$99.00

In FAR 23 LOADS, author Hal C. McMaSter leads you through the procedure of calculating
the loads on your airplane to the requirements of the Federal Air Regulations. Your personal
computer does the tedious calculations without an error. The procedure is illustrated through
the detailed sample calculation of loads for a typical four place airplane.

The results are in a format that is acceptable to the FAA. The book and programs are becoming
a standard. They are used in 26 countries. Most important is that reliable loads are available for
you to substantiate the strength of your airplane by analysis or test. The FAA requires that
loads be calculated to the requirements of FAR 23 Subpart C for certification. Your
experimental airplane should meet the same requirements for your own safety.

The programs cover weight estimation, weight and inertia, weight-cg envelope, surface
geometry, spanwise and airplane aero coefficients, design speeds, flight envelope, compressi-
bility, wing sweep, flight loads, engine mount loads, landing loads, control surface loads and
selection of critical loads for turboprop or reciprocating powered single and multi-engined
airplanes.              '           ^! , .1:.^:'1:1'.,^;:^1-:";'1,1.:-       ' "' ! !   !   ! '

FAR 23 LOADS will be an invaluable aid to the engineer, student, experimental airplane
designer, airplane manufacturer, airplane modification shop or DER.

Aero Science Software
. 7415 Tanglewood Ct.
' Wichita, Kansas 67206
(316)682-1644

Copyright (C) 1988, 1989, 1990, 1991, 1992, 1993 by Hal C. McMaster

All rights reserved.
No part of this work may be reproduced or transmitted in any form
or by any means, electronic or mechanical, including photocopying
and recording, or by any information storage or retrieval system,
except as may be expressly permitted by the 1976 Copyright Act or
in writing from Hal C. McMaster.

Requests for permission should be addressed in writing to

 Hal C. McMaster
 Aero Science Software
 7415 Tanglewood Court
 Wichita, Kansas 67206

TABLE OF CONTENTS

PREFACE .................................................... 1

INTRODUCTION. .............................................. 3

USAGE, REGISTRATION AND DISTRIBUTION.................. 5

DISCLAIMER............................................ 8

SET-UP AND BACKUP INSTRUCTIONS ........................ 9

RUNNING BASIC PROGRAMS ............................... 12

FAR 23 LOADS DISK.................................... 13

OVERVIEW OF FAR 2 3 LOADS ............................. 15

WEIGHT ESTIMATION......................................... 23

WEIGHT AND INERTIA FOR SINGLE CONFIGURATION AND LOADING...31
WEIGHT VS CENTER OF GRAVITY FOR A RANGE OF LOADINGS....... 45

AERODYNAMIC SURFACE GEOMETRY.............................. 61

STRUCTURAL DESIGN SPEEDS AND MANEUVERING LOAD FACTORS..... 85

AERODYNAMIC COEFFICIENTS AND AIRLOADS. .................. .101

LOADS AND BALANCING CALCULATIONS FOR FLIGHT ENVELOPE..... 159

SELECTION OF CRITICAL LOADS.............................. 189

AILERON LOADS............................................219

FLAP LOADS ............................................... 225

WING INERTIA............................................. 231

NET WING LOADS ...........................................243

ENGINE MOUNT LOADS ....................................... 253

LANDING LOADS ............................................263

ABOUT THE AUTHOR.........................................287

PURCHASE FORM............................................289

REGISTRATION FORM........................................ 290

INDEX....................................................291

i i

 COMPUTER PROGRAM SOURCE CODE LISTINGS

WTESTIMA.BAS, Wt Estimate for Empty, Gross & Components... 24

WTONECG.BAS, Wt vs CG for a Single Loading............... 33

WTENV.BAS, Wt vs CG for a Range of Loadings............ 48

WINGGEOM.BAS, Aerodynamic Surface Geometry................ 63

STRSPEED.BAS, Structural Design Speeds & Load Factors ..... 89

MACHLIM.BAS, Mach Limit Lines............................ 96

AIRLOADS.BAS, Aerodynamic Coefficients & Airloads........ 105

TAU.BAS, Correction Factor for Slope of Lift Curve..117

FLTLOADS.BAS, Balancing Calculations for Flight Envelope.166

SELECT.BAS, Selection of Critical Loads................ 196

AILERON.BAS, Selection of Critical Aileron Loads........ 221

FLAPLOAD.BAS, Selection of Critical Flap Loads........... 227

WINERCWT.BAS, Wing Inertia Loads........................ .233

NETLOADS.BAS, Net Wing Loads............................ .245

ENGLOADS.BAS, Engine Mount Loads.........................255

LANDLOAD.BAS, Landing Loads for Tricycle Gear............ 264

LGFACTOR.BAS, Estimate Landing Load Factor...............284

iii

FIGURES

Flow Chart FAR 23 LOADS................................... 22

Beach Banana Airplane, Side View.......................... 53

Diagram, Useful Load Envelope & Structural Limits......... 56

Wing, Plan View........................................... 66

Vertical Tail, Side View.................................. 72

Horizontal Tail, Plan View................................ 78

Diagram, Operating Limits - Structural Speeds & Altitude..99
Diagram, Spanwise Lift Coefficients - Cruise............. 131

Diagram, Spanwise Lift Coefficients - Landing............ 143

Diagram Cr max vs ^acn Number. ............................ 164

Flow Chart, FLTLOADS.BAS................................. 165

Diagram, V-n Flight Envelope - Cruise.................... 186

Diagram, V-n Flight Envelope - Landing................... 187

Diagram, Chordwise Distributions for Horizontal Tail.....214

Chordwise Distributions for Vertical Tail................ 217

Diagram, Net Wing Loads, Cond PHAA Case 22...............251

IV

PREFACE

FAR  23  LOADS  is a series of  computer  aided  engineering
programs  to calculate airplane flight and ground  loads  meeting
the  requirements  and intent of of Subpart C of Part 23  of  the
Federal Air Regulations.

The  software  programs  were originally  written  in  BASIC
language  on a Tandy 1000 and an Epson FX-85 printer. The  manual
was  written  with Wordstar 4.0.  Version 2.0 was prepared  on  a
COMPAQ  DESKPRO  and an Epson FX-85 printer  with  WordStar  4.0.
Version  2.01  was  prepared on a 386SX computer  and  a  Houston
Instruments  Jet-Pro 360 printer with WordStar 5.5.  The  current
version  2.02  was  prepared on a 386SX computer  and  a  Houston
Instruments Jet-Pro 360 with WordStar 7.0.

The programs may be run on any IBM compatible computer  with
an  Epson  compatible  printer. Before serial  number  30148  the
program disks were in basic compressed binary format readable  by
the  basic  interpreters. Program disks serial number  30148  and
after are in ASCII format readable by both the basic interpreters
and the basic compilers.

The  minimum  configuration required is  an  IBM  compatible
computer,  one double-sided disk drive, 384K memory and an  Epson
compatible  printer. Two disk drives are recommended. For a  high
performance  airplane with dive drag (dive brakes, gear  extended
or partial flaps) operating above 20,000 feet, 640K memory may be
needed.

TRADEMARK ACKNOWLEDGMENTS

IBM, IBM PC, XT and AT are registered trademarks of International
Business Machines, Inc.

Tand- is registered trademark of Tandy Corporation.
EPSON and FX-85 are registered trademarks of Epson Corporation.
MS-DOS is a registered trademark of Microsoft Corporation.
COMPAQ is a registered trademark of COMPAQ Computer Corporation.

WordStar  is  a registered trademark  of  MicroPro  International
Corporation.

Jet-Pro  360  is a registered trademark  of  Houston  Instruments
Corp.

FAR 23 LOADS

INTRODUCTION

I wrote these programs to provide a method to calculate  the
loads on a conventional airplane meeting the requirements of  the
Federal  Air  Regulations  (FAR). Years  ago  I  participated  in
writing  some  of the loads reports for Beech  Aircraft  by  hand
using pencil, sliderule, and  mechanical four function mechanical
calculator.

That  wasn't  too  bad  in the  fifties  when  the  book  of
regulations  was not so thick and lawyers were not the  principle
input.  In fact we used one set of aerodynamic  coefficients  for
all  conditions  for the airplane. These were  "sea  level"  air-
planes. They were unpressurized and flew at not more than Mach .4
so  we avoided considerations of compressibility effects  due  to
altitude and speed. But when we began to pressurize and  increase
speeds  on  our "corporate" airplanes we could not  ignore  this.
Then  we had a new set of aero coefficients for every  speed  and
altitude. That's when we turned to the computer.

We  had  noticed  that all the  loads  reports  before  read
essentially  the  same  except  that  the  numbers  changed   for
different  airplanes.  So  we not  only  computerized  the  loads
calculations but we just went ahead and wrote the reports on  the
computer.

Let  me go back to the "sea level" airplanes. Even the  high
performance single engine unpressurized airplanes with  naturally
aspirated engines were beginning to feel the compressibility. But
this  was  hidden with the reduction in speed with  altitude  for
flutter clearance. We were in effect reducing speeds at  altitude
to keep the mach number about Mach .4 or less.

I was given permission by Beech Aircraft to write and market
these  programs  for  the  personal  computer.  They  assume   no
responsibility for them in any way. Beech has progressed to  more
sophisticated methods for their advanced airplanes. The technolo-
gy  used in the programs of this book is more practical and  cost
effective for today's FAR 23 airplanes and kit airplanes.

Today all good performing singles and twin engine  airplanes
should  consider compressibility effects. These programs  provide
the  means  to make these calculations and record  all  the  data
systematically.

The current version of FAR 23 LOADS is Version 2.02 which is
the fourth release. It incorporates the corrections in the latest
errata sheet for Version 2.01. The programs have been in use  and
updated  during  my consulting work for more  than  seven  years.
Users  of  the book and programs have  provided  corrections  and
suggestions for improving the programs. The original programs and
examples  are retained but variations of the programs  have  been

3

FAR 23 LOADS

added  to   the program disk to include sweepback  effects,  con-
centrated  weight inertia loads and calculation of Tau, the  cor-
rection  factor  for the slope of the lift curve of the  wing  to
account  for the deviation of the wing planform from an  ellipse.
Two new programs were added in version 2.01 to calculate  aileron
loads and flap loads including propeller slipstream effects.

The individual programs have been identified as  copyrighted
and not disclosed to anyone except for very limited beta testing.
The  manual for this version is brief. The source  code  programs
are  provided in the manual and on disk and are internally  docu-
mented to some extent. The individual programs are very  interac-
tive since the input is specifically requested on the screen. The
overview  of each program, the commentary, the specific  interac-
tive  program requests for data and the sample input  and  output
should guide you to useful results.

A fictitious airplane called the Beach Banana 36 is used  as
as the example data for most of the programs. The geometric  data
is  taken  from a 20th scale model of an airplane  of  a  similar
name. All data is derived from published information and  changed
to  represent typical data for a high performance  single  engine
airplane such as produced by Piper, Beech, Mooney and Cessna.

All  programs  were written from scratch in  basic  language
based  on memory of similar routines I wrote in fortran  language
in  the sixties. I previously used sequential files in  the  data
base  for weights and inertia programs in my consulting  calcula-
tions. When I prepared version 1.0 of FAR 23 LOADS I switched  to
random access files, I needed the help of Thomas Dwyer and  Marg-
got  Critchfield  who wrote "Programming in  Style".  I  modified
their  concept to adapt to my situation. This credit was  printed
in  version 1.0 of FAR 23 LOADS but accidentally omitted  in  the
next printing.

INTRODUCTION

USAGE, REGISTRATION AND DISTRIBUTION OF FAR 23 LOADS PROGRAMS

PURCHASER'S RIGHTS

Users  of  FAR  23 LOADS should be aware that  the
programs  and  the User's Manual that make up the  FAR
package  fall under the scope of the 1976 Copyright Act

Hal C. McMaster,
copyright on them.

the owner of AERO SCIENCE SOFTWARE,

computer
23.  LOADS
and  that

holds  a

AERO  SCIENCE  SOFTWARE does not sell a license to  use  its
programs but actually sells copies of them in a manner similar to
the way publishing companies sell books.

The  FAR  23 LOADS program disk is not copy  protected.  The
legal  owner  may  make back-up copies as  a  protection  against
accidental destruction.               ,

The original disk, a back-up copy or a hard disk copy may be
used, but only one of them may be used at one time. This would be
similar to the use of a book.  Any other use would be a violation
of the copyright because the user paid for only one copy.

DISTRIBUTION

The  author  and  AERO   SCIENCE   SOFTWARE
distribution  of copies of the disks included in
package  to.  serious* prospective  buyers  under
conditions:

authorize   the
the FAR 23 LOADS
the   following

1. Only registered purchasers of FAR 23 LOADS programs may
distribute evaluation copies of the FAR 23 LOADS program disks.

2. The distribution of copies is for evaluation purposes
only. Use of the programs on a regular basis or with the
intention of applying results is only permitted to   those
purchasing the FAR 23 LOADS package. The recipient of the
evaluation copy must be instructed by the donor, in advance, of
this specific condition.

3. No charge whatsoever may be collected in any form by the
registered owner from the prospective buyer for the distribution
to the prospective buyer.

4. The registered owner of FAR 23 LOADS package believes the
prospective buyer has a need or use for this type of program.
Evidence of this might be that the prospective buyer is an ama-
teur or professional airplane designer; engineer; engineering
student; experimental airplane home builder; modifier of ultra-
light, kit or certified aircraft; aircraft modification shop; or
manufacturer of kit, ultralight or certified aircraft.

FAR 23 LOADS

5.  The  registered owner of FAR 23 LOADS must  support  the
prospective  buyer through set up and running of at least one  of
the  18  programs in the FAR 23 LOADS series,  using  the 'sample
input disk files or input data from the manual for programs with-
out disk file input.

6.  The  registered  owner of FAR 23  LOADS  must  mail  the
prospective buyer's name and address to

Hal C. McMaster
AERO SCIENCE SOFTWARE
7415 Tanglewood Court
Wichita, Kansas 67206

within  30 days of the distribution of the FAR 23  LOADS  program
and  document disks to the potential buyer.

7.  The evaluation disks copy must be  complete,  containing
all  the files on the original FAR 23 LOADS program and  document
disks  including the file to print the evaluation manual.  Copies
of  the disks may be made using the DISKCOPY command. This is  to
provide the prospective buyer with all the data files and program
files necessary to evaluate his areas of interest. The  potential
buyer may make a copy of the evaluation manual (Version 2.0  less
diagrams,  program  listings and sample output)  by  typing  COPY
D: EVALMANU. DOC LPT1 (where D is the drive that the Document  Disk
is in and LPT1 is the printer port) at the DOS prompt. The evalu-
ation manual is about 70 pages long. The manual may be viewed  on
the monitor by typing TYPE D:EVALMANU.DOC at the DOS prompt.

8.  If the prospective buyer purchases version 2.02  of  the
FAR  23  LOADS package from AERO SCIENCE SOFTWARE at  the  retail
price of $99.00 then AERO SCIENCE SOFTWARE will mail the distrib-
uting  donor a check for $25.00 within 30 days after the  buyer's
check has cleared the bank providing the donor's letter in item 6
above  preceded the receipt of the buyer's check. This  offer  is
good  till January 1, 1995. To order, use the form at the end  of
the manual. To make a copy of the form, type COPY  D: PURCHASE. DOC
LPT1 (where D is the drive that the Document Disk is in and  LPT1
is the printer port).

REGISTRATION

Purchasers  of  the  complete  FAR  23  LOADS  package   are
registered on receipt of payment in full when purchased  directly
from Aero Science Software. Purchasers from other sources  should
mail  in the registration form to Aero Science  Software.  Regis-
tered  owners  of  the FAR 23 LOADS package may  be  notified  of
enhancements  and  corrections that might be  developed.  Notices
will  be mailed to the address at registration or as up dated  by
the purchaser.

INTRODUCTION

The  author will provide assistance to registered owners  in
operation  and application of the FAR 23 LOADS   programs.  Tele-
phone  to   316-682-1644  or write to  the  address  above.  Aero
Science Software shall reserve the right to limit the amount  and
frequency  of such assistance and to institute a charge for  such
services.

SUBMITTAL TO FAA

The FAA may request a copy of the manual including  listings
of  the loads programs to substantiate the quality of your  basic
loads submitted for certification. You may provide them with your
copy  of the manual for review as proprietary  information.  They
should not divulge your reports or the copy of the manual to  any
one else. You may purchase a replacement copy of the book FAR  23
LOADS for $29.50 including shipping and handling in the USA  from
AERO SCIENCE SOFTWARE.

UPGRADES

With  each printing of FAR 23 LOADS we  incorporate  sugges-
tions  from  the  users for improving the programs.  We  plan  to
develop  enhancements including tab loads, tail  dragger  landing
loads,  tip tank loads, water loads and making the programs  more
user  friendly.  Future versions  may include some of  these  en-
hancements.  Upgrades will be provided to registered owners at  a
reasonable charge.

7

FAR 23 LOADS

DISCLAIMER

The  FAR  23 LOADS software package has been tested  by  the
author  in actual applications in his computer aided  engineering
consultation  work.  The results of the major individual programs
in  the package compare well with results from programs  used  in
the industry.

The  author and AERO SCIENCE SOFTWARE provide these programs
on  an "as is" basis and do not guarantee,  warrant or  make  any
other  representation regarding the use of these programs or  the
use  of  results  produced  from  these  programs.  The  user  is
responsible  for the engineering validity of the program  results
and the suitability of these programs to his application.

In  no  event  will the author or AERO SCIENCE  SOFTWARE  be
liable to the user for any damages,  including any lost  profits,
lost savings or other incidental or consequential damages arising
out of the use of or inability to use these programs, even if the
author  has been advised of the possibility of such  damages,  or
for any claim by any other party.

Only   the   FAA  or  their  Designated  Representative   is
authorized to inspect and issue an airworthiness certificate  for
any aircraft with the exception of an ultralight according to the
Federal  Air  Regulations.  The Federal Air Regulations  covering
ultralight  aircraft  are  based  on  the  assumption  that   any
individual  who elects to fly an ultralight aircraft has assessed
the dangers involved and assumes personal responsibility for  his
own  safety.  The  author  and AERO SCIENCE  SOFTWARE  assume  no
responsibility  for  damages resulting from flight  of  airplanes
which were designed or modified using any of these programs.

INTRODUCTION

SET-UP AND BACKUP INSTRUCTIONS

The  disk provided with FAR 23 LOADS package may be used  as
it  comes out of the package without modification.  We  recommend
that  you  make back up copies immediately and file the  original
disk in a safe place.

You  may wish to rearrange some files  and include your  DOS
operating  system  on  your "work"  or  "operational"  disk.  The
following  paragraphs will show you a way of accomplishing  this.
We  assume that you can "boot" your computer and arrive at the A>
prompt.

WITH TWO FLOPPY DISK DRIVES
"Work" Disk

1.  Insert the DOS disk in drive A:  and insert a blank disk
in drive B:.

2.  Format  the  disk in drive B:  with the  command  FORMAT
B:<ENTER>.  If  you want to include the DOS operating  system  on
your  "work" disk,  format the disk in drive B:  with the command
FORMAT B:/S<ENTER>

3.  If  you included the DOS operating system on the  "work"
disk  then type in the command COPY BASIC.COM B:<ENTER> and  then
the command COPY PRINT.COM B: .

4. Replace the DOS disk in drive A: with the original FAR 23
LOADS  program  disk.  Be sure the original disk  has  the  write
protect notch  covered.

5. To copy the program  files from. the original FAR 23 LOADS
program  disk to the above newly formatted disk type the  command
COPY *.BAS B:<ENTER>.

Your "work" disk is complete. Cover the write protect notch.

Data Disk

You  will  need to prepare a data disk for input and  output
files.  The following paragraphs will show you how to  accomplish
this.

1.  Format another disk without installing the DOS system on
it as in paragraph 1 and 2 above.

2. Insert the copy of the original program disk in drive  A:

and your newly formatted "data" disk in Drive B: .

FAR 23 LOADS

3.  Type the commands COPY M2002576 B:<ENTER>, COPY  WTENV36
B:<ENTER>,  COPY WTAFTCG B:<ENTER>, COPY BBFLTLDS B:<ENTER>,  and
COPY BBSELECT B:<ENTER>. These commands copy the sample files  to
your "data" disk.

Your "data" disk is complete.  The write protect notch must
not  be  covered  for open files during running of  most  of  the
programs.

WITH ONE FLOPPY DISK DRIVE
"Work" Disk

1. Place the DOS disk in drive A: and at the prompt A>, type
FORMAT<ENTER>. If you want to include the DOS operating system on
your "work" disk type the command FORMAT/S<ENTER>.

2.  When  prompted,  remove your DOS disk and insert a blank
disk in drive A: and press <SPACEBAR> to start formatting.

3.  If you formatted the "work" disk with the DOS  operating
system  on  it,  insert the DOS disk in drive  A:  and  type  the
command  COPY  BASIC.COM<ENTER>  swapping the DOS  disk  and  the
"work" disk as prompted. This will put the file BASIC.COM on your
"work" disk. Then do the same for the file PRINT.COM.

4.  Remove the newly formatted disk and insert the  original
FAR 23 LOADS program disk in drive A:.

5. To copy the program files from the original FAR 23  LOADS
disk type the command COPY *.BAS <ENTER>.

6.  When prompted remove the original FAR 23 LOADS disk  and
insert the newly formatted disk and press <SPACE BAR>.

7.   You  will  be prompted to swap the disks several  times
before all the files have been copied.

Your "work" disk is now complete.

Data disk

You  will need to prepare a data disk for input  and  output
files.  The  following paragraphs will show you how to accomplish
this.

1.  Format another disk without installing the DOS system on
it as in paragraph 1 and 2 above,



2. Insert your copy of the original program disk  drive  A:

10



INTRODUCTION

and  type  the command COPY M2002576<ENTER>  swapping  the  newly
formatted  data disk and the program disk as prompted. This  will
copy the sample file M2002576 to your data disk. Do the same  for
sample files WTAFTCG, WTENV36, BBFLTLDS and DESELECT.

Your  "data" disk is complete.  The write protect notch must
not  be  covered  for open files during running of  most  of  the
programs.

11

FAR 23 LOADS

 RUNNING BASIC LANGUAGE PROGRAMS

All of the programs on the FAR 23 LOADS disk are  in Basic

language. They can be run with the following procedure.

1.  Boot the computer with your DOS disk as you usually  do.
At  the A> prompt type the command BASIC <ENTER> (or  GWBASIC  or
BASICA) . The DOS disk may then be removed.

2.  Insert  your  "work" disk containing the  FAR  23  LOADS
programs  in  A  drive.  At  the  OK prompt  type  the   command
LOAD"filename.BAS" <ENTER>. Or you may put the "work" disk in any
drive.  In  that  case  at the OK  prompt  type  in  the  command
LOAD"d:filename.BAS"  (d:  is the letter of the disk  drive  your
work  disk  is  in  and filename.BAS is the  name  of  the  Basic
program.)

3. Type the command RUN <ENTER>

4. Respond to the questions asked by the program.

When the program asks for one piece of information,  respond
by typing in the answer and then pressing <ENTER>. Example:

WHAT IS THE CHORD OF THE WING, INCHES? 42.5

When  a  series of values are asked for,  you  separate  the
answers with commas. Example:

WHAT  ARE  THE AREAS OF THE VERTICAL  TAIL,  HORIZONTAL
TAIL IN SQ FT? 14.5,32.6

When questions request a yes or no answer,  you may  respond
with  Y,  YES,  YEA,  NO,  NAW  N etc.  Only the first letter  is
significant.

5. Run these BASIC programs with CAP LOCK on.

6.  For those of you  modifying the programs or  customizing
the  output  -- CAUTION. The spacing of blanks in the  PRINT  and
LPRINT statements may be incorrect in the program listings in the
manual (due to word wrap and aligning of the word processor). Use
the BASIC listings on the program disk.

7. The programs are in ASCII format which an be read by  the
basic compilers as well the basic inperptreters. If you are using
Quick Basic or another basic compiler, follow the instructions in
the compiler manual.

12

INTRODUCTION

FAR 23 LOADS DISK

The following table describes the contents of the program disk.

FILE NAME
WTESTIMA.BAS

WTONECG.BAS
WTENV.BAS
WINGGEOM.BAS
STRSPEED.BAS

MACHLIM.BAS
AIRLOADS.BAS

AIRLOAD4.BAS

TAU.BAS

FLTLOADS.BAS
SELECT.BAS
AILERON.BAS
FLAPLOAD.BAS
WINGINER.BAS
NETLOADS.BAS
ENGLOADS.BAS
LANDLOAD.BAS
LGFACTOR.BAS

DESCRIPTION

Basic program to estimate empty, max take-off and
component weights

Basic program to calculate weight, cg and inertia
for one particular loading of the airplane

Basic program to calculate envelope of weight and
cg for the full. range of possible loading

Basic program to  calculate  aerodynamic  surface
geometry

Basic program to calculate  FAR minimum design
speeds and chosen design speeds

Basic  program to calculate Mach limit lines

Basic program to calculate spanwise aero coeffic-
ients,  airplane less tail coefficients and span-
wise airloads

Basic program to calculate spanwise coefficients,
airplane less tail coefficients  and  spanwise
airloads for sweepback and high mach air loads

Basic program to calculate correction factor for
slope of the lift curve of the wing

Basic program to calculate V-n diagram data
Basic program to select critical flight loads
Basic program to calculate aileron loads
Basic program to calculate flap loads
Basic program  to calculate  wing inertia  loads
Basic program to calculate net wing loads
Basic program to calculate engine mount loads
Basic program to calculate landing loads
Basic Program to estimate landing load factor

13

FAR 23 LOADS

M2002576

WTENV36

WTAFTCG

BBFLTLDS
BBSELECT
PHAABB36
ACCELROL
TORSBB36

Sample  data  file  for input  to WTONECG.BAS  or
WTENV.BAS (data base for up to 200 items)

Sample  data  file  for  input to WTENV.BAS' (data
base for up to 100 items)

Sample data file  for  input to WTONECG.BAS (data
base for up to 100 items)

Sample data file for input to FLTLOADS.BAS
Sample data file for input to SELECT. BAS
Sample data file for input to NETLOADS.BAS
Sample data file for input to NETLOADS.BAS
Sample data file for input to NETLOADS.BAS

14

INTRODUCTION

OVERVIEW OF FAR 23 LOADS

Introduction

Although  you  may  be  familiar  with  the  calculation  of
airplane loads, it might be helpful to see how we intend for  the
individual  computer programs to be used.  A set of  basic  loads
acceptable for submittal to the FAA can be achieved by completing
the  series  of  programs using your data. These  loads  are,  of
course, suitable as the basis for substantiating the strength  of
a structurally sound home built or experimental airplane.

Purpose

The  purpose  of  the series of basic loads programs  is to

provide  the  means  to  calculate a set  of  loads  meeting the

requirements  and  intent  of Federal  Air  Regulations  Part 23
Subpart C covering flight loads;  horizontal tail loads;  control

surface and system loads; vertical tail surfaces; wing flaps and
special devices; engine loads and ground loads.

Federal Air Regulations Part 23 Subpart C - Structure

General includes the following FAR paragraphs:

23.301 Loads

23.303 Factor of safety

23.305 Strength and deformation

23.307 Proof of strength

Flight loads include the following FAR paragraphs:

23.321 General

23.331 Symmetrical flight conditions

23.333 Flight envelope

23.335 Design airspeeds

23.337 Limit maneuvering load factors

23.341 Gust load factors

23.345 High lift devices

23.347 Unsymmetrical flight conditions

23.349 Rolling conditions

23.351 Yawing conditions

23.361 Engine torque

23.363 Side load on engine mount

23.365 Pressurized cabin loads (not available yet)

23.367 Unsymmetrical loads due to turbopropeller

engine failure (not available yet)
23.369 Special conditions for rear lift truss (not

included)

23.371 Gyroscopic loads for turbine powered airplanes
23.373 Speed control devices

15

FAR 23 LOADS

Control surface and system loads

23.391 Control surface loads 23.397-23.459 occur in

conditions described in 23.331-23.351
23.395-23.415 Control Systems (not included)

Horizontal tail surfaces include the following FAR
paragraphs:

23.421 Balancing loads

23.423 Maneuvering loads

23.425 Gust loads

23.427 Unsymmetrical loads

Vertical tail surface loads include the following FAR
paragraphs:

23.441 Maneuvering loads

23.443 Gust loads

23.445 Outboard fins (not included)

Ailerons, wing flaps and special devices
23.455 Ailerons
23.457 Wing Flaps
23.459 Special Devices (not included)

Ground loads include the following FAR paragraphs:

23.471 General

23.473 Ground load conditions and assumptions

23.477 Landing arrangement (available for tricycle

configuration only)
23.479 Level landing conditions
23.481 Tail down landing conditions
23.483 One-wheel landing conditions
23.485 Side load conditions
23.493 Braked roll conditions
23.497 Supplementary conditions for tail wheels

(not included)

23.499 Supplementary conditions for nose wheels
23.505 Supplementary conditions for ski-planes

(not included)
23.507 Jacking loads (not included)
23.509 Towing loads (not included)
23.511 Ground load; unsymmetrical loads on multiple

wheel units (not included)

Water loads include the following FAR paragraphs:

23.521 Water load conditions (not included)

Emergency landing conditions

23.561 General (not included)

Fatigue evaluation

23.571 Pressure cabin (not included)

23.572 Wing and associated structure (not included)

16

INTRODUCTION

General Overview

The  basis for most of the detail flight loads for  the  FAR
paragraphs above are the flight envelopes or V-n diagrams of  FAR
23.333  and  23.345 and the computations to  balance  the  linear
normal and drag accelerations and the aerodynamic lift, drag  and
moments about the center of gravity at each required point on the
diagrams.  This  can  amount to 584  balanced  conditions  for  3
configurations,  4 altitudes and 12 cg's.  For smaller low  level
airplanes a practical approach would include 2 configurations,  2
altitudes and 8 cg's for a total of 216 balanced points. You  can
see  the advantage of the computer in making these  calculations.
Searching the all this data for the critical conditions affecting
the flaps, ailerons, wings, horizontal stabilizer, elevator, tab,
vertical  fin,  rudder, fuselage etc is a  tremendous  task.  The
micro computer can help us do this work with a minimum of  effort
and elimination all arithmetic errors.

The  data  needed  to make the  V-n  balancing  calculations
consists  of  weight and center of gravity,  aerodynamic  surface
geometry,   structural  speeds  and   aerodynamic   coefficients.
Computer  programs  are provided for calculating  this  essential
information  and are discussed in the following overviews of  the
individual programs.

The above data is then entered into the flight loads program
which  produces  a matrix of balanced load data for  the  several
hundred conditions. This data consists of the wing load,balancing
horizontal tail load, the load factor, the drag factor, the angle
of attack,  the speed, the mach effect, the lift coefficient, the
total  load on the airplane and the name and case number of  each
condition.

The  above  matrix of data is searched by the  selection  of
critical  loads  program for the critical structural  loads.  The
program also calculates the angular acceleration conditions which
are  derived as increments added to the linear  accelerations  of
the balanced conditions. It then selects the critical  structural
loads  for the angular accelerated conditions. These include  the
accelerated  roll  wing loads, checked and  unchecked  horizontal
tail loads etc.

The  wing  spanwise airloads are calculated by returning  to
the  aero coefficients program with the coefficient of  lift  and
speed for the specific critical wing conditions from selection of
critical loads program.

The  wing inertia program calculates the inertia loads  from
the  wing panel weight,  wing geometry and the linear and angular
accelerations for the selected critical wing conditions.

The net wing loads are obtained by algebraically adding  the
wing inertia loads to the wing air loads.

17

FAR 23 LOADS

Separate  programs  calculate the aileron, flap  and  engine
mount loads.

The  landing loads program calculates the landing loads from
landing  gear  geometry,  landing load factor and weight  and  cg
data. The program prints out a matrix of loads consisting of nose
and  main  gear vertical,  drag and side  loads,  linear  inertia
factors  and unbalanced angular moments all with respect to  both
ground reference and airplane coordinate reference.

This  overview  indicates that this  computer  aided  design
approach  can produce a relatively complete set of airplane basic
loads.  The  programs are based on the Federal  Air  Regulations,
text  references used in the industry and years of experience  in
certification process of FAR 23 airplanes.

A flow chart pictures the above overview on page 22.

Overview of the Weight Programs

Three weight programs are provided. The first estimates  the
empty  weight,  maximum take-off weight and the weight  of  every
significant  component of the airplane. It does this in  response
to seven questions.

The second and third weights programs use a common data base
which  is  derived  from the weight data from  the  first  weight
program combined with the locating dimensions from the three-view
drawing of the airplane.

The  second weight program calculates the weight, center  of
gravity  and inertias about three axes of the airplane  and  also
with  respect  to the principal axis for a specific  loading  and
configuration.  This program is used for the four points  on  the
structural  limits  diagram  (aft  gross  weight,  forward  gross
weight, forward regardless of weight, minimum weight). These four
points  are  the  weight and cg data input to  the  flight  loads
program.

The   third  weight  program  calculates  the  envelope   of
discretionary useful loading. This program includes a small  data
base   for  entering,  adding,  deleting,  changing  and   moving
component weight data. The component data can be placed in  empty
weight,  minimum weight or useful load categories from which  the
program  will calculate the minimum flight weight, sort the  data
in  ascending and descending fuselage stations and calculate  the
envelope  enclosing  all possible loadings.  From a plot  of  the
envelope of useful loading, the four structural limit points  can
be selected to include the most desirable and practical loadings.

Overview of the Aerodynamic Surface Geometry Program

18

INTRODUCTION

For  each  aerodynamic surface, the program  calculates  the
surface area, aspect ratio, mean aerodynamic chord (MAC, actually
the  mean geometric chord), spanwise location of the MAC and  the
fuselage  station  of  the leading edge of  the  MAC  for  either
symmetrical or unsymmetrical surfaces. The necessary data to make
the  calculations  are the coordinates defining the  leading  and
trailing edge of the surface.

Overview of the Aerodynamic Coefficients Program

The aerodynamic coefficients program calculates the spanwise
basic and additive lift, drag, and moment coefficients, the  span
wise stall coefficients, the airplane less tail coefficients  and
the  equations  for the lift moment and drag coefficients  to  be
used in the flight loads program. After the flight loads  program
and selection of critical loads program are run, the  aerodynamic
coefficient  program is used to calculate the spanwise air  loads
for the critical wing conditions.

Overview of the Structural Speeds Program

The  structural  speeds program calculates the  FAR  minimum
required  speeds  and  load factors. It then  brings  the  chosen
speeds  and  load  factors  up to  the  minimum  requirements  if
necessary and adjusts the structural speeds for the FAR  required
operational relationships. The only data necessary to make  these
calculations  are the gross weight, wing area, maximum  speed  at
sea level and stall speed or Cr MAX-

Overview of the Flight Loads and Balancing Calculations Program

The  flight  loads  program  receives  the  data  from   the
geometry,   weights,  aero  coefficients  and  structural   speed
programs  from which it makes the balancing calculations for  all
points  on  the  V-n diagrams. There is a V-n  diagram  for  each
combination of configuration, weight and cg, and altitude.  There
may be up to three configurations --- cruise, enroute (drag flaps
or  brakes) and landing. There are four weights and cg's ---  aft
gross weight, forward gross weight, forward regardless of  weight
and  minimum weight for cruise and enroute, four for landing  and
possibly  four more in case landing gear is lowered for  drag  in
the enroute configuration.

Four   altitudes   are  necessary   for   high   performance
turbocharged  or  turboprop  airplanes ---  sea  level,  shoulder
altitude  (initial mach limitation), 20,000 feet (change in  gust
rules),  and maximum operating altitude. There are 20  points  on
the  V-n  diagram for cruise, 16 for enroute and 14  for  landing
configuration.  The  landing configuration is done at  sea  level
only. The number of conditions for a high performance airplane is
584 and for a simple kit airplane 216.

19

FAR 23 LOADS

For  each condition, the balancing calculations produce the

speed,  normal  load  factor, angle of attack (RW  to  WL), mach

effect  (Glauert correction), lift coefficient, wing  load, tail

load and drag load. This matrix of data is printed out with case
number and name on paper and saved as an input file to the selec-
tion of critical loads program.

Overview of the Selection of Critical Loads Program

The selection of critical loads program searches up to  6424
elements  of  the  matrix of flight load file  for  the  critical
structural  loads in the balanced conditions. It then  calculates
the  pitching,  rolling  and  yawing increments  to  add  to  the
balanced  conditions  as  required  by FAR  23  for  the  angular
accelerations due to maneuvers and gusts and selects the critical
structural loads for the angular acceleration conditions.

This  program selects the critical conditions for  the  wing
for  bending  and torsion during balanced, pitching  and  rolling
flight.  It calculates and selects the horizontal tail loads  for
up and down balancing load with flaps retracted and extended, for
up and down checked and unchecked maneuver load, for up and  down
gust load and for unsymmetrical load.  It calculates and  selects
the  vertical  tail loads for critical maneuver load  for  sudden
rudder  deflection,  for maneuver load for yaw to  sideslip  with
rudder  deflected, for maneuver load for yaw with rudder in  neu-
tral  and  for  side gust load at cruise speed.  It  selects  the
critical conditions for the fuselage.

Overview of Wing Inertia Program

The  wing  inertia program calculates the  spanwise  inertia
loads,  shears  and moments in balanced  and  accelerated  flight
along the quarter chord of the wing.  Input data required are the
inertia factors which are obtained for the selected critical wing
conditions, the wing panel weight, the ratio of area densities at
the tip to the root, the wing plan form geometry and the dihedral
angle of the wing reference plane and the waterline of its inter-
section with the center plane of symmetry at the quarter chord.

Overview of Net Wing Loads

The  net  wing loads are calculated by algebraically  adding
the  spanwise  airloads  and the inertia for  vertical  and  drag
shears,  moments and torques about the quarter chord of the wing.

Overview of Aileron Loads

Aileron  loads are calculated at maneuver speed for  maximum

20

INTRODUCTION

deflection and at cruise speed and dive speed for reduced deflec-
tions as specified by regulations.

Overview of Flap Loads

Flap loads are calculated for maximum deflection at speeds
up to maximum flap speed for maneuver, gust and slipstream ef-
fects.

Overview of Engine Mount Loads

Engine  mount  loads are calculated for  vertical  and  side
inertia,  thrust, engine torque, and in the case of  turbine  en-
gines gyroscopic forces and torque due to sudden stoppage.

Overview of Landing Loads Program

The landing loads program calculates the loads for  tricycle
landing  gear with spring or oleo struts. The main and nose  need
not be the same type. The inputs needed for this program are  the
landing gear load factor, the assumed lift factor during landing,
the  station and waterline of the axles for the  static  position
and  the  25 percent compressed position if oleo or  100  percent
compressed if spring strut, the rolling radius of the tires,  the
distance  between the main wheels, the tail down bump  angle  and
the  weight and cg for the structural limits. The dimensions  and
formulas  of FAR 23 Appendix C are the basis for  these  calcula-
tions.

A  program  is also provided to estimate  the  landing  load
factor  since  test data is usually not available in  the  design
stage.  The  load factor in the landing loads   program must  be
revised  if it is less than that determined by  tests  which  are
required for certification.

21

FAR 23 LOADS
Flow Chart

K    Start



WEIGHT ESTIMATION

With only a sketch of your airplane it is possible to make a
very  reasonable  weight estimate of the empty  weight,  take-off
weight  and  the weight of each significant component.

Statistically  there is a ratio of empty weight to  t-ake-off
weight of approximately .62. This varies slightly with the number
of seats, endurance at cruise speed, number and type of  engines,
pressurized or not, etc.

But  the actual take off weight is a function of the  useful
load. The useful load consists of just three items. The weight of
the persons occupying all the seats in the airplane, the  baggage
and the fuel for a specified endurance at cruise speed.

Then the take-off weight is calculated by:

Mto^useful^1-1^
Where K= ratio ^empty^to

The component weights follow statistical percentages of  the
take-off  weight  closely  for all  except  the  powerplant.  The
powerplant  and its components are a percentage of the  installed
engine  weight. These are a function of the rated horse power  of
the engine.

The  percentages  are derived from data  on  many  airplanes
under  12500  pounds take-off weight. This data is  available  in
technical books, some of which are referenced at the end of  this
discussion.

If you will answer the following few questions presented  on
the monitor when you run the basic program WTESTIMA.BAS, you will
have reasonable weight data to use as input to the weight inertia
program,   WTONECG.BAS,  and  the  range  of  loadings   program,
WTENV.BAS:

How many engines

What is total horse power

What type of engine

How many hours endurance at cruise speed

How many seats

What is total baggage weight

Is cabin pressurized

References:

The Design of the Airplane by Darrol Stinton
Fundementals of Aircraft Design by Leiand M. Nicolai
Synthesis of Subsonic Airplane Design by Egbert Torenbeek
Supersonic and Subsonic Airplane Design by Gerald Corning

23


26

WEIGHT ESTIMATION

Example output for Estimated Weight for Two Place Trainer:

ESTIMATED WEIGHT DATA FOR TWO PLACE TRAINER
INPUT

MAX CONTINUOUS HP 65

NUMBER OF ENGINES 1

NUMBER OF SEATS 2

HOURS AT CRUISE POWER 3

MAX BAGGAGE WEIGHT 40
UNPRESSORIZED
RECIPROCAL 4 CYCLE ENGINE

OUTPUT

MAX TAKE OFF WT 1216

USEFUL LOAD 453

EMPTY WEIGHT 763

W(EMPTY)/W(TO) .62

WING 126

FUSELAGE 119

TAIL 28

NACELLE 17

LANDING GEAR 69

CONTROLS 18

TOTAL STRUCTURE 379

ENGINE INSTALLED 199

(INCLUDES PROPELLER(S)) ( 19 )

FUEL SYSTEM 21

EXHAUST ,29

OTHER ENGINE DETAILS 35

TOTAL POWRPLANT 285

INSTRUMENTS & NA7 EQUIP 5

PNEUMATICS 1

ELECTRICAL 29

ELECTRONICS 0

FURNISHINGS & EQUIPMENT 53
ENVIRONMENTAL & ANTI-ICE 3

HISC OTHER SYSTEM WT 0
TOTAL SYSTEMS WEIGHT 94

OPTIONS & MISCELLANEOUS 3
EMPTY WEIGHT 763

PILOT 170

PASSENGER NO. 2 170

BAGGAGE 40

FUEL 73

USEFUL LOAD 453

27

FAR 23 LOADS

Example output for Estimated Weight for Six Place Single Turbo-
charged Recip:

ESTIMATED WEIGHT DATA FOR SIX PLACE SINGLE TURBOCHARQED RECIP
INPUT

MAX CONTINUOUS HP 250

NUMBER OF ENGINES I

NUMBER OF SEATS 6

HOURS AT CRUISE POWER 3.5

MAX BAGGAGE WEIGHT 60
UNPRESSURIZED
TURBOCHARGED ENGINE

OUTPUT

MAX TAKE OFF WT 3805

USEFUL LOAD 1408

EMPTY WEIGHT 2397

W(EMPTY)/W(TO) .63

WING 394

FUSELAGE 373

TAIL 89

NACELLE 55

LANDING GEAR 217

CONTROLS 57

TOTAL STRUCTURE 1187

ENGINE INSTALLED 543

(INCLUDES PROPELLER(S)) ( 78 )

FUEL SYSTEM 58

EXHAUST 79

OTHER ENGINE DETAILS 95

TOTAL POWRPLANT 777

INSTRUMENTS & NAV EQUIP 16

PNEUMATICS 3

ELECTRICAL 91

ELECTRONICS 0

FURNISHINGS & EQUIPMENT 167
ENVIRONMENTAL & ANTI-ICE 11

MISC OTHER SYSTEM WT 0
TOTAL SYSTEMS WEIGHT 294

OPTIONS & MISCELLANEOUS 138
EMPTY WEIGHT 2397

PILOT 170

PASSENGER NO. 2 170

PASSENGER NO. 3 170

PASSENGER NO. 4 170

PASSENGER NO. 5 170

PASSENGER NO. 6 . 170

BAGGAGE 60

FUEL 328

USEFUL LOAD 1408

28

WEIGHT ESTIMATION

output for Estimated Weight for Pressurized Twin  Turbo-

ESTIMATED WEIGHT DATA FOR PRESSURIZED TWIN TURBO PROP

INPUT

MAX CONTINUOUS HP
NUMBER OF ENGINES
NUMBER OF SEATS
HOURS AT CRUISE POWER
MAX BAGGAGE WEIGHT
PRESSURIZED
TURBOPROP ENGINE

OUTPUT

WT

MAX TAKE OFF
USEFUL LOAD
EMPTY WEIGHT

W(EMPTY)/^(TO)

WING

FUSELAGE

TAIL

NACELLE

LANDING GEAR

CONTROLS

TOTAL STRUCTURE

1500

2

8

4.2

160

12462
4985
7477
.59

1291

1223

291

181

711

186

3887

ENGINE INSTALLED 935

(INCLUDES PROPELLER(S)) ( 491

FUEL SYSTEM 99

EXHAUST 234

OTHER ENGINE DETAILS 164
TOTAL POWRPLANT

INSTRUMENTS & NA7 EQUIP '147

PNEUMATICS 0

ELECTRICAL 335

ELECTRONICS 0

FURNISHINGS & EQUIPMENT 570
ENVIRONMENTAL & ANTI-ICE 147

MISC OTHER SYSTEM WT 98
TOTAL SYSTEMS WEIGHT

OPTIONS & MISCELLANEOUS 672
EMPTY WEIGHT

PILOT 170

PASSENGER NO. 2 170

PASSENGER NO. 3 170

PASSENGER NO. 4 170

PASSENGER NO. 5 170

PASSENGER NO. 6 170

PASSENGER NO. 7 170

PASSENGER NO. 8 170

BAGGAGE 160

FUEL 3464

USEFUL LOAD

1435

1483

7477

4985

29

FAR 23 LOADS

30

WEIGHT AND INERTIA FOR A SINGLE CONFIGURATION AND LOADING

The  program  WTONECG.BAS calculates the weight,  center  of
gravity and moment of inertia for a single load configuration  of
an  airplane.  Inputs required are the  coordinates,  weight  and
moment  of  inertia  for each of all of  the  components  of  the
airplane  and useful load for that particular loading. "The  total
weight  of  the airplane and useful can consist of  a  few  large
components or as many detail components as desired.

The  maximum number of components in the data base is 100 by
default  or you may choose any number. Two sample data files  are
provided on the program disk.

The  first, WTAFTCG, is a data base permitting  the  default
maximum  of up to 100 components consisting of 24 components  for
the Beach Banana 36.

The second sample file, M2002576, is a data base  permitting
up  to 200 components and consists of 56 items. This  sample  was
taken from NACA Technical Note 575 entitled Estimation of Moments
of  Inertia of Airplanes from Design Data. The same data  appears
in the book. Analysis and Design of Flight Vehicle Structures  by
E. F. Bruhn. You will find the results  check closely with theirs
and would be the same except for three minor numerical errors  in
their calculations, but then they didn't have a PC.

Equations

The equations used to calculate the center of gravity are:

X =SUM(X^)/SUM(Wi)
Zcg=SUM(Z^)/SUM(Wi)

where X, is the fuselage station of a component
Z^ is the waterline of a component
W^ is the weight of a component

i is the identifying number of the component

The equations used to calculate the moment of inertia about
the airplane center of gravity referenced to airplane coordinates
are:

I^SuMCWiy^+SuMCW^z^+SUMCI^)
I^SUMtW^x^+SUI-KWiZi^+SuMCI ^)
I^SUMCW^x^+SUMCW^y^+SUMtl^)
I^=SUM(W^Zi)

where x^=X^-X^-

Yi^i-^cg

z,=Z,-Z^g

31

FAR 23 LOADS

The equations used to calculate the moment of inertia about
the center of gravity referenced to the principal axes are:

TAN2A=2I^/(I^-I^)

Ixp=Ixxcos A+IzzsIN A-lxzsIy2A

yp  yv   i        ~>
I-I^SIN'A+I^COS^A+I^Sl^A

Discussion

Airplane  weight  and  center of gravity are needed  in  the
calculation of balanced flight and landing  conditions.  Airplane
inertia  is  needed  in the calculation of maneuvering  and  gust
flight conditions and unbalanced landing conditions.

This  program is used to calculate the usual four points  on
the  weight  structural  limits  diagram  --- aft  gross  weight,
forward  gross weight,  forward weight regardless of  weight  and
minimum weight.

The  aft gross weight cg is usually about 30 percent of  the
wing  mean  aerodynamic chord.  The forward gross  weight  cg  is
usually about 20 percent of the MAC and the forward regardless cg
is  usually about 15 percent.  These cg's are established by  the
aerodynamic!st and approved by the project engineer.

The minimum weight cg falls where the airplane empty  weight
plus a 170 pound pilot and a half hour of fuel at max  continuous
power  calculates  to  be.  This can  be  modified  by  permanent
ballast  to bring it inside the weight structural limits  diagram
if necessary.

The maximum weight (gross weight) must not be less than  the
empty  weight  plus 170 pounds for each seat and a half  hour  of
fuel at max continuous power. The maximum weight must not be less
than  the  empty weight plus a 170 pound pilot and fuel  full  to
tank capacity.

Fuel  may be assumed to be used at the rate of .5 pound  per
HP per hour.

Note: Inertia of a rod about its cg is:

I^g = WL'^/ll  LB-IN2

Examples:

I       = 505*442/12 = 81,473

lxx wing = 330*402^/12 = 4,444,110

Compare with accurate calculation on page 238

32


38

WEIGHT AND MOMENT OF INERTIA

Example input for Weight Data File WTAFTCG:

AIRPLANE WEIGHT AND INERTIA
WEIGHT DATA FOR BEACH BANANA AT AFT CG USING DATA FILE WTAFTCG

ITEM	COMPONENT	WEIG!	3T		X	Y		Z		IXX	IYY	IZZ
1	WING, OUTBOARD	330	.0	97	.87	0	.00	87	.73	4444110	133485	4444110
2	HORIZ TAIL	42	.0	270	.36	0	.00	111	.00	0	0	0
3	VEKT TAIL	23	.0	276	.93	0	.00	137	.76	0	0	0
4	MAIN GEAR WHEE	45	.0	97	.00	0	.00	69	.00	0	0	0
5	MAIN GEAR STRU	110	.0	97	.00	0	.00	78	.00	0	0	0
6	NOSE GEAR WHEE	9	.0	1	.00	0	.00	52	.00	0	0	0
7	NOSE GEAR STRU	40	.0	 1	.00	0	.00	65	.00	0	0	0
8	FLIGHT CONTROL	57	.0	123	.00	0	.00	105	.00	0	0	0
9	NACELLE	62	.0	21	.00	0	.00	92	.00	0	0	0
10	ENGINE INSTALL	505	.0	22	.00	0	.00	92.	.00	52604	81473	81473
11	PROPELLER	74	.0	-10	.00	0	.00	100	.00	0	0	0
12	SYSTEMS	88	.0	60	.00	0.	.00	100.	.00	0	0	0
13	FURNISHINGS	175	.0	105	.00	0	.00	100	.00	0	0	0
14	UNUSABLE FUEL	12.	.0	73	.00	0.	.00	80.	.00	0	0	0
15	FUSELAGE STRUC	250	.0	99	.00	0.	.00	80.	,00	0	1131020	1131020
				END	OF	EMPT'1	r WE	SIGHT	IT:	EMS----
51	PILOT	170.	.0	75	.00	0.	.00	100.	.00	28730	24480	4250
52	30 MIN FUEL	71.	.0	70	.00	0.	.00	82.	.00	86975	0	86975
				END	OF	MINII	1UM	WEIGt	IT	ITEMS--
61	COPILOT	170.	.0	75	.00	0.	.00	100.	00	28730	24480	4250
62	3RD PERSON	170.	.0	111	.00	0.	,00	100.	,00	28730	24480	4250
63	4TH PERSON	170.	,0	111	.00	0.	00	100.	00	28730	24480	4250
64	5TH PERSON	170,	.0	150	.00	0.	.00	100.	.00	28730	24480	4250
65	6TH PERSON	170,	0	150	.00	0.	00	100.	00	28730	24480	4250
67	FUEL TO GR WT	409.	.0	70	.00	0.	,00	87.	00	501025	0	501025
68	BALLAST	78.	.0	103	.70	0.	00	90.	00	0	0	0
				END	OF	DISCI	SET:	:ONAR^	r wi	EIGHT ITE	MS -----

39

FAR 23 LOADS

Example output for Inertia using WTAFTCG:

CENTER OF GRAVITY, WEIGHT & INERTIA FOR
BEACH BANANA AT AFT CG OS ING DATA FILE WTAFTCG

CENTER OF GRAVITY AND WEIGHT

XBAB (FUS STA) ZBAK (WATERLIME) WEIGHT (POUNDS)
84.99936       92.57932       3400

INERTIAS WITH RESPECT TO AIRPLANE COORDINATES

IXX IYY IZZ IXY UNITS

1201.527 2058.21 3022.766 134.4063 SLOG FEET SQUARED

5566051 9534614 14002900 622634 LBS INCHES SQUARED

INERTIAS WITH RESPECT TO PRINCIPAL AXES
IX(P)         IY(P)         IZ(P)
1191.662      2058.21       3032.631
5520349      9534614      14048600

UNITS

SLUG FT SQUARED

LBS INCHES SQUARED

THETA

4.198394 (DEGREES, MEASURED UP FROM WL & AFT FROM CG)

40

WEIGHT AND MOMENT OF INERTIA

Example input for Weight Data File M2002576:

AIRPLANE WEIGHT AND INERTIA
WEIGHT DATA FOR MODEL 575 AT AFT GROSS WEIGHT USING DATA FILE M2002576

ITEM	COMPONENT	WEIG	HT		X	Y		Z		IXX	IYY	IZZ
I	C S NOSE	108	.8	102	.00	0	.00	57	.00	261229	0	261229
2	C S BEAM	204	.6	121	.00	0	.00	57	.00	491245	0	491245
3	C S RIBS	84	.2	148	.00	0	.00	55	.00	202164	33680	235844
4	FLAP	22	.0	180	.00	0	.00	53	.00	48598	0	48598
5	0 P NOSE	104	.6	105	.00	156	.00	65	.00	184514	0	184514
6	0 P BEAM	155	.6	120	.00	156	.00	65	.00	274478	0	274478
7	0 P RIBS	89	.8	139	.00	156	.00	64	.00	158407	17601	176008
8	AILERONS	31	.4	172	.00	156	.00	62	.00	55390	0	55390
9	HORIZ TAIL	87	.1	367	.00	0	.00	96	.70	176378	0	176378
10	VERT TAIL	31	.4	352	.00	0	.00	125	.00	110200	10174	31
11	FUS SKELETON	314	.0	176	.00	0	.00	81	.00	69394	1576590	1570000
12	ENG MOONT	40	.5	60	.00	0	.00	80	.00	5184	5184	5184
13	TURTLEBACK	48	.5	254	.00	0	.00	80	.00	15181	57861	56648
14	FIREWALL	11	.0	70	.00	0	.00	80	.00	2200	1100	1100
15	STEPS	2	.0	170	.00	20	.00	70	.00	0	0	0
16	COWLING	70	.0	50	.00	0	.00	80	.00	16940	15470	15470
17	CABIN & W S	66	.5	146	.00	0	.00	108	.00	2394	106400	108794
18	FOOT TROUGHS	2	.0	77	.00	5	.00	68	.00	0	0	0
19	FLOOR REAR	9	.5	210	.00	0	.00	66	.00	608	1368	1976
20	WING FILLETS	18	.5	142	.00	20	.00	58	.00	0	18944	18944
21	BOT COWL &SIDE	27	.0	140	.00	11	.00	75	.00	0	24300	24300
22	ARREST DOOR	1	.3	284	.00	0	.00	63	.00	5	0	5
23	TAIL WHEEL PAN	4	.0	365	.00	0	.00	84	.00	100	0	100
24	SIDE DOORS	17	.0	143	.00	18.	.00	82	.00	1088	28288	27200
25	BAGGAGE DOOR	1	.8	165	.00	0.	.00	63	.00	720	0	720
26	FABRIC & DOPE	13	.0	254	.00	0.	.00	80	.00	4394	15509	15509
27	TAIL CONE	7	.5	385	.00	0.	.00	91	.00	120	0	120
28	COWL STA 1 t 2	12.	.0	110	.00	0.	.00	95	.00	1200	0	1200
29	CHASSI RETRACT,	232.	.4	115	.00	54.	.00	51.	.00	0	23240	23240
30	RETRACT MECH	28.	.6	110	.00	25.	00	67.	.00	0	0	0
31	WHEELS	91.	.0	141	.00	54.	.00	56.	.00	0	0	0
32	TAIL WHEEL	26.	.0	360,	,00	0.	00	74.	.00	26	0	26
33	ENGINE	1049.	.0	33,	,00	0.	00	80,	.00	253858	253858	253858
34	ENG ACCES	90.	.6	52.	.00	0.	00	83.	00	9060	0	9060
35	ENG CONT	11.	.0	103.	.00	10.	00	76.	00	0	0	0
36	PROP	222.	0	9.	.30	0.	00	80.	00	177600	89300	89300
37	STARTER SYSTEM	37,	.0	56.	.00	0.	00	85.	00	148	333	481
38	LDB SYSTEM	26.	0	69.	.00	0.	00	82.	00	1274	0	1274
39	FUEL SYSTEM	82.	0	128.	.00	0.	00	80.	00	22058	20008	25666
40	INSTRUMENTS	38.	0	102.	.00	0.	00	92.	00	2432	60800	65232
41	SURF CONTROL	81.	5	160.	,00	0.	00	71.	00	123962	130400	254362
42	FURNISHINGS	160.	0	156.	00	0.	00	80.	00	108160	400000	508160
43	ELECT EQUIP	100.	7	128.	,00	15.	00	81.	00	0	0	0
44	HOIST SLING	6.	0	115.	00	0.	00	102.	00	864	0	864
45	RADIO	142.	7	178.	00	0.	00	85.	00	5137	0	5137
50	OIL	75.	0	71.	00	0.	00	85.	00	3675	0	3675
				END	OF	EMPTY	 WE	:IGHT	ITE1	IS-------
101	30 MIN FUEL	195.	0	132.	00	0.	00	85.	50	35295	43095	39390
102	PILOT	200.	0	105.	00	0.	00	90.	00	33800	28800	5000
				END	OF	MINIM	UM	WEIGH	T n	FEMS----
121	REST OF FUEL	585.	0	132.	00	0.	00	85.	50	105885	129285	118170
122	VERY PISTOL	3.	9	195.	00	14.	00	75.	00	0	0	0
123	SMOKE CANDLES	4.	0	184.	00	14.	00	96.	00	0	0	0

41

FAR 23 LOADS

Example input for Weight Data File M2002576 Cont

124	FLOAT LIGHTS	9	.0	190	.00	14.00	72.00	0	0	0
125	CHART BOARD	3.	.7	80	.00	3.00	94.00	0	0	0
126	DRIFT SIGHT	1.	.6	222	.00	14.00	84.00	0	0	0
127	FIRST AID	4.	.0	165	.00	10.00	57.00	0	0	0
128	LIFE RAFT	34.	0	136.	.00	0.00	101.00	306	0	306
129	OBSERVER	200.	.0	205.	.00	 0.00	89.00	33800 :	28800	5000
				END	OF	DISCRETI	ONARY WE]	[GHT ITEMS

42

WEIGHT AND MOMENT OF INERTIA

Example output for Inertia Output Using M2002576:

CENTER OF GRAVITY. WEIGHT & INERTIA FOR
MODEL 575 AT AFT GROSS WEIGHT USING DATA FILE M2002576

CENTER OF GRAVITY AND WEIGHT

XBAR (FOS STA) ZBAR (WATERLINE) WEIGHT (POUNDS)
115.8659       78.0418        5325.301

INERTIAS WITH RESPECT TO AIRPLANE COORDINATES

IXX IYY IZZ IXY

3044.844 6549.09 9033.307 152.01

14105180 30338530 41846610 704183

UNITS

SLUG FEET SQUARED

LBS INCHES SQUARED

INERTIAS WITH RESPECT TO PRINCIPAL AXES
IX(P)         IY(P)         IZ(P)
3040.989      6549.09       9037.164
14087320     30338530      41864480

UNITS

SLUG FT SQUARED

LBS INCHES SQUARED

THETA

1.453245 (DEGREES, MEASURED UP FROM WL & AFT FROM CG)

43

FAR 23 LOADS

WEIGHT VS CENTER OF GRAVITY FOR A RANGE OF USEFUL LOADINGS

The  program WTENV.BAS calculates the the envelope of weight
vs  center  of gravity for all possible  combinations  of  useful
load.  Inputs  required  are  the coordinates and weight  of  the
components of the airplane included in the empty weight,  minimum
weight and all the discretionary loads you wish to consider. Note
that the  data  base  subroutine is the same as the  one  in  the
program WTONECG.BAS.

Run  program  WTENV.BAS with your full data base  of  weight
information. Then plot the envelope and choose the the points for
your  weight  structural  limits  diagram  to  include  the  most
desirable  and  practical loadings to keep the center of  gravity
within   the   range  of  percent  of  MAC   specified   by   the
aerodynamic!st.  The  aerodynamicist probably will also limit the
gross  weight  to  provide the performance needed  for  take  off
distance, climb and service ceiling.

Your  selected  weight and cg points for gross  weight  aft,
gross  weight forward and forward regardless will probably not be
exactly  on the envelope.  Using the data base for the  envelope,
delete  weight  items in the useful load to represent  a  loading
close  to  and below (less weight than) one  of  your  structural
limit  points.  You will have to place ballast (for analytical or
structural test purposes) to achieve the chosen weight and center
of gravity of the structural limit point.

The  ballast weight and station can easily be calculated  by
hand and checked with program WTONECG.BAS. Start with the  weight
and  cg  of  that point on the envelope which  is  close  to  but
slightly less weight than the structural limit. Use the following
equation to find the ballast weight and its station:

^B^L^^A-W/^L-^^
WB=WL-WA

where Wr is weight of chosen structural limit

XL is fuselage station of chosen structural limit
W^ is weight of point on envelope
XB is fuselage station of point on envelope
Xn is fuselage station of ballast

If  the  fuselage  station of the ballast is  not  contained
within  the fuselage,  then use the next lower  (lighter  weight)
point  on  the envelope and repeat the calculation  for  fuselage
station and weight of the ballast.

Use program WTONECG.BAS to calculate the inertia and confirm
the weight and cg of the structural limit.

45

FAR 23 LOADS

An example of setting the structural limits and  calculating
the  ballast to match the weight and cg of the  structural  limit
follows.

The  aerodynamic 1st or you set the limits of the  structural
diagram, for the Beach Banana 36 like this. The gross  weight  is
set at 3400 pounds to achieve desired climb and stall speeds. The
aft  gross  weight  cg limit is set at 31  percent  of  MAC.  The
forward  gross  weight  cg limit is at 20  percent  of  MAC.  The
forward  regardless of weight cg limit is set at 13 percent  MAC.
These are typical limits for aerodynamic considerations.

The  actual fuselage stations for the structural limits  are
calculated from the wing geometry data as follows:

X(aft gross)=63.641+.31(69.246)=85.1
X(fwd gross)=63.641+.20(69.246)=77.49
X(fwd regardless)=63.641+.13(69.246)=72.64

The  resulting  envelope  of all possible  loading  and  the
Structure  limit envelope are plotted on the figure in the  pages
following.  I use Micro Soft Chart to do my plotting. You can  do
this by hand or use any commercial plotting program. You can  see
in the figure that the Beach Banana 36 can be loaded with six 170
pound people with full fuel and not exceed the gross weight limit
or  the  aft cg limit. That meets the requirement  of  FAR  23.25
which  requires all seats at 170 pounds and at least a half  hour
of fuel at max continuous power.

The program does not print out the empty weight or its cg in

this  version. You could calculate it by running the  WTONECG.BAS

program or a simple hand calculation like this.

X         W         =    M
Min Weight     73.09     2063           150,785
Less pilot     75        -170      =    -12,750
Less 30 m fuel 70        - 71      =    - 4,970

Empty Weight 75.03 1822 133,065

The ballast weight and ballast fuselage station are
calculated like this:

Aft Gross Weight

Ballast weight = 3400 - 3322 = 78
85 x 3400 = 3322 x 84.56 + 78 x X^a
Then X^ = 103.7

Forward Regardless of Weight

Ballast Weight = 2800 - 2642 = 158
72.64 x 2800 = 2642 x 72.74 + 158 x X^8
Then X^^ = 70.97

46

WEIGHT vs CG FOR RANGE OF LOADINGS

Forward Gross Weight

Ballast Weight = 3400- 2982 = 418

77.49 x 3400 = 2982 x 77.10 + 418 x X4ig

Then X4ig = 80.27

47


52

WEIGHT vs CG FOR RANGE OF LOADINGS

Beach Banana Airplane, Side View



53


54

z

87.73
111.00
137.76
69.00
78.00
52.00
65.00
105.00
92.00
92.00
100.00
100.00
100.00
80.00
80.00

100.00
82.00

100.00
100.00
100.00
100.00
100.00
110.00
87.00

FAR 23 LOADS

Diagram, Useful Load Envelope & Structural Limits



s
a

p<

^

56


58

WEIGHT vs CG FOR RANGE OF LOADINGS

Example output for Envelope of Loadings using M2002576:

ENVELOPE OF DISCRETIONARY LOAD FOR MODEL 575 OSING DATA FILE M2002576

ADDED XBAR ZBAR WEIGHT

MINIMUM WEIGHT 109.30 76.41 4480.1

CHART BOARD 109.27 76.42 4483.8

REST OF FUEL 111.90 77.47 5068.8

LIFE RAFT 112.06 77.63 5102.8

FIRST AID 112.10 77.61 5106.8

SMOKE CANDLES 112.15 77.62 5110.8

FLOAT LIGHTS 112.29 77.61 5119.8

VERY PISTOL 112.35 77.61 5123.7

OBSERVER 115.83 78.04 5323.7

DRIFT SIGHT 115.87 78.04 5325.3

MINIMUM WEIGHT 109.30 76.41 4480.1

DRIFT SIGHT 109.34 . 76.41 4481.7

OBSERVER 113.42 76.95 4681.7

VERY PISTOL 113.49 76.95 4685.6

FLOAT LIGHTS 113.64 76.94 4694.6

SMOKE CANDLES 113.70 76.95 4698.6

FIRST AID 113.74 76.94 4702.6

LIFE RAFT 113.90 77.11 4736.6

REST OF FUEL 115.89 78.03 5321.6

CHART BOARD 115.87 78.04 5325.3

59

AERODYNAMIC SURFACE GEOMETRY

The program WINGGEOM.BAS calculates the geometry for all the
aerodynamic  surfaces  on the airplane.  These include the  wing,
aileron,   aileron  tab,   flap,   horizontal  tail,   horizontal
stabilizer,  elevator,  elevator  tab,  vertical  tail,  vertical
stabilizer,  rudder  and rudder tab.  The smaller  single  engine
airplanes  usually have tabs on only the elevator or none at  all
if the horizontal stabilizer is adjustable in flight.

The input required is the coordinates of the points defining
the  leading  edge  and the trailing edge.  Two points  define  a
straight  leading  or  trailing edge.  Three  points  define  the
leading  edge  of  a wing with a leading edge  extension  at  the
inboard end of the wing like a Beech Bonanza. Three points define
a straight leading edge with a straight raked tip.  A Complex  or
curved  leading  or  trailing edge can be define by a  series  of
points assuming short straight lines between points.

The program prints out the area, aspect ratio, MAC, and butt
line and fuselage station of the leading edge of the MAC for each
of the aerodynamic surfaces. This output data is needed as  input
to the programs for structural speeds, flight loads and balancing
calculations, and selection of critical loads.

EQUATIONS

The equations used to calculate the geometry for surfaces

symmetrical about the center plane of the air plane are:

ALH=SUM(Cidy)

S=2Am

YBAR=SUM(yiCidy)/ALH

XgAR=SUM(XiCidy)/ALH

MAC=SUM(Ci2dy)/ALH

AR=(2y^p)2/S

where Arusarea on one side of plane of symmetry
S=total area of surface
Yg^p=butt line of MAC

Xg^p=fuselage station of mid point on MAC
MAC=mean aerodynamic chord (mean geometric chord)
AR=aspect ratio
y^jo=butt line of most outboard point on wing

61

FAR 23 LOADS

The equations used to calculate the geometry for
unsymmetrical surfaces are:

A=SUM(Ci<3y)
YBAR=SUM(YiCidy)/A
XgAR=SUM(XiCidy)/A
MAC=SUM(Cj2dy)/A

AR^Ytip-Yroot)2^

The equations to calculate the fuselage station of the
leading edge and 25 percent point of the MAC are:

XLEMAC=XBAR-> 50MAC
X25MAC=XBAR-25MAC

62


65

AERODYNAMIC SURFACE GEOMETRY

Example output for Wing Geometry:

AERODYNAMIC SURFACE GEOMETRIC PROPERTIES

WING
SYM ABOUT CL

COORDINATES OF LEADING EDGE

POINT NO      FUS STA (XLE) WING STA (YLE)

1            45            0

2            64.31301      46.5

3            72            201

COORDINATES OF TRAILING EDGE
POINT NO      FUS STA (XTE) -WING STA (YTE)

1             146           0

2             116           201

THE SURFACE IS DIVIDED INTO  20  INCREMENTS OF DY

AREA/SIDE  MAC
13257     69.246

ELEMENT DATA
ELEM      XLE

YLE(MAC)   XLE(MAC)   ASPECT RATIO
87.854     63.641     6.095

XTE

AREA

1	47.	.087	145.	250	5.	.025	98.	163	986.	.538
2	51.	.261	143.	.750	15.	.075	92.	.489	929.	.513
3	55.	.435	142.	250	25,	.125	86.	815	872.	.488
4	59,	.609	140.	.750	35	.175	81.	.141	815.	.464
5	63.	.783	139.	250	45.	.225	75.	467	758.	439
6	64	.750	137.	.750	55	.275	73.	.000	733	.654
7	65.	.250	136.	.250	65.	.325	71.	.000	713.	.554
8	65	.750	'134.	.750	75	.375	69.	.000	693.	.454
9	66.	,250	133.	.250	85.	.425	67.	.000	673.	.353
10	66	.750	131.	.750	95	.475	65.	.000	653.	.253
11	67	.250	130.	.250	105,	.525	63.	000	633.	.153
12	67	.750	128.	.750	115	.575	61.	.000	613.	.052
13	68	.250	127.	.250	125	.625	59.	,000	592.	.952
14	68	.750	125	.750	135	.675	57.	.000	572.	.852
15	69	.250	124.	.250	145	.725	55.	.000	552.	.752
16	69	.750	122.	.750	155	.775	53,	.000	532.	.651
17	70	.250	121.	.250	165.	.825	51.	,000	512.	.551
18	70	.750	119,	.750	175	.875	49.	,000	492.	.451
19	71	.250	118	.250	185	.925	47,	,000	472.	.350
20	71	.750	116	.750	195	.975	45	.000	452.	.250

67

FAR 23 LOADS

Example output for Aileron Geometry:

AILERON
NOT SYM ABOUT CL

COORDINATES OF LEADING EDGE

POINT NO      FUS STA (XLE) WING STA (YLE)

1             116.38        109

2             107.744       190

COORDINATES OF TRAILING EDGE

POINT NO      FUS STA (XTE) WING STA (YTE)

1             116.38        109

2             129.522       110.401

3             117.642       190

THE SURFACE IS DIVIDED INTO  100  INCREMENTS OF DY

AREA/SIDE  MAC        YLE(MAC)   XLE(MAC)   ASPECT RATIO
932     11.645    147.866    112.236     7.036

68

AERODYNAMIC SURFACE GEOMETRY

Example output for Aileron Forward of Hinge Line Geometry:

AILERON FORWARD OF HINGE LINE
NOT SYM ABOUT CL

COORDINATES OF LEADING EDGE
POINT NO      FUS STA (XLE) WING STA (YLE)

1             116.38        109

2             107.744       190

COORDINATES OF TRAILING EDGE
POINT NO      FUS STA (XTE) WING STA (YTE)

1             116.38        109

2             118.993       109.279

3             109.705       190

THE SURFACE IS DIVIDED INTO  100  INCREMENTS OF DY

AREA/SIDE  MAC        YLE(MAC)   XLE(MAC)   ASPECT RATIO
187      2.320    147.495    112.276    35.171

69 .

STRUCTURAL DESIGN SPEEDS AND MANEUVERING LOAD FACTORS

You  may  select the structural design speeds  and  maneuver
load  factors  providing  they are not  less  than  the  minimums
specified  by  FAR 23.335. The relationships  between  structural
design  speeds must also meet the minimum margins between  speeds
specified by FAR 23.335.

The  program STRSPEED.BAS calculates the minimum  structural
design  speeds  and  load factors. It verifies  that  the  chosen
structural  design speeds are not less than the minimum  required
or  brings  them  up to meet the minimum  requirements.  It  then
verifies  that the margins between the structural  design  speeds
are  not less than the minimum relationship required  or  adjusts
them to meet the requirements relative to cruise speed. Then  the
program calculates the mach limitations at altitude for V^ and Vp
when you specify the shoulder altitude. Mach limitations will  be
discussed  in a later paragraph.

The  program  STRSPEED.BAS also permits you  to  choose  the
category  in  which  you will  certify  the  airplane  ---normal,
utility  or acrobatic. An airplane may be certified in more  then
one category.

EQUATIONS

All  design speeds are in knots equivalent airspeed  (KEAS).
The equations used to calculate maneuver load factors are:

N(min)=2.1+24000/(W+10000)

IF CAT="N" and N(min)>3.8 THEN N(min)=3.8

IF CAT="U" THEN N(min)=4.4

IF CAT="A" THEN N(min)=6.0

IF N<N(min) then N=N(min)

IF CAT="N" OR CAT="U" THEN NNEG(min)=-.4N(min)

IF CAT="A" THEN NNEG(min)=-.5N(min)

IF NNEG>NNEG(min) THEN NNEG=NNEG(min)

IF CAT="N" OR CAT="U" AND NNEG>-.4N THEN NNEG=-.4N

IF CAT="A" AND NNEG>-.5N THEN NNEG=-.5N

where CAT=Category

N=chosen load factor

N(min)=FAR minimum required load factor

NNEG=chosen negative load factor

NNEG(min)=FAR minimum required negative load factor

"N"=normal

"U"=utility

"A"=acrobatic

The equations used to calculate structural design cruise and

85

