. Congratulations to them on the 100^ anniversary of their first flight. Too bad about the windstorm - if the Flyer hadn't been wrecked, their afternoon flights would have gone for miles. Special thanks to my reviewers - Peter Garrison, Todd Hodges, David Lednicer, Michael Niu, and David Raymer. As always, thanks to those who taught me - the list grows each day.
(This page intentionally blank) IV
FOREWORD BY PETER GARRISON (author of Technicalities Column, j%46L4ZZME, desigpier of Melmoth 1 & 2) You have to be crazy to want to design your own airplane. Welcome to the club. I started thinking about it when I was 20, began the design of the real thing when I was 25, and flew it when I was 30. How much of every waking hour I spent thinking about airplane design I don't know, but I can say that the subject ranked right up there with women and money. Since I had no engineering training or mathematics beyond high school algebra, I had a great deal to learn. The enterprise requires a lot of miscellaneous knowledge that can be acquired only piecemeal and sometimes by chance; the annoying thing is that you want to get started right away. When I began, there were fewer places to learn about it than there are today. To find a yellowing copy of K. D. Wood's ?lzrp/ane Design was cause for rejoicing; and yet I might extract from the whole book only one or two tidbits that applied to the problem at hand. Things are different today. Quite a few amateurs have designed successful planes, and even made livings from selling plans and kits. The EAA and the Internet disseminate information widely. The personal computer has put tremendous analytical and graphical power into the hands of designers. There is as much learning to be done as ever, but much less searching. The great problem for the beginning designer is in/egraiion: to know how to think about the multifaceted task ahead, in which every choice influences every other one so intimately that it seems impossible to know where to start. Dan Raymer has a knack for cutting through this Gordian knot. His remarkable textbook, ^Zrcrq/f Design: ^4 Concept#/ yfyproaei, manages to bring together every aspect of airplane design at the precise intersection of the theoretical and the practical. It combines professional experience with an unusual directness and clarity of expression. The book you hold in your hands does the same, but at an even more accessible level, and with reference to the class of airplane that an amateur designer is likely to undertake. It shows you how to think about the problem; what steps to take to begin a design, and in what order. It introduces you to the complete spectrum of the designer's concerns and arms you with a vocabulary of concepts that you will flesh out through further reading. It won't - can't - be the last book on airplane design that you buy; but it should be the first. I wish Td had it in 1963. Peter Garrison, Los Angeles, CA, Oct 2002 v
(This page intentionally blank)
TABLE OF CONTENTS Dedication Foreword by Peter Garrison CHAPTER 1 INTRODUCTION 1 WHO AM 1 AND WHY DID 1 WRITE THIS BOOK? WHAT IS A HOMEBUILT? A PLAIN PLAN FOR PLANE PLANNING STEP RIGHT UP, GET YOUR FREE DESIGN SOFTWARE PLEASE READ THE FOLLOWING CAUTIONS: 1 2 4 5 6 CHAPTER 2 SO, YOU WANT TO DESIGN A HOMEBUILT? 7 WHY? WHAT DO YOU WANT IT TO DO? SO, RAYMER WANTS TO DESIGN A HOMEBUILT 7 7 8 CHAPTER 3 HOW BIG SHOULD IT BE? 11 POWER LOADING WING LOADING AIRPLANE SIZING ENGINE SIZING AND SELECTION WING GEOMETRY AIRFOIL SELECTION TAIL GEOMETRY FUSELAGE SIZE 11 13 16 22 24 32 35 39 CHAPTER 4 STUFF IN SOME STUFF 41 You AND ME AND A DOG OR THREE THE RUBBER MEETS THE ROAD IN GOES THE ENGINE STUFF SOME STRUCTURE FUEL TANKS 41 45 51 55 63 vii
CHAPTER 5 DRAW A SMOOTH OUTSIDE 67 CONIC LOFTING FLAT-WRAP LOFTING WING/TAIL LOFTING RAYMERS DR-4 SAFETY TWIN MEASURE WHAT YOU DREW 67 73 74 79 80 CHAPTER 6 BUCKLE UP FOR SAFETY 83 CRASHWORTHINESS FLUTTER 83 84 CHAPTER 7 ANALYZE IT 87 AERODYNAMICS PROPULSION PRELIMINARY STRUCTURAL SIZING WEIGHTS ESTIMATION STABILITY 87 91 97 105 113 CHAPTER 8 RANGE & PERFORMANCE 117 STALL SPEED TAKEOFF DISTANCE RATE OF CLIMB MAXIMUM AND CRUISING SPEED RANGE HELP - 1 DIDN'T GET THE RANGE/PERFORlMAiCE 1 WANTED! 117 117 118 118 120 122 CHAPTER 9 LET'S MAKE IT BETTER! 123 CHAPTER 10 AND IN CONCLUSION 127 vm
LIST OF FIGURES /zgMry 7. 7?/z/zyr _ Z^7^4 Sa/y7/_ PHz^za - Ear/- *^a^z^<c/^a^.y /Zgz^z*y 2. pz/._ jZg^z^/re J. D7--4 TZz^zYza?/ &^z'z^z'z^g G/ap^^/z /ZgMry 4. TTpp/C^a? / .Z^^Z^zZey pLyco/nz'Hg 0-2333^ y7gZ^/re J. P?c0f a3a/_ PZp C^/^a^Z^aT? /ZgMry 6. 7Cpe^^^^zz/^gyCo44p/^j^(^.r?z^c7/y pEt/Zp^.^^ /zgMry 7. 7Zz_ ^7^^^a//_ _ WZzg^a'yya- .23.- 6*^C/^^r^j^77JZz)ey_ yZgz^z/y & EZa/Zzag /^Z^y A<y^a^zy .4^a?a^z?//^^/^j2^zZ_ C^Z^a/r/- AP4C_ yZgz^z/y 9^. (aac^J/ey-^-(a^/^z^^Z/*^7/yyz^7?4^aza^z7a^/az7zaM_ CAor^ PP^ C? yZgz^z/y 76^. Canard jCyyoMf ^rr &0a^z7zzy /Zg^^y 7 7. G7z//-WZZzg //ozey^zz/f - 'PCwP^g _ p^a-^a? /zgMry 72. yl^z'Z(?roz &zzzzg GzZ&ZZay. /Zg^z*y 73. Z/yazZEja^r TLzgzzZ .4 z'rcraf yzg^^y 74. Paz/ Z 5zzZag / Ua/^Zz^az- (Tc^rZC^^^zZ^z/Z yZgz^z/y 73. jr^^Ca/ Z 'a^z'Z/Zl4azf3^z^^y jyZz^^^^^3yT-P7z^z7Z - .y^c^z^jaZ^zz p/a/^/z^yp^^? yZgzzry 76. Paz/ Z4t7^c^z^Z7^z^7/^^^zz/.Ja?y3azza2 ./^^^z^a^1^<aa^ /ZgMry 77. (9/zZz/z^^zn! zaaayaz^e^. 7^</^Za_ .Z^z^(^./azzr pyaazZz/^^r yZgz^z*y 7& ^zrcza/DDy.yzgzz 77Zryy^-^^a^^^w Er^a^a^^z'z^g Jry/e^J^^aac^^ 7) yZgMay 79^. ./^z^z^/z/^^7^(^.TCza^ /ZgMry 26^. 7Zr^.^Za^zz/.^^zr^y paaa^zz/ /ZgMry 27. ZZaMa^^Zy PCz^^a(a^z'z^g- (^a^a/y pC/azzz_ /Zg^^y 22. Eaz76/raggyy^aaaa'ag Gyar A/yzzZ jZg^^^y 23. M9.y/7az7 WZ^y^a?- p^^y^^zz/ jZg^^z/y 24. Laa/Zzag 7^^/Zra^^aM^j/ jZg^^z/y 23. Eagz'ay C^c^apaa^zz /zg^z^y 26. S'yaZyz?7zZyaMa (ao(zZza^g ,Sy/^i^^^az - 7racZar yzgzzz/y 27. Syy/^Za^/./yaa^zaz^ia- CaaZzag ^Syz^i^^^a- - pzz./^a^zT /zgMry 2& Pa/^za^^/Zy .XJ^z7.4z^^^^z (2ay/Z j/7ar_ /Zg^z*y 29. Jaas^e^/^c^z^^ *^^/^zacz^zz7'^c^Z.4^jrrz^z^gyzraya^^ /Zg^z^y 30. A/aZar 7/7a^zaz^Z azZza- TZa^^y Gyar.4#acZzy7 /Zg^z*y 37. ^^a'z^^^ (C/^J^^z^Z^j^(aMEz-*Er^^^zc^^Z^z^jyy /zgMry 32^. Jy^^^^azaZa^gy J5^^aza- (aa^z^zz/a^/^^aag^^ /zgMry 33. ZaZzzg*7Zz^^7 Z .aaz^/7 /zgMry 34. Pa9a^Z ^/Z^iM/^z^z/yy -ZZZz^^y &- Paaz Z (jrzzp? /ZgMry 33. A/yz^a?- Jaary/c^z^^ .S'ZzzcZMry Jaga^7/y 36. A/y?Za/_ ^Zzag &z^z^z^(/Zaz^y /Zgz^z/y 37. //Z-calap?aaz7y 7Zz^z/^Zaap P^aZZ .^Zaz^z?Z^a7^6? /zgMry 3<S. Jaa^^z- Pao^z^A^ pCaat^z^Zza^r^J7c^a^(^zZaZ/Z.y /zgMry 39. CaaZc (Zz^jnyy Caa^yZzacZZaa /zgzzz*y 46^. (7z^zzZ- CMrvr -ppa?r_ Ezzz/.y /zgz^//y 47. p^^zzaa^Za<z/aZzc7_ CazZra - .aZz^a^.yP^^?rp^z^(7aVy /Zgz^z*y 42^. pCaagaZM/Zaaa- Caaaz^7^^/- .aZay^J--^ZZz^y- &_ Tap- PZyaAy ^gz^z/y 43. (7z^zzZy .Laa^z^z/ ZMaZag T^a — ^gz^//y 44. Caaz'cr wzZ/z (/Z^a^jz^^Zz^g^ .7/^a — ^gz^?/y 43. Caaz'y (/azZag.Zz^J^^^^za^^ (^zz^z^^a/ Z.aazyJa/r77a^a ajo bo ^^Z)QoQo-t^bo^'-^^^Z)OoOo'^L^-^L^bo^^Oo'^0\-^bo^^Qo'^^\bo^^^OoOo'^)L^4^boboO\^) ix
yzgzrz 46. Eoz/E^z^z . CozzzcO'zg 74 yZgMre 47. yl zryoz/ Zoyoo/ az? Mz'z^^ P^^^o^/Z/orz% 76 yzgzrz 4& E/o^Z-z^</p zA/og Zo^<^<^j/ 76 y?gzrz49. 77-^7 77 yigorz 66^. ^P/'o^g E7/EE 7P y^^^^orz 67. Eoyzzzr . DZ^-^4 TWo Poyoo/ 79 y/gMrz 62^. F^^yyz/zr \ Z^E^-^4 &/&/y 7W^zo P^zr^sp^z^c/z/V^z^z' TO y/gorz 62. Eoz/E^z^z z/^j^^z^?^.Tz^o Cz^/cz/z^i^7zzz <37 y/gorz 64. P^?7z/9/Z/^(zJ Po/z/nz Cz^/c^a^/z^i^/zz (^.2 y^^^^orz 66. Pozzz Po/ZF C(^/^(^z?^/zyor Z^zgA//4ircrro/ P3 yzgMrz 66. 7^-^6^7 7oz7 w^FZA Fo76r^zc E^^voZor z^^774^J^J P6 y^z^^^^rz 67. F7zppz4ZZrzz jor APzx^zzzz^/M Z^z/7 Cz^^^^^z//^^Zz^^jo 97 y^goro 63. Z/y^(^zzz^cy ?//..* 2-6E&Z7 ^^J^z'z^7E yzz^c/A Pro^^^o/E* 93 yzgMro 69^. E/yc^E^o^cy 77/?; 3-6/oZzJ PZ^;^zo?/E jzYc?A Pro^^^o/E' 94 y^z^^oro 66^. Az/X^^(7--jz7^c?A P^r^op Jlz^^^^./Zzzz^Z Eocfpr 96 67. Cooz/og E^r^o^g - ^7Az zzZ zz^z Ao^Z 96 yzgzrz 62^. C^z^rrAz^z AZ?/z!^/ZA 2 9^(2 yzg7^7rz 63. Pzzp/(/7z7 ZP^^jog P/^r^T^^/TzroZ J^/^^a^/z/A 99 yigMrz 64. 7roz PfrocZorz 7 6^2 y^T^^^jrz 66. 7roz P^^/Mj^zz^/7 ; AZ/^ZA^^zE' z?^^4^7z^z^z?Z^^.AE?ZAzJ ^Pzors j^Z^2 y^^^^orz 66. Co/opoozoZ ZE^g/7/^Z^^/Z'zz (Pj/pzoz^/x 767 yzgiorz 67. E^o^g^zo^z WEzgAZ Pr^z^o^z^Z/z^z j^.^0 yigorz 63. PEoiZaJ G7^6^zp zfE^zg^^Z E^^7^7zzZ 777 yzgiorz 69^. Tz^P^zo/yC^^^/(^z/Z7/zZ^z CAarZ j^.^3 y^^^^orz 76^. E7?-4 APzx^zzzz^/z zzJ Croz^z 720 y?gMrz77. E^E^-^4^JZ^^/^^?C/(^/?7^6 726 y^T^^^^rz 72. E^E^-^4 . zc/ E^z7Zz (/^z^zzzzzz^/z(Zz^ 7 J^6 x
Chapter 1 INTRODUCTION Who am I and why did I write this book? My name is Dan Raymer. I've spent my career in the design of new aircraft concepts, with 10 years in the Advanced Design Department of North American Aviation (then part of Rockwell, now part of Boeing), followed by a few years in futuristic spacecraft design at Aerojet, and then as Director of Advanced Design for Lockheed. For the last ten years I have headed my own company specializing in aircraft conceptual design, design reviews, and design software development. A few years back I wrote a design textbook aimed at college seniors and working engineers called Denigi.* CowcepMa/ I'm proud to say that it is widely used both in industry and in university design classes. I also teach aircraft design engineering classes - over two thousand engineers and students have taken my Aircraft Conceptual Design Short Course. Organizations such as NASA, Boeing, Lockheed, BAE-Systems, and SAAB have brought me in to train their engineers in aircraft design methods. In the design textbook and short course I've tried to present aircraft design as it is done by "big" industry - the methods that I learned from the guys who designed the B-l, B-70, X-15, and many others. I used these methods when running the early design studies for X-31, and in developing Rockwell's design concepts for its entries in the programs that became the B-2, F-22, T-45, and numerous others (other than X-31, we lost them all, but not due to my design concepts -1 think). While my work experience is "big industry" oriented, I've always been interested in homebuilt aircraft. I grew up building and flying original-design model aircraft and have belonged to EAA for many years. Some day I'll design, build, and fly an original design homebuilt aircraft - just as soon as the kids are grown and the bank account is full. In the meantime, I've given a number of forum lectures at the EAA AirVenture (Oshkosh) on how "big industry" does the design of a new aircraft and how those methods apply to homebuilt aircraft. Several subjects seem to be especially 1
interesting to homebuilders - how to develop the actual configuration drawing itself, and how to quickly analyze the design and then optimize it so that you get the most range, payload, and speed out of the selected engine. There are other aircraft design books aimed at non-professionals. They are full of useful information, but to me they don't seem to cover all the required topics evenly. One book is mostly structural design, another focuses on performance but doesn't tell you how to actually the design, another is mostly selection and construction of a kit, etc... There are also aircraft design books for professionals, including my own* , but these are full of big equations and they try to provide methods for every imaginable type of aircraft. Too much for homebuilders! So, I decided to write a design book for homebuilders, covering these topics and many others. My goal was to give step-by-step instructions for starting with a dream and a blank sheet of paper and winding up with a credible design layout that could be built and flown by a regular person. In writing this book, I've tried to take the industry methods and distill them down to their bare essence as applied to homebuilts. Since I'm not trying to turn you into aeronautical engineers, the theoretical developments are not included. For proof of the methods and additional information, see my design textbook^ In writing this book, I've made some assumptions and restrictions: * You are familiar with basic aircraft terminology (wing, tail, aileron, propeller, lift, etc...) * You are not afraid of sharp pencils, pocket calculators, data tables, or medium¬ sized equations. * You are interested in designing a "normal" homebuilt - no flying saucers, exotic materials or engines, flying cars, supersonic jets, etc.... * You understand that, while this book will get you started, you'll need more information and should go to other books and seek experienced help in design, construction, and flight test. Your local EAA chapter is a great place to find help, and the FAA will work with you before they authorize you to begin flight test. What is a Homebuilt? Almost as soon as the airplane was invented, companies were formed to mass¬ produce them. The Wrights, Bleriot, Curtis, and others built and sold airplanes to the newly formed military air services of the various nations as well as to wealthy sportsmen. An instruction manual for an early Curtis tells you how to take it out of * If you are serious about designing your own plane, you may want to pick up a copy of my textbook (reference 1). It has better methods for many of the simplified methods in this book, and has more complete explanations of terms and equations. However, it is written to a technical audience and has a lot of material that is not relevant to design of propeller-powered homebuilts. Also, it's not nearly as fun. 2
its packing box, assemble it, and, should you not have an instructor pilot handy, teach yourself to fly it. Almost as early, people built and flew their own planes. Brazilian-born Alberto Santos-Dumont published "homebuilt" plans* worldwide for his 1909 De/noAyeZ/e, in Popular Mechanics magazine in the USA. Built partly of bamboo, this flew on 20 horsepower and could be called the first ultra-light. Another early article told how to build and fly a braced biplane hang-glider. I wonder how many aviation careers were started by the construction and flight of one of those - or prematurely ended. Typical of pre-WWI homebuilders were two brothers named Loughead who built an original-design seaplane in a garage in 1913. The plane flew well but nobody could pronounce their last name correctly, so they changed it to spell like it was pronounced - "Lockheed." As time went on, airplanes became more common and safety more important. In response to numerous crashes, regulations were issued that increasingly restricted the average citizen's freedom to design, build, and fly an original design, especially in controlled airspace. Essentially, homebuilts had to be certified by the same expensive procedures as production aircraft. Homebuilding by amateurs practically died out until 1946 when the government, with the encouragement of people like George Borgardus, Paul Poberezny, and Steve Wittman, released new rules permitting properly-inspected and documented homebuilts to be built and flown virtually anywhere a similarly-equipped production plane could be flown. The Experimental Aircraft Association (EAA), founded by Poberezny, continues to work with the FAA on rules and procedures for experimental aircraft airworthiness certification. I'm a member, and you should be too. Today, there are more homebuilt aircraft built per year than production lightplanes. Homebuilts span the spectrum from under-254 pound ultralights to the 6,800 lb Grand 51, a turbine-powered P-51 copy available in kit form for a mere $355,000. Most homebuilts flown today are kit planes, a radical shift from the situation even 25 years ago when plans-built designs like the Wittman Tailwind and the Thorp T-18 were prevalent. However, the rarest of all continues to be the original-design homebuilt - the subject of this book. What is a homebuilt? The FAA officially calls them "Experimental-Amateur Buill," and defines them as aircraft ' 7/? e /nq/or /?orbon o wbz'cb 7 e been ybbnca^ a^nzb/^^ by wba /be consbMcb'on /yq/ecf so/e/y ybr own e<Mcaff'on orrecrefon" (FAR 21.191, see Appendix I). The phrase "major portion" has been interpreted into the so-called "51% Rule." Basically, if you can convince the FAA that you built 51% of the plane, it can be certified as a homebuilt. * Santos-Dumont was also an aviation idealist who never tried to patent his technical contributions, didn't charge for publication of his plans, and donated his prize money to his mechanics and to the poor. 3
Otherwise there are no special requirements such as use of certified engines and materials, or certain design practices or analysis methods. You don't even legally need to get a licensed aircraft mechanic to inspect it, nor a trained engineer to double-check your calculations (although it's not a bad idea). The FAA may request that the builder hire (at his own expense) a "Designated Airworthiness Representative (DAR)" to inspect a homebuilt, and also recommends that homebuilders call upon the assistance of EAA "Technical Counselors" who will review the aircraft during construction. A key part of convincing the FAA that your aircraft is safe to fly is documentation. Save your calculations in a well-organized notebook. Keep all receipts for the materials, supplies, and components you purchase. Photograph every step of the construction, and save sample pieces and test specimens. There are other requirements you must follow and paperwork you must submit to get an experimental certificate. The FAA publishes a number of homebuilt-related Advisory Circulars (AC90-89A, AC20-27E, AC20-139, and AC65-23A). A recent Sport Aviation magazine article by Lawrence^ summarizes the newest experimental certification regulations. A Plain Plan For Piane Planning This book follows, step-by-step, the design of your aircraft concept. No introductory lessons in aerodynamics, no math review, and especially, no derivation of equations! The design steps in this book will work for most concepts, and you should be able to modify these methods if you have something unusual to consider. We begin by deciding what you want your homebuilt to do, and how to set your design requirements. Next, your requirements are used to estimate how big the aircraft should be, how big the wing should be, and how big an engine you should buy. If you already have selected an engine, you'll work backwards to determine what airplane capabilities you can hope to get out of that engine. Selection of wing geometry comes next, along with airfoil selection and tail geometry and size. Following that is a discussion of the things that you must put inside the aircraft. These include yourself and the passengers and baggage. Landing gear design, engine installation, propeller sizing, and fuel tank design are then considered. Then come the methods used to "loft" your airplane. This is the actual creation of the drawing, and the book explains how to develop smooth external shapes either on a drafting table or in a CAD system. Methods are given for analyzing the airplane you just drew, including aerodynamics, structure, weights, stability, propulsion, and performance. Last comes an introduction to design optimization - how to change your design concept now to make it a better airplane when it is built. 4
In my engineering textbook I provided two design examples - a homebuilt aerobatic single-seater and an advanced supersonic fighter. At the time, I'd hoped to actually build the homebuilt concept but never got around to it. For this book Fve designed another homebuilt airplane, and hope to build it someday. My basic concept for this design (to be called DR-4) is to create a low-cost twin for training and recreational flying with a design approach that minimizes engine-out controllability problems. Also, I want to use a fairly inexpensive in-production engine that can be bought with off-the-shelf components such as propeller and accessories. I want a lot of range and hopefully a pretty good cruising speed. And, Fd like a pony while I'm wishing. Throughout the book you'll see how this overall wish-list was turned into a design concept, in a series of boxed discussions and drawings. To repeat the warning from my textbook, DON'T BUILD IT! This is a first-pass conceptual design only. It would take probably a year of design effort before this concept could be built and safely flown, and along the way changes to the overall layout may be required. Hopefully, I'll do that some day and you'll see me in the pattern at Oshkosh. Step Right Up, Get Your Free Design Software Really! The Excels spreadsheet software used to make sample design calculations throughout this book is available on the website as described below. You can use it to make your own design calculations including sizing, performance, and range estimates. However, you do not „ , to have the spreadsheet to design and analyze an airplane - you can do it all with a pocket calculator using the methods in this book. Original purchasers of this book are authorized to download the spreadsheet and use it at no additional charge (must be downloaded within one year of purchase). All others must send in a registration fee as described on the website. Look for De.ngK " Please note that the spreadsheet has a usage and license agreement to protect this litigation-averse author! Also, ExceP" itself is not included with this offer - you must have your own copy to run the Simplified Aircraft Design Spreadsheet. A crass commercial plug: Please visit my company's website, where you'll find lots of stuff of interest to aircraft designers including sample design conceptual layouts, recommended books for aircraft design and analysis, a glossary of aerospace terms and acronyms, free and not free design software including and the ybrcra? Dez/g? information about upcoming design short courses, advice for inventors, and a huge listing of design related links. 5
Piease Read The Following Cautions: * Airplanes kill, casually and without malice. Nobody, and no book, can guarantee that an aircraft design is 100% safe. Even if you do "all the right things" in its design, construction, and flight test, any aircraft can have hidden failure modes that are only found the hard way. Early Leaijets crashed because water vapor would freeze inside the elevator, causing flutter. A celebrity (and excellent pilot) died in a well-proven homebuilt design apparently because a minor change to the fuel system put the selector valve in an awkward location, causing distraction during climb-out. Some WWI fighters crashed because nobody anticipated a forward load on the wings during pull-ups. If you just want to fly, a production aircraft or a proven homebuilt design is safer than a one-off original design. But, there are few thrills in life that could compare to the first flight of an airplane you designed and built yourself. * Be ve?y careful if you are trying to modify a plans or kit design. Sometimes a seemingly-innocent change, like reshaping the turtledeck and wing fillet to make the airplane "cooler" looking, can change the airflow enough to make it impossible to get out of a spin, or increase loads on the tails enough to cause fatigue or outright failure under some condition. Even something that would seem to make the plane stronger, like using thicker skin gages, may actually make it weaker (by overloading adjacent structure). This book offers some methods that can help you to calculate the performance effects of your changes, but no book can guarantee the safety of such changes - only a careful and expert engineering analysis can do that to a high level of confidence. Don't expect help from the original designers - they hate it when people try to modify their designs, and may be legally liable if they even comment on your proposed changes. * In what follows, I've tried to present useful and reliable methods for designing a homebuilt aircraft. I've done my best, but there may be errors due to typos, my use of information from other sources that is wrong or inappropriate, or my own ignorance. There may also be errors of omission - some factor that is life-or- death important for your design may not even be mentioned here. Therefore, please note the following legal statement: 7Aa aoZAo^ jprznZar, jPAA/ZdAee ant/ tZZSrrZAaars a/* dAds AaaA ataAa aa uwrraaZAs ar cZaZms as da carrgcZASs, cawpZOZaAss, ar a<Z#aacy a/dZAe Zt/arTaaZZaa eacdased yar aay papAse ZA&aJ&ag dAe dAssga, coaZTacZZa, aad yZZgAZ a/ aZrcaZ. reader assaazas a// reypaastMzgy yar dAe ase a' dAe eacZased aafataazZMa aad ds rvaraed /a ZadepeazeazZZy verd#? add eadOssed dOorataZda Ae/are ase. 7Ae aadAar, jwdaZer, paAddsAer, aad dZz?zddAad^s ay dAds AaaA assume aa ZdaAdZZZy yar aay dassas ar ddaMages, ddrecd ar caaseawadiad, ras^add^^ yraw dAe ase ay dAe eacdased Zfeyo?7aeidZaa. In other words, I hope that this book helps you to realize your dream of flying your own aircraft design, but please don't sue me if it crashes - even if you did it "just like Raymer says." 6
Chapter 2 SO, YOU WANT TO DESIGN A HOMEBUILT? Why? The first question has to be, "Why?" Good used pianes can be bought for about the same total price, if you include a reasonable cost for your labor. This is especially true when you consider the greater resale value of, say, a clean C-172 as compared to the one-and-only "YourName-Special." If you just want to build an airplane, a plans- built or kit plane is less work, safer, and probably has a greater resale value than an original design. Good reasons for designing and building your own homebuilt probably include one or more of the following: 1. No existing design does quite what you want your airplane to do. 2. You want something really unique - a flying "who I am." 3. Self-education and/or validation of what you know about airplanes. 4. The glorious challenge of it all (people climb a mountain "because it was there" - we design and build an airplane "because it wasn't"). 5. Price - an original design or a plans-built homebuilt may actually cost you less than a used airplane or a kit-built homebuilt if you ignore your labor "cost" and can successfully scrounge for a good used engine and avionics. 6. Flight test of your original design concept or technology ("they laughed at the Wright Brothers"). pM/or one/ // too?? ge/OOM %7/e?/ MtZ&y.yyoM %/ow w/?afjoM orc (%9/Kg What do you want it to do? So, the first step in design is to write down exactly why you want to design a homebuilt. What do you want that airplane to do? Perhaps you just want it to fly, and fly as well as possible within your budget and the limits of your design and construction skills. Write that down. Think about what you want to do with the airplane - where will you fly, what and/or who do you want to take with you, what speed do you hope to reach? Think about planes you've flown and how your design should compare with them. Think about what sort of pilot you are (or others who may fly the plane). Should the plane be real stable and easy to fly, or a little "hotter" - more challenging and more fun to fly? Write down numbers for these thoughts - range, payload, top speed, stall speed, rate of climb, etc... Make two columns - a column of "goals" (what you'd like it to do), and a matching column of "thresholds." Thresholds are the minimum capability you can accept - if your design can't do "X" you don't even want to waste time building 7
it. Think hard, and be tough and honest with yourself. If you ask for too much, and you design to a ridiculous set of requirements, you will waste a lot of time and the answer that comes out probably won't really do what you wanted it to. Remember that it is pretty normal for an aircraft to be able to carry a full cabin of large people, or a lot of heavy payload, but not both at the same time. Make sure that your requirement isn't more severe than the way the aircraft will actually be flown or you will drive up the weight and cost. So, Raymer Wants to Design a Homebuiit What are my reasons for designing an airplane, other than to have an example for this book? I confess a lot of it would be #2 above - the ego gratification of showing up at Oshkosh or my local airport and having people say, "what the heck is that?" The first reason above applies to this particular concept - some people including myself would like a second engine for flying to Catalina Island or over the Rockies at night, and virtually all existing homebuilt designs are single engined. Number 6 also applies - I have what I think is an original concept for a safer twin. Despite the extra engine, twins have a safety record no better than single engine aircraft. The problem is that the loss of one engine during takeoff or go-around causes such a large yawing moment that control is all-to-often lost. A normal twin has a center fuselage with engines in wing-mounted nacelles, which moves them far away from the centerline creating large yawing moments. Burt Rutan's Boomerang is asymmetric with one engine in the fuselage and another in a second, smaller fuselage, placing the engines closer together. My idea is also asymmetric to bring the engines closer together, but adds one more wrinkle - the extra engine is a wing-mounted pusher. Since a propeller's thrust line moves towards the downward-moving blade when the airplane is at an angle of attack, this arrangement puts the thrust axis of both propellers even closer to the aircraft lateral center during the critical climb-out phase. What about the scary warning above? Hopefully, after all these years in the business I "really know what I am doing'" and can design, build, and fly such an unusual concept without getting my name in the newspapers the hard way. And, I'll be very, very careful! Below are my first sketches of this concept, done on a napkin at the Oshkosh Applebee's a few years back. Notice how I hadn't yet decided on a few things, like whether the horizontal tail would be symmetric to the centerline, symmetric to the fuselage, or all on one side. I later decided that I'd better use a T-tail arrangement to get the horizontal tail above the propwash from the too-close pusher engine. From my overall design desires described in the last section, I wrote down design-to requirements, and included two well-known production designs for comparison. 8
7. \ DE 4 TW/E - iS^c/i&s* DESIGN REQUIREMENTS FOR DR-4 * Twin engine (piston-prop) * Affordoblz production znginz * Two-szot, duol control * Stoblz but rzsponsivz * Enginz-out minimum control spzzd < Stoll spzzd * Build it in o two-cor gorogz * Pzrformoncz ot lzost os good os C-172, ond lots foster Gool Threshold C-172 C-310 Mox Lood (Crzw+boggogz) 500 380 743 1007 (lbs) Rongz (mox lood, no reserves 2000 800 551 615 (nmi) Moximum Spzzd 200 150 122 207 (kts) Mox Cruise Spzzd 180 125 117 194 (kts) Rotz of Climb - Szo Level 1500 800 645 1662 (fpm) Rotz of Climb - Engine out 500 200 n/o 370 (^m) Stoll Spzzd - flops down 43 61 43 67 (kts) Minimum Control Spzzd 43 61 n/o 81 (kts) Tokzoff Distoncz 1200 2000 1525 1700 (ft) Londing Distoncz 1200 2000 1250 1790 (ft) It is often difficult to comporz quotzd numbzrs for diffzrznt oirplonzs. Spzzds moy bz ot diffzrznt oltitudzs, ond moy bz rzportzd os indicotzd or os truz oirspzzd . . Truz Airspzzd (KTAS) is thz octuol vzlocity through thz oir (no wind^). Indicotzd oirspzzd (KIAS) is whot is shown on your oirspzzd indicotor (duh!). This will bz lzss thon truz oirspzzd ot oltitudz bzcousz thz oir is lzss dense, ond thz instrumznt works on przssurc. Ignoring colibrotion zrror o^d Moch effects, thz truz oirspzzd is thz indicotzd oirspzzd dividzd by thz square root of thz density rotio (p/po). Wz of/wayy use truz oirspzzd in rongz ond performoncz czlculzt^ion^s^. 9
7P&? ybr 67/7 676bv677<n?6? ^/^jz%6^/^.^/ra/or M^yZZ^^g /?O7MebM;76%e''.y Zow-^-^^^.^y COJW/^6^.yZZy y6^j7^^6A^/Z?b CO/^-y/M^c^//?^/?. Moe Z^y ^7?^67/// ZZyy 6^.y ;'M6%?x7e(7 by ZZZy Zarg^y yzzy */ Zby Z?Z^6^^Z - bz\y y&yf 67/^6^^^Z y/zcA OMZ Zby yTonZ/ &?6^//^^b Co^/^^r^^^zZyy (7?MrZ 7?MZ//zy W67y Z67^/^<y6Z W7?ZZ T^ocbwy// #^or^/Zb ^Myn'can Zo b^MZZzZ Z7 bzzZ Zby /pro'ycZ W6^.y 7yvyr ^72^6^^^^^. Too b^63^Z - WOM/z/ /Z67vy bey^M^- 10
Chapter 3 HOW BIG SHOULD IT BE? Always an important question; we find the answer one of two ways. If you have already picked or bought an engine, then we do it one way. If not, we do it another way. In either case we start by finding a reasonable value for the "Power Loading." Power Loading Power loading is a term that dates back to the earliest days of aircraft design, and is simply the weight of the aircraft divided by its power (W/hp, W in lbs). Power loading is a "backwards" term because a high power loading indicates a small engine. Power loadings typically range from 10 to 15 lb per horsepower for homebuilt aircraft. A aerobatic or high-speed aircraft may have a power loading as low as 6 to 8, and a few exhibition planes have power loadings under four (lower number = bigger engine). Power Loadings Wo (tbs) Hp Wo/Hp Vmax (kts) Baby Ace 950 65 14.6 113 Great Lakes 1618 200 8.1 120 Kitfox 1550 125 12.4 122 Pazmany PL2 1447 150 9.6 133 Pitts SIS 1150 180 6.4 153 CA65 1500 125 12.0 156 MiniImp 1000 115 8.7 174 KR-2 900 80 11.3 174 T ail wind 1425 145 9.8 179 T-18 1500 180 8.3 182 Cozy 2050 220 9.3 198 Lancair ES 3200 300 10.7 208 Lancair 360 1685 180 9.4 226 Lancair IV 3200 350 9.1 274 Berkut 2000 260 7.7 304 Meyers 360 1650 230 7.2 347 Power loadings for typical homebuilt aircraft are given above, sorted by maximum speed. The faster aircraft tend to have lower power loadings (ie. bigger engines) as you'd expect. However, the class of aircraft also has a big effect - notice that the aerobatic aircraft like the Pitts have lower power loadings than the general trend. Data on about 60 homebuilts were used to make the following Power Loading 11
estimation equations. The equations labeled "smooth design" are generally for molded composite aircraft, but a clean and carefully built metal design could also match these equations. Fixed-Gear Normal Design: Retract-Gear Normal Design: % = Fixed-Gear Smooth Design: = 248^"" / Ap Retract-Gear Smooth Design: % =680 Acrobatic: =172T *'6i ""M RagWings: % =5111^75 /%? "ax Ultralights: -325T "'75 Use one of these equations to estimate your required power loading based on desired maximum speed (kts). If you have already picked or bought an engine, it is now easy to determine how "big" (heavy) your aircraft should be. Simply take the power of the engine(s) and multiply by the power loading. However, there is no guarantee that this aircraft weight will give you the range you were hoping to get. WeTl find that out later. If you haven't yet picked an engine, you'll make some calculations in the chapter on "sizing" that will tell you how big the aircraft should be to get the range you want, and then that weight can be used to find how much horsepower you need. Then, you can pick an engine (or change your requirements if the answer is unaffordable). For the DR-4, I'll pick the engine later. I calculate power loading to meet my goal of 200 kts maximum speed as: Retract-Gear Normal Design: = 276(200)-63 =8.8 12
Wing Loading Nyxt wy dete/mine how big thy wing should be. Wy _ ll do this fi/st as a /atio, thyn latyr use that /atio to find the actual wing a/ea in squa/e feet. This /atio is callyd thy "Wing Loading," and is anothe/ te/m dating f/om the ea/liest days of aviation. Wing loading ("W/S") is the weight of the akc/aft divided by the wing a/ea (units of lbs py/ squa/e foot, o/ "ps^f'). Wing loading is anothe/ "backwa/ds" te/m - a big numbe/ means a small wing. Fo/ gene/al aviation and homebuilt ai/c/aft, typical values /ange f/om about 10 to 20 lbs/fff. Wing loading, like powe/ loading, is set to meet some c/itical pe/fo/mance /equi/ement. Fo/ high-pe/fo/mance ai/c/aft such as fighte/s and jyt transports, the/e a/e seve/al /equi/ements that may be c/itical such as maneuve/ability o/ go-amund, and we have to check them all. Fo/ homebuilt ai/c/aft, though, things a/e simple/ - it is almost always the stall speed that will set the wing loading. To find out how big the wing has to be to give us the stall speed we want, we simply have to make su/e that lift equals weight at the stall. Befo/e we can p/oceed we need to int/oduce the idea of "coefficients." Coefficients a/e /atios that we use to compa/e and estimate numbe/s of inte/est. Most coefficients that we use a/e called "nondimensional," because we make sui*e that the/e a/e no units (dimensions) in the te/m, such as feet o/ pounds. How do we get /id of the unwanted units? By dividing the actual value by some /elated values with the same units. Lift in pounds is turned into a nondimensional coefficient by dividing by seve/al lift- /elated values. Obviously, a bigge/ wing has mo/e lift, so let's staR by dividing the actual lift in pounds by the wing a/ea in squa/e feet (ft^). This isn't enough to turn lift into a nondimensional numbe/, though. We need to divide by some mo/e units. As you would imagine, the faste/ you go, the mo/e lift you get. It turns out that the lift is di/ectly /elated to the p/essu/e of the air blowing against the ai/plane, which is found using the squa/e of the speed of the ai/c/aft. But, at highe/ altitudes the ai/ is less dense, which means less lift. This intuitive unde/standing of the "blowing" fo/ce of the ai/ can be w/itten as an equation based on velocity and ai/ density. This is called "dynamic p/essu/e" o/ 1 T^2 Dynamic P/essu/e: ^ = — Z" The density of the ai/ is called "p" (G/eek lette/ "/ho") and /educes as you go up in altitude. It is also /educed when the ai/ is hotte/. Values a/e given in Appendix B. Note that thy speed has to be in feet pe/ second - to conve/t f/om knots (kts) multiply by 1689, and to conve/t f/om mile-per-hour (mph), multiply by 1467. Do this BEFORE you squa/e the speed. 13
For stall speed calculations, we can use the sea level standard day value of 0.00238 slugs/cubic ft (if you think slugs are slimy things that live in your garden, see below * ). Sometimes we use a value of 0.00189 slugs/cubic ft which represents Denver on a hot summer day (-5,000 ft field elevation). If we divide actual lift (L) by the wing area (6) and by the dynamic pressure of the air (<?), we get a nondimensional numbed that we call the "lift coefficient," or Q. On the other hand, if we can somehow estimate this lift coefficient, we can easily use it to calculate lift as shown below: Lift Coefficient: or, Lift: Now let's play with that equation a little bit. We want lift equal to weight - make it so. Then divide both sides by wing area * and you get: Wing Loading: Where This useful equation calculates the wing loading that will exactly give us the stall speed we desire. The stall speed we want is used to find dynamic pressure %, and the lift coefficient CL is the maximum lift coefficient, reached just before stall. What values should we use for these? Stall speed is a major factor of flying safety - each year some people die due to "failure to maintain flying speed." A plane with a high stall speed is trickier to land and requires more experience and continuing practice. When an accident does occur, the physical injury to human bodies is related to the square of the speed (it's the unwanted kinetic energy you possess that kills you). FAR 23 certified aircraft (under 12,500 lb takeoff weight) must stall at no more than 61 knots unless they are multi-engined and meet certain climb requirements. While * To engineers, g/ngy are the British units of mass, not Mass is the property of objects to resist accelerations - in outer space bodies have mass even when they have no weight. By definition, a mass of one slug will accelerate by one ft/sec^ if pushed by a one pound force. We measure weight in pounds, which is the British units of force, but in everyday life we also use the word "pounds" as units of mass. If we say that something "weighs 210 pounds," we really mean, "this object has enough mass that it will press down with a force of 210 pounds when in an Earth-standard gravitational field." This also means that I have to stop eating my famous Low-Drag Cheesecake (see my website for the recipe). t If you are checking my math and can't get the units to cancel, remember that one slug =one lb /(ft/sec^ 14
not stated in any design specifications, a stall speed of about 50 knots would be considered a reasonable safe stall speed for a trainer aircraft or one to be flown by low-time pilots. Also, the approach speed, which is an important factor in landing distance, is defined by a safety allowance of 30% higher than stall speed. So, if you desire a certain approach speed, divide it by 1.3 to get the stall speed you need. We also need the maximum lift coefficient (highest value of Ci). For a typical homebuilt aircraft, Q* will be about 1.4 without using flaps. With flaps, that increases to about 1.8, but we'll probably only use the flaps for landing. If we do use them for takeoff, well deflect them less to avoid excess drag, so the maximum lift coefficient will only be about 1.6. These numbers are conservative - if you use really big expanding "Fowler" flaps like on a Cessna 172 you can get about 0.3 more, but they are more expensive and difficult to build. Also, they create huge pitching moments. A canard design like the Rutan Long-EZ gets extra lift from the canard so it seems to have a higher maximum lift coefficient, about 2.4 or so. This is because the lift coefficient is based on just the wing area. If the coefficient were based on the combined areas of the wing and canard, the number would be about the same as for any other design. Note that these canard designs usually don't have flaps because the wing is too far behind the center of gravity - you can't make it balance! Later we'll make a better estimate of C^x, to revise the wing area for the second drawing* . By the way, see how nice it is to use nondimensional coefficients? I don't even know what your design looks like, and I can give you an approximation of its maximum lift coefficient! So, get to it - make a preliminary estimate of wing loading using this equation. For the DR-4, I use a stall speed of 60 kts (sea level standard day, and assume moderate flaps giving a maximum lift coefficient of 1.6. Stall speed (kts) 60 Takeoff air density (slugs/ft^3) 0.00238 Wing CLmax 1.6 Dynamic pressure (psf) 12.2 Wing loading (W/S) (psf) 19.6 (light box for inputs, dark box for results) * Second drawing? Who said anything about a second drawing? Well, you'll spend several years or more building your baby, so you should put in an extra day or even a week in the early stages to get it right. In industry, we never build the first drawing - often we get to the h0 overall concept drawing before we lock in the design and start designing the parts. We'll just do two of them - trust me, it'll be worth it! 15
At first I tried to use my 43 knot gool voluz for stoll, but the colculotzd wing looding of 10 mode the drog too high when I got to thz sizing colculotions (L/D=5.3). I hod to come bock to this point ond stort over, using o higher volue (I chose 60 kts). Whot obout biplones? Biplones go bock to the down of oviotion ond hove two moin zdvzntzges. First, thz two wings con broce zoch other forming o strong ond lightweight structure. Second, biplones con hove o lorge totol wing oreo, ie. o low wing looding, without o ridiculous wingspon. However, biplones hove higher drog bzcousz of their structural brocing ond thz interference between thz two wings. Select wing looding for o biplone just os before, bosed on desired stoll spzzd. Biplones work best when thz two wings hove obout thz some oreo ond geometry. Loter wz will odjust drog colculotions for the biplone configuration. Airplane Sizing Now on to the most importont initiol colculotion - how big should thz oirplonz bz? As it soys obove, if you've olrzody picked on engine ond you've colculotzd thz power looding you need, then the weight of the zircrzft is simply the power times thz power looding. All done - move on to thz next section! (but you won't know until loter how for thz plonz will fly). Otherwise, wz hove to colculotz thz storting weight of on oirplone thot con just exoctly moke thz rongz requirement (this is colled "Tokeoff Gross Weight," or "TOGW," or "Wo"). Thz colculotion is colled "sizing," ond is one of the most importont colculotions in oircroft design. Wz stort with zstimoting C^o ond A?, needed to colculotz drog. Cpo (pronounced "see dzz zero") is thz "porositic" drog coefficient, ond is thz port of the drog thot doesn't chonge when thz lift chongzs. X (pronounced "K") is thz "drog due to lift foctor" - it 16
lets us estimate the drag on the wing caused by the creation of lift. The drag due to lift coefficient is A? times the square of the lift coefficient. The parasitic drag is mostly related to the total "wetted area" of the design. Wetted Area (Swet) is the total surface area of the aircraft, including the top and bottom of the wings, the top, sides, and bottom of the fuselage, and both sides of the tails. Later we will measure Swet from your drawing - for now, we ' ll approximate it. The wetted area can be estimated using a ratio to the wing area. Since the wing area is defined as the top-view projected area, the wetted area must be at least twice the wing area (top of the wing plus bottom of the wing). Actually, even for a pure flying wing the wetted area is larger than two due to the area around the leading edge. We can invent a ratio of total wetted area to wing area, or Swet/Sref. Sref is the "reference" wing area, a precise definition of wing area (S) that we will look at later. This ratio Swet/Sref is slightly greater than two for a tailless flying wing design (-2.2), and can be as high as 7-8 for some designs. Typical homebuilt values are provided below. Later you will measure this ratio from your drawing - for now, use one of these values as an approximation. This wetted area ratio Swet/Sref is then multiplied by a number that takes into account the overall "cleanliness" of a typical design to arrive at a parasitic drag coefficient Coo. This is called an "equivalent skin friction coefficient" or C%, as shown in the table below. So, we can find the parasitic drag coefficient using these estimates as follows (If your design is really strange, you may need to adjust these estimates up or down): Parasitic Drag Coefficient*: Swet/Sref Single Engine Twin Engine Conventional Design 3.8 4.6 Canard-Pusher 4.2 5.0 Tailless Flying Wing 2.2 2.8 * Here we are using a drag coefficient Cpp that is based on this wing reference area Sref There is another version of a drag coefficient that is based on the/ronRa/ area of a body. Yet another form of drag coefficient is simply the actual drag in pounds divided by the dynamic pressure q. Unlike the others, this isn't a nondimensional number and has units of square feet, so we call it the "drag area." All are useful at different times. 17
Cf. Single Engine Fixed Gear Single Engine Retract Twin Engine Retract Sailplane Average Design 0.0090 0.0058 0.0048 0.0038 Smooth Design 0.0065 0.0050 0.0045 0.0030 Clean Stmt-braced 0.0080 Dirty Biplane 0.0140 P-51 (flight test data) 0.0053] Rutan Voyager 0.0041 The next thing we need to calculate is the drag-due-to-lift factor A?. There are really complicated ways to estimate this, but for most homebuilt designs a good approximation is: D rag-due-to-lift-factor: 1 _ 0.424 0.755/t" Aspect ratio ("A") is the square of the wing span divided by the total wing area (Sf We don't measure aspect ratio - we pick it. For most homebuilts, the aspect ratio is somewhere between 6 and 8. A higher value gives lower drag and therefore more range and climb rate, but is usually heavier and may reduce roll response. Now we can estimate the lift-to-drag ratio. L/D is the main measure of aerodynamic "cleanliness" for an aircraft. Since the lift equals the weight in level flight, L/D really tells us the drag. Divide the aircraft weight by the L/D and you get the total drag in pounds. For example, a 1,000 lb airplane flying with an L/D of 10 would have 100 lbs of drag, and therefore need 100 lbs of thrust to maintain level flight. To calculate L/D, we need the Cpo and X terms we calculated above plus the dynamic pressure "q" during cruise. This is found from the "q" equation above using cruise velocity (ft/sec) and the air density at cruise altitude (see Appendix B). The wing loading (W/S) we already determined, but we have to adjust it a bit since the weight is reduced by the time we are cruising. Multiply the takeoff wing loading you determined above by 0.98 to approximate an average cruise wing loading since the airplane weighs less during cruise - it has already burned off part of its fuel. Lift-to-Drag Ratio: L D 1 The fuel bum of the engine is expressed as engine specific fuel consumption (SFC, or Cbhp) . This is fuel consumption rate expressed as a ratio of the brake horsepower produced. This is typically about 0.4 to 0.6 pounds of fuel used per hour per horsepower produced. You can get the value of Cbhp from the company that builds the engine you plan to use, or just use 0.45 - it's about right for most modem piston aircraft engines. To have consistent units in the fuel fraction equation below, this 18
must be converted to pounds of fuel per per horsepower produced. So, use 0.45 divided by 3600, or a specific fuel consumption of Cbhp =0.00013 lbs/sec/bhp. We also need an estimate of propeller efficiency. Prop efficiency is called rp, pronounced "ate a pea." This is the ratio of the thrust power you get out of your propeller compared to the engine power you put into it. Efficiency of zero means that no thrust is produced, whereas an efficiency of 1.0 means that all of the engine's power is converted into thrust. Use 0.75 for now - later we'll calculate a better value. Now we can find our fuel fraction (Wf/Wo), using a variation of the Breguet range equation. This was developed in the early days of aviation and is still one of the most important equations in aircraft design. The Breguet equation actually calculates the re/naim/ig weight of the aircraft after the cruise, so the weight fraction of the fuel that was burned is found as one minus the fraction found using the equation. Fuel Fmcti°n: = 1 - 0.9755^'° The 0.775 term is an approximate allowance for additional fuel used during takeoff, climb, descend, and landing, suitable for most homebuilts. If you're not familiar with "e" it's a number like "pi" (n) that shows up a lot in engineering equations, and approximately equals 2.7183 (like pi, its exact value cannot be calculated). Most scientific calculators have an e* button you can use for this equation - don't forget the minus sign. In this equation, "R" is the range in . e . . To convert nautical miles (nmi) to feet multiply the value by 6076. To convert statute (regular) miles to feet, multiply by 5280 (I knew that one, you say!). One final thing about fuel fraction - we should include a small allowance for a less- than-perfect engine and for the last drops of fuel that cannot be used by the engine. Six percent extra is normally used (multiply Wf/Wo by 106), but for a homebuilt with simply shaped tanks and a tuned-up, fairly new engine, this may be conservative. OK - now you can calculate fuel fraction for your design. Do it. For the DR-4,1 figure that my concept is about halfway between a single and a twin, so I select Swet/Sref and Cfe values halfway too. I pick an aspect ratio a little on the high side, because I want the chord length to be shorter so the pusher propeller is not too far to the rear. I assume cruise at 10,000 ft, 180 kts, and get: Swet/Sref 4.2 Cie 0.0053 Aspect ratio (A) 10 19
Cruise air density (slugs/ft^3) 0.00176 Cruise velocity (kts) 180 Cdo 0.0223 K (=l/piAe) 0.0424 W/S cruise 19.2 Cruise velocity (ft/sec) 304.0 Dynamic pressure (psf) 81.3 L/D cruise 9.57 I assume the values above for the DR-4 engines and propellers, adjusting SFC to be per-second. Then I calculate the Breguet equation for a range of 800 nmi, with adjustments as described above: Engine SFC (lb/hour/bhp) 0.45 Prop Efficiency (cruise) 0.75 Engine SFC (lb/sec/blip) 0.000125 Breguet Exponent 0.1539 WEWo 0.1641 Wf/Wo with allow. 0.1739 We also need to determine the empty weight, which we estimate as a fraction of the takeoff weight (We/Wo). This empty weight includes all of the aircraft's structure (what you must build) plus the engine, avionics, equipment, controls, landing gear, and other stuff that you bolt in to make a complete airplane ready to fly. We includes basically everything other than fuel, people, and payload. How do we estimate it, before we've even made a good drawing? Luckily, empty weight fraction is a nondimensional ratio that doesn't change much for different airplane designs. Because of this, we can develop simple equations that predict it. It turns out that the best way to predict it is with the aircraft's takeoff gross weight Wo. A reasonable equation is given below. The constant term "a" depends on the type of design - typical values are provided in the table * . Empty Weight Fraction: "a" Single Engine Twin Engine Metal or Wood Design 1.19 1.40 Composite Design 1.15 1.35 We're almost done. The Sizing Equation below calculates the aircraft weight Wo that just meets the range requirement we used ("R" in the fuel fraction equation). The weights of the people and payload come from your requirements. A normal weight See Appendix E if you wish to do a better job of estimating "a" for your design. 20
allowance fo/ people is 180 pounds each, but pe/haps 200 lbs is mo/e /yalistic these days fo/ cheesecake-eating adult males. Sizing Equation: So, now you can size you/ ai/plane. Calculate all the te/ms above, and wait a minute, to find Wo I need to know We /Wo, but to find We /Wo, I need to know Wo. Yup - nobody said it would be easy. To find the answe/ we need to "ite/ate." That's what enginee/s say when they /eally mean, "keep guessing until you get the /ight answe/ . ' " Fi/st guess a likely value fo/ Wo. If you have no idea, use 1,000 lbs. Then calculate We /Wo fom the equation above, and use it to calculate Wo. If you/ calculated value equals you/ guess - wow a/e you lucky! Othe/wise guess anothe/ value fo/ Wo which is highe/ o/ lowe/ depending on whethe/ the calculated value was highe/ o/ lowe/, and keep guessing until you hit it. If you don't want to tty that itemtion stuff, you can also find the /ight value fo/ Wo by making a simple g/aph. On the ho/izontal axis place 4-5 diffe/ent guesses of Wo. On the ve/tical axis put the calculated values of Wo fo/ those guesses. Connect the dots to make a line. Then d/aw a st/aight line f/om the graph's 0-0 point up at a 45- deg/ee angle whe/e the guess value of the ho/izontal axis equals the calculated value on the ve/tical axis. The point whe/e these lines c/oss is you/ answe/ (see below). Fo/ the DR-4,1 assume the empty weight f/action will also be somewhe/e between a single-engine ai/c/aft and a no/mal twin, so I use "a"=1.25 (a bit close/ to the single). Fo/ weight ca/ried I used the minimum th/eshold, 2 people at 180 lbs each plus 20 lbs of baggage. I'll be able to cany mo/e fo/ sho/te/ tnps, but don't want to inc/ease my akc/aft's weight and cost by t/ying to cany mo/e ove/ the longest distances. I then guess values of Wo between 1,000 and 2,500 lbs, calculate the empty weight f/action, and use it and the fuel f/action to make a calculated value of Wo. The g/aph below shows the sized /esult to be just less than 2,000 lbs. 21
3000.0 0 500 1000 1500 2000 2500 3000 Wo Guess J. DE-4 /KzYEz/ &zz/7g I decided to use 2,000 ibs as the design weight for the first drawing to leave a little margin in case things don't work out as hoped for. By the way, I first tried to reach my goal range of 2000 nmi but there was no usable answer. Engine Sizing and Selection y?gMre 4. TizrcnT/? Engz^e (Lyco/Kzng 0-2J5) Skip this section if you've already selected an engine - too bad, because this is the easiest calculation of all. We previously calculated Power Loading, and now have calculated takeoff gross weight (Wo). To find out the horsepower that wed //%<? to have for our design, simply divide the weight by the power loading: 22
Horsepower Required: TTp - If you have two or more engines, divide by the number of engines. Now look for a good, affordable engine that has about that much power. See Appendix D for data on typical engines used in homebuilts, but don't be limited by these. There are many possibilities including production aircraft engines, engines produced just for homebuilts, modified automobile engines, and even-more-exotic possibilities. Many companies have the information you need on their website - see the links page at my company's website One caution - anything other than a production aircraft engine was probably not originally designed to the reliability levels required for FAA certification, and may have more risk of an in-flight failure. So be careful! But, many homebuilders are having great success with non-traditional engines. For further discussion related to engine selection and installation, the book F/rewa// Forward by Tony Bingelis^ is recommended (as are all his books). If you find a great engine that just misses the required amount of power, grab it anyway and adjust your Wo to a lower value to keep the Power Loading you previously estimated. You will lose a bit of range, probably. We also need to pick the propeller diameter. Often there is a propeller that is already used with the engine. If not, we'll decide on the diameter now since it will have a big effect on thrust produced and on our landing gear length when we lay out our design. The following empirical equations seem to work: Diameter (2-bladed prop): D = 1.83 Diameter (3-bladedprop): D = 1. If the propeller diameter is too large, the tips may approach sonic speeds in high¬ speed flight causing a loss of thrust and a lot of noise. To avoid this we calculate the tip speed using the following equation (n is revolutions per second_RPM/60). Make sure tip speed is less than 950 ft/sec (850 if using a thicker wooden prop). Tip Speed: ; D m ft V m A/sec For the DR-4, my power loading of 8.8 and takeoff weight of 2,000 lbs says that I need at least 228 hp. I select the two Australian Jabiru 33OOs, a 4-stroke engine which puts out a maximum of 120 hp and has a good cruise SFC. This engine is relatively small and is designed for both tractor and pusher installations. I will use a 2-bladed prop in front and a 3-bladed prop in back to reduce the chances of a "beat" type interaction between the props. The above equations indicate that the 2-bladed prop should be 6 feet whereas the 3-bladed prop should be 5 ft (diameter). 23
Wing Geometry Now thot wz hove colculoted tokeoff gross weight, wz con colculotz thz wing oreo - it is simply thz oircroft tokeoff gross weight divided by thz tokeoff wing looding. Wing Arzo: We need to decide on the octuol wing geometry. Wz don't just drow something cool. Instzod wz pick volues of certoin porometers ond use them to mokz the wing drawing. One of these we've olreody discussed, thz Aspect Rotio (A=b^/S). When wz pick ospect rotio, wz ore reolly picking the wing spon since thz wing oreo wos olreody found to give us thz correct stoll speed. Wing spon is octuolly the moin foctor in drog-duz-to-lift. A lorger spon results in lower drag-due-to-lift. But, o lorger spon is usuolly heovier so wz must pick o suitoblz compromise for ospect rotio. After drowing the oirplone wz con do on ospect rotio trode study to find the best voluz to usz. Another importont geometric poramzter is thz "toper rotio" or "2c" (Greek letter "lombdo"). Toper rotio is just the tip chord length divided by the root chord length. The only tricky port is, the root chord isn't the chord where the wing meets the side of the fuseloge. For oerodynomic purposes, thz root chord is ot the center of the oirplone ond is found by extending straight lines from thz wing leoding ond trailing edges. This con be seen in figure 5. Root Chord Tip Chord yigMre 3776 77/? Notice the dotted lines thot form o tropezoidol shopz, sort of o simplified wing. This is thz "reference wing," ond its totol oreo is thz Sref thot wz mentioned previously. 24
The actual wing is shown shaded, and ignores the part of the reference wing that is covered by the fuselage while including the change in wing area due to fillets and wingtip shaping. This actual wing area is called the "exposed" wing area, or S.xp * WeTl use this later to calculate the wing wetted area. Tapering of a wing is used mostly to change the spanwise lift distribution - how much of the lift occurs at what spanwise location. This has a desirable effect on drag if done properly. Ideally, we want the lift to be "spread" from tip to tip in the shape of an ellipse. A wing with no taper has too much lift out near the tips. By tapering the wing, we make it look a little more like an ellipse, as shown in figure 6. Notice that we can get even closer to an ellipse by having a straight center section and tapered outer wing panels. It is a bit more difficult to build, but many homebuilt airplanes have "double-tapered" wings like this. Wing taper may also reduce structural weight, because the root chord is longer so the wing is deeper at the root. This provides a greater leverage for handling the wing bending moments. This allows the skins to be thinner. For a larger aircraft with an unswept wing, a taper ratio of about 0.4 will usually provide the best compromise between aerodynamics and structural weight. For smaller aircraft like most homebuilts, this weight savings due to taper may not apply since the skins can only be so thin. Also, a small airplane can experience tip stall problems if the tip chord is too short. It is therefore suggested that the taper ratio be no less than 0.5 (tip chord equals half the root chord). Many successful homebuilts use an untapered wing (2=1) which is much easier to build - the ribs are all the same. While the drag will be slightly worse, an untapered 25
wing does have another advantage - it tends to stall starting at the root which makes the airplane more controllable in stall. Like many things in aircraft design, you the designer must decide. Now we can start the design layout by drawing this reference wing using Sref, Aspect Ratio, and Taper Ratio, with the following equations: Wmg Span: - ^46^ Root Chord: C = Tip Chord: Go on - draw the reference wing on a piece of paper, in the drawing scale you are using for your layout (probably 1/10 . or 1/20^ for a typical homebuilt). Or, create the reference wing outline in your CAD system in full scale. If you are designing a large or high-aspect ratio airplane you may want to check the calculated wing span against the hanger you hope to use. Typical general aviation hangers have doors about 40 feet wide. YouTl have to decide on the wing sweep - it's OK just to make it look cool, but realize a few things. If you make the sweep too great, you will lose some lift (by the cosine of the sweep angle, so 60 degrees of sweep will cost you half your lift). Also, too much sweep tends to make the wing stall first at the tip - the reason for those extra drooped leading edges and vortilons on Long-EZs and the like. Swept wings are more prone to flutter than straight wings - make it stiff. But, swept wings have definite aerodynamic advantages - starting at about 450 kts! If you want to sweep the wing forward you really have to know what you are doing. A forward-swept wing is naturally prone to "divergence" - the fancy way engineers say, "the wing gets ripped off unexpectedly." Get expert help, or don't even try it! Sweep is called "A" (upper case Greek letter "lambda"). In figure 7 you can see the precise definition of wing sweep for lift calculation - it is actually the sweep of the line at 25% of the chords that matters in subsonic flight. Zero is best, but 5-10 degrees is about as good. 26
^g^re 7. 77?e IFZ'T^zg (2.5% o/ CjZc^^rTLLT?^) Now we come to the first thing that we'll do to make the airplane stable. We need to design the airplane so that its center of gravity and the wing are in the "right" location with respect to each other. What is "right"? To find this, we first need to find something called the "mean aerodynamic chord," or "MAC." In equations, the length of the MAC* is a "C" with a line over it, pronounced "C-bar." We will find the MAC using an old graphical method, shown in figure 8. First draw a line from a point at the middle of the root chord to a point at the middle of the tip chord (the 50% chord line). Now go behind the root chord by a distance equal to the tip chord and mark a point. Then go in front of the tip chord by a distance equal to the root chord, mark a point, and draw a line to the other point you marked. Where it crosses the 50% chord line is the location of the MAC, which you can now draw and measure. Or, the length of the MAC can be calculated using the equation below. Mean Aerodynamic Chord: 2)l + + A" 3 J 1 + A c = Actually, there is a technical difference between mean aerodynamic chord (MAC) and mean chord (C-bar), but we commonly mix terminologies and use the notation C-bar for MAC in our equations. Don't worry about it! 27
& Fy/z^ng (^F^(Q Thz MAC is sort of on overoged chord, ond thz entire wing tends to oct os if oil its orzo were concentrated ot the MAC. In other words, whotzver the MAC would do by itszlf, the entire wing does. This includes making lift and producing pitching moments. For an airfoil by itszlf, the point of neutral stability is 25% of chord back from the leading edge. So, for a wing, the point of neutral stability is 25% of MAC bock from thz leading edge of the MAC . Find this point and mark it on your drawing. For a double-tapered wing, find thz MAC of each panel separately, find thz 25% point of each, and find an averaged point weighted by the areas of thz panels. 28
If your airplane had no fuselage or tail and the center of gravity was located at exactly the 25% MAC point, it would be neutrally stable. When you add tails to the plane it gets more stable, which is good. In industry we usually put the center of gravity a little further to the rear, at about the 30% MAC point, but we do sophisticated analysis and wind tunnel tests to make sure it works. For a homebuilt, let's just keep the center of gravity at 25% MAC. How do we keep the center of gravity at 25% MAC? When you first draw the airplane, try to make it so just by eyeball. Later we will measure from your drawing where the center of gravity wound up, and fix it if needed. Notice in figure 9 the center of gravity symbol, a circle with two quarters filled in. Put this on your drawing as a target. What about canards? Homebuilts use a type of canard known as a "lifting canard, ' ' which really acts like an extra wing. Canards make the airplane very unstable unless the center of gravity is put way forward of the wing's 25% MAC location. The problem with canard and tandem wing designs is that the canard (or front wing) turns the flow before the back wing sees it. If the nose comes up, the canard gets the full extra lift from the increase in angle of attack, but it also turns the flow. The back wing sees only a smaller change in angle of attack, so it gets less extra lift. More extra lift in front and less extra lift in back tends to give a nose-up pitching moment, but we need a nose-down pitching moment for stability. The only solution is to shove the center of gravity far forward, which forces the canard to carry more than its fair share of the aircraft's weight. As a starting point, lay out the airplane so that the center of gravity is at a point between the 15% MAC locations of the wing and canard, weighted by their areas (see illustration and equation below). Please realize that this is only a rough starting point for your first drawing - you should get expert help to finalize the design of a canard airplane * . Before flying the VariViggen, Burt Rutan tested it thoroughly using an instrumented model mounted on the roof of his car (poor-man's wind tunnel!). CG Location for Canard Airplane: " (where Xwng and X^M-d are measured at the 15% MAC point for each) * Reviewer Peter Garrison says it stronger: "7%e Aayzc pro?/em o ?Ae canard con/igi/na/ion zs /Aa/ // you ge/ z * wrong, you're pr-o?ai?/y dead wAereay /Ae convention con/igura/ion Ay nzucA moreybrgzvzng dlnd /low do youyznd on/ i/you've go/ t/ie canard rigA/ wz/Aont extensive and Aazardony /ey/ing, .pun cAute, etc? / wou/d s/rong/y connye/ wou/d-Ae de^ignery againy/ nuder/a^ing (origina/) canard pro/ec/y " 29
7 0. Canard Layoff j&r We need to set the dihedral. This is the upward angle most wings have when seen from the front. More dihedral makes the airplane more stable in roll, but also makes it less responsive in roll and makes it wobble from side to side in gusty winds. A high wing gets a slight positive dihedral effect so a little less actual dihedral is needed. A low wing design will almost always need some dihedral because the fuselage above the wing acts like negative dihedral, making the airplane unstable in roll. Wing sweep also acts like dihedral, with 10 degrees of aft sweep acting like one degree of dihedral. The table below gives reasonable values for dihedral. Dihedrat Low Wing Mid Wing High Wing Unswept Wing Swept Wing (5) to (7) (3) to (7) (2) to (4) (-2) to (2) (0)to(2) (-5) to (-2) Use 2-3 degrees less dihedral for an aerobatic airplane to make it about neutral in roll stability. If you want a flat center section with the dihedral only on the outer wing panels, draw it so the wing tip is at about the same height as it would be if the dihedral started at the center. Watch out - if the dihedral break occurs much more than 50% out on the span, you can get excess and maybe uncontrollable rolling near the stall. If you use a gull wing like on the saucy little design below, the dihedral guidelines for a low wing should be used with perhaps 1-2 degrees more dihedral. 30
77. Gz//--F7?g - "Lovwg Low " We also need to decide how big to make the ailerons. This is related to the size of the flaps, if you have any. With big flaps there is not as much span left for ailerons, so they have to have a large chord. But, when you do that the rear spar has to be further forward, which may increase weight and also takes away fuel volume. Aileron sizing guidelines are provided below. If you use most of the wing trailing edge for ailerons (no flaps), they can be just 10 or 12% of chord. If the ailerons are less than half-span, you may need 20-30% of chord to get adequate roll control. AUeron Chord/Wing Chord y?gMre 72. Tf/eron &z//7g For the DR-4 wing, I select taper ratio = 0.5. Sweep will be about zero at the quarter¬ chord, with 5 degrees of total dihedral. Wing area is 2000/19.55, or 102.3 square feet. With aspect ratio of 10 the span is 32 ft, with a mean chord of 3.32 feet. Root chord is 4.26, and tip chord is 2.13 ft. 31
Airfoit Selection The choice of airfoil affects the airplane's lift, drag, and stability especially near the stall, and also affects the weight of the aircraft. In general, an airfoil will have more lift if it is thicker, has a more-round leading edge, and has more camber (the curvature from front to back). It will also have more drag. Airfoils with a lot of camber tend to have a greater pitching moment requiring more trim force, adding to the drag. An airfoil with a fairly sharp leading edge may have less drag but is more prone to a sudden and uncontrollable stall. Some airfoils are especially designed to encourage laminar flow, where the air flows smoothly from front to rear. On a normal airfoil the flow will go from laminar to turbulent flow not too far back from the leading edge. Turbulent flow has higher drag, but is better at staying attached around the back of a body (the reason for the dimples on a golf ball). If a laminar flow airfoil is selected, it must be almost- perfectly fabricated, usually with molded composites. Watch out for a tendency of laminar airfoils to have sudden stall characteristics. A thick airfoil has more depth for structure so the wing will be lighter, at the expense of higher parasitic drag. However, a super-thin airfoil (<10%) really doesn't reduce total aircraft drag by much unless you are going over 450 kts. A thicker airfoil also provides more room for fuel, control linkages, and landing gear. All in all, a thickness of 12-16% is probably most suitable for homebuilts. Today's design "pros" usually have new airfoils designed for each new aircraft. In the past, designers did what most homebuilders do today - select a proven existing airfoil. The actual coordinates (points to draw the airfoil) along with lift, drag, and pitching moment for the NACA airfoils can be found in the widely used book "Theory of Wing Sections^." This is an enhanced version of the 1945 NACA Report 824, currently available at the NASA-Langley website. Other airfoil data can be found at an extensive University of Illinois website (see the Links page for the current URL). Typical airfoils^ used in light aircraft are shown and listed below. NACAOOQa <^Z^CA0009 NACA 23012 32
CpMvenZMMia/ Root Airfoii Cimax Tip Airfoii Cimax Ae/onca C3 Cla/k Y 1.65 Clark Y 1.65 Bede BD-4 NACA 64-415 1.60 NACA 64-415 1.60 Bede BD-5 NACA 64-212 1.50 NACA 64-218 1.50 Beech 35 Bonanza NACA 23016.5 1.60 NACA 23012 1.60 Bellanca Skyrocket 11 NACA 63-215 1.60 NACA 63-215 1.60 Bellanca Citab/ia NACA 4412 1.60 NACA 4412 1.60 Bellanca Decathlon NACA 1412 1.60 NACA 1412 1.60 Bowe/s Fly Baby 1-A NACA 4412 1.60 NACA 4412 1.60 Cessna 152 NACA 2412 1.65 NACA 0012 1.55 Cvjetkovic CA-65 NACA 4415 1.55 NACA 4415 1.55 Gar/ison Melmoth NACA 65A316 1.50 NACA 65A316 1.50 Hughes H-l Race/ NACA 23012 1.60 NACA 23006 1.60 Loving WR-1 Love NACA 2412 1.65 NACA 2409 1.65 Mu/phy Rebel NACA 4415mod 1.55 NACA 4415mod 1.55 Neico Lancai/ 320 NLF(l)-0215F NLF(l)-0215F No/th Ame/ican Navion NACA 4415R 1.55 NACA 641 OR Pa^]m^^)/PL-12 NACA 63-615 1.60 NACA 63-615 1.60 Pazmany PL-4 NACA 63-418 1.60 NACA 63-418 1.60 Pipe/ PA-28 Che/okee NACA 65-415 1.60 NACA 65-415 1.60 Pipe/ PA-38 Tomahawk NASA GA(W)-1 1.70 NASA GA(W)-1 1.70 Pitts S-1C NACA M-6 1.50 NACA M-6 1.50 P/escott Pushe/ NLF(l)-0215F NLF(l)-0215F Questai/ Ventu/e NACA 23017 1.60 NACA 23010 1.60 Rand Robinson KR-1,2 RAF-48 RAF-48 Schempp-Hi/th CiIrus Wo/lmann 66-196 Wo/lmann 66-161 Stodda/d-Ham^. Glasai/ NASA GA(W)-2 1.80 NASA GA(W)-2 1.80 Taylo/ Ae/oca/ NACA 43012 1.65 NACA 43012 1.65 Van's RV^-^, 4, 6, 8 NACA 23013.5 1.60 NACA 23013.5 1.60 Wittman Tailwind NACA 4309 1.60 NACA 4309 1.60 CanarJ D^e^signs Airfoii: Canard Airfoil: Rear Wing AASI Jetc/uze/ NASA LS(l)-0417mod NACA 23012 Cana/d Aviation SC Epple/ 1232 FX 63-137 Co-Z Cozy RonczR1145MS Epple/ 1230 mod Gy/oFlug Speed Cana/d Epple/ 793 Epple/ 1231 QAC Q2 GU25-5(11)8 Epple/ 1212 Rutan 32 Va/iViggen SP NACA 4414 Wo/tmann FX60-126 Rutan 33 Va^ze GU25-5(11)8 NASA GA(W)-1 mod Rutan 61 Long EZ RonczR^1145MS Epple/ 1230 mod Velocity RonczR^1145MS Epple/ 1230 mod VFW-FokkerVC 400 RAE 102 RAE 102 33
Different airfoils are designed to have their lowest drag at different lift coefficients. Airfoils with a lot of camber are good at lower speeds (high lift coefficients), but have extra drag in high-speed flight. Uncambered airfoils are good at high speeds (low lift coefficients), but have lots of drag when flying at low speeds. The "design lift coefficient" (C/^gn or C/J is the lift coefficient the airfoil is best at, and can be found by looking at the lift-vs-drag data for an airfoil you are considering. It is smart to make sure that your airplane will be cruising at about the chosen airfoil's design lift coefficient. We find the lift coefficient during cruise using the wing loading equation we saw before: Wing Loading: where 9 = and So Cruise Lift Coefficient is: c Calculate q using air density and flight velocity at cruise, and don't forget, V is in ft/sec. Typical values of cruise lift coefficient are about 0.2 to 0.5. Anything over 1.0 is probably a mistake! One more thing to consider - we normally place the airfoils at some incidence angle to the fuselage. We try to set the airfoils so that they are at the correct angle of attack for creating the lift we need during cruise, with the fuselage at zero angle of attack so that it doesn't create unwanted drag. Calculate the lift coefficient during cruise as above, then find the angle of attack (a) that gives that lift coefficient. A simplified version of wing theory calculates this as: Angie of Amdc (degrees): a = [10 + 18/ /]+ Or if wing is swept: = C 10 + 18cos((iw^p)/4 cos(AMp) "A" is the wing aspect ratio. The last term, 6//, comes from your airfoil data. An airfoil with camber (curvature) makes lift even at zero angle of attack, so the calculated angle of attack is too large. In the airfoil lift vs. angle of attack, find the angle of attack that gives zero lift. This should be a negative number (-1 degree for the NACA 23015). We add this negative number, so the angle of attack is reduced (by 1 degree for the 23015). If you use an airfoil with a lot of camber, don't be surprised if the adjusted incidence angle is very small - the VariEze has a wing incidence angle of only 1/10/ of a degree. 34
What about twist? We often twist the wing 2-3 degrees, with higher airfoil incidence at the root and a lower incidence at the tip. This is called "washout" and makes the wing stall first at the root because it has a higher angle of attack. Note that the incidence angle calculated above is the airfoil angle at the MAC, no/ the centerline wing root airfoil or the airfoil at the side of the fuselage. Lay out the wing so that the MAC is at the desired incidence angle and the twist begins at the MAC, with reduced incidence outboard and increased incidence inboard of the MAC. For the DR-4 wing airfoil I select the NLF(l)-0215F (15%), which has good structural depth and exhibits laminar flow even at lower Reynold's numbers. It also has a reasonable maximum lift coefficient (1.6). However, it has a fairly large pitching moment (-. 15) so I'd better make sure the tail is large enough. Tai! Geometry Airplanes have tails for one purpose - to make moments. Moments are made by having some force act at a distance ("moment arm") around the point of rotation. We all learned about moments as children, playing on a teeter-totter. Two kids close to the pivot can be balanced by one kid sitting far on the opposite side (until he jumps off - ouch!). For tails, the moment arm is measured from the MAC of the tail to the MAC of the wing" . The force made by the tail is its lift (up or down), which depends on the size of the tail (area S). If you multiply distance in feet by area in square feet, you get cubic feet (ft^), which are the units of volume. Years ago somebody invented a nondimensional coefficient that considers this, called the "tail volume coefficient." It is still the best way to initially estimate areas for the horizontal (Sm) and vertical (Syr) tails. It uses tail moment arm length "L" and either the wing span "b" or the wing MAC (C-bar in the equations). * It would be slightly more correct to measure to the center of gravity, but the wing MAC is close to the e . g. and is used as a reasonable approximation. 35
74. 7hw7 S/zz^g Aj/ Co^czeMf Horizontal Tail Sizing^: ^ZTonzro^Kf^a^Z " ^/fy Vertical Tail Sizing: A C Q ^WlKg " ^PT We need reasonable values of the coefficients and to use these equations. These are found by measurements from successful airplanes. You can do this yourself, for designs similar to what you want to build, or you can use typical homebuilt aircraft values of 0.5 for the horizontal tail (0.7 if large flaps are used) and 0.04 for the vertical tail. For the DR-4 I use a vertical tail volume coefficient of .04 and a slightly large horizontal coefficient of.6 (because of the high moments of the airfoil). These give a vertical tail area of 13 and a horizontal tail area of 20, based on a tail moment arm of 10 feet. As I begin the layout IT1 have to check the tail moment arm and maybe revise these. 36
What about T-tails? The T-tail places the horizontal tail up high, away from the wake and downwash of the wing, so the tail works better. Also, the horizontal tail acts like an endplate so the vertical tail works better too. Both surfaces can be reduced in area about 5%. However, there is often a weight penalty for T-tails because the vertical tail has to carry the loads of the horizontal tail, and the fuselage sees greater twisting loads. Only a detailed structural calculation will tell you if there is a penalty, and how much it is. If you use an all-moving horizontal tail like on a Piper Cherokee or Pazmany PL-1, it will work a bit better than a separate elevator. Horizontal tail area can be about 10% reduced, but again, there is a weight penalty. If you use an all-moving T-tail, my suggestion is - don't push your luck by trying to apply both area reductions! For a V-tail, calculate the total areas required as if you would have regular tails then add those areas together. This is about the right area* for a V-tail. Set the two tail panels at about 45 degrees from horizontal. Be wary of V-tails and get some expert help. They are prone to lateral "wandering' ' and some have been reported to have poor spin recovery. Also, make sure that the control linkages are absolutely reliable 75. wz?/z (T-Th?/) - L(?<r/&K To actually lay out the tail on your drawing, you also need to select the tail aspect ratio, taper ratio, and sweep. These are not as critical as for the wing, and it is OK just to make the tails so they look like tails, provided they have the right area. Typical nice-looking values for homebuilts are as follows: Pythagoras was a lousy aircraft designer.
Tai! Geometry Horizontal Vertical Aspect Ratio Taper Ratio Aspect Ratio Taper Ratio Conventional 3 to 5 0.3 to 0.6 1.3 to 2.0 0.3 to 0.6 T-tail 3 to 5 0.3 to 0.6 0.7 to 1.2 0.6 to 1.0 Sailplane 6 to 10 0.3 to 0.5 1.5 to 2.0 0.4 to 0.6 Horizontal tail sweep is frequently set to provide a straight hinge line for the elevator. This makes it easy to connect the left and right sides, which reduces flutter tendencies. Some homebuilt airplanes use untapered horizontal tails (2= 1.0) to make them easier to build. Tail airfoils are not as critical as wing airfoils because the tail is usually generating very little lift. Often the old NACA four-digit symmetrical airfoils such as the 0009 are used for tails. Tail thickness ratio is usually similar to the wing thickness ratio, or perhaps a bit thinner. Elevators for homebuilts and lightplanes are usually about 45% of the tail chord, unless an all-moving tail is used as discussed above. Rudders are normally about 40% of tail chord (unless you want to try an all-moving vertical, like on the SR-71). The vertical tail plays a key role in spin recovery, and the horizontal tail can hurt its effectiveness. An aircraft in a spin is essentially falling vertically and rotating about a vertical axis. We need the rudder to stop the rotation, but if the horizontal tail is in the wrong place it may block the air from getting to the rudder. yigMre 7 6. Th?/ 7?ecovery In a spin the horizontal tail is at extreme angle of attack and is throwing a turbulent wake behind itself, extending upwards along roughly a 60 degree angle from the 38
leading edge and a 30 degree angle from the trailing edge. Our mission is to make sure that at least a third of the rudder area is no/ in that bad region. The first design in figure 16 couldn't be worse. At the stall, this rudder is entirely within the wake of the horizontal tail. The rudder will barely work. The second example shows moving the horizontal tail forward to "uncover" part of the rudder, improving rudder control. The third design, like a Corsair, moves the vertical tail forward and the horizontal tail to the rear. The last example, a T-tail, fully exposes the rudder. Watch out, though - the horizontal tail may find itself in the wake from the wing so the elevator may stop working just when you need it the most! Lifting canards are usually sized by deciding how to split the lift between wing and canard A typical split is to make the canard 25% of the total area and the wing 75% of the total area. You can use the area split of a similar design as a starting point. If you use a 50-50 area split, you have a tandem wing design. The geometry of a lifting canard or tandem wing should be designed the same way the wing was designed, rather than using these tail guidelines. One exception is the aspect ratio. Most canard homebuilt aircraft have the canard aspect ratio much higher than the aspect ratio of the wing. A lifting surface with a high aspect ratio will stall before one with a lower aspect ratio. This is nice, because it makes the canard stall before the wing, which lowers the nose. Done properly, the wing should never stall. See the previous discussion on locating the center of gravity for canard designs. Fuselage Size How big should the fuselage be? A wise man once said that the outside has to be bigger than the inside. Good advice. The actual fuselage length and cross-section shape will be determined as you make the layout, working back and forth between placing the internal components and getting a smooth and pleasing shape (see next section). As a rough approximation, the following equation will estimate the length of a typical homebuilt airplane, based on sized takeoff gross weight (which we found above): Fuselage Length (starting guess): = 3.6 Of course, this estimate should only be considered a starting point. The layout you make will find its own length based on fitting everything inside, and making a smooth faired shape from nose to tail. There is considerable debate about the best value for fuselage fineness ratio (length/diameter). Numerous design books such as the classic Hoemer Fluid Dynamic Drag/ say that the lowest drag occurs when the fineness ratio is around three. However, most airplanes including homebuilts have much higher fineness ratios. 39
Analysis indicates^ that the best fineness ratio really is about three if your design needs to have a pretty large cross-section area, and it is not tight on volume (in other words, you can make it as short as you want). This is typical for a small airplane, especially one with side-by-side seating as shown below. The shortness of such a design requires larger tail areas to get the desired tail volume coefficient, which increases wetted area. Also, some people just don't like the egg¬ like appearance, or are scared about controllability despite favorable analysis and flight test. An alternative is to add a tailboom to the back of the fuselage, which can be smoothly faired to the fuselage forming a tadpole-looking design. This is common in sailplanes. If the cross-section area is not so much of a problem, but you need to enclose a certain amount of volume, then a fineness ratio of around six will have less drag. This is more typical for larger aircraft or for smaller aircraft with tandem seating. One more suggestion for fuselage design - don't start the tapering of the back end until past the trailing edge of the wing (see above design). Otherwise, the wing and the fuselage will be tapering at the same time, which makes the air more likely to separate, increasing drag. 40
Chapter 4 STUFF IN SOME STUFF One of the most import things we do in aircraft design layout is creating a smooth and aerodynamic outside shape while arranging and installing all the things that need to go inside. You have to do these at the same time, but I cant have you read two chapters at the same time. First let's look at the stuff that goes inside - then we ' ll look at getting a smooth outside shape. The end result will be a design layout drawing called a "three-view" because it shows, well, three views (side, top, and rear - see example below). This drawing will be the master plan for doing the design of the parts and the structural pieces that you will build. Also, we will use this three-view to calculate drag, weight, and performance. So, this drawing is very important and you should do it right. z^gi/re 7& X/rcrq/? Design Drawing (re/erence 7) You and Me and a Dog or Three Lots of homebuilt design projects begin with somebody sitting on the floor on a stack of pillows, moving them around until a comfortable position is found, then measuring the results. This is a perfectly good method, but you also want to make sure that other people can fit inside too. Of course, if you are big enough then your own body can be used as a "worse-case" for cockpit sizing. I'm told that the reason a 41
certain production four-seater has such a generous cockpit is that the chief designer was a really, really big guy. The other way to design the cockpit is to use a "standard-man" drawing like the one below. This guy is about 6'2", but his shoes and helmet add two more inches. Make a tracing on stiff paper of all the parts separately, in the drawing scale you are using, then cut them out and attach them using bent over thumbtacks. Then you can move him around to the desired position and trace him on your drawing. 95th percentile Man This standard man is about 26 inches wide at the shoulder. Most light planes don't really have enough room for this big guy. A typical light plane has 18-22 inches of width per person and 35-40 inches of headroom from the seat cushion to the ceiling. For this 95^ percentile standard man, a light plane feels more like a tight sweater than an airplane. What about when some smaller people want to fly your plane? For production and some homebuilt airplanes, the seat slides back and forth and/or the rudder pedals adjust in and out. These mechanisms are rather complicated for no-kit homebuilders, so maybe a simpler approach can be devised. Perhaps a large cushion can be used by smaller people, or the seat back can have several snap-in attachment points, or maybe you can loan the short pilots some 1970's-style platform shoes.... If you have two or more seats, you have to decide how to place them. Many two- seaters have the seats one behind the other (tandem). This makes the fuselage narrower, which lowers drag, and even better the pilot can't hear the passenger 42
complaining. If companionship is desi/ed, side-by-side seating is called for You can somewhat /educe the dmg penalty by having the second seat a little to the /ea/ so that the two peoples' shoulde/s ove/lap, allowing less side-to-side separation between seats. Rutan's Boome/ang has all the seats stagge/ed this way. FAR23 Section 783 sets doo/ /equipments including safety pmvisions, and should be /eviewed. While it doesn't set a /equipment fo/ light ai/c/aft, fo/ commute/ ai/c/aft it pqui/es that doo/s qualify as eme/gency exits, with "a /ectangular opening of not less than 24 inches wide by 48 inches high, with come/ /adii not gpate/ than ony-thi/d the width of the exit." If you have two o/ mo/e seats, FAR 23 Section 807 /equi/es an eme/gency exit on the opposite side f/om the doo/, that is "a clea/ and unobst/ucted opening la/ge enough to admit a 19-by-26-inch ellipse." Homebuilts aren't pquipd to follow FAR23, but it is a nice safety suggestion. Most planes also have a baggage compartment of some so/t. If you hope to sell you/ design to othe/s, the myste/ious connection between flying and golfing should be conside/ed. At Rockwell, ou/ design compute/ p/og/am had compute/-gene/ated golf clubs that could be placed into ou/ designs fo/ the milita/y. It always got a good laugh, but the pilots app/eciated it because, in /eality, it is common fo/ pilots to thrnw thei/ clubs in when going on an ove/night flight to anothy/ base. Othe/ people have diffe/ent needs - the Boome/ang has a baggage compartment sized fo/ skis. A key concern fo/ the ffont of the ai/c/aft is the ovemose vision angle. On you/ layout, d/aw a line f/om the pilot's eye fo/wa/d, at a downwa/d angle just touching the top of the cowling o/ whateve/ else p/events you f/om seeing fu/the/ down. T/y to give yourself at least a 10 deg/ee ovemose vision angle - Fo/mula One /ace/s /equi/e 15 deg/ees ovemose vision. Most fighte/s have a 15-deg/ee ovemose vision angle and most t^spo/ts have about 20 degpes. An ideal fo/ebody design would let you see the /unway a few hund/ed feet in font of the ai/plane, when the nose is up as high as it can go. Many light planes ap not so good, and fo/ most biplanes you cant see the /unway in ftont of you - the /eason fo/ S-tums. You must also plan enough space fo/ the instmment panel. You should decide what instmments and avionics you want to install and get thei/ dimensions, then lay out the panel to make sup you have enough /oom. While 1/8" is conside/ed the minimum sepa/ation between instmments, using a %" minimum separation will make the panel mo/e ngid and will look "cleane/" too. Don't be tempted to extend the panel so fa/ downwa/d that you/ knees ap t/appyd - you need to be able to get out of the ai/plane quickly, just in case. You need plenty of space behind the panel fo/ the depth of the instruments and avionics, plus extra /oom fo/ wi/ing and hoses, with /oom left ove/ fo/ getting at eve/ythrng (1 ft is good). Somehow you must p/ovide fo/ getting at the back of the inst/uments fo/ maintenance when the ai/plane is completed. The ai/c/aft of figu/e 20 has a clea/ nose like a helicopte/, so the instrument panel is on a pedestal. 43
20. Pane/ There are surprisingly few instruments legally required for VFR flight, per FAR 91. They are: 1. Airspeed Indicator 2. Altimeter 3. Magnetic Compass 4. Tachometer 5. Oil Pressure Gauge 6. Oil Temperature Gage (water temp for liquid-cooled engine) 7. Fuel Quantity Indicator 8. Landing Gear Position Indicator (if retractable) Most of us would also like to have: 1. Rate of Climb 2. Turn Indicator** 3. Slip-skid Indicator (ball)** 4. Clock 5. Directional Gyro** 6. Artificial Horizon* * 7. Com. Radio * 8. VOR 9. Transponder with altimeter encoding * 10. Ammeter and/or Voltmeter 44
More good stuff on my holiday list: 1. Glideslope with marker beacons 2. Outside Air Temperature 3. Accelerometer 4. Cylinder Head and/or EGT 5. DME 6. GPS 7. Moving Map GPS feature 8. Radar Altimeter 9. Autopilot 10. Radar Stormscope 11. Norden Bombsite (just kidding maybe) * Required to fly into Class A, B, or C airspace ** Required for IFR (Please double-check these as FARs may change at any time.) Dimensions and layout guidance for instruments and avionics are provided in the Aircraft Spruce & Specialty Catalog^, a recommended resource for designers even if you buy your stuff elsewhere! The Rubber Meets the Road Layout of the landing gear is very important. It has to be done just the right way or the plane will be dangerous to land, and may not even let you take off. There is a wealth of experience in the right way to design landing gear, going back 80 years or more, and you shouldn't stray very far from the proven methods. First, you must size the tires. There are statistical and analytical methods to do this (see my textbook), but for homebuilders, just pick tires that are on an airplane of about the same weight. If you select existing wheels, tires, and brakes from some common airplane, you can buy them from an airplane junkyard. Your landing gear will need some spring and damping action, normally provided using oleo shock absorbers. Some homebuilts use bending gear legs such as seen on light Cessnas and on the Wittman Tailwind and Rutan Long-EZ. These are usually a bit heavier and don't dampen the bouncing as well, but they are cheap and easy to fabricate. Some really small homebuilts just attach the wheels directly to the aircraft, relying on the tire itself for all spring and damping action (ouch, ouch). Whatever type of shock absorbing is used, you need to decide the 'stroke' of the shock absorber. This is the total possible motion of the wheels as the plane bounces up and down. The required amount depends mostly on the vertical speed of the airplane at touchdown. For general aviation and homebuilt airplanes, the stroke should be at least 6 inches, and 10-12 inches is better. The 'static' position of the wheel is the position when the airplane is sitting on the gear at takeoff gross weight. Typically, the shock absorber is deflected by about 2/3 of the total stroke at the static position. 45
The down location of the landing gear is critical. For tricycle landing gear, the length of the landing gear must be set so that the tail doesn't hit the ground on landing. This is measured from the wheel in the static position assuming an aircraft angle of attack for landing that gives 90% of the maximum lift (see your airfoil data for a rough approximation). This tail-down angle ranges from about 10-15 degrees for most types of aircraft, and can be seen in the figure below. 27. 7rzcyG Loy—Mg Gar ZqyoW The "tipback angle" is the maximum aircraft nose-up attitude with the tail touching the ground and the strut fully extended. To prevent the aircraft from getting stuck, tipped back on its tail, the angle off the vertical from the main wheel position to the center of gravity (c . g.) should be greater than the tipback angle or 15 degrees, whichever is larger. However, too large of a tipback angle makes it difficult to lift the nose for takeoff, and can also lead to catastrophic "porpoising." If the nose wheel is carrying over 20% of the aircraft's weight, the main gear is probably too far aft. Qn-the other hand, if the nose wheel is carrying less than 5% of the aircraft's weight, there will not be enough nose-wheel traction to steer the aircraft. The optimum range for the percentage of the aircraft's weight that is carried by the nose wheel is about 8-15%, for the most aft and most-forward e . g. positions. 46
The "overturn angle" is a measure of the aircraft's tendency to overturn when landing in a crosswind or taxiing around a sharp comer. This is measured as the angle from the c . g. to the main wheel, seen from the rear at a location where the main wheel is aligned with the nose wheel (see figure 21). This angle should be no greater than 63 degrees. The layout of taildragger landing gear is shown above. The tail-down angle should be about 10-15 degrees with the gear in the static position. The most forward and most aft e . g. positions should fall between 16 and 25 degrees back from vertical measured from the main wheel location. If the e . g. is too far forward the aircraft will tend to nose over, and if it is too far back it will tend to groundloop. To prevent the aircraft from overturning the main wheels should be separated by at least 25 degrees off the e . g., as measured from the rear in a tail-down attitude. Propeller ground clearance has a big effect on your landing gear layout. FAR 23 requires a minimum of 7 inches ground clearance for tricycle gear and 9 inches for taildraggers. With a flat tire and the strut fully compressed the prop must not hit the ground. To avoid the propeller pulling up and striking small objects on the ground, it is a good idea to have at least 10 inches of ground clearance. 47
Free-swivei negative rake Forward Steerable positive rake Trail Trail 2J JVohe/7b777 The nosewheel or tailwheel must be capable of being castored (turned). We use different geometry if the wheel is free to swivel or is steerable, as shown above. Nosewheels can be steerable or free to swivel. If the nosewheel - is free to swivel, the pilot steers the aircraft on the ground using only the brakes. This increases brake wear and presents a great danger if one brake fails during takeoff or landing. Tailwheels are always designed as if they are free to swivel. Steerable tailwheels are connected to the rudder pedals by soft springs that don't affect the wheel dynamics. High-powered tailwheel aircraft like WWII warbirds may have provisions for locking the tailwheel during takeoff and landing. The castoring can cause "wheel shimmy," a rapid side-to-side motion of the wheel that can tear the landing gear off the airplane. We avoid shimmy by proper selection of the rake angle and trail as shown above. In some cases a shimmy damper is also required. This can be a hydraulic plunger or simply a pivot with a lot of friction. For a wheel that is free to swivel, shimmy tendencies are lessened by using a small negative angle of rake (4-6 degrees) and a trail equal to 0.2-1.2 times the tire radius. If the trail is less than the tire radius, a shimmy damper is more likely required. 48
For steerable nosewheels on tricycle-geared aircraft, a steering linkage is connected to the rudder pedals to provide positive control of the turning angle * . To reduce the control forces, we use a rake angle of up to 15 degrees and a trail of about 20%. Big decision - retract the gear, or not? For a slow aircraft, say, under 120 kts, retracting the landing gear is probably more trouble than it is worth. Retractable landing gear is heavier, more complicated to build, and greatly increases the chances of a gear-up landing. Retractable landing gear also messes up the structure of the wing or fuselage where it retracts, and takes away internal volume that could be used for other things. Really, the only advantage to using retractable landing gear is drag reduction. An airplane that retracts its landing gear has an L/D that is about 20% better than a fixed-gear design. Also, this best L/D occurs at a higher speed. Together, these give more than 20% greater range on the same amount of fuel. As a comparison, the Cessna Cardinal comes in retractable and non-retractable versions. The retractable version has a maximum range of 1050 nmi at a best cruise speed of 121 kts, compared to the fixed-gear version with range of 712 nmi at a best cruise speed of 109 kts. Maximum speeds are 156 kts and 139 kts, on a similar engine. The retractable version weights 175 lbs more, or a 12% increase in empty weight. However, it is difficult to draw direct conclusions since the takeoff gross weight for the retractable version was increased 300 lbs. Also, there is 12% more horsepower in the retractable version, but by itself this increases speed less than 5%. * The nosewheel steering is usually connected via springs to allow some self-centering, but the springs are hard enough that the dynamic response of the nosewheel is as if a rigid connection were used. Note that airliners often have a separate steering wheel rather than a connection to the rudder pedals. 49
If your gear is to retract, you need to draw it in the down position, place the pivot point, and swing the gear into the retracted position. Remember that the shock absorber will extend when you take oif, so the gear length that must be retracted is longer (see figure 24). r —r Dotted is static position 2-. jRtefraf on 50
In Goes the Engine First decision: engine in front (tractor) or engine in back (pusher)? My textbook has a big technical discussion on the pros and cons of each, but you probably don't care. If you like pushers, make it a pusher" . If not, make it a tractor. Either one can produce a good airplane. The engine compartment for a piston engine is normally no/ a part of the fuselage structure. The engine is bolted to a steel-tube motor mount that is itself bolted to the corners of the fuselage, transferring the engine loads to the structure. Between the engine and the fuselage structure it is a good idea to leave a foot or so of space, which will be used for installing batteries, cabin heat ducts, hydraulic reservoirs, and the like. Also, if you might ever want to put in a larger engine it is a good idea to provide extra room now so that the nose doesn't have to be extended. A firewall is needed, to keep fire away from people and the airplane structure. This is typically a 0.015-in. steel sheet (stainless or galvanized) or a fireproof ceramic cloth (Fiberfrax) attached to the first structural bulkhead of the fuselage. The firewall should not be broken with cutouts (such as for a retractable nose wheel). All controls, hoses, and wires that pass through the firewall have to be sealed with fireproof fittings. The cowling (skin) around the engine is usually a non-structural, aerodynamic fairing. Some or all of the cowling should be removable to let you get at the engine for maintenance. Small doors are also needed so that you can check the oil level and drain fuel before flight. ^Fg^re 25. Engy/ic Cow/Mg * Try to position a pusher propeller no less than 30% of wing chord behind the wing trailing edge or you'll lose thrust and gain a lot of vibration. 51
Cooling is a major concern. 10% or more of the engine's horsepower can be wasted by the drag associated with taking in cooling air, passing it over the engine, and exiting it. To minimize this cooling drag, the cooling-air mass flow should be as small as possible and used as efficiently as possible. For efficient use of cooling air, it should be ducted to a tight compartment above or below the engine so that it can only escape by flowing through the cooling fins on the cylinders. Traditional cowlings (see above) use sealing flaps that press against the cowling skins when they are attached, but this may allow costly leakage. A better design for cooling has a fully sealed box ("plenum") forcing the air through the cooling fins - but such a design is heavier and makes maintenance more difficult. Two examples of sealed plenum systems are shown below - one for a tractor, and one for a pusher design. For the tractor installation, the top of the box is removed in the photo. In both designs, the cooling air enters the plenum box from the left, and is forced down through the cylinders. In the pusher installation, the cooling air exits through the "tubes" at the bottom-right. Note that the engine exhaust pipes also exit through these tubes. The exhaust gases going out actually pull the cooling air out as well, providing a free "pumping" action to improve cooling. 26. P/Mm/K Coo/wig - Prohor 52
27. Coo//pg - P^A^r Typical air-cooled engines need about 1 pound of cooling air massflow per second per 100 horsepower of the engine. Recent optimization studies^^ indicate that the best intake slows the air to 30% of the aircraft flight speed (climb speed in the worst case). This results in the following equatior Cooling Intake Area: Results are in square feet. Vcim is the climb speed in feet per second (=kts* 1.689 or =mph* 1.467). This is usually the critical condition for cooling. The cross-section shape of the intake hole as seen from the front is not so important, but the internal flow will be better if the intake hole is about the same shape as the cooling plenum chamber it connects to. The lips of the cooling intake should be well rounded to allow air to flow in from all angles. Also, the cooling intake should not be too close to the prop spinner for a tractor engine - 3 to 6 inches is a good clearance. It's better if the air that flows over the spinner doesn't go into the cooling intake. * An inlet area formula from a lecture many years ago by John Thorp can be manipulated to yield the same equation with the (2.2) replaced by (3.0), ie., a slightly smaller intake. In some existing homebuilts this factor is as high as 4, indicating an even smaller intake. This author suggests sticking with 2.2. 53
An old rule-of-thumb says that the exit area should be about 30% larger than the intake area. This rule was intended to keep the cooling air velocity constant from the inlet to the exit, considering the momentum loss of the air passing over the engine. Recent analytical optimizations have shown that an exit area slightly .wwa/Zer than the intake is actually better. According to these results maintaining constant internal velocity really isn't so important. This author measured the cooling air inlets and outlets of dozens of homebuilt and production lightplanes* , and found that the ratio (Aexit/Ainlet) varies from 0.5 to over 4! Many of the designs have a ratio of 1.3, indicating that the old rule-of-thumb described above is still in use. This author suggests designing to a ratio Aexit/Ainlet of 0.8 and providing adjustable cowl flaps that open to a ratio of 2 or more. Adjustable cowl flaps let us change the exit area in flight, which changes the cooling airflow (see below). It isn't necessary to vary the cooling intake area because the cooling airflow always adjusts to the exit area. yZgMe 2& %r/o&/e Ew7 /irea Cow/ The cooling air exit is usually at the bottom of the cowling. This keeps the heated air away from the cockpit and also allows leaking fluids such as gasoline and oil to drain out the bottom. Better cooling flow will result if the cooling exit is in a low-pressure region such as the top of the cowling or over the wing. Peter Garrison's new Melmoth 2 has the cooling exits on top of the cowling at the very front, where aerodynamic analysis has revealed a low pressure region. However, if you have cooling exits in front of the windscreen, beware of oil and smoke covering the canopy and causing instant IFR! Perhaps you saw me under your plane at AirVenture (Oshkosh) 2002, tape measure in hand. 54
Stuff Some Structure You have to define the overall concept and arrangement of the structure before you can design the actual pieces of structure you will build. The overall arrangement of structure is done in the very first three-view drawing, and includes the wing box, wing carrythrough, fuselage bulkheads, fuselage longitudinal structure, and attachment locations for the engine, landing gear, tails, and anything else that is big, heavy, or highly loaded. The main thing to worry about in designing a good structural arrangement is the provision of good "load paths." These are simply the structural elements by which opposing forces are connected. For example, the engine's weight pushes downward, and ultimately this download is opposed by the lift of the wing pushing upwards. Between the engine and the wing there will be some structural pieces (motor mount, fuselage, and wing attachment). Together, these are the "load path" for those opposing loads. Good load paths are short, straight, and continuous (not broken up in any way). The ideal way to provide good load paths is to make them zero-length, by putting the weight loads of the aircraft directly on the lift loads (wing) of the aircraft. In the Pazmany PL-1, the pilot and passenger are literally sitting on the wing box - the fuselage never sees their weight. Carried to the extreme, minimization of load path length leads to the Spanloaded Flying Wing concept where the weight forces are spread out along the wing to match the lift forces. For a normal design, just try to consider how the structural load will "flow" from weight load to lift load, and make sure that there is some good structure between them. Since the wing provides the lift force, load-path distances can be reduced by locating the heavy weight items as near to the wing as possible. It is also a good idea to avoid cutouts in the highly loaded portions of the structure such as the wing box or the middle of the fuselage. Several important concepts in structural arrangement are illustrated in figure 29. The skin of the engine cowling is not carrying a structural load other than its own loads. The first fuselage bulkhead, which is also the firewall, picks up the motor mount 55
loads. The cockpit a/ea is, unfo/tunately, a la/ge cutout in the fuselage at the wo/se possible place - the middle, whe/e the bending loads a/e the gfeatest. This /equi/es ext/a strengthening as shown by the top beam /unning f/om moto/ mount to the end of the canopy cutout. Quite likely this beam would be extended back to the tail (not shown). Bulkheads a/*e p/ovided to t/ansfe/ the wing loads - notice how the bulkhead at the end of the cockpit cutout is lined up with the back of the wing box. In the tail, a single bulkhead takes the loads of the ho/izontal tail, ve/tical tail, and tailwheel. This wasn't an accident! The fuselage will be lighte/ and easie/ to build if the design is airanged so that the big loads go into just a few bulkheads. In a good conceptual design, even the locations of the ai/plane components may be adjusted to make this happen. In this example, the landing gear loads go into the f/ont spar of the wing, and then into a small hiselage bulkhead. Alternatively, thy gea/ loads could have gone di/ectly into the fuselage, pe/haps attaching to the fi/st bulkhead (but make srne the gea/ layout guidelines above a/-e followed). A moto/ mount fo/ a composite ai/plane is shown below. Note how the nose landing gea/ is attached di/ectly to the moto/ mount, not to the fuselage structure. This makes sense, because the load path is sho/te/ f/om engine to nose gear when sitting on the gwund. The pictu/e on the /ight shows the back of the fi/ewall bulkhead with the fou/ moto/ mount backing fittings (black) bonded in place. These sp/ead the concent/ated moto/ mount loads out into the composite skins. 56
The liA force on the wing produces a tremendous bending moment and vertical shear load where the wing attaches to the fuselage. These are among the largest loads on the entire airplane, and you must decide how to handle them. Some approaches make for lightweight structure but give high drag, while others do the opposite. Wing carrythrough structure must also handle the twisting moments created by the wing. These result from moments about the airfoils themselves, plus moments produced if the airfoil center of lift is not centered on the wing structure, plus the potentially large moments when flaps are deflected. There are three types of wing carrythrough structure suitable for homebuilts, shown in figure 31. The "wing box carrythrough" is used for many airplanes. The box carrythrough arrangement continues the wing box through the fuselage. The fuselage itself isn't exposed to the bending moment of the wing, which reduces fuselage weight. The box is also good at carrying the torsional loads, which are kept distributed in the box skins. The box carrythrough can be a constant-section straight part going perpendicularly through the fuselage, as shown, or it can be an extension of the wing panel boxes that meet at the center of the fuselage forming a "V" if the wing is swept. 57
W)NG BOX CARRYTHROUGH BEND!NG BEAM The "bending beam" carrythrough is common on sailplanes and is increasingly seen on homebuilts of all types. The wing panels are bolted to the side of the fuselage to carry the lift forces. However, the bending moment is carried through the fuselage by a beam that connects the two wing panels. The beam is not attached to the fuselage so the bending moments don't go into the structure of the fuselage at all. Frequently there is a separate bending beam for each wing half, which makes it easier to attach and remove the wings (see below). 58
One clever design provides two different bolt attachments for the opposite ends of the wing panels' bending beams. The higher locations provide reduced dihedral for better aerobatic flying! Normally a bolt towards the rear of the wing prevents the wing from twisting but doesn't carry bending loads into the fuselage. In some designs (Piper Tomahawk), a bending beam is used which is built into the fuselage and bolted to the wings. Low-speed aircraft can use an external bracing strut to deal with the bending moments. This approach is usually the lightest of all, but it has a substantial drag penalty from the strut. This penalty is worse at higher speeds, while the weight saving is the same at any speed. The only way to know if a strut-braced carrythrough is better for your airplane is to design it both ways and analyze them. The loads on a strut-braced airplane are a bit strange, and this may affect your layout. The wings and struts are attached with bolts that act like pivots, so there are no bending loads passed into the strut or fuselage. The wing lift loads are roughly balanced on the inside and outside panels, so there is actually little vertical lift at the point where the wing attaches to the fuselage. In fact, if the wing span outboard of the strut attachment is much larger than the inboard portion, there may actually be a net download ( "W") where the wing attaches to the side of the fuselage. S3. PfM* Most of the lift is carried by the tension in the strut ("a"), which passes that lift load down to the of the fuselage. So, the fuselage is actually sitting on the bottom strut attachment fittings (y) rather than hanging from the wing attachment fittings. The tension in the struts is greater than the lift on the wing due to the angle (divide the lift by the cosine of the angle from vertical), so don't try to use too flat a strut angle. Also notice the compression loads in the inner wing panel and upper part of the fuselage ("7?" and "c"), and the tension load in the lower part of the fuselage ("e"). While it is possible to use strut bracing on a low wing, it is uncommon because it puts the strut in compression, which works poorly. Also, the strut on the top of the wing creates a greater aerodynamic penalty than on the bottom. 59
Aircraft wings usually have the front spar at about 20-30% of the chord back from the leading edge. The rear spar is usually at about the 60-75% chord location. Additional spars may be located between the front and rear spars forming a "multispar" structure, but this is not common for small aircraft. Homebuilts usually have just two spars, and some have just one main spar (located at the point of maximum airfoil thickness). If the wing skin over the spars is an integral part of the wing structure, a "wing box" is formed which in most cases provides the lightest wing weight. A wing box is naturally good at resisting twisting loads. If a wing box is not used, such as for a fabric-covered wing, then internal bracing must be used to prevent excess wing twisting (see below). 3^. iSVrMcfH/re - Wing & 7hw7 Wing ribs are spaced to provide stability to the wing skins, and are about 1-3 feet apart for light planes. For fabric-covered wings, ribs should be no more that 15" apart'c. If the plane flies faster than 130 kts, reduce that spacing by 0.068(\kts-130). This goes to zero at 350 kts, and so will you if you try to fly a fabric-covered wing that fast! You have to decide what materials to use - the main options for homebuilders are wood, metal, and various forms of composites. Wood construction normally features built-up structure with fabric skins (see figure 34), but can also be used in load¬ bearing stressed panels and sandwiches. Metal homebuilts are normally either welded tube truss structure (fabric covered) or stressed-skin aluminum construction (see figure 35). 60
^gv/^ 36. Af^^^/ M^^;?g (BD-3) Fo/ the composites, Ae/y a/e a variet/ of mate/ials fo/ the fibe/ including glass, g/aphite, and bo/o^. Alternatives fo/ the mat/ix mate/ial include epoxy, polyeste/, and vinylester fesins. Composites can be fab/icated in solid fofm with built-up substructure (spa/s, /ibs, f/ames), as built-up flat sandwich panels with foam o/ 61
honeycomb core materials, or as full-depth sandwiches in which the entire part is filled with the foam core. Composites can be fabricated in molds, or can be done in a "moldless" method using shaped foam core. One can also make wooden sandwiches such as a spruce or birch skin over a balsa core. Much has been written on the technical pros and cons of the various materials (see my textbook), but you should select the materials that you are most comfortable with. Certainly a good aircraft can be built from any of these options. Some random thoughts to consider: * If your aircraft will be parked outside for years, all forms of aircraft structure are in danger of structural weakening. Wood rots and is eaten by bugs. Most composites are weakened by heating and ultraviolet radiation from the sun (this is why we usually paint them white). If water gets into a composite sandwich - look out! Metal structure is probably the most weather-tolerant, but even metal can corrode if water gets in. But, after years of design and construction work you'll probably want to keep your "baby" in a hangar anyway. * Metal fabrication is a skill. Anybody can learn it, but learn it you must, especially if you will fabricate 100% of your original design (remember, no quick-build kits for original designs). Set aside some time to get really good at cutting, drilling, deburring, riveting, and maybe welding before you start cutting into your expensive metal stock. Buy good tools, too. You'll save time and money in the long run. These comments are especially true if you want to fabricate compound-curved metal surfaces by hand. * Metal parts that are extensively worked (90 degree bends, etc...) are often fabricated from soft annealed aluminum then heat-treated to increase strength and relieve the internal stresses caused by working the metal. Plan to send them out for professional heat-treatment - this is no job for amateurs. However, if bend radii guidelines are carefully followed it is possible to fabricate metal parts from tempered metal without subsequent heat treatment. Pazmany^ is recommended for an overview of metal construction techniques. * Composite fabrication is also a skill, although many would say it is an easier skill to learn than metalworking (others disagree). If you plan to design and build your own composite wing, I'd recommend designing a smaller test piece and analyzing and building it, then testing it to destruction to see if it carries the 62
load you thought it would. It's good fabrication practice, and good verification of your design and analysis methods. Also, be aware of the health and safety aspects of composite fabrication - especially, use gloves and goggles, and work in a well-ventilated area. Even with precautions, many people develop allergies after working with composites for a while. And, watch out for urethane foams. Urethane sanding debris is microscopically sharp and bad for your lungs, and it must never be cut with a hot wire because it emits poisonous gases when melted. Great material, otherwise! * Gluing, bonding, and all forms of composite fabrication depend on extreme cleanliness, precise control of temperature and humidity, exact mixing of the adhesive or matrix, and careful preparation of the surfaces. Unfortunately, once parts are fabricated it is difficult to visually tell if they were made correctly (fiberglass is somewhat transparent allowing you to somewhat see problems). In industry we use expensive testing machines to look for voids and debonds, and we find them often. Use extra safety margins in the design of such structure to allow for undiscovered imperfections. * The strength of a glued or bonded joint depends on how well the pieces fit together. They must match for the glue to work well. This is especially important for scarf joints where you are joining long pieces of wood together. If nails or screws are used they are mostly to clamp the wood while the glue dries, and are often removed later to save weight. It's the glue joint that matters. * If you want your design to be really, really clean aerodynamically, molded composites are probably the way to go. But a well-designed, well-built flush- riveted metal design can come close. * Composite raw materials are more expensive to buy, but don't forget that when you make a metal airplane you buy and throw away a lot of cut-off scrap pieces (roughly 25 percent by weight). With composites, this is down to roughly 5% unless you do stupid things like spill a pot of coffee on your fabric or leave your resin can open. * If composites are to be used, be aware of a peculiarity of composites that will affect your overall design concept. Composites really don't like concentrated loads. Most materials don't, but composites don't! Wherever loads are concentrated, such as where a wing or tail panel attach, you will probably need to transfer the load from the composite part to a metal fitting, or add a large number of additional plies in that region, or both. This adds weight. So, if possible try to design the airplane so that concentrated loads are avoided. For example, rather than fabricate the wings in two panels that are bolted to a separate carrythrough structure, consider making the wing as one piece, tip-to- tip, with only a lift load transferred to the fuselage. Rather than fabricate the vertical tail as a separate piece that must be bolted on, consider making the vertical tail an integral part of the fuselage, and so on. Fue! Tanks Unless you're designing a glider, you'll need to include some fuel tanks on your drawing. While not terribly large, the fuel tanks will carry 10-20% of the aircraft's weight in a typical homebuilt, so they'd better be in the right place and attached to some strong structure. 63
The most important concern is that the fuel tanks be near the aircraft center of gravity. This way, the c . g. will be in about the same location whether the tanks are empty or full. There are also safety considerations - wed rather not be bathed in fuel during a crash or because of a minor fuel leak, nor do we want fuel spilling over a hot engine or exhaust pipe. Typical locations for fuel tanks are shown below. A tank that is directly behind the engine and above the pilot's toes is close to the aircraft's e . g. and provides short fuel lines. This is perhaps less safe in the event of a crash or leak. Many planes have fuel in the wing box and/or wing leading edge. Such tanks often stop part way out the span because the wing gets too thin. Fuel is also carried in the wing box where it passes through the fuselage on some planes but again, this may compromise safety in the event of a leak or a crash. Note that fuel pumps are required if fuel is carried inside a low wing. Canard-pusher aircraft like the Long-EZ often have fuel in wing strakes (highly swept triangular panels at the leading edge of the wing root). These are used on supersonic fighters like the F-18 to generate more lift at high angles of attack, but for a subsonic homebuilt their main aerodynamic effect is an increase in drag due to the extra wetted area. They are put there y— to provide fuel tanks near the center of gravity. Where else could you put fuel on such designs? 64
Fuel tanks for homebuilts are either of discrete construction, or are "integral." Discrete tanks are separate components that you fabricate and bolt into the airplane. You can say "look honey - I finished the fuel tank." With integral tanks you never get to say that because the tank is just an existing part of the aircraft structure which has been sealed off to hold fuel. Often, we use part of the wing box as an integral tank. In our sizing calculation we found the of fuel required (multiply fuel fraction by sized takeoff gross weight). To determine the size of the tanks we need to divide fuel weight by fuel density, which is 6 pounds per gallon for aviation gasoline (7.5 for oil). Then we need to divide by 7.5 to convert gallons to cubic feet. If you are designing a discrete tank you can probably determine the dimensions to give you the required cubic feet of fuel. Remember to allow for skin thickness and for any internal structure in the tank. For an integral tank in the wing or wing box, it is difficult to determine up front how big to make the tank to hold the required volume of fuel. Basically, you have to draw something reasonable then measure it, and revise it until the tank volume is adequate. Methods to estimate volume of tanks are provided in the next chapter . You should also make an allowance for skin thickness and for internal structure, which includes wing ribs and spars. A conservative allowance is 15% of volume (so the usable volume is only 85% of the volume measured to the outside moldline). A lesser allowance, perhaps 5%, would be suitable if your design has just a few internal ribs and no spars in the region you've selected to be a fuel tank. If you skipped the sizing calculation because you had already selected an engine, you must determine the fuel weight another way. You can't pick fuel weight to give you the range you want - that's cheating! The problem is, when you add that fuel weight to the empty weight and the weight of the people and payload you want to carry, you'll probably get a heavier takeoff gross weight so you'll have a higher power loading than you wanted (ie., more weight per horsepower equals less performance). Instead calculate the allowable fuel weight as follows: where the empty weight fraction We /Wo is found from the equation in the sizing section. Later we'll estimate empty weight using better methods. If this amount of fuel doesn't give you the range you were hoping for, you'll need to increase Wo. If you keep the same engine, you'll wind up with lower performance - perhaps too low for your needs. The other choice is to find a larger engine, but this will bum more fuel requiring an even larger airplane (find the right answer by redoing the sizing calculations). Or, you can change the requirements for weight of people and payload. 65
EXerna/ TAree-PAw, EM/aA Phr^zEze e^^o//eyy E Ezz/aA^. AT^As As* ^awe z^Aez/ ^ar^E //?e revo/Mow /A /zoA^/AMz/EzE,^, a/?E ^v^A /wore, coAV/AceE Z/zazz.yaAEy ^^^^6y reaEy aazz/E <?//7E Z/^?^^rr o^w/A azTyEaAe. 66
Chapter 5 DRAW A SMOOTH OUTStDE Now it's time to make ou/ fi/st good design layout d/awing. Sharpen some #2 pencils and tape down a nice piece of d/afting pape/, o/ turn on you/ CAD system if you have a good one and know how to use it. Undoubtedly you'vy made some sketches of what you want you/ ai/plane to look like. Pin them to the wall in f/ont of you and use them fo/ guidance, but don't be su/p/ised if you/ final design layout looks somewhat diffe/ent. Lay out the wing t/apezoidal geomet/y, and ditto fo/ the tails when you get fa/ enough along that you know what the tail arm will be (see discussion above). Lay out the engine, and the cockpit, and the landing gea/, and any othe/ majo/ internal components. If using pape/, make these layouts on sepa/ate pieces of papy/ so they can late/ be t/aced onto the final d/awing in the /ight locations. On a CAD system, you should be able to d/aw them now and move them into place late/. Conic Lofting "Lofting" is the p/ocess of defining the exte/nal shape of the ai/plane. Lofting gets its name f/om shipbuilding. The definition of the hull shape was done using eno/mous d/awings in the loft ove/ the shipya/d, so they called it "lofting." Ship lofting was done by measunng and smoothing points f/om doss-section and top view ("wate/line") d/awings, and the/e was a lot of a/two/k involved. This led to e/ro/s and mismatches, but these could be fixed du/ing p/oduction using hamme/s and welding to/ches. This lofting method wo/ked OK fo/ ai/daft in the ea/ly days, but when ai/planes got faste/ the lofting e//o/s we/e unacceptable. A new and bette/ method of lofting was developed at No/th Ame/ican Aviation and used fo/ the fi/st time on the P-51 Mustang. This method, now conside/ed t/aditional, is based upon a mathematical cu/ve fo/m known as the "conic." The nice thing about the conic cu/ve is that it is ve/y easy to d/aw a good one, and it is also easy to make conic cu/ves that flow smoothly f/om nose to tail. A conic cu/ve is d/awn starting with just fou/ points. Two of these aTe the desi/ed star! and end points ('^4 " and "2?"). At those end points, the cu/ve sta/ts and ends in the di/ections of lines (tangent angles) that inte/sect at a point "C. " Between the end points ^4 and B, the cu/ve goes th/ough anothe/ point called a "shoulde/ point," o/ "B, " which is simply some point on the conic you want to d/aw. 67
y?gure 39. Cowc Curve Co^^rucOo/? The first step in drawing a conic (see figure 39) is to draw these four points ^4, 7?, C, and & In the second step, lines have been drawn from ^4 and Z?, passing through 6* and continuing further. These two lines are said to be "shot" from the endpoints through 1$ and are reused to find many points on the curve you are trying to draw. The remaining steps show how to find one point on the conic. In the third step a line is drawn from point C, crossing the two lines we just drew. Draw this line anywhere between the tangent lines (4-C and B-C). Every line you draw will create another point on the conic. In the last step, lines are drawn from ?! and Z? through the points just found in the last step. Where these lines cross is a point on the desired conic curve, shown by a star. This process is repeated two more times in figure 40, creating two more points. Keep doing that 5-10 times, connect the dots, and you have a very nice conic. y?gure 40. CtMue Curve - T&re 68
While this seems complicated at first, with a little practice you can construct an accurate conic in less than a minute. Notice a very important fact. The conic is created by those four points - two end points, the tangent intersection, and a shoulder point. If you control where those go, you completely control the shape of the conic. That is how we will get a good fuselage shape from nose to tail. This is shown below. Three conics form a portion of the upper fuselage of some airplane. The conics are parts of cross-sections, which for some reason are important, probably because some major component such as the engine is inside at that location. Such cross-sections are called "control sections" or "control stations" because they control the shape of the body. We design just a few control stations (perhaps 5-6) and use them to create all the other cross sections we need to design the body. The conics of the control stations are connected with smooth lines running from front to back called "longitudinal control lines," running through the four points that define the conics. Note that the top line connects all the ^4 points, the bottom line connects all the 2? points, and other lines connect all the C points and all the S points. If we could "read" the locations of the four points ^1, 2?, C, and S for another cross section, we could easily draw it. 69
y?gnro 42 Long/SHS/nt?/ Con/ro/ Ls/^7^ -sSMe & To/? FSow^ In figure 42, the longitudinal control lines are drawn in side and top view. This makes it easy to "read" the locations of the points ^4, 2?, C, and & This is done by measuring the distance from the centerline in top view and the distance above or below the dotted reference line (s=0) in side view. Locating the 2? point is shown in the illustration - the others are done the same way. The tangent lines ?1-C and 2?-C do no/ have to be at right angles (90 degrees). We often design it that way so that the .4 and C longitudinal control lines are the same in side view and the 2? and C lines are the same in top view, as in this example. How do we draw the longitudinal control lines? They can be made using conics, just as was done for the cross-sections. It is also common to use a "spline," a long piece of thin plastic that is bent to the desired shape and held down with pointed weights (get these at a good art and architecture supply store). You can even use a good set of "french curves" (they are called something else in France, by the way, same as french fries). The important thing is that the longitudinal control lines must be smooth with no breaks, and they must pass through the appropriate points. On a CAD system there are various spline functions you can use. One problem arises with this method of lofting. The locations of the shoulder points (6) can be difficult to control, creating conics that are either too square (shoulder point too close to Q or too flat. A better method of using conics involves a special ratio which directly controls the shoulder point's distance from C. This method seems tricky at first but actually takes less work once you leam how to do it. The method is based on a ratio we call the "conic shape parameter," or p ("rho" in the Greek alphabet). We use p instead of a shoulder point to control the shape of the 70
conic between the endpoints. In fact, we use p to 4 4 a shoulder point and then draw the conic as before. How do we find the shoulder point? This is shown in figure 43. We start with the points .4 , B, and C, as before, but do not have a shoulder point & Instead we have a value for p. This is a ratio from zero to one, where zero would give a straight line from 4 to B whereas one would give a squared-off conic going from B to C to B (actually we never use zero or one - real values of p range from about .2 to .9). To draw the conic, we first draw a line from 4 to B and find its midpoint D. Then we draw a line from D to C. We place a shoulder point B on this line at a point which is p times the length of this line from D to C. In fact, p by definition is the length of the line from D to B divided by the length of the line from D to C. What value of p do we use? If we use p = 0.4142 and the lines from 4 to C and from B to C have the same length, our conic is actually a portion of a circle. We can use p = 0.4142 for all the conics from nose to tail and get circles when needed, and nicely rounded conics everywhere else. We can also change p from nose to tail. The next figure shows a portion of a body where p starts as 0.4142 (circle) but increases to 0.95 at the back, making a nearly square conic. This is commonly done on the bottom of airplanes to make more room for landing gear, but can be used wherever a squared-off cross section is desired. 71
yzgwe 4V. Cc^zzzcz w^zVA C/:^z^z^g^zzg 7?Ao (^ An "auxiliary control line" can be used to control the value of p as shown in figure 45(the auxiliary control line for p is at the bottom). This is a graph of the desired value of p from nose to tail, with p starting at some lower value at the nose (here 0.4142) and increasing to a higher value at the back to make the conic more square. When we draw another cross-section we just have to read from this graph the value of p that we should use for that section. Notice that by using this approach, we no longer need a longitudinal control line to control the location of the shoulder points (5) - we do it with p instead. A key point - if the value of p varies smoothly from nose to tail, and the conic endpoints and tangent intersection point are controlled with smooth longitudinal lines, then the resulting body will be smooth. This method is a very powerful tool for designing smooth surfaces such as aircraft fuselages, canopies, and nacelles. 72
V.5. (A/^g Confro/ L ybr 7?7?o Hat-Wrap Lofting If you build from wood or metal, or plan to use metal to make molds for your composites, it will be easier to build if you avoid compound-curvature as much as possible. Compound-curvature means that the shape curves in all directions like a ball. A cylinder or cone curves in only one direction and is called "flat-wrapped," because it can be formed by wrapping a flat sheet around some substructure. There are several ways of lofting a surface so that compound-curvature is avoided. One obvious way is to make the surface out of flat pieces like the fuselage of a BD- 4. Usually this has a large drag penalty and the flat sheets may "oil can" in and out, so single curvature is generally better. A simple technique for designing a flat-wrapped surface is to use a constant cross section. Most commercial airliners use a constant circular cross-sectional shape over most of the fuselage length. Any cross section shape will provide flat-wrap if the cross section doesn't change. You can also get flat-wrap by tapering the same cross-sectional shape from front to rear. For example, a cone is a flat-wrap surface produced by tapering a circular cross section. You can make a fairly complicated shape by connecting together various flat-wrapped cones, cylinders, and flat pieces as shown below. To find out if a shape can be made from flat-wrap, try making it from a sheet of paper. 73
46. CoKKefng Wings and tails can also be flat-wrapped. If the wing or tail is a trapezoid, and the same airfoil is used throughout with no twist, then the surface will be flat-wrapped automatically. You simply scale the airfoil points to the desired chord length. If the wing has twist or a change in thickness ratio, or if different airfoils are used, then flat wrap is much more difficult to attain. The method to use in this case is described in the next section. Wing/Tai! Lofting Lofting of wings and tails starts with the layout of the trapezoidal wing planform, as we already saw. We may modify the trapezoidal planform, such as rounding off the wing tips. Then we scale the airfoils to the chord length at each desired spanwise location. A common way to draw the wing is shown in figure 47. We lay out the airfoils rotated flat onto the planview (top) of the wing. This lets us easily see the airfoil shape and twist from root to tip. 74
47. ^/r/b;7 Loyoz// 077 fFz7?g ^/^77/br^ Often we want to use dif^rent airfoils at root and tip. We may also twist* the airfoils with the leading edge more nose-down out towards the tip, to avoid tip stall. Sometimes we give the tip a higher thickness ratio (/7c) or increased camber to reduce tip stall. For any of these, we lay out the root and tip airfoils then interpolate to find the other airfoils in between. There are two ways to interpolate - linear and flat-wrap. Linear interpolation is what you get if you take the airfoil points at root and tip, and connect them with straight lines to form the surface of the wing. This is no/ what we want because it makes a surface that isn't flat-wrap. Linear interpolation connects airfoil points that are at the same ^n^n/ of chord length. To get flat wrap, we need to connect airfoil points that have the same g/. . If the tip airfoil is twisted or has a different shape or thickness ratio, points at the root will not have the same slope as the same percent-chord at the tip so,...., no flat-wrap. The method to get flat-wrap by connecting points of the same slope is shown in the next figure. Notice we lay out the wing in planview with airfoils laid flat, as before. We start by finding the point on the tip airfoil that has the same slope (angle "X") as a point on the root airfoil. We project those points to the chord line of each airfoil and connect them with a straight spanwise line (1). * It is common to twist the airfoils around the trailing edge as shown here, but you can also twist around the quarter-chord, leading edge, or some selected spar location. Also, the airfoils need to be the correct chord length .e r we rotate them for twist. Usually this is trivial, but a large amount of twist will shorten the airfoil so it has to be scaled in length by 1/cos (airfoil incidence). 75
w.l Next we "swing" those two points (at root and tip) down onto their chord line (3). We connect them with another spanwise straight line. Now, for each airfoil we wish to create, we find a point which is the intersection of the line drawn in (3) with the desired chord line. We "swing" this point up above the spanwise line found in (1). This is a point on the desired airfoil forming a flat-wrapped wing. It's actually simple and fast once you've done it several times, but the first time, If you are using a CAD system, be careful. It may not have flat-wrap capability and may only do linear interpolation. If so, you'll have to construct flat-wrap interpolated airfoils exactly as described above using your CAD system rather than a drafting table. It is common in building sandwich composite wings to use the hot-wire technique to cut foam blocks to the wing shape. The root and tip airfoil shapes are pasted to opposite ends of the foam block with numbered tic-marks going around the contour. The builder and a friend move the cutting wire around the airfoil shapes, counting off the tic-marks as they go. 76
If the tic marks are marked using the airfoil points, which are at constant percents of chord, the resulting foam core is a linearly interpolated wing, no/ a flat-wrapped wing. The difference is minor and unimportant if composite skins are laid up on the foam core. However, if a rigid wood or metal skin is to be bonded to the wing core then there may be a problem. If there is quite a bit of twist or the root and tip airfoils are quite different, the use of an interpolated layout core may prevent good bonding at the middle of the wing, where it is slightly depressed compared to a proper flat¬ wrap lofting. To fix this, don't use constant percent tic-marks. Instead lay out the tip airfoil tic- marks to give the same slope as the same number at the root section. Then cut the wing as usual. This is actually what we are doing with the flat-wrap layout procedure above. 49. 74-7 IFzng Ti'/Zef Another important wing lofting job is the wing fillet. This is the "smoothing" between wing and fuselage seen on many airplanes. It serves several purposes. First, it reduces the interference drag, where the airflow around the wing and the fuselage has bad interactions that increase turbulence, vortex flow, and separation. Also, a good wing fillet can fix stability problems. Sometimes the disturbed flow at the wing root will cause vortices to be formed. These vortices can flow back to the horizontal or vertical tail and reduce their effectiveness. In some cases, such vortices help put the airplane into a spin or make it difficult to get out of a spin. Unfortunately, there is no good way to determine if a wing fillet is needed other than wind tunnel or flight test. Even a low-wing aircraft may not need one if the fuselage is shaped correctly, with the cross-section not tapering smaller until after the trailing edge of the wing. Normally, it is a good idea to use a fillet for a low wing airplane, and consider adding one to other airplanes if problems are found in flight test. An extreme example of a wing fillet, on the Hughes H-l racer, shown above.
A wing fillet works by pushing the wing and fuselage airflows away from each other. There are many ways to lay out a fillet. Some airplanes have a fillet which is nothing more than a straight "board" from fuselage to wing, either vertical or at some outward angle. The usual way to design a wing fillet is by a circular arc, tangent to both the wing and fuselage. Typically a wing fillet has a radius of about 10% of the root-chord length. The fillet circular arc is perpendicular to the wing surface, so the arc is vertical to the wing only at the maximum thickness point of the wing. At the leading edge, the arc is in a horizontal plane. The fillet arc radius may be constant, but it will probably work better if the radius expands towards the rear. This is done using an auxiliary radius control line. Note that the starting radius must be equal to the fillet radius shown in the wing top view. Also, the fillet radius is usually increasing towards the rear of the aircraft, to minimise airflow separation. Some aircraft have a fillet only on the rear part of the wing. In this case the fillet starts, with sero radius, at the wing's maximum thickness point. . 78
Raymer's DR-4 Safety Twin My design layout fo/ the DR-4 is shown above. The d/awing cente/line is the t/ue cente/line of the wing and ho/izontal tail, but the fuselage is offset f/om this cente/line. Dimensions a/e in inches - the design is 22 feet long with a 32 ft span and a wing a/ea of 102 squa/e feet (as dete/mined in the analysis desc/ibed p/eviously). The 2-man cockpit is 40 inches wide and yes, that's the "big guy ' ' shown inside. .57. T&yy/ey '3 DR-<7 y Tu/M D^ggLayoff A vent/al fin is used below the fuselage to limit the tail-down angle so that the pilot cannot cause the pushe/ p/op to strike the g/ound. Vent/als a/*e also good fo/ spin /ecove/y. Flaps a/e employed on the inboa/d po/tion of the wing - tentatively a single uninte//upted split flap since a ^gula/* flap could not be used unde/ the pushe/ nacelle. Howeve/, a split flap will c/eate mo/e d/ag if used fo/ takeoff. Fu/lhe/ study is needed. 79
I already see problems that I want to fix on the next layout - I'm worried about runway junk getting thrown into the prop so I want to move the gear either inward or way outward. Also, the gear up location in the wing is very tight. I'm still not sure about the horizontal tail and suspect I'd be better off centering it on the vertical tail, even though that would cause a slight rolling moment with elevator deflection and trim. I need to do a more detailed layout of the engine installations, and must get installation drawings from the manufacturer. There is a slight overlap of the two propeller disks, which may or may not be a problem. I'd like even more overnose vision, but like so many designers before me I hate to make the plane goofy-looking and draggy by raising the cockpit any farther. But, all in all I think it's not too bad for a first layout. Measure What You Drew You've drawn it, now you've got to measure it. We need certain numbers off the drawing for analysis. Some you already have, like the wing and tail reference areas and geometry. Others are simple distances - I assume you can figure that out by yourself! For drag and weight analysis we need the wetted areas. As discussed above, wetted area is the actual external surface area. If the plane drops into water, it's the total outside area that will get wet (not counting certain areas inside the cabin). In figure 5 we saw the exposed wing area (Sexp - shaded area on the drawing). The actual wetted area of the wing will be double this area (top and bottom), plus a little more area around the leading edge. A reasonable approximation of the wetted area of thick wings and tails is found by: Wing or Tail Wetted Area: 5^ = ^exp - 977 + 0.52((/c)] 80
For the fuselage, the proper way to measure wetted area is to measure the perimeters of all the cross sections then do a graphical integration (see my textbook). A pretty good approximation can be found by measuring the top view and side view areas of the fuselage. If the fuselage were a square cross section like a BD-4, the wetted area would just be double the side view area plus double the top view area, or four times the average of the side view and top view areas. Since most homebuilts have more rounded cross sections, a good approximation is: Fuselage Wetted Area: If your fuselage is square in cross-section, use 4.0 instead of 3.4. If it is circular or oval in cross-section, use 7 (=3.142). For most designs, 3.4 is pretty close. y?g%re -53. 7iye/#ge Tire# 81
Another important measurement is the volume and location of the fuel tanks. The proper way to do this is by measuring their cross-section area at several locations and doing a graphical integration. A simpler method is to measure the cross section area (S) at opposite ends and calculate the volume from: Volume Approximation: The length between sections "L" must be measured perpendicular to the end cross¬ sections. An even simpler approximation is to "guesstimate" averaged values of length, width, and height, and multiply them together for volume. This is pretty crude, and you'd better oversise the tanks a bit to allow for measurement error. 82
Chapter 6 Buckie Up for Safety Crashworthiness Of course, yoM would never crash your new homebuilt design, but your building partner you're not so sure about. Just in case, give it some serious thought during the design process. To provide some protection in a crash, the aircraft should be designed to act like a shock absorber. The structure between the ground the plane hits and the people inside should crush in a controlled fashion over distance and time. The worst thing is to have extremely hard structure between the ground and the people. In crashes of 4-seaters it is tragically common that the back-seat passengers survive a crash, while the pilot and front seat passenger do not. Those in front were sitting on the hard wing box so the load went immediately into their bodies. In back, the seats are on legs that collapsed downwards. Good design practiced is to have people sitting on seats with energy absorbing foam cushions and seat legs that collapse downward without breaking loose. For a front-mounted engine, the motor mount can be designed so that it bends upwards and rearwards under a crash load. This will absorb some of the crash energy. Also, avoid a sharp edge on the bottom of the firewall. When the cowling crushes, a sharp edge will dig into the ground causing a rapid deceleration (see figure 29). If that edge is scarfed to the rear the airplane will "skip" and slide rather than dig in and stop. Many fatalities occur because the front of the airplane collapses driving the control wheel backwards just as the pilot is being thrown forward. That is why a good safety harness, properly attached to some strong structure, is so essential. See the harness vendor for proper installation geometry. This is also a good argument in favor of a sidestick controller. Even with a regular centerstick the pilot's head can be thrown down on the top of the stick with non-aesthetic effects. 83
While we want the structure between the ground and the people to collapse, we do no/ want any deformation of the passenger compartment itself. Think of an egg - the growing chick is inside a hard shell that won't deform, but the whole egg is inside a nice so A straw nest (or a nice soft carton at the store). Some obvious things - make sure nothing heavy is placed where it will break loose and strike people. Make sure the battery isn't where it can splash people with acid if it ruptures. Avoid sharp edges, protruding knobs, and other people-stabbers in the cockpit, and put padding where heads are likely to hit. Provide good emergency exit capability, even if the plane flips over. Speaking of which, provide a rollover structure of some sort. Make sure the fire extinguisher is handy and won't break off, playing "hide-and-seek" just when you need it most. Ditto for your emergency flashlight. Several of these safety concepts are shown above. No, I don't know where the wing box goes either. But a single bending beam could go right behind the seat, attached to the rollover bulkhead. An option being used more and more on homebuilts is the "ballistic" parachute. In an extreme emergency the pilot hits a button and a parachute shoots out, lowering the whole airplane safely. Probably the airplane will sustain major damage anyway, but the people should survive. Contact the vendor for installation instructions. Ftutter Flutter is a dynamic interaction between the aerodynamics and the structure of an aircraft. It occurs when some structural deflection of the aircraft such as wing bending causes an aerodynamic load that tends to push the structure to more deflection during each oscillation until structural failure is reached. There are many possible flutter modes. An aileron with its center of mass well behind its hinge line will tend to lag when accelerated upwards by oscillating wing bending. This lagging is similar to a flap deflection, increasing the wing lift and amplifying the wing bending. On the way back down, the aileron lags upward, driving the wing down even further. Similar flutter modes occur in elevators and rudders that have center of masses behind their hinge lines. Early Learjets were crashing because water was freezing inside the elevators behind the hinge line, causing flutter. This was difficult to uncover because the ice melted by the time the accident investigators got to the scene. Even a trim tab or servo tab may cause flutter if it has its center of mass behind its hinge line. The solution to this control surface flutter is obvious: don't allow the center of mass to be behind the hinge line! Instead, add mass balancing in the form of weight ahead of the hinge line, and ruthlessly avoid weight behind it. A control surface is said to be statically balanced if its chordwise center of gravity is on its hinge line. Many World War 11-vintage planes had fabric-covered control surfaces to keep the center 84
of g/avity fo/wa/d to avoid flutte/. This is shown below along with a mass balance indicated by an a/row. The/e are many diffe/ent types of mass balance othe/ than the one shown. 56. P-57 y / wzf^A 7^^/^?^/^ E/e^uxf(^^r <7%/ My Cont/ol su/face flutte/ is mo/e likely if the/e is play (looseness) in the cont/ol linkages o/ play in the turn tab linkage. Fo/ this /eason, stiff push/od linkages a/e p/efe//ed ove/ wi/e cables, which tend to sketch. Also, pilots should always inspect cont/ol linkages befo/e flight. The shaping of the cont/ol su/faces has an effect on flutter They should neve/ be convex, bulging out into the ai/flow, because it sets up unstable flow at the t/ailing edge. Instead, they should be flat-sided which is also easie/ to build. It is desi/able to have a beveled t/ailing edge. A cont/ol surface that is "fattened" at the hinge line will tend to /eattach the flow, imp/oving flutte/ cha/acte/istics. This discussion ba/ely touches on the c/ucial subject of flutte/. Unless you/ ai/plane flies ve/y slowly, /efe/ to a good /efe/ence on the subject at some time du/ing you/ design effo/t. 85
n x2.2^j L i...... c X i - -b - ;7 ! [ P'. '! t ! 1 -....- [' j l....Z5l f { 1 } So#%?/e J Aoywer 0^/7 ADS *s^7 /^^rogro^w^, wz'Z/z /z/?-/o-(7^rog ro^z^zo ca/c?M/^^^z(^zzj^. D^a/7 7 worry - 7/ ca^j^(?M/afe ZD Mzng 7^^?y0oZy a /?ocAe ca^^^c^^^<aZ^zr/ 86
Chapter 7 ANALYZE IT Now we've finished the drawing. Let's analyze it to see if it does what we hope it does, and to find out how to improve the design in the second drawing*. These methods are simplified, as promised in the title of this book. However, the results here should be pretty close for a normal homebuilt. For better methods, see my textbook among others. Also, there are various computer programs for aircraft analysis including my own RDS-Homebuilt (see If you get such a program, use these simplified methods to check your results - it is very easy to misunderstand the inputs of a sophisticated program and get a silly answer! As mentioned in the Introduction, original purchasers of this book get to download for free the Excel^ spreadsheet software yLrcrq? at This was used to make many of the calculations below for the DR-4 design example. You are welcome to use it to make your own calculations including sizing, performance, and range estimates. Or, you can do all of these calculations with a pocket calculator so that you are sure of your results. Aerodynamics For the drag calculation, we'll use a better version of the same method we used before but with our measured value of wetted area rather than a guess of the wetted area ratio. Also, we ' ll do a better job of including the drag of fixed landing gear and bracing struts or wires. In Chapter 3 we used an "equivalent skin friction coefficient" or Cf. that takes into account the overall "cleanliness" of a typical design to arrive at a parasitic drag coefficient COo. Select the appropriate value from the table below. Add up all the wetted areas for wings, tails, fuselage, canopy, and what-have-you, and multiply it by the Of. value as follows: Parasitic Drag Coefficient: Cpp - Cf. Single Engine Twin Engine Sailplane Average Metal Design 0.0058 0.0048 0.0038 Smooth Composite 0.0050 0.0045 0.0030 where Sref is your wing reference area. Previously the drag of fixed landing gear and wing struts was included in suggested Cf. values, but now we will estimate those separately. These values are "gear up." * No, I wasn't kidding about the second drawing. Sorry! 87
To this "clean" drag we will add additional drag for fixed landing gear, struts, bracing wires, and any other "junk" that may be on your airplane that isn't on a clean, cantilevered, retractable gear design as assumed by the values in this table. We will estimate this additional drag using values of drag divided by dynamic pressure (D/%, pronounced "D-over-%"). DZ? has units of square feet and is sometimes called the "drag area." DZ? divided by the wing reference area (Sref) yields a parasite drag coefficient that can be added to the Cpo that was found above. In the table below, values for DZ? are based on a unit* frontal area. In other words, multiply these values times the frontal area of the components on your design to get the value of DZ/. For something like a wire or strut, the frontal area is the width times the length. For a tire it's about 90% of the width times the diameter. Then, divide by your wing reference area to get the additional Cp#. For fixed landing gear, add 20% to the sum of these values for interference. For struts and bracing wires, add 5-10%. Drag Area D/q per unit frontal area Exposed Wheel & Tire 0.25 2nd Wheel in T andem 0.15 Streamlined Wheel & Tire 0.18 Wheel & Tire in "Pants" 0.13 Round Strut or Wire 0.30 Streamlined Strut (.166<t/c<33 0.05 Flat Spring Gear Leg 1.40 Fork or Irregular Fitting 1.0 to 1.4 Speed brake - fuselage 1.00 Speed brake - wing 1.60 Windshield - smoothly faired 0.07 Windshield - sharp edged 0.15 Open Cockpit 0.50 Next we need to estimate the drag due to lift factor, "'A?. " Again, the previous method is pretty good. Let's use a more general version of that equation: I Drag-due-to-lift-factor: A = As before, aspect ratio ("A") is the square of the wing span divided by the total wing area (Sf Now we have a new term - "e." This is the "Oswald's Span Efficiency Factor," and is a correction to the aspect ratio that takes into account a less-than-ideal In "engineer-speak," "unit" often means "per one of them' 88
spanwise lift distribution and the effects of flow separation on the wing. Before, we assumed that e was about 0.75, which is a pretty good estimate for most homebuilts. A very-well-designed airplane might approach an e of 0.85, if you are lucky. If you used an untapered wing (2=1), the induced drag factor (A3 will be about 6% higher since the wing will have a relatively poor spanwise lift distribution. If your design uses properly shaped winglets you can approximate their benefit by multiplying your aspect ratio by 1.2 in the A? equation. This lowers the drag. For biplanes, the aspect ratio is the square of the longer span divided by the total area of both wings. If both wings have the same area and span, and are separated by a gap of about 30% of their span, then the span efficiency factor (e) is about 1.4 - a surprising result since 1.0 would be an ideal monoplane. But, remember that the effective aspect ratio is very low since the areas of both wings are included. So, the biplane is still worse than a monoplane where the monoplane's wing has the total area and the same shape as the biplane's wings. For the drag-due-to-lift of other biplane geometries see my textbook, or any old aerodynamics book. The maximum lift coefficient of the wing (C??) determines the stall speed so we need a better estimate. For high-aspect-ratio wings with moderate sweep and a large airfoil leading edge radius, the maximum lift depends mostly upon the airfoil characteristics. The maximum lift coefficient of the "clean" wing (no flaps used) will be about 90% of the airfoil's maximum lift coefficient. Sweeping the wing reduces the maximum lift by the cosine of the sweep. Maximum Lift - Clean: =0.90;^ cos((M??p) Where C* is the airfoil's maximum lift and "sweep" is the quarter-chord line sweep. The 0.9 factor is an adjustment for lift losses near the wingtips. For C* see your airfoil data* . To get more lift for takeoff and landing, most airplanes use a flap of some sort. A flap is a part of the wing trailing edge that deflects downwards to increase camber, which increases lift. There are many types of flaps. A plain flap is simply a hinged portion of the airfoil, typically with a flap chord of 20-30% of the airfoil chord. For most airfoils, the maximum lift occurs with a flap deflection angle of about 40-45 deg. Note that ailerons and other control surfaces are a form of plain flap. * The airfoil data used must be at a similar which at sea level equals 6368 times velocity (ft/sec) times wing MAC (ft). For a homebuilt, Reynolds Number is typically around 1 to 20 million. You don't need to find data at exactly the same Reynolds Number, but be suspicious of maximum lift data if it is at a Reynolds Number that is higher than your design's by a factor of 2 or 3. Also, don't use the "smooth surface" data unless your airplane looks like perfect, clean polished glass. However, the "standard roughness" data is probably too rough unless you stuccoed the wing - use a value in between. 89
The split flap is like the plain flap except that only the bottom surface of the airfoil is hinged. This produces virtually the same increase in lift as the plain flap. However, the split flap produces more drag and much less change in pitching moment, which may be useful in some designs. Split flaps are rarely used now but were common in the 1930'sand 1940 ' s. The slotted flap is a plain flap with a slot between the wing and the flap. This permits high-pressure air from beneath the wing to blow over the top of the flap, which tends to reduce separation. This increases lift and reduces drag. The Fowler-type flap is like a slotted flap, but mechanized to slide rearward as it is deflected. This increases the wing area as well as the camber. Fowler flaps can be mechanized by a simple hinge located below the wing (like a Navion), or by some form of tracked arrangement inside the wing (like many Cessnas). Aft flaps do not increase the angle of stall. In fact, they tend to reduce the stall angle by increasing the pressure drop over the top of the airfoil, which makes the flow likely to separate causing a stall. To increase stall angle, leading edge flaps and slots are used but are uncommon on homebuilts. It is very difficult to accurately calculate the Cf obtained when flaps are used. A quick approximation starts by finding the maximum lift coefficient of the "clean" wing as above. To this we add a lift increase for the flaps based on their size. Max Lift Coefficient: f = f* Q AT"* A max L max CVean ' / max Lift fncrease delta Cl-max Plain & Split Flaps 0.9 Slotted Flaps 1.3 Fowler Flaps 1.3 c7c As for the wing itself, the lift is reduced when the flap is swept. For the flap, the important sweep is the sweep of the hinge line (sweepm) The term (pronounced "delta C L max") is the lift increase you get from the flap, taken from the table above. Or, you may find a better number in your airfoil data or in Appendix C (the difference between the clean wing and the wing with flaps). For Fowler flaps, the extra lift you get depends on the amount that the chord length increases (c' is the new chord length, c is the original chord length). If flaps are used for takeoff they are opened only part way, so use lift increments of about 60-80% of these values. The term Snapped is no/ the area of the flaps. Sapped is the area of the wing that has the flaps as illustrated in the next figure. 90
.5 7. 7^1//? C^/cMt:^^77^ Watch out for big flaps, especially Fowler flaps. They create huge nose-down pitching moments and can also mess up the flow on the ailerons near the flaps. Another problem - they make a powerful downwash that can actually stall die horizontal tail, causing an abrupt nose-down event! For the DR-4, I measure my as-drawn wetted areas as follows: fuselage & canopy 178, wing 175, horizontal tail 41, vertical tail & ventral 26, and nacelle 12, for a total of 432. With wing reference area of 102, the measured Swet/Sref comes out to 4.22, which is almost exacdy my earlier guess (I promise, I didn't cheat!). Using the same C% value gives us the same ' we calculated before (.0223). For a comparison, I calculated the drag of this design using RDS-Professional and got .0209 at 10,000 A, 160 kts, so maybe these simplified methods aren't so bad. Also, RDS drag-due-to-lift results are equivalent to an Oswald's efficiency factor of .81, but I'll continue to use the more-conservative 0.75 as recommended above. Propulsion As mentioned, in this book we are sticking to conventional piston-prop propulsion systems. Good enough for Wilbur and Orville - good enough for us. If you want to use a turboprop or turbojet, and can afford one, you'll have to adjust these design methods accordingly. To begin with, we need the power and fuel consumption of our selected engine at different altitudes. If possible, get it all from the engine manufacturer. If not, you can assume that Cbhp (specific fuel consumption) is about 0.4 to 0.6 pounds of fuel per hour per horsepower produced. Use 0.45 for a modem engine in good condition, and 0.55 or so for an oldie or not-so-goodie. You can easily find the sea-level power of your engine, but what about the reduced power at higher altitudes and hotter days? It's the reduction in air density (p) that reduces power in both cases. There is an old equation from the Wright Aeronautical Company (1934) that still does a pretty good job of accounting for the air-density effect upon power. This equation indicates that at an altitude of 20,000 A, a piston engine has less than half of its sea-level power (70% at 10,000 A). 91
Density effect on Power: 7 = JP 7.55 Where P = power, p = air density, and po = air density at sea level To calculate range and performance weTl need an estimate of the thrust we'll get from our propeller. In the sizing section we defined the propeller efficiency (r)p) as the ratio of the thrust power you get out of your propeller compared to the engine power you put into it. We used 0.75 as a rough guess - it's time to calculate a better value. Actually, you may not need to calculate r(p. If you are using a propeller that is normally used with your engine, you may be able to get a table of propeller efficiencies or even a table of thrust and fuel consumption at different speeds and altitudes. If not, read on. We determine propeller efficiency from two key parameters - the "advance ratio" and the "power coefficient." The advance ratio ' V ' ' (roughly equivalent to the wing angle of attack) is related to the distance the aircraft moves with one turn of the propeller. Advance ratio is sometimes called the "slip function" or "progression factor." The power coefficient is a nondimensional ratio that expresses how much power we are putting into our propeller compared to its diameter and rotation rate. Thrust Produced: T _ 550%/%?%, Advance Ratio: nD Power Coefficient: 550)/%? V = velocity (ft/sec) n = propeller rotation rate (rev/sec) D = propeller diameter (ft) p = air density at that altitude (slugs/cubic ft) bhp = engine brake horsepower at that altitude Propeller data is available from the manufacturers as well as various NASA/NACA reports. This data is provided in many different formats. Propeller efficiency data typical of the props used on homebuilts are provided below as a function of advance ratio and power coefficient, which you calculate using the equations above for each flight speed. A thick wooden propeller will have efficiencies about 10% worse than these values. 92
Don't forget to divide RPM (revolutions per znzKM/e) by 60 to get rev/sec! Also, remember V is in ft/sec and D is in feet, not inches. I mess these up all the time and wonder why my calculated 7 value isn't on the charts below. Prop Efficiency Eta-P 1.000 0.800 0.600 0.400 0.200 0.000 0.500 1.000 1.500 2.000 2.500 3.000 Advance Ratio J Cp 0 = .18 0 = .05 H = .12 D = .26 ] = .35 .5& E^c7<?Hcy .* 2-M<3<3M PhrZhAE PZVcA J*ropE//Er 93
Prop Efficiency Eta-P 1.000 H 1 —1 — — - 6.806 ! X t r y /p 0.400( r p t 0.200 0.000 0.500 1.000 1.500 2.000 2.500 3.000 advance Ratio J Cp 0 = .075 H = .15 <1 = .25 0 = .35 .475 yigMe ^9^. E^ycyency z^p/ 3-A/^^ Phz^y'^^A/^ P^yVc^/Z Prope/Zer I^ the propeller is of variable-pitch design, its pitch is adjusted to the optimum blade angle ot eoch flight condition to produce o constont engine RPM and to keep the prop working in an efficient manner. For such variable-pitch propellers, find the value of propeller efficiency from one of these figures for each velocity and use it to calculate thrust at each speed. If a fixed-pitch propeller is used, the blade angle cannot be varied in flight to maintain engine RPM at different flight conditions. Since the RPM and therefore horsepower will vary with velocity, the efficiency and thrust will be reduced at other speeds. What you must do is to pick a "design speed" for the propeller. The prop will be shaped so that it is best at that speed, but it will be worse at other speeds. Use figure 58 or figure 59 to find the "on design" efficiency of your prop (ie., efficiency at the design advance ratio J). 94
100 .90 \ 70 \ .60 J .40 .50 .60 .70 .80 .90 1.00 1.10 1 20 1.30 -^design 60. Prep fhc/or An adjustment for fixed-pitch propeller efficiency at an off-design advance ratio is provided in figure 60. The efficiency at the design speed is multiplied by the ratio found in this chart at another advance ratio (J). Some production airplanes offer a "cruise prop" and a "climb prop" as purchase options. Those are just props with different design speeds. Actual design of the prop for your plane is not covered in this book, and can wait until later. Or, you may just buy a good prop for your selected engine. Propeller efficiency must be corrected for scrubbing drag. This is the extra drag caused by the propwash blowing down the side of the fuselage, tails, and wing root. A reasonable estimate is a 5% loss, so multiply your propeller efficiency by 0.95. A pusher design does not have scrubbing drag because the propwash isn't blowing on the airplane. However, the propeller itself is operating in air already disturbed by the fuselage and wing, causing a loss in thrust. Coincidentally, a reasonable correction is also a 5% reduction in efficiency. If the tip speed of the propeller gets too close to the speed of sound, shocks will form causing losses in efficiency. At 300 kts, these losses can reduce thrust by 10-20% or more. If your design will exceed 200 kts and/or has a large, fast-turning propeller, you should include corrections for tip Mach effects or your top speed estimate will be way too optimistic (see my textbook). Cooling drag represents the momentum loss of the air passed over the engine for cooling. This depends upon the detail design of the intake, baffles, and exit, and is 95
very difficult to estimate. In addition, there is miscellaneous engine drag that includes the drag of the oil cooler, air intake, exhaust pipes, and other parts. In our calculations we can deal with the cooling and miscellaneous drag in one of two ways - either add it to the aircraft total drag, or subtract the cooling drag from the propeller thrust. We will use a version of this latter approach. Data from various airplanes indicates that about the best we can hope to do is a cooling and miscellaneous drag that is 6% of the total thrust, while a more-typical engine installation for homebuilts will lose 8-10% of the total thrust. A crude, open¬ engine cooling scheme as shown below may cost 15-20% of thrust. As a simplified estimate, reduce your horsepower by the appropriate percentage before calculating thrust. 67. Coo>?Kg Drag - 7%e a^ JW & Sometimes we need to know the static thrust (thrust when airplane is not moving). Our thrust equation above has the velocity in the denominator - if you put in zero for speed the equation explodes in your face (try it - I warned you). There are more complicated methods you can use, but a reasonable rule-of-thumb says that static thrust is about 60% higher than the thrust at 100 kts. For the DR-4, I have a 2-bladed prop in front and a less-efficient 3-bladed prop in back. The pusher prop will also suffer from being in a disturbed flowfield, so the total thrust needs to be reduced. As a rough approximation of this, I analyze both props as if they were 3-bladed props and applied a 5% thrust reduction to account for scrubbing drag and the pusher prop losses. The thrust calculation at 10,000 ft, 150 kts is shown below. The selected Jabiru engine cruises at 2700 rpm, producing 105 hp at sea level. At 10,000 ft it will produce 70% of this, or 74 hp. From the calculated J and Cp, I read the efficiency of a 3-bladed propeller as 0.89 which I reduce 5% for scrubbing drag to 0.85. Assuming a 6 percent cooling drag power loss gives the calculated thrust of 128 lbs per engine. I assume constant-speed propellers will be used (I hope they exist!) so thrust at other speeds is calculated the same way. 96
Advance Rat.o: y = -L_ '5°'' *6,89 =1 J26 nD 2700*5/60 550 Mp 550*74 Power Coefficient: .00176 *(7700660)3 5' Thrust Produced: y,_ 55^(^^/%p)7p " r 550 *44 * .94 * . 85 150 8=1.689 = 128.4 (lbs) Preliminary Structural Sizing Structural sising is the calculation of the thicknesses of the structural parts required to safely withstand the expected loads, including a factor of safety. In high-performance aircraft we do structural sising over the whole aircraft and then taper the material thicknesses to just exactly meet the required strength. This is done with expensive manufacturing methods such as machining, chem-milling, or complicated variations in the number of composite plies. For small aircraft including homebuilts, it is more common to select just a few different skin thicknesses (gages) and use the same gage over a pretty large region, such as the entire tail. For example, much of the Piper Tomahawk is made from aluminum 2024-T3 that is 0.020" thick. This is used for aft fuselage sides, wing box skins, and horisontal tail skins. Very thin skins (0.016") are used for lightly loaded structure such as rudder and aileron. Skins that are 0.025" thick are used for the aft fuselage top and bottoms and the side of the fuselage in the cockpit area. The thickest gage, 0.032", is used for inboard leading edge skins and for the wing box at the root. The small Sonerai kit plane has wing spars of 0.040" aluminum 2024-T3, and has ribs, ailerons, and wing skins of 0.025." The fuselage and tails are of 4130 steel tubing, fabric covered. There is also some 4130 steel sheet metal in the fuselage. The landing gear is of solid-spring design, made of aluminum 2024-T351 that is 5/8" thick. The canopy is 1/8" molded Plexiglas. The fuel tank is aluminum, and the cowling is fiberglass. The popular RV-6 is also mostly aluminum 2024-T3. Wing skins are 0.032" inboard, reducing to 0.025" outboard. Spars are built-up of 0.032" to 0.040" thicknesses. Ailerons are 0.016" with stiffeners. Tails are 0.032" with 0.016" control surfaces. The fuselage varies from 0.040" up front to 0.025" over the back two-thirds. 0.125" aluminum extrusions are used for longerons and angle reinforcements, with bulkheads of 0.025" to 0.032" aluminum. The RV-6 motor mount is 4130 steel tubing, and landing gear is a steel spring. Cowling is fiberglass with 0.020" stainless steel firewall. 97
Burt Rutan's Voyager is perhaps the ultimate application of non-autoclave, wet¬ layup composites as used by homebuilders. Its basic structural weight was only 938 lbs, but it could support a takeoff weight of 9794 lbs - more than ten times as high. The wing skins are graphite-epoxy sandwiches, with 0.014" thick face sheets over 0.25 honeycomb core. The fuselage is similar except that Kevlar is used in the cockpit area to allow the radios inside to work. Peter Garrison's new four-place Melmoth 2 is typical of a modem all-composite homebuilt, made largely from foam core sandwiches with glass-epoxy and carbon¬ epoxy face sheets (skins). The fuselage skin sandwich typically has 2 plies of bidirectional cloth, totaling about .020" thick, on each side of a half-inch-thick polyester foam core. 62. GarrMtK 2 However, the weight of this sandwich construction is equivalent to that of 0.036" thick aluminum sheet. The weight savings we hope to get from composites don't seem to apply to small structures such as homebuilts (and Melmoth 2 is a large homebuilt). The wing skins of Melmoth 2 are unusual in having a bidirectional carbon inner skin (0.016" thick) and a glass outer skin (0.018" thick) over a 1/4" thick foam core. All torsional loads are carried by the inner skin, which is also the liner of an integral fuel tank occupying almost the entire wing. All of the wing and empennage spars are of carbon-epoxy construction. The tail surfaces are solid foam cores skinned with two or three plies of unidirectional E-glass. The ailerons, flaps and trim tabs are all carbon. The trim tab skins are only .005" thick - hands of The Melmoth 2 canopy is made of three different thickness of acrylic: 1/4" for the windshield, 3/16" for the side windows, and 1/8" for the rear window. 98
Garrison's first Melmoth was of all-metai construction, making him one of few people to design and build both a metal and a composite homebuilt. Comparing the two experiences, he says, " Wzen 7 y/a?7eZ /7e yeconZ azzp/ane, 7 z7 woM/Z 7e z/zzzcA E,r/ 7?M^^/z yeenzeZ 7, ,7/, /^o /Mm OM/ azryz^^^/ney Z/z a y,w 7zz.^z^/?a(7 7 yb^M/7,7 coM/?oy;'7e cozy/^r^Mc/^zo^j? o/ yo/?7zyffcafeZ /o 7, y^^r /wore coz?^/z7a/e7 ,zj/z(7 Mz/z6^-^(7^J?^^^Mznzj/^^g /T^/zzz znefa/. 77^e w,zg7/y a/ /7, /wo azzyz/aney ar^e a7a^z^^/ /7, ya/we. 77^e w^azz)? aa7^a^z^j^<ag, o/ cawy/ayz/ey way /7, a^7?z/z'7y /a yorw c?a^w/^^aM77(7 cz^jrv,y ,a^yz/y - 7%/ 7'w yz^zr, /7a/ 7? /7, 26y^ea^r^y 7 ,??(/z^/ an /7e y,c^a?z^(7 azrg/a^a^g^, 7 cazn/Zfz 7 7av, /ea^r^z^^^a, /a Hye a /p/anzy7zz?g 7a?/z/?^(^jr a^^?(7 an Eng/zy7 w7e,/ y'zfy^/ ay we//. P7eweZ aey/7e7'ca^/^/y^, ev^e?7 a ge/yec/ c?a/?2/^(ayz7e a^z7y^^/a/ze (az^^a' //zzz^e zy z^(a/ /zezyec/? zy /eyy yafzy/yzng /7a^j? a z^^^j/a/ a/ze 7ecaMye z/y /^<e/yec/^za^^z zy yMjp^^zzyz^zz^^/ an<7 ca^j? 7e aZZe^/ /a/ez^. 77zere 'y /^^a way /aya^Ae goo (7 we/a/warA^". But, this author has seen Melmoth 2 and it is truly beautiful! Structural sizing is serious business, and not something to be "simplified." Mess it up, and it messes you up. Luckily, we can test our structural sizing and fabrication with the aide of nature's own laboratory tool - sand. Plan on doing sandbag tests of every structural item on the plane - wings, tails, fuselage, landing gear, motor mount, and more. Flip it over and load it up! I'm not going to try to provide simplified structural calculations that are easy to use, but good enough to trust your life to. Can't be done. Instead, let me offer two sample calculations to give you a feeling for structural analysis. You can also use them for preliminary, first-guess structural sizing. After that, you should dig into a good structures book and do it right. However, you don't really need to do final structural sizing until your overall design concept is finalized, not until after you've make your second drawing. j?g/zre 63. 5^z'7K9/z^e(7 l%T?g ^^r^Mc/z^z^^/ Tna/yyzy 99
A simplified model of the loads on a cantilevered wing is shown in figure 63. The total wing lift equals the aircraft weight times the load factor (L = nW). Well assume that the lift is uniformly spread across the wing, so the total lift acts, on average, at a point half way out the span (we are ignoring the fuselage, which is shown just so you'll know it's an airplane). This creates a moment at the wing root which equals the lift on one side (nW/2) times the moment arm distance (half the semispan, or b/4). At the wing root, this moment must be "fought" by a reaction moment to stop the wing from rising up and breaking off. This "fighting" is done by a compressive force C in the top skin, and a tension force T in the bottom skin. These must equal each other or the wing will slide to the left or the right in our picture. The moment arm created by C and T depends on the distance between them, which is the wing average depth (thickness "t"). That is why a thicker wing is better for structure. If the lift moment equals the wing root reaction moment, and T=C, then: ??%%% Equating Moments: = /C , oo C = T = 8 8/ As can be seen at the bottom left of the figure, these compression and tension loads are distributed into the wing skins at the root. If the load is evenly distributed, the stress in the skin is the total load divided by the area carrying it (skin thickness times length of skin carrying the load). Now we simply need to find out the thickness of our chosen material to carry that much load. On the tension side (bottom), we can find the material allowables in a structures book or the material producer's data sheets. For aluminum 2024T3, a typical value for ultimate tension stress (Ftu) is about 60,000 psi. For safety we normally design to no more than 2/3 of this value, which is about the stress where it begins to permanently deform like plastic. We can then calculate the skin thickness required to keep the stress below this value. On the compression side things are more complicated. Pull on a piece of paper, then push on it. Big difference! Under compression, sheets of material will buckle at a very low load. The load a sheet can carry in compression depends on how well it is supported. That is why we use stiffeners on skins, and why sandwich construction is so good (the skin is supported everywhere). Structures handbooks have charts of test data on skin panel buckling under load. You simply have to determine the load and the skin geometry (thickness and how it is supported), then read the answer from the chart. Sounds easy, huh!? There is another significant structural loading shown in figure 63. The vertical lift of the wing has to get "transferred" into the fuselage to hold up the airplane. This lift force is opposed by the "shear" force shown acting downwards on the wing spar. The shearing stress is the force divided by the area. In this case, the area of concern is the vertical area (next to that downward shear arrow). 2024 aluminum can typically take 100
about 40,000 psi in shear (FgJ. Again, we only use 2/3 of that value to provide a factor of safety. If you are designing a composite airplane, you cannot go to a table or chart to get the allowable tension, compression, and shear values. You have to actually design the composite material itself, by selecting the fiber material, the matrix (resin) material, the number and alignments of the fiber plies, and the curing process. These choices result in substantially different material properties. The properties of a composite material are not simply the algebraic sum of the properties of the individual ply layers. To do it right requires tensor calculus equations and a pretty good computer program. Even then, in industry we always do coupon testing to determine design allowables for the selected materials and ply orientation. There is a designer's rule of thumb for composites called the Ten-Percent Rule ' that gives a quick strength approximation for typical composites. This rule reasonably assumes that most of the load is carried by the plies that are running in the direction of the applied load. The rule is simple - just add the number of plies times the strength per ply, but multiply all plies that are not running in the direction of the applied load by 0.10. Note that many of the plies must be at 45 degrees to the main load to give good shear and torsional strength. Needless to say, this rough approximation is on/y for initial sizing purposes and should not be relied upon for a final design analysis! A good technical introduction to composite materials is provided in reference 21. For homebuilders, Hollmann provides an excellent overview of composites^ and of sandwich structure^. Another important wing load not shown on this simplified figure is the torsional load. The lift on the wing will not be exactly centered on the wing spars, so a twisting load about the spars will be created. This is complicated to analyze and is beyond the scope of this book - consult a good structures book (see below). Another common type of aircraft structural problem is a truss structure motor mount. We need to know the loads in the tubes, to determine the tubing gages required. There are several ways to solve this. One simple method is the combined method of moments/method of shears. 101
64. (numbers are dimensions in inches) T/ws A4^i^7/c^Oy ^q)weK^q/o^^SZ?ear.y yig^Mrg 66. 102
We start by pretending to cut away the top tube. If we did this, the load of the motor (nWengme) would pivot the motor downward around the bottom weldment. We will solve for the load in the missing top tube that prevents this from happening. Do this by equating moments around the bottom weldment as if it were a pivot point (figure 65 top): Equate moments: (4000)(19.6) = 7^ (20) so Fc= 3919.2 By the way, don't confuse Fc with a notation for a compression force. Here Fc is just the name of that unknown force -1 could have called it "Ralph." You can see just by looking that this top tube must be in tension. Repeat this method for the bottom tube. The calculation is a little more complicated because we need to include the angle of the bottom tube - its force is acting at an angle of 11 degrees to the moment arm distance, so the effective force in the direction perpendicular to the moment arm is reduced (multiply by cosine of 11). We get: Equate moments: (4000)(69.6) - 7^ 30 cos(l 1) so Fp = -9463 Fp is a negative number. What is a negative force? One that is in compression. We would expect this for the bottom tube. So, we've solved for two of them - how do we get the third answer? Get out that saw you used to cut the top and bottom tubes, and cut the whole thing off (figure 65 bottom). Now find the missing force that stops the whole thing from floating away. Add up all the forces in the horizontal direction - their sum must equal zero or off it goes! Solve for the missing force: Sum Horizontal Forces: 3919.2 + 7^ cos(22) + (—9463) cos(l 1) - 0 so Fp-5775 We could have done it the other way - add up all the forces in the vertical direction. They also must add up to zero. Don't forget the engine. Sum Vertical Forces: - 4000 + 7^. sin(22) - (-9463) sin(l 1) - 0 so Fp=5775 Same answer either way, and a good way to check our result. Actually, there are probably tubes on both sides of the airplane so these loads are divided in two. Also, they are probably at some angle when seen from above so the loads in the tubes will be increased by dividing by the cosine of the angle. Now that we have the loads in the individual tubes we can find the thicknesses required. On the tubes under tension, it's the same calculation we used for the wing 103
skins. Calculate the total area of the metal, divide force by area to get stress, and compare it to the metal's allowable stress including a factor of safety. On the compression-loaded tubes, we have a similar problem to the skins. Take a drinking straw and pull on it, then push on it. When you push on it (compression), it buckles sideways long before the actual material fails. For tubes under compression we go to charts in structures handbooks that give us the buckling loads for columns based on thickness and length of column. Pick a tube that won't buckle for the calculated load. Often the gages we select for structural parts have nothing to do with the structural calculations. If a part is lightly loaded, the stress analysis may tell us to use aluminum foil from the kitchen. Bad idea. Thrown rocks and dropped tools will dent it, curious kids will bend it, and a bird will go right through it at 200 kts. To avoid this, we define a "minimum gage" for our design, which means just what it says. No matter what the stress analysis says, that skin thickness or tubing wall thickness is the thinnest we will use. The 0.016" aluminum used for lightly loaded structure on the Tomahawk is probably a realistic minimum gage for homebuilts. For composite skins the minimum gage is thicker because super-thin composites are brittle and prone to impact damage. Sandwich structure helps that a bit. In any case, the allowable minimum gage on your project is your call - and also your problem later! The problem of minimum gage has an interesting side effect. A small airplane may have much of its structure sised by minimum gage, not by stresses. This provides ample structural margin for increased loads. Because of this, a small airplane may have no weight penalty for using a T-tail or gull wing or another design approach that would penalise a larger design, precisely because the skins are already oversised. To do the structural sising or the after-construction testing, we need to know what the loads will be. Again, this is serious business and takes some real effort. For homebuilt aircraft, the loads approximations in FAR 23 are reasonable and reflect almost 100 years of design experience. Plan to study FAR 23 and other books to learn about this subject. My own textbook has 63 introductory pages on loads and structural calculations including the classical methods for tension, compression, shear, bending, torsion, column buckling, panel buckling, truss analysis, shear webs, and more. For an easy-to-read, intuitive understanding of structural analysis I recommend Rhodes's "Stess Without Tears'?." A book by Hiscocks*? has a thorough treatment of light aircraft loads. Of course, everybody involved in aircraft structural design and analysis has a well-worn copy of Bnum's. I also like the structures books by Peery*? and by Niu^?'. These can be found in the bookstore on my website. 104
Weights Estimation Estimation of the weight of the design you've drawn is the next thing to do. It isn't easy. We haven't fully drawn all the parts yet so we cant simply multiply material densities times the volumes measured from the drawing. Some parts we haven't even thought of yet, and we may not make a layout of them until we get to building that section of the airplane. But, we have to estimate the total empty weight now, to find out if our airplane will give us the range and performance that we wanted. This includes the parts we haven't drawn or don't even know we need! We do this with a combination of historical analogy, statistics, component selection, and structural analysis. We start with mostly analogy and statistics, and replace our earlier estimates with better numbers found from selection and analysis as the project advances. ana/ogy is simple. I'm designing a canopy a whole lot like a Long-EZ canopy - I'll bet it will weigh about the same. If it is a bit different in some way, I scratch my head and make up an adjustment to the weight. Often the adjustment is based on a ratio - weight divided by some area. If our canopy is smaller than a Long- EZ canopy we may find the weight per square foot of canopy area and apply it to our own canopy's area. For other components such as landing gear we may make an adjustment based on the takeoff gross weight. methods are similar, but we use more than one existing component to estimate the weight. For example, we may calculate the weight per square foot of several different airplanes' canopies and note that they are about the same. Take an averaged value and you've done a "statistical regression analysis. ' " You can use this value to predict the weight of your canopy. Maybe you've spotted some sort of trend in the numbers - perhaps the faster planes have a higher weight per square foot of canopy area than the slower planes. You can graph weight per square foot versus maximum speed and, if a trend appears, draw a line and use it for weight prediction of your airplane. A sample of this is the engine weight vs. horsepower graph provided below. The Wengim/bhp values calculated for the engines of Appendix D showed an obvious trend - the higher power engines had a lower weight ratio, so a graph was prepared showing this. Often such statistical weight relationships follow an "exponential" equation. This means that if you plot the data points on a piece of log-log graph paper, you get a straight line. We can use this line, or make an equation from it of the form Y=aX^. We saw such an equation in our estimation of empty weight fraction We /Wo . This is also regression analysis, but the sort you can actually get paid for doing! One simple and popular form of weight estimation statistic is the "percent of Wo" method. An example is "most homebuilts have landing gear which is 5% of Wo, so my design will too." This isn't a bad way to begin looking at weights, and serves as a useful check on your final estimate. However, this really doesn't "predict" the weight because it isn't based on your actual design layout. Maybe your landing gear can land on snow, water, soft dirt, and an active volcano. It is going to weigh more 105
than 5% of Wo, I promise! Component to gross weight ratios for homebuiits are provided below. Statistical equations get a lot more complicated. Over the years many weights engineers have made sophisticated equations for predicting aircraft component weights. Often these start as a structural analysis of a simplified model of the component. For example, the wing could be modeled as a simple tapered box with a tapered lift loading. From this, engineers can develop an equation that gives the skin and spar thicknesses required to withstand the loads. Then the volume of material can be found and multiplied times the material density for a weight estimate of this simplified part. However, real airplanes have much more complicated geometry and loadings. The weight engineers take actual data on existing aircraft and adjust the terms of the simplified equation until its results better match the actual numbers. A few of these equations are useful to homebuilders and will be provided below. Cow/wHenf se/ec/Zon refers to actually picking off-the-shelf components for various things " . Typical examples include engines, propellers, wheels, tires, brakes, avionics, actuators, batteries, etc... If the part you've selected really does work for your design, this weight estimate is, of course, very accurate. If you have to modify the part, look out! Finally, we can estimate component weights by actual ana/yw-y and selection of thicknesses and gages. Then, we multiply the total volume of material by the material densities. This was briefly introduced in the last section, and you'll want to do such analysis before beginning fabrication. Don't forget to add weight for fasteners, finishes, and fittings. This method should give the most accurate weights estimates, but it takes a lot of time. The empirical equations work pretty well for initial weight estimation and are much easier to calculate. You must use your own experience and judgement in deciding what methods to use, and when. Below are some suggested methods for estimating the weights of different parts of the airplane, suitable for analyzing your first design layout. More data and methods are available in the Weight Engineers Handbook^, a recommended resource for designers. Also, the publications of the Society of Allied Weights Engineers are useful. No weight analysis method gives the "right" answer. Only you can determine how each part will actually be built, and therefore what it will weigh. Remember, when you do a weights estimate early in the design process you aren't really "calculating" the weight. Instead, you are "promising" the weight. If you don't meet your promises when you build the plane, it will weigh too much and perform poorly. I recommend against trying to reuse major structural parts such as existing wings, tails, and fuselages in your design. It seems that everyone who tries it finds that the cost savings are less than expected, and the performance penalties are greater than estimated. Besides, such designs are usually ugly. 106
We often begin our weights analysis with a top-down weight estimation called a "weight budget," which indicates how much the different components normally weigh on an airplane of that takeoff weight. Weights are estimated using historical ratios to total takeoff weight. Below are the averaged W/Wo values for typical homebuilt and light airplanes detailed in Appendix F. You can use these ratios, or pick an airplane similar to yours and ratio based on its weights. WM/o As we develop a better weight estimate for the different components we can check them against the weight budget to see if we are doing something historically and hysterically stupid. Now on to the "real" methods! For the major structural components, the following statistical equations from the Rockwell AeroCommander Division^'' seem to do a pretty good job even for small homebuilts. British Units are used such as pounds and feet. Dynamic pressure "q" was defined and calculated above. "S" terms are areas (square feet). "A" terms are quarter-chord sweeps. Wjg is the "design gross weight" which for light planes is the same as the takeoff gross weight. Use the as-drawn value. 107
Wing: %% = weight of fuel in wings. If zero, skip this term (=1) Az = Ultimate load factor (1.5 times limit load factor) Horizontal Tail: ^Aonzona/ — 0.01 t<21/ -0.12^ x 0 .043 1-0.02 \Cos'A„,y Vertical Tail: = 0.073^ 1 + 0.2— 7 ^1007/c aCOSA^y \-^0.49 ^17 4 ^c°s A.J 10.039 Zf/% = height of horizontal tail on vertical tail (0=conventional, l=T-tail) Fuselage: 5)-= fuselage wetted area (square feet) L, = tail length, wing quarter-MAC to tail quarter-MAC L = fuselage structural length (excludes cowling) D = fuselage structural depth ^r^= weight penalty due to pressurization, if used These equations assume conventional aluminum construction. If you build your design from hand layup fiberglass over thick foam cores it will probably be about 10-15% heavier than these values. Fiberglass, designs where the skins and substructure are molded of thin sandwich construction (vacuum bag-cured) and bonded together will probably weigh about what the equations predict, or perhaps 5% less mostly because of reduced fasteners and fittings. If unidirectional carbon is used for the spars, the wing weight may be 10% lighter or more. If you use graphite (carbon)-epoxy sandwiches the weights should be much less than the values predicted by these equations. If expertly designed and fabricated, you can expect about a 10-15% weight savings for wings and tails, and a 5-10% weight savings for the fuselage. But, the material cost will be very high. 108
The Nemesis Formula One racer was built of non-autoclave carbon epoxy over foam core sandwiches and attained even better weight reductions^, but the guys who did it had dayjobs at Scaled Composites and the Lockheed Skunkworks - not exactly your average homebuilders! Nemesis totally dominated Formula One racing until they got tired of winning so much and retired it to the Smithsonian. If your wing is strut-braced it will weigh about 18% less than the weight calculated by this equation. A biplane's wings weigh roughly 25-50% less than these calculations would indicate. A steel tube fuselage will weigh about 80% more, and a wood fuselage will weigh about 60% more. These adjustments may not apply to a very small design due to the effect of minimum gages, as discussed above. To get a good weight estimate you'll probably have to do some structural analysis to size the major skins or tubes, and add up their weights. According to Piper's experience, a T-tail PA-28 has a 38% heavier tail group than the conventional tailed PA-28. That sounds high for a homebuilt, and some argue that a small homebuilt has no T-tail weight penalty due to the minimum gage effect. I'd split the difference and assume a 16% penalty until a detailed calculation proved otherwise. For a small plane it's just a few pounds anyway. Another way to estimate the weights of these main structural components is the statistical "pounds-per-square-foot" method. This method may actually give a better result than the fancy equations if based on data for a similar design. The table below is based on various homebuilt and light aircraft. For the fuselage, the area to use is the wetted area. For the wings and tails, the area to use is the exposed planform area, no/ the wetted area (which is more than double the exposed planform area). Weight Est. wing ib/sq-ft horiz ib/sq-ft vert ib/sq-ft fu setage ib/sq-ft Metal 1.1 to 2.0 0.9 to 2.0 0.9 to 2.0 1.2 to 1.4 Fiberglass 1.6 to 2.2 0.9 to 2.0 0.9 to 2.0 1.2 to 1.4 Carbon 1.2 to 2.0 0.9 to 2.0 0.9 to 2.0 0.7 to 1.2 Fabric (braced 1.0 to 2.0 0.8 to 1.5 0.8 to 1.5 1.4 to 1.8 For a better estimate find weight data on an aircraft similar in both design and construction to your own, and find these weight/area ratios. Best of all - if you can - is to actually do the structural design and analysis, and from that select the material thicknesses. Then simply multiply volume times density. Simple, huh?! Densities of a number of aircraft materials are provided in Appendix G. These include metals, wood, composites, and miscellaneous materials such as acrylic, glycol and rubber. Please note that these are just typical values, to use during initial design. You should verify all data with the material vendors making sure that it is the material that is appropriate for your application. 109
Other weight items for homebuilts can generally be found by selection of components, or are small enough that a good guess is good enough. Engine weight should be readily available. Weights of typical homebuilt engines are provided in Appendix D and are plotted below as pounds per horsepower. Note that this weight ratio reduces for the more-powerful engines. Engines have an installation weight that adds to their basic weight. This includes the propeller, mounts, exhausts, and other piping and plumbing. These can be individually estimated or can be approximated as about 30%, added to the engine weight. Other weight data and ratios are provided in Appendix H, including canopy, landing gear, avionics, instruments, and more. These should allow you to make a reasonable estimate of your total weight. When the weights are estimated, we write them down in a standard format as shown below. This helps us to remember everything and also makes it easier to compare our plane to similar planes. Besides, it just looks more professional. At this point, the professional designers usually put in an "empty weight allowance." This is just a chunk of weight to account for a sad truth - the weight always goes up during detail design and fabrication. A minimum allowance is 5% of empty weight, and some people use a 10% allowance. Put this weight allowance on your weights statement just above the total empty weight. 110
STRUCTURES GROUP EQUIPMENT GROUP Wing Horizontai Tait Verticai Tai! Ventrai Tai! Wingiet Fuseiage Canopy Naceiie/cowiing Motor Mount Main Landing Gear Nose Landing Gear Fiight Controis instruments Hydrauiics Eiectricai Avionics Air Conditioning Anti-icing Furnishings & Equipment 1 Empty Weight Aiiowance] 1 PROPULSION GROUP [TOTAL WEIGHT EMPTY 1 rn Engine Ar induction USEFUL LOAD GROUP Cooiing Crew Exhaust Fuei Engine Controis Oii Misc. Engine instaiiation Passengers Propeiier Payioad Starter Fuei System [TAKEOFF GROSS WEIGHT! a y?gare &aA7^ar^/ Gro^//? IT^/gh^ Tor/naf One important t^ng to remember about the standard group weight format: Kot/ never, ever change fhe /aheo/0gro.xy we/ghf an i7A This should always be the weight that you used when you drew your airplane (Wodrawn) * That weight was used to select the sises of the wing, tails, engine, and landing gear. If you change it, you must change them all and make a new drawing. Also, it is used in the weight estimating equations and if you change it, your answers are wrong. Instead, use this sheet to calculate the ^Re/ w?gA as whatever is left from takeoff gross weight after subtracting the empty weight and the rest of the useful load group. When you've calculated fuel weight this way, the empty weight plus the useful load group including fuel adds up to Wo-drawn . Later we'll use this available fuel weight to calculate the range. Another thing we have to calculate is the center of gravity. This is easy, once we've found the weights of the components. First pick a "datum. *" In English, this is the reference point for measuring lengths. It can be any easy-to-find location, such as the front of the engine or the front of the firewall. Don't pick the tip of the spinner - you'll get confused later when you put on a bigger one. Some people use a datum far in front of the airplane so that all distances are positive, even if the design is changed. For each component, measure the distance from the datum to the center of mass of the component. For wings and tails this is at about 40% of MAC. For the fuselage it 111
is probably at about 40-50% of the structural length. For other components, try to get correct data, or find the center of volume, or just guess. The errors on the smaller items will cancel out. On your group weight statement add another column for moments. For each component, multiply its weight times its distance from the datum and write that down. Add them all up, and divide by the takeoff gross weight. That number is your center of gravity in feet behind the datum. Hopefully this is near the "target" c . g. you used when drawing the airplane. Don't panic yet, though - save it until after you've calculated the static pitch stability. Then, determine what combination of loading would give the most-forward and most-aft e . g. locations (perhaps a heavy pilot, full fuel tanks, and nobody in back gives you the most forward e . g. whereas a petite pilot, empty tanks, and a big passenger in back give the aft-most e . g. ). For each loading condition, calculate the center of gravity. The weight reporting format and e . g. calculation is included in the spreadsheet yhrcrq/? DeygK " available for download at www. cow. One final thing - during design and fabrication the center of gravity always seems to move away from the engine (ie., rearwards for a tractor aircraft). In early analysis, err on the side away from the engine. It takes very little ballast at the tail to fix it if the e . g. finally winds up too far forward, but it takes a lot of ballast at the nose if the opposite is true (anyone know where to buy a solid-lead propeller spinner?). For the DR-4, I use the above equations for fuselage, wing, and tails without any adjustments except a 16% penalty on the vertical tail for being a T-tail. Thus, I'm assuming either a metal structure or a foam/fiberglass construction, not a molded sandwich construction. I may change my mind on this later. I assume an aerobatic limit load factor of 6, yielding an ultimate load factor of 9. For other components I largely rely on ratios from similar airplanes and from actual component weights, and add a 10% empty weight margin resulting in the following weights. As can be seen, the fuel weight is just about what the sizing calculation said was needed - what luck! The center of gravity is at 7.8 ft, a little aft of the target on the drawing. 112
DR-4 Weights Weight ibs Loc ft Moment ft-ibs Weight ibs Loc ft Moment ft-ibs STRUCTURES 661.0 5600 EQUIPMENT 69.0 429 Wing 276 6.5 1794 Fiight Controis 10 5.5 55 Horizontal Tait 24 21.0 504 instruments 10 5.5 55 Verticai Tai) 18 19.0 342 Hydrauiics 2 6.0 12 Ventrai Tait 8 17.0 136 Eiectricai 12 6.0 72 Fuseiage 155 9.0 1395 Avionics 15 5.0 75 Canopy 15 8.0 120 Air Conditioning 0 Naceiie on wing 50 9.0 450 Anti-icing 0 Naceiie/cowiing 30 7.5 225 Furnishings & Equipment 20 8.0 160 Motor Mount 10 7.5 75 Main Landing Gear 56 9.0 504 (% We Aiiowance) 10 Nose Landing Gear 19 2.9 55 Empty Weight Aiiowance 114.1 7.8 891 PROPULSION 411.0 28771 [TOTAL WEIGHT EMPTY 12551 7.8 9797 Engine 340 7.0 2380 Air induction 3 7.0 21 USEFUL LOAD 744.9 Cooiing 3 7.0 21 Crew 180.0 8.0 1440 Exhaust 8 7.0 56 Fuei 358.9 7.5 2692 Engine Controis 2 7.0 14 Oii 6 5.0 30 Misc. Engine inst 5 7.0 35 Passengers 180 8.0 1440 Propeiier 30 7.0 210 Payioad 20 10.0 200 Starter 10 7.0 70 Fuei System 10 7.0 70 TAKEOFF GROSS WEIGHT 2000.0 7.8 15598 Crew+Pass+Pid, No Fuei Crew+Pass,No Pid,No Fue) Crew on)y, No Fue) Crew on!y, Fuii Fue! 12907 12707 11267 13958 o tL 1641.1 1621.1 1441.1 1800.0 Stability The center of gravity we just calculated may or may not match the "target" we used to draw the airplane. Actually, we don't care. What we really care about is, do we have the stability we want? Most people have an intuitive understanding of stability. If disturbed, a stable airplane will return to its original condition. If pitch is the "condition" being considered, a stable airplane that suddenly finds itself nose-up will tend to put its nose back down. An unstable airplane will increase the nose-up condition until stall occurs. The usual textbook illustration of stability is a marble in a bowr - if "disturbed" by being moved up one side, the marble will go back down to the lowest point. Like an airplane, though, the marble will not immediately find the lowest point but will oscillate back and forth a bit before settling down. If you've sized the vertical tail correctly and provided a reasonable amount of dihedral, a normal aircraft configuration should have acceptable roll and yaw stability. You must check it later with some stability calculations, but it's probably close enough that you can press on to the second drawing without further ado. Use your imagination in the absence of a stupid drawing of a marble in a bowl. 113
However, the pitch (longitudinal) stability needs to be checked immediately, and often the wing must be moved in the second drawing to fix it. There is no way around it - calculating pitch stability takes some ugly equations. LeTs start with one that gives us the "Neutral Point" - if your plane had its center of gravity exactly here, it would have perfectly neutral stability. If the nose comes up, it just stays there. fTafe. //ya% yzsV yyzcAea/ M/p /Az\y AaaA ana/ are yzppz'ng AraagA /a yee z/*joatz wan/ /a /?My I A /p/eaje, Aeey? y7z/??zng/ 77?zj /^<age Aa?L war^L^/^, Mg/zef^Z efM^ZzanL zn /Ae w/^^a/e /^a?a/T a^j?(/ ?7 pyy^wy 7a^zL ar A7zzry?/ry I revenge /^z^ j^a/ya^^/a /^z^.re/) Neutral Point: 7L y — y -)- y y " y -k y ^7aiZ7erm where: cosfweep) 10 + 18 cos(swefp) / ,4 A^„g= location of quarter chord of wing MAC Am? = location of quarter chord of horizontal tail MAC = (o . 2'25^,,. 0.0675^„„, + 0.011) If%ejge=naximum fuselage width; Ty^,^/^^^gg^Lf^s^(^l^^age length L^j = (distance from front of fuselage to 25% of wing root chordd)///^ z ; ) Q _ or I ?a:7 LTL7i7gn?w '^7^aL7Ld^c^w^n^w^aM^° The .85 value in the tail term adjusts for the wing wake effect on the dynamic pressure seen by the tail. If you have a high T-tail, use .95. CLttaii is found with the same Cm equation used above for the wing, but using the tail aspect ratio. is the effect of the wing turning the airflow before it reaches the tail. This reduces the tail's effectiveness, and ranges from approximately 0.3 for a low tail close to a tapered low aspect ratio wing, to about 0.8 for a T-tail a normal distance behind a high aspect ratio wing. For most normal designs, =0.6 is probably reasonable (=0.7 for a T-tail)*. For a better number, see the downwash derivative estimate in my textbook. Notice how a T- tail benefits twice - less downwash effect, and less wing wake effect. Too bad they are usually heavier. 114
The term with the elevator area is an adjustment for the fact that the pilot doesn't firmly grip the control stick - the plane is flown with a light touch. If the nose comes up, the air blowing on the bottom of the elevator will lift it slightly and the pilot won't even notice that the stick has moved back a bit. This slightly reduces the nose¬ down pitching moment we need for stability, so the airplane is a little less stable. As a first approximation, this term reduces the tail effectiveness by an amount equal to half of the ratio between elevator and tail areas. Since we are making this adjustment, we are calculating the "Stick-free Neutral Point." Now you can calculate the Neutral Point. So what? We rarely want an aircraft that is neutrally stable, so we try to design it so the center of gravity is forward of the neutral point. In fact, the distance between the center of gravity and the neutral point will tell us how stable the airplane is. We divide this distance by the wing mean aerodynamic chord, which gives us something we call "static margin." A" - A" Static Margin: 5W -——— Where: 2) + A + A_ 3 J 1 + A (we measured this on our wing drawing) c = What does it mean? The static margin is a simple and direct measure of stability. We want ours to be about 12 to 20% (ie., 0.12 to 0.20) for a nice-flying, stable design. For sportier handling, shoot for 8-12%. Anything less than 8% had better be a serious aerobatic plane for expert pilots. By the way, these suggested values include an allowance for a propeller in front, which is destabilizing. If you have a pusher propeller you can reduce these by 3-5%. After calculating your design's static margin (stability), you may need to move the wing for the second drawing. Move it to the rear if the static margin is too low, and to the front if it is too high. You can try a few locations in the equations above to find the right amount to move the wing * . PLEASE, do not fly your airplane without doing a better stability calculation than this simplified estimate. These methods are great for use during design layout, but get a good stability and control book and do a better calculation before trusting your life to the answers! And no, building and flying a model airplane is not proof that the real airplane will fly OK, unless you know how to do a proper dynamic scaling analysis. Hint - if you do it right, the model is probably too heavy to take off under its own power! Also note that I have not attempted to provide a quick method for calculating the stability of canard and tandem wing designs. You can adjust these methods to * But Dan - in college I learned to leave the wing where it is and change the size of the tail until I get the correct amount of stability. Sorry. Wrong. 115
remove the downwash effects on the tail (which is now in front of the wing) and then add the effect of the canard's downwash on the wing. However, the results will be pretty crude. I wouldn't trust my life to a new canard design without hiring somebody to run some aerodynamic analysis on it, and/or testing a pretty good model. But, such analysis is getting cheaper by the day, so don't let me discourage you completely. Stability calculations for the DR-4 found a wing Cm of .0847, a tail Cm of .077 (aspect ratio of 6), a fuselage K term of .031, and a tail K term of .0092. This gives a neutral point of 8.4 feet. With the calculated center of gravity at 7.8 ft, a stick-free Static Margin of 19% is obtained. This is stable, more than I'd prefer. As a check I ran the better calculation in RDS-Professional and found a stick-free Static Margin of 14%, so I could move the wing forward a bit on the next drawing to make it a little less stable. Or, I could leave it where it is for safety and as an allowance for the mysterious tendency of the c.g. to drift to the rear as time goes by! 116
Chapter 8 RANGE & PERFORMANCE We've made estimates for aerodynamics, weights, and propulsion, and checked the stability. Now we can do better calculations for stall speed, takeoff distance, rate of climb, maximum speed, cruise speed, and range. These are the most important performance parameters for light aircraft - if you want to calculate some other performance values, please refer to my textbook. Many of these calculations are also in the spreadsheet "Roy/Mer Des/gn available at www.a/rcrq/?^;M-<co?w and included in the original purchase of this book. See details in the introduction. StaH Speed Stall speed is calculated just as we did it before, by setting lift equal to weight. However, we'll take the equations we used to find wing loading and solve them for the stall speed, based on the wing area we have on our drawing. Also, we can now use our better estimate of the maximum lift coefficient. For air density (p) we usually use the sea level standard day value of 0.00238 slugs/cubic ft or the Denver hot day value of 0.00189. Stall Speed: Hopefully this result matches the stall speed we set as our requirement. If not, we must change the wing loading (and area) for the second drawing. For the DR-4, the wing maximum lift coefficient will be 90% of the airfoil's value of 1.6, or 144. The split flaps are over about 40% of the wing by area. If used for takeoff, they add (.9* . 4* . 9=. 194) to the lift, for a total of 1.63. However, I'd expect a little less due to the interactions with the fuselage and wing nacelle, so I'll assume 1.6, which is the same value used for the initial wing sizing. With this, stall speed calculates to be 60 kts as desired. Takeoff Distance For takeoff distance, the graph below provides a simple estimate from your wing loading, your power loading, and your maximum lift coefficient. We've already found all of these. Calculate your value for the "takeoff par^m(^f^t^r^'" using the equation below, find it on the graph, go up to the desired line, and go left to read off your takeoff distance. For the Denver hot-day takeoff multiply the T . O . P. by 126 (.00238/.00189) to adjust for reduced air density before using the graph. 117
Takeoff Parameter: r.CLP. = 1.21 /%? 4000 3500 3000 2500 2000 1500 1000 500 0 Over 50 ^Ground Ro!) 100 150 200 250 300 350 400 T akeOff Parameter For the DR-4,1 get takeoff par<Mneter= 123.2 yielding a ground roll of about 850 ft. Rate Of CHmb Rate of climb is found from the thrust and aerodynamic coefficients. L/D is found from the equation above, using chmb speed V to calculate q. Velocities are in feet per second, as before. Most light planes climb best at around 70 kts, but you can change the chmb speed until you find the best climb speed for your design. Rate of Climb: r 1 Z/D Maximum and Cruising Speed Maximum and cruising speed are found the same way - we look for the speed where thrust equals drag. For cruise speed, choose a power setting (often 75%). You can And the speed by guessing different speeds and calculating thrust and drag until you get it right, or you can find speeds using a graph (spreadsheet program or that dead¬ tree stuff). Pick four or five different speeds and for each, calculate thrust using the equation provided in the Propulsion Analysis section (repeated below). Don't forget to reduce the horsepower for cooling drag and to apply the corrections for scrubbing drag and 118
other thrust reductions. Then, calculate total drag using the aerodynamic coefficients we estimated above. Plot the curves and look for the place where the thrust curve crosses the drag curve. Thrust Produced: Calculate thrust twice - once at 100% power, and once at your engine's preferred cruise power setting (perhaps 75%). Total Drag: where Lift Coefficient: D = <*((C.+XC/) A c % Dynamic Pressure: The weight "W" is the aircraft's weight during cruise. Previously we multiplied the takeoff wing loading (W/S) by 0.98 to approximate an average cruise wing loading - do that in the lift coefficient equation. This adjusts for the fuel already burned by the start of cruise. I calculated speeds and rate of climb for the DR-4 using a calculation table. Data from this table was then graphed. As can be seen, the DR-4 does just meet its intended cruise speed of 180 kts and reaches a maximum speed of 220 kts. Rate of climb is well over the goal of 1500 fpm. To assess engine-out rate of climb the power loading was increased by more than double (2.05 times) to account for the loss of an engine plus the extra windmilling drag. This gave an engine-out rate of climb of 850 fpm. Then the Cpo drag coefficient was doubled as an approximation of the extra drag with gear and flaps down, which gave a rate of climb of 600 fpm. Better estimations for engine-out and for gear and flap drag are in my textbook. Vkts Total Thrust lbs Cruise Thrust lbs CL CD Drag lbs Climb (Ips) 50 867 537 3.1156 0.4342 279 1520 100 588 364 0.7789 0.0480 123 2401 150 416 258 0.3462 0.0273 158 2003 200 301 187 0.1947 0.0239 245 580 220 267 166 0.1609 0.0234 290 -263 119
1000 Vetocity - kts 70. D7!--Z A%2X7/?mw <7M<% Cr^M7.ye S/?e<7 Range We calculate the range using a version* of the same Breguet equation we used for initial sizing. First we have to find out how much the aircraft's weight will change during our cruise, expressed as weight a* the cruise divided by weight the cruise. Unless somebody falls out, the only way that a homebuilt airplane's weight Actually, this is more like the original version - it solves for range given the aircraft's change in weight. We adjust it to include other fuel usage. 120
changes in flight is by burning fuel. So, the aircraft weight after burning the fuel is {Wo-WJ. However, some of the fuel will be used for takeoff, climb, and landing. When sizing the airplane before drawing it, we used a factor of 0.975 to allow for this. Applying this allowance to the Breguet equation yields the following approximate range calculation: Range: 0,, D 0.975)% ^0 — where L D 1 + (r/3)— % If you wish to include a 6% fuel allowance as described in the sizing chapter, divide Wf by 106 before using it in this equation. Remember, Cbhp must be in pounds of fuel per second per horsepower produced, so divide it by 3600 if your data was given as "per hour." Results are in feet (oh, so that's why I thought my plane could circle the globe six times!). Divide by 6076 for nautical miles. For the DR-4, I find the propeller efficiency from the calculated advance ratio (below) and reduce it 5% to 0.85. With this efficiency I estimate range as 964 nmi - below my goal, but over my threshold of 800 nmi. I find that by lowering cruise speed to 120 kts the range increases to about 1500 nmi, but that is over 12 hours of flying time! Don't forget to change the propeller efficiency for the different Advance Ratios. Cruise speed (ft/sec) 304.02 Cruise Advance Ratio J 13512 Cruise q (psf) 81.3 Cruise W/S (psf) 19.2 Cruise L/D 9.6 Wfuei (total) (lbs) 365 Wfuei (usable) (lbs) 344 Wfuei (cruise) (lbs) 294 log term 1 177691 Range W 5854552 Range (nmi) 964 121
Hetp -1 didn't get the range/performance I wanted! If you are way off, you'll need to make the plane bigger, which probably means a bigger engine. Or, you can reduce the weight carried (throw out those golf clubs, or put your co-pilot on a diet). In either case, you'll need to redo the sizing calculations and then revise your design drawing and analyze it again. Luckily, we ' re using simplified methods so it won't take too long. If you are not too far off, you may be able to fix things by a bit of optimization. Read on, young apprentice! 122
Chapter 9 LET'S MAKE !T BETTER! We are almost ready to do the second design drawing. Hopefully the second one will be good enough to take into detail design and construction. We've already learned a lot, and if you want, you can skip this whole section and just do the second drawing. Before we dive into the next drawing, we can try to improve on some of our early guesses. We made lots of them. The most important guesses we made were the power loading, wing loading, aspect ratio, taper ratio, and airfoil thickness. We'd like to know if the values we picked are good, or if different picks would give us a better airplane. We do this with trade studies, called "parametric" because we will vary the design parameters. We simply change the parameters, recalculate range and performance, and look for the best combination of parameters for our airplane. For example, we could just change the aspect ratio. Make it a larger number, and recalculate. Then make it a smaller number, and recalculate. Then, a simple graph would tell us the best aspect ratio to use. In industry we optimize a number of variables* at the same time because the different parameters "t^k" to each other. The best airplane probably has a different wing loading %' a different aspect ratio from our initial guesses. You wont find that "best" airplane if you just change the variables one at a time. However, this sort of optimization is too much work for most homebuilders, so let's try to reason our way through some of the variables. First of all, the wing loading (W/S) will usually be set by stall speed for homebuilts, so we don't have to optimize that. Just double-check after making the layout that the stall speed is met, and if not; revise the wing loading (area) for the next drawing. Power Loading (W/hp) will be set by performance needs - if performance is not met, revise the power loading until it is (which means resizing your design then finding a bigger engine). If you change the other design variables the drag will change, so the required power loading will change. This is especially true for aspect ratio and airfoil thickness ratio. Optimizing wing sweep is important for high-speed aircraft, but for homebuilts the optimum sweep is obvious - it is zero. Sweep for subsonic airplanes only adds weight and drag, while reducing lift. For homebuilts, sweep is used for other reasons such as to allow balancing the aircraft (like all those swept-wing canard pushers). So, we can forget about optimizing sweep. This leaves three important variables that we can try to optimize - aspect ratio, taper ratio, and airfoil thickness ratio. To optimize these we want to change our design and * See my textbook for industry optimization methods. 123
calculate the effects on the plane's performance and range. To do that, we need to estimate the effects on weight and drag for these changes. For the weight, you can use the wing weight equation to find the expected changes in weight, even if you didn't use this equation to estimate the weight of the baseline. The wing weight equation has each of these parameters raised to a power. Aspect ratio is raised to the 0.6 power, taper ratio to the 0.04 power, and airfoil thickness ratio to the (-0.3) power. If we make changes in these parameters, the weight should change as follows: \0.6 Aspect Ratio (A): zz zz x 0.04 Taper Ratio (A): V^3 Airfoil Thickness Ratio (t/c): These may give incorrect results if the wing structure is mostly minimum gage, or if the structural concept is unusual, or for some other reason. In such cases only a detailed design and structural analysis of each trade study change will determine the weight effects of these changes. This takes too much time, so these equations are probably the best approximations available. What about drag? For aspect ratio, simply recalculate the drag-due-to-liff factor (/Q. For taper ratio, the effect is fairly small unless you go from A=0.5 to A=1.0, in which case we previously said to increase K by 6%. Parasitic drag is not greatly affected and can be ignored. Remember, a taper ratio much less than 0.5 can cause dangerous tip stalling for small aircraft. The effect of airfoil thickness ratio on drag is mostly a change in parasitic drag, and is properly found from the airfoil data. If airfoil data at different thicknesses is not available, an approximation based on NACA airfoils can be used. Also, the parasitic drag changes only for the part of the drag that is from the wing, so we have to adjust for the relative wetted area of the wing, as follows: Drag adjustment for (t/c): (o.°05 + 0.02('/e.„.,,) ,_ Y (0.005 + 0.02(/ / c = c 1 + The terms {.005+.02(t/c)} are approximations of the airfoil parasitic drag for different thicknesses, based on NACA airfoils. If you have actual drag data for different thicknesses of your airfoil, use it instead. 124
Now you can make trade studies. Change the design parameters (aspect ratio, taper ratio, and airfoil thickness ratio) up and down, say, by plus and minus *5%". For each variation, calculate the change in wing weight, and use it to revise the as-drawn empty weight you calculated before. Also calculate the changes in parasitic drag and drag-due-to-lift factor. Recalculate all the performance values including the range, for each of these parametric variations. Lots of work - it sure is easier if you use a spreadsheet like the one that goes with this book, or a design program like RDS. Now we can graph the answers and hopefully find a better airplane. For each design parameter, plot the parameter on the horizontal axis against the resulting range on the vertical axis. Also plot the calculated values of the performance on the vertical axis. Find the lowest or highest value of the design parameter that meets each required performance value. Then, you can readily see the value of that design parameter that gives maximum range while meeting all performance requirements (see sample below). So, now you can make your second drawing based on everything you've learned from the first drawing. Don't be afraid to make changes - you should never "fall in love" with your first drawing. Change the wing geometry if the optimization showed a better arrangement. Fix any problems you uncovered. Try to make it smaller, lighter, and simpler. Then, do the calculations again and decide if this is the one. Take your time, and do as many iterations as it takes until you see no further ways to improve your design. Then, go and build it! For the DR-4, I've already described the improvements to the drawing that I'd like to investigate. As far as optimization, I did an aspect ratio trade and got the following results: A A/Abase Wwing/ Ww-base Deha We We-new Range Max Speed Cruise Speed ROC 6 0.60 0.74 -73 1182 1165 212 175 2200 10 1.00 LOO 0 1255 964 220 180 2400 14 1.40 1.22 62 1317 760 221 181 2500 * In industry we would do them all at the same time, for every possible combination of the parameters. You should just do them one at a time - first aspect ratio, then taper ratio, then thickness ratio. 125
2500 Aspect Ratto ygHre 72. These results are interesting*. The DR-4 was designed with a rather high aspect ratio to keep the pusher propeller further away from the wing trailing edge. This chart indicates that the range would actually improve with a lower aspect ratio, not due to aerodynamics but due to the weight savings (which allows more fuel to be carried). The only performance limitation is that the extra drag for a lower aspect ratio will slightly reduce cruise speed, and our desired speed can't be maintained if the aspect ratio goes much below 10 (see arrow in figure). It would be worth investigating whether the cruise speed could be met using a lower aspect ratio and a bit lower power loading (lower design weight) or some aerodynamic cleanup, or both. Or, just drop down to 175 kts, use a lower aspect ratio, and still meet the range requirement. Aren't trade studies fun??!! Be aware, though, that these results are only true if the calculated weight adjustments above are true. If lowering aspect ratio doesn't actually save any weight, perhaps due to the effects of minimum gage, then these results are nonsense and the highest possible aspect ratio should be used. * Notice that speeds were multiplied by 10 to make them easier to read on the same scale - divide by 10 to read them. 126
Chapter 10 AND IN CONCLUSION I hope you have enjoyed this book. I enjoyed writing it. May it help you to design your dream, and may your dream become a reality. While simplified, the methods presented in this book are real and are not too different from the methods used by the big companies. As stated before, no book can guarantee 100% safety. Be careful, be patient, and be alert. Use other resources - friends who have built planes, your local EAA chapter, and your friendly neighborhood FAA representative. Buy other books and study them - especially structures and controls books. This book is about the overall design concept - other authors have presented the detail design of aircraft including engine installation and systems. You still have a lot of work to do before you are ready to start "cutting metal" (or "gluing strings"). When you are done with the design and have built your plane, be even more careful. Do structural and systems tests before flight. Do a slow and careful flight test program (and perhaps get an experienced test pilot to do the initial flights). Start with taxi tests, going faster and faster without trying to take off. On the first flight, just take it up, check the controls, and bring it down. Gradually expand the flight envelope, adding stall tests, maximum speed, and (if appropriate) spin tests. Wear a parachute the whole time, even if you have a ballistic chute. Fly off the required hours and even more, before taking along a passenger. Be methodical, document each test you perform, and don't hurry no matter what. Then, give me a call - I'd love a flight in the "YourName-Special"! 127
(This page intentionally Mank) 128
APPENDIX A - Abbreviations A Breguet C CAD Cantilevered Q) Cpo Q FAR fineness ratio JAR A/D AE psf AW ED^ SFC /A? 7E EOGD D^IP IW a (alpha) P (beta) T (gamma) A (lambda) A (Lambda) P (rho) = Aspect Ratio (span^/reference area of wings and tails) = Classical range calculation method = Specific Fuel Consumption = Computer-Aided Design = Wing with no bracing struts or wires = Drag Coefficient = Zero-lift Drag Coefficient = Lift Coefficient = Wing Design Lift Coefficient = Wing Design Lift Coefficient (NACA terminology) = Federal Aviation Regulations (USA equivalent of JAR) -Lengih/diameter (usually of fuselage) = Joint Aviation Requirements (European equiv. of FAR) = Lift-to-Drag Ratio -Leading Edge (wing or tail) = pounds per square foot = Power-to-weight ratio of aircraft (engine power/%) = Aircraft design software \ A)&ngn = Specific Fuel Consumption = Airfoil thickness/chord length -Trailing Edge (wing or tail) = Aircraft Takeoff Gross Weight = Thrust-to-weight ratio = Wing loading (weight/area) = Aircraft Empty Weight = Empty Weight Fraction = Fuel Weight = Fuel Fraction = Aircraft Takeoff Gross Weight = angle of attack = angle of sideslip = dihedral = taper ratio = sweep = air density, also conic shape parameter 129
APPENDIX B - Air Properties and Conversions STANDARD DAY HOT DAY (+15 degC)HOT DAY (+24.4 degC Altitude Density Speed of Sound Density Speed of Sound Density Speed of Sound (ft) Slug/fT3 (ft/sec) siujgftM (ft/sec) Sl-ug/tr3 (ft/sec) 0 0.00238 1116.4 0.00226 1145.1 0.00219 1162.8 1000 0.00231 1112.6 0.00220 1141.4 0.00213 1159.1 2000 0.00224 1108.7 0.00214 1137.6 0.00208 1155.4 3000 0.00218 1104.9 0.00208 1133.9 0.00202 1151.6 4000 0.00211 1101.0 0.00202 1130.1 0.00196 1147.9 5000 0.00205 1097.1 0.00196 1126.3 0.00191 1144.2 6000 0.00199 1093.2 0.00191 1122.5 0.00186 1140.4 7000 0.00193 1089.2 0.00185 1118.6 0.00181 1136.7 8000 0.00187 1085.3 0.00180 1114.8 0.00176 1132.9 9000 0.00181 1081.4 0.00175 1110.9 0.00171 1129.1 10000 0.00176 1077.4 0.00170 1107.1 0.00166 1125.3 11000 0.00170 1073.4 0.00165 1103.2 0.00161 1121.5 12000 0.00165 1069.4 0.00160 1099.3 0.00157 1117.7 13000 0.00160 1065.4 0.00155 1095.4 0.00152 1113.8 14000 0.00155 1061.4 0.00150 1091.5 0.00148 1110.0 15000 0.00150 1057.3 0.00146 1087.6 0.00143 1106.1 16000 0.00145 1053.2 0.00141 1083.6 0.00139 1102.2 17000 0.00140 1049.2 0.00137 1079.6 0.00135 1098.3 18000 0.00136 1045.1 0.00133 1075.7 0.00131 1094.4 19000 0.00131 1041.0 0.00129 1071.7 0.00127 1090.5 20000 0.00127 1036.8 0.00125 1067.7 0.00123 1086.6 ISO Std Day ISO Hot Day AF-N 421 Hot Day 130
UN)T CONVERSIONS FOR DESiGN Muitipiy by To Obtain Reverse Design Usage ft 12 inch 0.0833 Distance ft 0.00019 mite 5280 Distance ft 0.00016 nauticai mite 6076 Distance ft/sec 0.5921 kt 1.6889 Velocity ft^^ec 0.6818 mph 1.4667 Velocity gaiion 0.1337 ft*3 7.4806 Fuei votume gaHon 231 inch*3 0.0043 Voiume horsepower 550 ft-tb/sec 0.0018 Power kt 1.1510 mph 0.8688 Veiocity kt 1.6890 ft/sec 0.5921 Veiocity )b 16 ounce 0.0625 Weight mite 5280 ft 0.0002 Distance mite 0.8684 nauticai mite 1.1515 Distance nauticai mite 6076 ft 0.0002 Distance nauticai mite 1.1515 mite 0.8684 Distance METRiC CONVERSIONS FOR DESiGN Muitipiy by To Obtain Reverse Design Usage ft 0.3048 meter 3.2808 Distance ft/ib 0.6720 m/kg 1.4882 Fuei to ciimb ft/min 0.3048 m/min 3.2808 Rate of Ciimb ft/sec 0.3048 m/sec 3.2808 Veiocity ft*2 0.0929 m*2 10.76 Area gaiion 0.0038 m*3 264.2 Voiume gaiion 3.7850 ttter 0.2642 Voiume Horsepower 0.7457 kWatt 1.3410 Power kt 1.8520 km/h 0.5400 Veiocity R^^/sqft 4.8824 kg/sqm 0.2048 Wing ioading ib/sqft 0.0479 kN^fsqm 20.88 Pressure ib^/hr/ib 28.32 mg/Ns 0.0353 Specific Fuei Cons. ib!5-f 0.0044 kN 224.8 Force ibts-m 0.4536 Rg 2.2046 Mass or weight nmi 1.8520 km 0.5400 Distance nmi/ib 4.0830 km/kg 0.2449 Specific Range seconds/ib 2.2046 sec/kg 0.4536 Specific Loiter siug/ft^3 515.21 kg/m*3 0.0019 Density ^2 means squared (area) ^3 means cubed (volume) 131
APPENDIX C - CLmax - NACA Sections^ ap%y /SOM cW*/b<7 4/r*b?f w^?A /Xqp ^Oh oWb^f 132
J ZC If AhyMwtw :#c/*&7 Z/!r g<?c/^w7, — o F o -O ./ F 1 er A .4 f/ r J Z * A V r—- Lz W. a X? (cr LJ - t ! ' PAWa CW*/iw7 /F /F <4r-p7 /M-^<ar^ o/ c^a^ 4^-Av/ wWy ATaxMwww L//?, A^iG4 64 i'r/bi/.s Maxr/)^:^w! A//?, 7^(C4 63^4ir/^fi/s Note: Cu is the design hft coefficient for the 6-series airfoils 133
APPENDIX D - Engine Data Model [ bhp] RPM] Weight] lb/hp VW (Great Piains conversion) 1600cc 2180cc 57 3600 160 76 3600 168 2.01 2.21 Lycoming 0-235 C 0-320 0-360 O-540-E 10-360 115 2200 215 160 2200 255 100 2270 270 260 2270 360 200 2270 293 107 159 150 1.42 1.47 Continental C-75 0^^200-A 0-300 10-360 TSIO-550-E 75 2227 160 100 2270 220 145 2270 260 195 2200 327 350 2270 433 2.24 2.20 1.05 160 1.24 Franklin 4A-235-B31 6A-350-C1R 125 2877 276 220 2877 292 165 135 Rotax Rotax 377 Rotax 582 Rotax 914 F 35 6570 61 63 6500 63 100 5500 141 1.74 100 1.41 Jabiru Jabiru 2200A Jabiru 33OOA Jabiru 600A 00 3300 132 120 3300 170 100 2700 231 165 140 1.20 Other Hirth 3203 HKS 700E 65 6300 33 56 5800 121 1.12 2.16 av. 168 134
APPENDIX E - Empty Weight Fraction To make a better estimate of empty weight fraction (Wo/ We) before drawing your aircraft, we can use data from existing aircraft. Find the takeoff gross weight (Wo) and the empty weight (We) of several airplanes that are similar to what you plan to design (see Sport Aviation and visit airplane company websites to find these numbers). Divide to find Wo/ We, then plot each point on the figure below (go ahead - you paid for the book!). Now read off the value of "a" for the dotted curve that best passes by your points. For the sample (star) shown below, Fd estimate that "a"=1.3 since a curve halfway between the 12 and 1.4 curves would pass right through the star. 1^ We/Wo 1000 (dots indicate homebuilt planes, triangles indicate production planes) 's. *** ** "*** . * . A — A A v— A A A Phpdactran FZanes $ w Tfo/rrebaiO P&znes a; 1.3 1.6 1.4 1.2 1.0 Now go tell your friends you just did a regression analysis. (Woe Jbr aabanced readers 77rese carves assarne a /-.69y exponent on w/n'cb rny carve yrt ca/ca/atr'ons /rave rndicated rs reasonab/e ybr /ronrebar'/t ar'rcraf. Foa con/d do year own carve tbroagb se/ected arrcra/i dafa and yrnd both constant and exponent Tfowever, nra&e sare /bat /be exponent rs a snna// negative nanrber - r no/, yoar se/ected arrcra/i sa^rnp/e rs ^7^00%^.^ 135
APPENDIX F -Weight Statements STRUCTURES 225 615 594 286 361 267 554 774 1392 Wing 87 250 210 126 127 107 214 226 572 Horizontai Tail 10 60 45 21 30 13 27 37 63 Vertical Tail 7 25 20 10 12 3 14 20 34 Ventral Tail 8 Winglet Fuselage 89 210 200 76 95 77 166 353 339 Canopy 15 Nacelle/cowling 15 10 18 11 14 15 124 Motor Mount 10 14 3 12 12 Main Landing Gear 22 60 65 40 54 53 76 79 200 Nose Landing Gear 10 25 3 10 31 32 52 PROPULSION 189 380 402 148 272 240 270 345 703 Engine 146 340 286 140 226 217 199 254 353 Air Induction 3 1 1 16 Cooling 3 6 2 6 Exhaust 12 7 10 14 16 Engine Controls 4 2 2 2 15 Misc. Engine Inst. 13 10 5 1 14 16 Propeller 5 20 58 24 8 20 33 133 Starter 16 10 16 34 Fuel System 25 10 15 8 3 8 20 21 120 EQUIPMENT 26 44 154 9 73 13 129 159 821 Flight Controls 15 7 5 8 31 28 132 Instruments 5 5 10 16 5 6 3 80 Hydraulics 5 4 3 3 Electrical 10 8 49 15 41 38 182 Avionics 1 15 20 18 1 1 123 Air Conditioning 1 4 9 4 1 134 Anti-Icing 1 Furnishings 10 10 52 2 10 43 85 169 WEIGHT EMPTY 440 1039 1150 443 706 520 953 1278 2916 USEFUL LOAD 390 711 1350 210 719 230 547 922. 1358 Crew 180 230 340 170 170 200 340 340 225 Fuel 180 230 300 40 300 30 156 252 876 Oil 2 11 10 11 15 32 Passengers 200 300 170 300 225 Payload 28 40 410 0 69 0 40 15 0 TOGW(Wo) 830 1750 2500 653 1425 750 1500 2200 4274 136
APPENDIX G - Aircraft Material Densities !b/in*3 Aluminum - 2024 173 0.1000 Aiuminum - 7075 175 0.1010 Aiuminum - cast 160 0.0927 —] Aiuminum - Lithium 159 0.0920 Stee) -A.!S! a!!oy(4130) 489 0.2830 LU Stee! - Wrought Cr-Mo-V 486 0.2810 Stee! - AiSi 301 Stainiess 494 0.2860 Magnesium -AZ31B 110 0.0639 Titanium 6A1-4V 276 0.1600 Lead 708 0.41 Ash 42 0.0243 Baisa 9 0.0052 Birch 43 0.0250 Cork 16 0.0090 Q Q Mahogany 32 0.0185 o Oak 45 0.0260 § Pine 27 0.0156 Spruce (northern) 45 0.0260 Spruce (western) 28 0.0162 Birch P!ywood (.010") 89 0.0514 Birch Ptywood (.100") 49 0.0281 t- *g o § CL E-giass/epoxy 131 0.0760 0) O E-giass/poiyester 131 0.0760 CL CL 5 Kevtar/epoxy 90 0.0520 o UJ Graphite/epoxy 97 0.0560 o Boron-epoxy 126 0.0730 X (D U) Urethane foam (fuseiage) 2.0 0.0012 o > c s (D Ctark urethane (wings) 4.5 0.0026 > Q z < LU g O W c (D -D Styrofoam (wings) Poiyvinyi 2.0 1.9 0.0012 0.0011 0) O Aramid honeycomb (nomex) 3.0 0.0017 High-impact Acryiic 70.8 0.041 Safety Gtass 168.0 0.0972 O Rubber 94.0 0.0544 (D Water (pervo)ume) 62.4 0.03613 Giycoi (Ethyiene) 69.6 0.04028 Aicohc^! (methyi) 50.5 0.02922 Fibergtass insuiation 1.5 0.00087 gef cojrr^c/ yrow 137
APPENDIX H - Equipment & Other Weights Factor (tbs) Weight Definition Retractable Landing Gear .05 to .06 Wgear/Wo Fixed Landing Gear .04 to .05 Wgear/Wo Adjustment for taiidragger gear 0.85 maingear-nosegear spiit 70%-30% maingear-taiiwheei spiit 80%-20% Piston Engine instaiiation inci. Propetter 0.3 Winstaii/Wengine Propeiier 0.15 to 0.25 per horsepower Spinner 2 to 4 each Motor Mount .03 to .05 per horsepower Fuei system (per hp) 0.05 per horsepower Aiuminum Fuei tank (ib/ibs-fuei) 0.06 Wtank/Wfuei Paint - typicai 0.04 per square foot Wing/fuseiage Fabric -instaiied & doped 0.1 per square foot Controi Surface Fabric -instaiied & doped 0.07 per square foot Fiight Controi System 0.01 Wfc/Wo Pitot's cockpit controis 10 per piiot Controi Surface Piano Hinge 0.1 per foot Hydrauiics System 5 typicai totai Eiectrica! System 0.02 Weiect/Wo Battery - reguiar 15 to 30 each Battery - aerobatic 20 to 40 each Avionics 15 to 20 typicai totai instruments 10 to 15 typicai totai Tachometer 1 to 3 each Other instruments 05to 1.5 each Com/Nav Radio 1 to 6 each Transponder, DME, or GPS 2 to 6 each Emergency Locator Transmitter 4 to 8 each Autopiiot 10 to 25 each Canopy 1.5 per square foot Aircraft Baiiistic Parachute 0.025 Wchute/Wo Furnishings totai 5 to 20 per person Seat 15 each Parachute - seatpack 25 each Parachute - backpack 18 each 138
APPENDIX I -Experimental Aircraft FARs §21.191 Experimental certificates. Experimental certificates are issued for the following purposes: (a) 7?(e.yea?c? Testing new aircraft design concepts. new aircft equipment, new aircraft installations, new aircraft operating techniques, or new uses for aircraft. (b) S%owM?g regM/af/on.y. Conducting flight tests mid other operations to show compliance with the airworthiness regulations including flights to show compliance for issuance of type and supplemental type certificates, flights to substantiate major design changes, and flights to show compliance with the function and reliability requirements of the regulations. (c) Crew ZrazmKg. Training of the applicant's flight crews. (d) ExH/'M'on. Exhibiting the aircraft's flight capabilities, performance, or unusual characteristics at air shows, motion picture, television, and similar productions, and the maintenance of exhibition flight proficiency, including (for persons exhibiting aircraft) flying to and from such air shows and productions. (e^4zr raczng Participating in air races, including (for such participants) practicing for such air races and flying to and from racing events. (f)Arhr%ef Use of aircraft for purposes of conducting market surveys, sales demonstrations, and customer crew training only as provided in §21.195. (g)OjPeragng azrcra/7. Operating an aircraft the major portion of which has been fabricated and assembled by persons who undertook the construction project solely for their own education or recreation. (h)<9per#igMg az'rcra/?. Operating a primary category aircraft that meets the criteria of §21.24(a)(1) that was assembled by a person from a kit manufactured by the holder of a production certificate for that kit, without the supervision and quality control of the production certificate holder under §21.184(a). §21.193 Experimental certificates: general. An applicant for an experimental certificate must submit the following information: (a) A statement, in a form and manner prescribed by the Administrator setting forth the purpose for which the aircraft is to be used. (b) Enough data (such as photographs) to identify the aircraft. (c) Upon inspection of the aircraft, any pertinent information found necessary by the Administrator to safeguard the general public. (d) In the case of an aircraft to be used for experimental purposes (1) The purpose of the experiment; (2) The estimated time or number of flights required for the experiment; (3) The areas over which the experiment will be conducted; and (4) Except for aircraft converted from a previously certificated type without appreciable change in the external configuration, three-view drawings or three-view dimensioned photographs of the aircraft. 139
§91.319 Aircraft having experimental certificates: Operating limitations. (a) No person may operate an aircraft that has an experimental certificate (1) For other than the purpose for which the certificate was issued; or (2) Carrying persons or property for compensation or hire. (b) No person may operate an aircraft that has an experimental certificate outside of an area assigned by the Administrator until it is shown that (1) The aircraft is controllable throughout its normal range of speeds and throughout all the maneuvers to be executed; and (2) The aircraft has no hazardous operating characteristics or design features. (c) Unless otherwise authorized by the Administrator in special operating limitations, no person may operate an aircraft that has an experimental certificate over a densely populated area or in a congested airway. The Administrator may issue special operating limitations for particular aircraft to permit takeoffs and landings to be conducted over a densely populated area or in a congested airway, in accordance with terms and conditions specified in the authorization in the interest of safety in air commerce. (d) Each person operating an aircraft that has an experimental certificate shall (1) Advise each person carried of the experimental nature of the aircraft; (2) Operate under VFR, day only, unless otherwise specifically authorized by the Administrator; and (3) Notify the control tower of the experimental nature of the aircraft when operating the aircraft into or out of airports with operating control towers. (e) The Administrator may prescribe additional limitations that the Administrator considers necessary, including limitations on the persons that may be carried in the aircraft. 140
INDEX p 13,24 T)P 19 51% Rule 3 advance rado 92 Advisory Circulars 4 ailerons 31 airfoil 4-, 28, 32, 34, 35, 36, 46, 57, 60, 74, 75, 76, 77, 89, 90, 117,123, 124, 125 Airspeed 9 , 44 AirVenttMe 1 ,54 aspect ratio 88 Aspect ratio 18, 19, 124 F bipllrne 3 , 16 , 89, 109 Breguet 19, 120 C cambee 34 canards 29, 39 cantilevered wing 100 Cbhp 18 17 center of gravity . . . 15, 27, 29, 35, 39, 46, 64, 84, 111, 112, 113, 114, 115, 116 Q 14 C?MMx 89 cockpii 42 composite materials 101 composites ... , 32, 60, 61, 62, 63, 73, 98, 99, 101, 104, 109 conic 67 Cooling 52, 53,95, 96, 142 crash 83 cruise speed 118 Z) Designated Airworthiness Representative 4 dihedral 30 drag due to lift factor 88 drag-due-to-lift factor 18 Dynamic Pressure 13 X EAA v, 1,2, 3, 4, 127, 142 empty weight . . . ,20, 21, 49, 65, 105, 110, 111, 112, 125, 135 F FAA 3 FAR 23 14 fineness ratio 40 flap 90 Flutter 84 forward-swept wing 26 fuel fraction 19 fuel tanks 64 G Garrison in , v, 142 7Z homebuilt 3 Z incidence angle 35 instrument panel 43 X A? 18 L L/D 16, 18, 20, 49, 118, 121, 129 landing gem- 45 Lift-to-Drag Ratio 18 load paths 55 Lofting 67 M MAC 27 141
maximum lift coefficient 89 Melmoth v, 54, 98, 99 Meta! 60 7V Neutral Poinn 114 o ovemose vision 43 overturn angle 47 P Parasitic Drag 87 Parasitic Drag Coefficient 17 Poberezny 3 Power loading 11 Power Loading 22 propeller efficiency ....19, 92, 94, 95, 121 pusher 51 e % 13 7? range 120 Rate of climb 118 Rutan 8, 15, 29, 43, 45, 98, 99 S Sexp 25 SFC 18 shimmy 48 5 , 87 , 112 , 117 Sizing 16 Sizing Equation 21 slugs 14 specific fuel consumption 18 speed 118 spin recovery 38 stability 113 Stall 14 Stall speed 117 Static Margin 115 Stick-free 115 structural arrangement 55 Structural sizing 97 strut-braced 59 T tail volume coefficient 35 tails 35 takeoff distance 117 Takeoff Gross Weight 16, !29 taper ratio 24 Technical Counselors 4 Ten-Percent Rule 101 Thrust 92 tires 45 tractor 51 trade studies 123 truss 101 T-tails 37 twist 35 r V-taii 37 W Wo 16 Weights 105 wetted area 17 wing carrythrough 57 wing fillet 77 Wing Loading 13 Wittman 3, 45 Wood 60 5, 23, 32, 87, 112, 117 142
REFERENCES 1 Raymer, D., DES7GM F Conc^epz/Ma/ yt^proacb, American Institute of Aeronautics and Astronautics, Washington, D . C., Third Edition 1999 2 Lawrence, E., 'Z4 TV^^w O^z^<^^r. E4F Simpz/i/ies Ro/weba/// C^j^j^zca^^zo^n wz7Z A/ew G^zZ^^?Z/zne", Sport Aviation, EAA, Dec. 1999 Bingelis, T., Fzrew^a// published by the author, 1983 4 Abbott, I., and von Doenhoff, A., Theory q/ lUng NeeZons, McGraw-Hill, New York, 1949. s Lednicer, D., TZe.^va^c^ozn^//c/c G^z^zT/e /oFir/bz7 (Fage (web site) Hoemer, S., F//Mz,7 ZT^y^n^j/nic Drag, Published by the author, 1958. Raymer, D., Enhancing ConcepsZza/ E^e^s^zgn a^z^zZ^^g MZ/Z^zz^z\y(^^^/?/zb^n^jry C/p/Zz^zZ^z^j/zZ^jn, Ph . D. Thesis, Swedish Royal Institute of Technology, Stockholm, Sweden, 2002 s anon., FYcra/? ^zrzzce & Special Co. (catalog), Corona, CA (yearly) 9 Lednicer, D., DnpMbzisZezZ Engine Coo/ingZ/Mz^ie^s, 2002 10 Becar, N., Sr^a^^^1^ica/7^ZS Design, Sport Aviation, May 1963 11 Pazmany, L., LZ^^/^ZzZ7y^^^^ane Can^zizzc^i^ion ybr F^zna^j^e^z^jr F^z/z7aZ^;rz, published by the author, 1970 12 Garrison, P., Unpublished personal e-mail communication, 9-11-02 13 Hart-Smith, L., 77i<e Ten Percen/ P^i^i/e/^jr P^r^ezanzzi^^ary Sizing <FZEoazcH.y Co^jn//^o^^^i7e SZrz^i^i/Mi^rez, Chula Vista, CA, May 1992 (SAWE Paper 2054) 11 Hollmann, M., Co^jn/p^o^^^zYe FireraZ Design, published by Aircraft Designs, Inc., Monterey, CA, 1991 13 Hollmann, M., Designing wYZ Core, published by Aircraft Designs, Inc., Monterey, CA, 1988 16 Rhodes, T., SYees H77Z<ozY Tea^s, Jacobs Publishing Inc., Indianapolis, IN 1990 13 Hiscocks, R., Design q^Ai'g/i/FYcra/?, Published by Patricia Hiscocks, Vancouver, BC, Canada, 1995 18 Bruhn, E., Fna/yzz's on (7 Design q/ Fbg/zf Fezaz\c/c S/^^Mc//j/^je^^ Tri - State Offsett, 1973. 19 Peery, D., Fiec^ea^ &/jzMc^/z^z^<es, McGraw-Hill, New York, 1950. 20 Niu, M., Fz'e/r^c^/ze &^e^i^<ciMr^a/ Design, Conmilit, Hong Kong, 1988. (available at website www.adairfeame.com). 21 Niu, M., Co^jnz^os^/7e Fz/yea/ne Sz^/^azc/^i^Jecs, Conmilit, Hong Kong, 1992. (available at website www.adairframe.com). 22 Anon., ^Feigaz Engineers EanTbooZ, Society of Allied Weight Engineers, Los Angeles, CA, 1986 23 Jackson, A., P^r^e^^iizninazy Design IFeig/zi EsZzzaZan Program, AeeoCommandee Div., Rept. 511-009, 1971. 21 Ericson, S., Sharp, J., and Valentine, J., 77^<e Feznesis slir Pacer, Weight Engineering Winter 1996, Society of Allied Weight Engineers 25 Abbot, I., von Doenhoff, A., & Stivers, L., SHninzary z^Fir^i/ Da/a, NACA Report 824, 1945 143