416yo 7x7 - dtic
TRANSCRIPT
AFFDL-TR-79-3032 • : ui.-"Volume T1
ADA08645 58
THE USAF STABILITY AND CONTROL DIGITAL DATCOMVolume HI. Implementation of Datcom Methods
416yo 7X7 .1350MCDONNELL DOUGLAS ASTRONA UTICS COMPANY - ST. LOUIS DIVISIONST. LOUIS, MISSOURI 63166
Reproduced From
APRIL 1979 Best Available Copy
TECHNICAL REPORT AFFDL-TR- 79-3032. VOLUME II 1E C: 'EFinal Report for Period 'August 1977 - November 1978
JUL 10 1980
A
Approved for public release;distribution unlimited.
0. AIR FORCE FLIGHT DYNAMICS LABORATORY0 AIR FORCE WRIGHT AERONAUTICAL LABORATORIES
C-) AIR FORCE SYSTEMS COMMANDIt' WRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433
SO 7 7 C38X..=.
NOTICE
When governint drawings, specificatiqons, or, other data are used fir anypurpose other than in connection with a defnitely related ,ovemrrawntprocurearent opextation, the United States Government thereby incur norespo•.sibility nor any obligation whdtsoever; and the fact that the govern-ment may have formulated, furnished, or in any way eipp lied the saiddrawings, specifications, or other data, is not to be regarded by inpli-cation or otherwise as in any manner licensing the holder or arW otherperson or corporation, or conveying any rights or permission to mannufaeti-re,use, or sell any patented invention that mny -in any way be related thereto.
This report has been reviewed by the Office of Public Affaizw (ASD•/PA) andis releasabZle to the National Technical Information Servioe (N2iS). AtNTIS, it will be available to the general public, includingoreign nations.
"This techn,.cazl report has been reviewed and is approved for pubZioation.
B., F. NIEHA USV.Acting Brwach ChiefControZ Dynamics BranchFlight Control Division
FOR TIHE COMfWDER
WORRIS A. OST9AAR•D
Acting ChiefFlight ControZ Division
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Copies of this report should not be returned unzless retur is required bysecurity considerations, contrictuaZ obligations, or notioe on a speoifodocumn t.
AIR PORCE/5H47/23 Juno 1IO0 - NO
elf-, • -.-- ,.m
_____ _ (r '7~L$//~00"UNCLASS IFIED)
sEcjUR7TY CLAS54FICAiTi..N Of T.f$r PAG jP'T-F.d
-Aý= TR-79-3032, VOTJNFIW T 1 I/ý T)~2C J
--I- T E(AdS 1,EPR PE4100 CAIOVERED
(/~ oh Wi~~as 'Sevn . V/ F,3615-77-C-3073jo ilasa&See VUkeliCh1 /
IPERFORM14G ORGANIZATION NAME AND0 ADDRESS 10 f'ROGR.AM EL.EMEr P
McDonnell Douglas Astronautc topn-t Loi 219&O~UINU~tics Boxa y-t 516i AFFDL Project No.
St. Louis, Missouri 63166 ~ ak8101
11. CONTROLLING OFFICE NAME AND .ODRESS KPWAir Force Flight Dynamics La') (FCC) Apr*t P7Wright-Patterson Air Force Base, WOhio 45433 155______________
14 MO0NITORING AGLM"V WANW-4 J%0OIFSS(II dileI'Ont I-o. Con'tlaling 0111-0) IS. SECURITY CLA;S lot this t.0ort)
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10. DISTRIBUTION STATEMENT (of this R.D..H,
Approvrd for public release; distribution unlimited.
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141. $UPPLE-AENTARY NOTES
None.
19 KEY WORDS (Co.,,t~no e~o.,e. 0,00 I1.t noc.tooo aen Identify by, block ftmobor)
USAF DATCOMAerodynamic StabilityHigh Lift and ControlLomputer ProgramFortran
20 AOSTITACT (Coýtnv~o O o.erI tOdo I ............ SAO Identifyp by block n~oe.)
* 7--ý-.This report describes a digital computer program that calculates staticstability, high lift and control, and dynamic derivative characteristics using
the methods contained in the USAF Stability and Control Datcou m s~~~
-.. 1476y. Configuration geometry, attitude, and Mach range capabilities are con-sistent with those accom~modated by the Datcom. The program contains a trim
option that computes control deflections end aerodynamic increments for vehicletrim at subsonic Mach numbers.,'Vcilume I is the user's manual and presents
DD 'J1473, EDI TION 01? 1 NOV 66 11 O§SO$.CTK UNCLASSIFIED
$9CURITY CLASI ATION OF 10N1S PAGE (Wheon 004 Enitletd4
811
UNCLASSIFIEDSLkCUMITY CLASSIFICATION Or TAIIS PLQOS(W 1 D#* *,.E) ,
---- program capabilities, input and output characteristics, and example problems.SVolume II describes program implementation of Datcom methods.,, Volume III dis-cusses a separate plot module for Digital Datcom.
T__ The program ,is written in ANSI Fortran IV. The primary deviations fromstandard Fortran are Namelist input and certain statements required by the CDCcompilers. Core requirements have been minimized by data packing and the use ofoverlays.
'User oriented features of the program include minimized input requirements,input error analysis, and various options for application flexibility.,
"*_.'h:. ! I;-..'. ±; : 1/ .. .
UNCiASSIFEDs$CURgTY CLA•SIFICATION OF tNIWS PA&GrMIM DaMa RAfhadl
I -I
FORE'JORD
This report, "The USAF Stability and Control Digital Datcom," describes
the computer program that calculates static stability, high lift and control,
and dynamic derivative characteristics using the methods contained in Sec-
tions 4 through 7 of the USAF Stability and Control Datcom (revised April
1976). The report consists of the following three volumes:
o Volume I,' Users Manual
o Volume II, Implementation of Datcom Methods
o Volume III, Plot Module
A complete listing of the program is provided as a microfiche supplement.
This work was performed by the McDonnell Douglas Astronautics Company,
Box 516, St. Louis, MO 63166, under contract number F33615-77-C-3073 with the
United States Air Force Systems Command, Wright-Patterson Air Force Base, OH.
The subject contract was initiated undfer Air ForcE Flight Dynamics Laboratory
Project 8219', Task 82190115 on 15 August 1977 and was effectively concluded
in November 1978. This report supersedes AFFDL TR-73-23 produced under
contract F33615-72-C-1067, which automated Sections 4 and 5 of the USAF Sta-
bility and Control Datcom; AFFDL TR-74-68 produced under contract F33615-73-
C-3058 which extended the program to include Datcom Sections 6 and 7 and a
trim option; and AFFDL-TR-76-45 that incorporated Datcom revisions and user
oriented options under contract'F33615-75-C-3043. The recent activity gener-
ated a plot modale, updated methods to incorporate the 1976 Datcom revisions,
and provide additional user oriented features. These contracts, in total,
reflect a systematic approach to Datcom automation which commenced in Feb-
ruary 1972. Mr. J. E. Jenkins, AFFDL FGC, was the Air Force Project Engineer
for the previous three contracts and Mr. B. F. Niehaus acted in this capa-
city for the current contract. The authors wish to thank Mr. Niehaus for his
assistance, particularly in the areas of computer program formulation, imple-
mentation, and verification. A list of the Digital Datcom Principal Investi-
gators and individual.s who made Fignificant contributions to the development
of this program is provided on the following page.
Requests for copies of the computer program should be directed to the
Air Force Flight Dynamics Laboratory (FGC). Copies of this report can be
obtained from the National Technical Information Service (NTIS).
This report was submitted in April 1979.
PRINCIPLE INVESTIGATORS
J. E. Williams (1975 - Present)
S. C. Murray (1973 - 1975)
G. J. Mehlick (1972 - 1973)
T. B. Sellers (1972 - 1972)
CONTRIBUTORS
E. W. Ellison (Datcom Methods Interpretation)
R. D. Finck
G. S. Washburn (Program Strature and Coding)
- ~iv{I ,
I I ,
TABLE OF CONTENTS
Section Ti tie Page
1.* Introduction . . . . . . . . .* . . .* . . . . . . . . 1
2. Pro gram Organization . . . . . *. . . .* . # -. 35
3. Equations for Geometric Parameters .* .... . . . . . 37
4.- Incorporation ofMethods. .. .... . .. .. .. .. . .67
5. System Resource Requirements . . . ..... . . . . . . . . 107
b. Program Conversion Modifications . .... . . . * **109
7. Program Deck Description . . . . #...... . . . . .. . 111
Reference s .* **** . . . .* . . . . . . .155
V
=110- -*. A -- -
LIST OF ILLUSTRATIONS
Figure Title Page
1 Overlay Program Structure.......... . . . . . . . ..... . .. 36
2 Planform Nomenclature ........... ......... . 38
3 Sweep Angle Nomenclature . . . . . . .... . . . . . 40
4 Exposed Mean Aerodynamic Chord Nomenclature. w . . . . . . . . . 42
5 Theoretical or Reference Mean Aerodynamic Chord Nomenclature . • 42
6 Special Wing Pitching Moment Geometry . . . .. . . . . . . . 43
7 Supersonic Nonstraight Wing Planform. 44
(AL <A )AS0 1I".48 Supersonic Nonstraight Wing Planform 4 . .... . .46
(AL > AL )0 19 Equivalent Dihedral Angle Nomenclature . . . . 48
10 Vertical Tail Geometry . . . . . 4q.
11 Supersonic and Hypersonic Body Geometry . ..... .... . 51
12 General Synthesis Nomenclature . . .......... . 52
13 Downwash Nomenclature". • . 54
14 Definition Sketch for Propeller Power Effect Calculations . . 57
15 Geometry for Determining Immersed Wing Parameters . . . * * * . 58
16 Geometry for'Determining Immersed Wing Parameters (Continued) .59
17 Geometry for Determining Immersed Wing Parameters (Concluded) * 60
18 Definition Sketch for Jet Power Calculations ....... . 61
19 Ground Effect*Wing and Tail Heights . . . . . ....... . 64
20 Ground Effects Planform Parameter AX . . .... ... . .. 65
21 Airfoil Section Module - Executive Routing . . . . . . . . . .. 70
22 Airfoil Section Module - NACA Designation Routine'.,. ..... * 71
23 Airfoil Section Module - Section Aerodynamics Routine ... 72
24. Airfoil Section Module - Section Maximum Lift 'ioutine ...... 73
25 Asymmetric Body Geometry Inputs • • . • ......... . . . 94
26 Potential and Vortex Lift Components .9.4..... .. . , 4
27a Correlation of a 95• V
27b Body Thickness Parameters .9........ .......... 5
28 Potential Lift Center of Pressure .,. ...... ....... 96
vi
_..._ _. . - i ". . . - ".. . . : . ' . 1,
LIST OF TABLES
Table Title Page
I Summary of Digital Datcom Methods . . . . . . . . . ... 2
2 Subsonic Data By Overlay . * . . . . . . ........... 31
3 Transonic Data By Overlay. . .. ... ....... . .. 32
4 Supersonic-Hypersonic Data By Overlay ........ ..... 33
5 Airfoil Section Module Routine Description . . . . * . . . ... 68
6 Programmed Transonic Second Levul Methods Summary . .. . .. 84
7 Digital Datcom Overlay'Description .. .. . . . . . . . .. 112
8 Frogram Common Deckso ............... . ... . 134
9 Digital Datcom Routine Description .. . . . ... . . ... 135
10 Control Data Blocks . .......... ... •..... .. 151
- -
SECTION I
INTRODUCTION
Digital Datcom calculates static stability, high-lift and control
device, and dynamic-derivative characteristics using the methods contained in
Sections- 4 through 7 of Datcom. The computer program also offers a trim
option that computes control deflections and aerodynamic data for vehicle
trim.
Even though the development of Digital Datcom was pursued with the
sole objective of translating the Datcom methods into an efficient, user-
oriented computer program, differences between Datcom and Digital Datcom do
exist. Such is the primary subject of this volume, Implementation of Datcom
Methods, which contains the program formulation for those methods in variance
with Datcom -iethods. Program implementation information regardirg system
resources necessary to make the program operational are presented in Sections
5 and 6.
Section 6 also lists each of the routines and references tieir appear-
ance in the program listings provided as a microfiche suppleiment to this
volume.
Users shou?.d refer to Datcom for the validity and limitations of methods
involved. However, potential users are fore-warned that Datcom drag methods
are not recommended for performance. Where more than one Datcom method
exists, the summary in Table 1 indicates which method or methods are employed
in Digital Datcom. Tables 2, 3, and 4 define the basic output data in each
Mach regime and shows the overlay in which each is computed.
The computer program' is written in Fortran IV for the CDC Cyber 175.
Through the use of overlay-and data packing techniques, core requirement is67,000 octal words for execution with the NOS operating system using the FTN
compiler. Central processor time for a case executed on the NOS system
depends on the type of configuration, number of flight conditions, and
program option selected. Usual requirements are on the order of one to'two
seconds per Mach number.
Direct all program inquires to AFFDL FGC, Wright-Patterson Air Force
Base, Ohio 45433. Phone (513) 255-4315.
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SECTION 2
PROGRAM ORGANIZATION
The Digital Datcom program consists of a MAIN program, EXECUTIVE,
subroutines, METHOD subroutines and UTILITY subroutines. The organiza-
tion and interfaces between these program components are shown in Figure 1.
The MAIN program performs executive functions that control and direct all
computations; the EXECUTIVE subroutines perform noncomputational tasks, which
include input data maniipulation and selection of output formats; UTILITY
subroutines perform standard mathematical computations; and METHOD sub-
routines implement the ,Datcom stability methods.,,
35
- • - - i Il.l.4
START
EXECUTIVE SubroutinesMAINPULATE INPUT DATA,PERFORM ERROR ANALYSISINITIALIZE ARRAYS TO 10SET LOGIC SWITCHES.
MAIN ProgramPERFORMS THE
METHOD Subroutines EXECUTIVE FUNCTIONSCALCULATE AERODYNAMIC OF ORGANIZING ANDCHARACTERISTICS AT PFDWRECTDNG THE TASKSANGLE OF ATTACK AND PERFOT ED'BY THEIN SIDE SLIP. OTHER PROGRAM
EXECUTIVE SubroutinesDUMP ARRAYS OF STOREDVARIABLES IN READABLE
UTILITY Subroutines - FORMAT, PRINTS APPROPRIATEPERFORL STANDARD OUTPUT HEADINGS, CASEMATHEMATICAL TASKS IDENTIFICATION INFORMATION,
REPETITIVELY REQUIRED AND, RESULTS OF COMPUTATIONS.BY METHOD SUBROUTINES.
END
FIGURE 1 OVERLAY PROGRAM STRUCTURE
36
Si~~~2 -
SECTION 3
EQUATIONS FOR GEOMETRIC PARAMETERS
One of the main features of the Digital Datcom program is that a
minimum of input data are requited. Minimal inputs require the program
to calculate basic geometric parameters required by the Datcom methods.
Equations for pertinent geometric parameters are defined in this section.
3. 1 PLANFORM PARAMETERS
The nomenclature used in the equations for calculating 'theoreti-
cal and exposed planform areas, taper ratios and aspect ratios are shown in
Figure 2. Equations for these parameters are presented below for a double
delta or cranked planform. Straight-tapered planform parameters are obtained
by setting b* /2 - 0.0, Cb -Ct, A* - 1.0 in the following equations:
b/ 2 - b/2 - b0 /2
b* 12) (b b/2)
Cb/ -Cr[l+(-x)r*,
S-b
wI obCW 0i
lnC /C
s3 -(C + C) b /2
* +*
SW 0
• ~ ~37 .- t-*"W N ftm= W _7
SI- (C.. - C).,
•,• • Li_• • " • m 1 b b,* ••-I•••-
o REQUIRED INPUTSALL PLANFORMS
- REQUIRED INPUTS,b. OUBLE DELTA
ANDCRANKED PLANFORMS
"INDICATES EXPOSEDPARAMETER
X; £ . - TAPER RATIO
A - ASPECT RATIO
S -AREA
bI , SEMI-SPANN% SUBSCRIPTS
I -k INBOARD PANEL
.............................0 - OUTBOARD PANEL
2 TOTAL WING
2
FIGURE 2 PLANFORM NOMENCLATURE
38
__ _ -2 __
S. •• _..~ ~~ ~ • • -• -, -. .. • - ."2- .'- " "-- - --,,,-*-,•di . . .. .
- I,
Swo (Cr Cb) bb/2 +S
- 4(b%/2) IS/
A* 0 4
*- 4Cb/2) 2/sW
Datcom methods use correlations that are based on wing sweep angles
measured at various chordlines. The nomenclature used to calculate sweep
angles is presented in Figure 3. Sweep angle equations are presented below
for a double ,delta or cranked wing. To obtain straight taper wing siweep
angles set C and A = 0 in the following equations:0
C1 - 4(1- A*ý/[A* (1 + 1*1)]
Co - 4(l - A* )/(A* (U + A*O)]
AuL tan 'CC, (r-n) + tanhm],
A% -tan 1 CC (r_-n) + tanAm 0
-1 ***(Andef cos- ](S, coo An, + SO-cos Ano)/S I
The nomenclature used to calculate the exposed mean aerodynamic chord
(MAC) for a double delta or cranked wing is shown in Figure 4. The param-
eters necessary to define the lateral and longitudinal location of the
exposed MAC are included. Equations to calculate and locate the MAC are
presented below. To obtain values for a straight-tapered wing set C* - 0,0o
Y*- 0, S* - 0 in the equations below:0 0
\c1 - 2C:(1 + A* + 2),/3(1 + A*)
C 2C Ub( +o + A*/MUl+ X
39
......I
(~\REQIUIRED INPUTS
ALL PLANFORMS
f REQUIRED INPUTS\-) DOUBLE DELTA
ANDCRANKED PLAN FORMS
m =PERCENTAGE CHORDAT WHICH SWEEP
AloolANGLE IS DEFINED
n =ANY CHORD LOCATIONAoo EXPRESSED IN
PERCENTAGE CHORD
FIGURE 3 SWEEP ANGLE NOMENCLATURE
40
24
=(s C + S C *)ISC 00
Y ( - b /2)(1 + 2X )/3(1 + X P-* * * * ,,
Y- (b /2)(1 + 2 X )/ 3 (l + X ) + b '2*O-, O-
Y s Y+S Y )/Sx , ^o * * .-* **
"Xo [SIY1 IanAoI +S(bb/2 tanAoI + (Yo -bb/ 2 ) tanAoo)]/S*
X -C /2 + X;V
Xr C /4 + X;
The theoretical or reference mean aerodynamic chord is calculated
with nomenclature of Figure 5 as follows:
C "2C ( + x + xI)/3(l + XI)
Cr (SI CI + S C)/S
xr Cr /4+Xr
Special geometric parameters are required to calculate wing pitching
moments. The nomenclature used to define these parameters is presented in
Figure 6. Equations' for these parameters are presented below:
*• "'~ / t* ~ b+ 1 * a o)I*r
(b b. , bb/2 tanAooI + 0)/C
AI 4(bbI 2 ) 2S,
A¥Y = bbl 4
(bo/2)' = bb/ 4 +'bo/2
41
• ' • - - ,---- • " . . . '---Y-,,-- 4
I IT
Xr
ClC
~Cg
FIGURE 4 TEXORETIADRREEEC MEAN AERODYNAMIC CHORD NMNLTR
NOMENCLATrE
74
0-c;-C-l-
I..
I \\I \I
I'I
C'bb
I I!II
--- _b_2--r b
FIGURE 6 SPECIAL WING PITCHING MOMENT GEOMETRY
43
"- I. • G,,•--r-• ....
-
.. . . .. . , ,- -
--. -•
GLOVE COMPONENT
BASIC WING COMPONENT
________ * TRAILING EDGE EXTENSION COMPONENT
A LEI
(S~g SS, GLOVE
Cr Cb
lrbw
Ct
b/2'
FIGURE 7 SUPERSONIC NON-STRAIGHT WING PLANFORM (ALE'o< ALEI)
44
im 4,
C cb t
Cb' = C + (b /2)'b t obb/2
0
(So) =.(Cb" + Ct.) (b */2)
* 2 *(A = 4[(b 0 /2) ](S0)
(Xo)' = Ct/C
Supersonic nonstraight wing analyses require the wing to be synthesized
from basic wing, glove, and trailing edge extension components as shown on
Figure 7. When the leading edge outboard sweep angle is greater than the
leaaing edge inboard sweep angle, an additional geometric parameter, S2' is
required and is shown in Figure 8.. Equations. for calculating geometric
parameters for the various wing components as required by the stability
methods are presented below.
All PlanformsbC-)-bTan
(C*)bw Cb + b - [ ][Tan ALE TanATE.0 0
* [(C) + C ] b*basic Sbw rbw t
* wing 2component 2
bw -bw
(C*)r bw
(Crg (Tan A ) (T- b°0
glove S* (C*) (.-bo*
g"component A' 4 "b°*1i
A* 2 2g S*•
A -0g
45
w, -,
~Sbw
LEI
J JA E I
LE0
FIGURES8 SUPERSONIC NON-STRAIGHT WING PLANFORM (ALEO,>ALEI)
46
.........
trailing
edge b* 2 (b-- -
extension e 2 7span
If > S*2 s- (tanLL 0 2 ( LE)
S1 S bw
Geometric parameters required for horizontal and vertical tail analyses
are identical to those for wings. Tail parameters can be calculated by
substituting tail geometry for wing geometry in the wing equations. Vertical
tail lateral stability calculations require additional geometry parameters as
shown in Figures 9 a and 9b. Equations are listed below:
Straight Tapered Vertical Tall
Cv a Cr - (Cr - Ct) (Z1 )l(b.,'2)
X -zH (TanK.I)
\on-Straight Vertical Tailb b*
ifZ v o2 2
b b* b* bX - +" +(R- Xv -(- - ') (TAN ,LEI) - (ZH + -1 ) TAN A
b b*
-V c t + (C% - ct)( )b b*
If Zl < v 02 2
X - i + - v. -H (TAN ALEo)
V 0C,, r C- r -Cb)(zF:)/ (bv b )....
2 2
For a horizontal lift'ing surface, an equivalent dihedral is defined as
follows:r b* )rl ) + 0o(
eqb*,
47
C - ~ - * .- ----~--- S
Ivbv
4 + ZN
_ C_________
FIGURE 9(a) STRAIGHT TAPERED VERTICAL TAIL GEOMETRY
----
A LEI
FIGURE. 9(b) NON-STRAIGHT TAPERED VERTICAL TAIL GEOMETRY
48
__ -+
(b/21ro-
FIGURE 10 EQUIVALENT DIHEDRAL ANGLE NOMENCLATURE
49
3.2 BODY PARANETERS
Longitudinal stability analyses for bod!es in the supersonic and hyper-
sonic speed regimes require the body to be synthesized in nose, afterbody,
and tail segment components as defined in Figure II. Geometry parameters for
the various body segments analyses are defined below:
RB iN + •A
tBT = B• B
d d! + d,cyl 2
Sp fJB r. (dx) Body planform area
02Sb ' 'd2 Body base area
4
a2fB r x (dx)0 Distance from nose of body to centroid of
Sp planform area
VB - fZb S (dx) Volume of body
0
If d2 > di, calculate flare angle f M TAN-11 "5(d 2 -d 1
L IBT
If d 2 < di, calculate boattail angle OB - .A_ 5(d1-d 2)
3.3 GENERAL SYNTHESIS PARAMETERS
Synthesizing and interference nomenclature for longitudinal and lateral
stability calculations are defined in Figure 12. The geometric' parameters are
presented In equation format below:
Xw,- (b/2 b'/2) TA. Ao1 cos (aQ,
Ax c- Xc s- + * w)
(Xac)v * (Xac*) C*; where (X /C*) i. calculated in wing pitching
moment subroutitne
*50 - -- "f
so-.
itif~ na [1=mop>
I'd,. d
POSSIBLE SUPERSONIC AND HYPERSONIC BODY CNFIGURATIONS
IN
NOE IA-IST- 0 NOTES:d~x d1 u dl NOSE AND TAIL SEGMENTS MAY BE CONICAL
< (AS SHOWN) OR OGIVAL
DIAMETERS dN d1 AND d7 ARE COMPUTEDFROM LINEAR N EROLaTION OF
IN INPUTS zi VS R
NOSE-AFTER BODY 1BTU 0
IINN
IA
NOSE-AFTER BCODY-IlL
dl.
I'0NOSE TA IL 'ST
djud
FIGURE 11 SUPERSONIC AND HYPERSONIC B3ODY GEOMETRY
51.
XWX
XCG-
-if2
I -(cr)H
7 318-
FIGURE -12 GENERAL SYNTHESIS NOMENCLATURE
52
(AXa)w =AXcg -(X A)w COS (az)w
AXN - (b/2 - b*/2)iH TAN AoIH COS (aci)H
(AXcg) H xcg - (XH + AX1 )
z*- z - TANH H H H A
(Xa)P n (Xa/C*)H C*
(Za) - - (Xa) SIN (ai) -zac H H ac H i H cg
A(Xac)H- (AXcg)H- (Xac)H COS (a i)H
¢XZ/4I- XH - (Xr)H COS (ai)H
Z' -Z + (C /4) SINciv w r i
Lf x +4AX +( o) TA A, + (b*)A -2 o 2 I 2
0 .
p 1X - Xcg + (Xr)w + C(r)'v4
ZP Zcg + (YR)v
3.4 DOWNWASH PARAMETERS
Downwash geometric nomenclature is defined in Figure 13. The equations.
presented below are used primarily in the subsonic speed regime:
z- ZH - xr SIN (¢i)1 - Zw + C SIN (ai)H -
ZH' TAN (cii)w
LTu L H -4L 1,1
AhH - Z'/Cos (Ci)w
53 1 P
" " " • • • i n |
___________...............................i)~
REFERENCE - -i
FIGURE 13 DOWNWASH NOMENCLATURE
54
E eff
C NOTE: t etf IS MEASURED INtef CHORD PLANE OF WING
4 Ctelf
A01
VORTEX SPAN - beff
(Cr)H
4
REFERENCE
I> xci
FIGURE 13 DOWNWASH NOMENCLATURE (CONCLUDED)
55
*oil
Ah2 - LT SIN (ai)w
h H 0Ah H+AhHh H .AH 1 +•H 2
9.2 = LT COS (01i)
Y - ARCTAN (hH/I 2 )
9.3 W (Cr) %- (Xr)
If bef f/ 2 < (b/2 - b*/2)%wteff0
C -C C-r Cb 71 (b ef/2)teff b2 - b*/2 eff
w
Eeff (beff/ 2 ) TAN AoI + C t /4eff
keff 1 2 (Eeff C )
If,b /2 > (b/2 - b*/2)eff 0
Cb - CtCt bo/2 [bff/2 - (b/2 - b*/2)]C *2eff 0w
Eeff ' (b/2 - b*/]) TAN Ao1 + [bff/ 2 - (b/2 b*/2) TAN Ao + C /40 w I ef0 V 0 t eff
I eff 1 2 .(E -Cr )ef r
3.5 POWER EFFECTS P.11.A METERS
Geometric parameters required to calculate propell'er-and jet power
effects are defined in Figures 14 through 18. Power'effects are only cal-
culated for longitudinal stability results in the subsonic speed regime.
56
i .______ _.__________
+Z
--- Xr a! p --- ' O ERo T I• _._
)( RPFPOWER ON S A
PRPROPELLER , C "' -I
+a- PLANE +z+it A / ZHF
MACý!MC IHORIZONTAL
4 " I TAILMACa rNRJSTA
+ a " " "- "XCG - -- ) 1-• "GCG
( -. ~ WING MAC +
+aiw4
= Xw +Xw COS %i-X t"• = Zw -Xrw SIN aiw
=P = aSCH+uit+uPii = ZT +Xp TAN a
. t = z, -ZT + [Xh h COSa, c -,X)TAN•'TI
= k COS jhahI. - X k-CSa,
4EFF = Z -Zh + IIh TAN (a'p_..EPOWER)
FIGURE 14, DEFINITION SKETCH FOR PROPELLER POW -R EFFECT CALCULATIONS
57
atom~ ~t
. ./,. o'\CASE! I /
SINGLE ENGINE
I Cti
2 2b2
C, -,b b f. ,ic =i Cr - .2 b * - b o/2J [ = [ .It I T ]; )
h,* ~bi j b!b 3(l +A)
,tL*X. =Y~TAN A
"I ' =
cA1 121 +I
Ai4
pti
3 (1 +N)
FIGURE 15 GEOMETRY FOR DETERMINING IMMERSED WING PARAMETERS
58
_ _ _ _ _ _, . .~..-- . . / 1-.;•.-o . ., , , . .4-
CASE?2ý," Ž( !2 - 2'Z
SINGLE ENGINE
bi 22
b
IE2
_ bo C oCt212 2 21=
C, -Cf bo,1
'I~~~b* 10 1 +C4C1jsI 2
'•" + •,~I TAN 0''o+s(.• TANAo,+(V,-•'.)TA i o) :
-, ,,( +,o; +• . , 2 ---------- + +[
" +,31) S.
-;.. x*
rI*
FIGURE 16 GEOMETRY FOR DETERMINING IMMERSED WING PARAMETERS (CONT'D) .
59
C~l s,~~~~~~
~ , ,..:+;.++~~~~~~~~~
= -•: I .+ ,+,••.,.••++.
CrCr
b/2
(cr -ct) YpIF b*'20.0 Crp Cr - /
IF yp b/2 -b*0i2 C - (Cr Cb/) -vt
* ~(Cb - Ct) (yp- b/2 +1 b'~oMIF yp>b/2- b0/2 Crp =Cb 02
S-'i2 [(bi29 r pIMMERSED AREA FOR TWO ENGIIIES
A*~ 0.um S~.
C1 Crp
FIGURE. 17 GEOMETRY FOR DETERMINING IMMERSED WING PARAMETERS (CONCLUDED)
60
J ~ 4~*
-X -
CTAI
T INLET MAh
TAI
Z'J(X+(~cS@~X)SIUZaT CGcS@
Zh z X
FIGUE 1 DEINIIONSKECH O E OERCLUAIN
61x
__ _ _ ___ _ __ _ *
~ ~ MA C
- - ~ ~ , - ~ . ~r-'-- -4
3.b GROUND EFFECTS PARAMETERS
Ground effects are only calculated for longitudinal stability results in
the subsonic speed regime. Lifting surface heights that are required by the
Datcom ground effect analyses are defined in Figure 19 and are presented in
equation format as follows:
Equations for Calculating hO;5b,"i
IF r, = 0 ANO (b 2))r 0.25 (b/2) hO.75b,7 h4.75C, , 5X TAN (aj)y
IF F,: 0 AND (b 2)r, > 0.25 (b!2) 0.75b,2 1 ht.75Cr z TAN r. (bi2w- 0.25 (b/7)I +AX TAN (ai w
IF r, 0 ANO (b 7)r,= 0.25 (b'2) ho.75b 2 2 ho.75C, + 0.7,5 " TAN ri+ AX TAN (a N
IF r, #0 AND (b 2)r,~ 0.25 (b,". NO.7$s, *: lt.M + [b/ - (b!7IQ TAN ri +
"b/2)r -OMb/2)l TAN F.,+ AX TAN (ai)e
Equations foc Calculating h
h a l'Z.5Ct + 40.75b/'2) ho.k75C HG + ZV 0.715 t TAN (aiW)
IF r. - AND (b/- • 0.25 (b'2) h * N. 75CC + 0.50 TAN to1~
IFr a 0 AND (bt- 0.25ci (11/7) h 1 +j*0,50 jTAN F@{(b/Pr~ -0.25Mj24. X TANi
IF r1 , IAND (bZir a U.S (bill h a hO7C -01.5 A A m
IF r, 0 AND (b,?ir 0.25 (b/) ha %0.75C, +0.50l1 W2) -k/2IQ .TAN r ,+
0.50 jký - 0.25 (01TAN r. + 0.50 aX TAN ,ij~
Equations for Calculating H
(h". G u 'ZR (7(,)W TAN I. 1V
IF r vi0.AND (r)W,U jh/7 - (b/')r,J 111 (lzI )
IF r, a AND (;,j - b/7 -2r~ WuTý) b(IW~2 ,71TAN r@
I F r $0ANO'(7y~w a t -H- (111~ Nuj,)..W TAN r,
IF r, J @ANI) (jý 10 - (b/2r41 H a Ib,2 - #bY A2I,4 rA + F i-, - (b/24, .b/21 TANr,
62
u ft .& wo w. ... . - " - • . . . . . . ' • " • • e • • - - - e•
Equations'for Calculating HH
(er )H= +-• TAN (oi!H
+++~ ~ ~ ~~H +0 2++ 14 (•)i++YH++++IF r1 = 0 AND
oyH - (b
1IF r. = 0 AND 7d b7H- (b?ýOhj)H = V;,4 +CyH + (b, 7* 1011 (b;27HiJ TAN r.
IF r. f 0 AND CdHlb? - (b.ý HH = (h-;- 4+ CriH TAN 1-HI 'H
'F r. i 0 AND -Y()" (,11 - (b.2),I- JH = (hC.4N+ J(b 2)H~ - (b,?Yc. HJTAN r 'H
+lrI~w.+ b2ý O - (b.7)1,1TAN r.H
Ground effect methods require calculation of a planform parameter,4X, in addition to the previously defined ground heights. This param-
eter is shown in Figure 20.
,63
--Lr
O'W
AC0.75-0.75C-
"C4 HPPLANEA SA lA
rr
0.75 ( 11/71 .%,
-~ -- - - - - - 0e
, ~ ~~~~~~1/4 CHORD ••.!07b2__.,
Z W
hcr 14 H G ( )WRFho.25Cr
VIEW A-A
GROUND
hO.75 Cl = HEIGHT OF 314 CHORD OF WING ROOT CHORD ABOVE GROUND
= HG + Zw-4.75 Ct TAN (a i) W
hcr 4 = HEIGHT OF l,'4 CHORD OF WING ROOT CHORD ABOVE GROUND
= hO.75Cr + G50 CITAN (a i) W
h0.75 VZ2. " EIGHT OF WING ABOVE GROUND AT 1,14 CHORD OF WING 75%, SEMI-SPAN CHORD
h AVERAGE ý EIGHT ABOVE GROUND OF THE 1/4 CHORD POINT OF WING CHORD AT 75% SEMI-SPAN
AND THE V4 CHORD POINT OF THE W/ING ROOT CHORD.
='C,50 Nh.75 IV2 + hO.75 Cr)
H z HEIGHT OF 1/4 CHORD POINT OF WING MEAN AERODYNAMIC CHORD ABOVE THE GROUND
Hm z HEIGHT OF 1/4 CHORD POINT OF HORIZONTAL TAIL MEAN AERODYNAMIC CHORD ABOVE THE GROUND
FIGURE 19 GROUND EFFECT WING AND TAIL HEIGHTS
. 64
Straight Tapered Wing
&X = 0.75Cj -0.75 (b,,?) TAN A'25
Cranked or Double Delta Wing
IF bo/.2 0.25 (b'2) aX= 0.75 Cr - 0.75(b/,2) TAN A2ý
IF b*0,j >025 kbi2) Ax 0.75Cr - TAN A25 b;/2 - 0.25(b/7)1 - TAN A251(b0) -lboI
Straight Tapered Wing. Cranked or Double Delta Wing
~Cr 07 C
I \
.--,..,,--.,-• -- 3/4 ^ 51/4• CHORD- CHORD 1A• CHORD A25 V/2
FIGURE 20 GROUND EFFECTS PLANFORM PARAMETER %X
65
S• - ,- ,. - , -•
SECTION 4
INCORPORATION OF METHODS
This section summarizes those methods which were incorporated into
Digital Datcom but were not defined in the Datcom Handbook or involve method
interpretation. Though some of the nythods included are not, in, general,
standard Datcom methods, they permit greater flexibility in using the pro-
gram, and provide output for some parameters which can be closely approxima-
ted or are difficult to obtain experimentally. All of the methods presented
in this section are referenced to Table I of Section I and the Datcom.
Methods, or procedures, not outlined in this section follow the Datcom method
and users should consult the Catcom for method limitations and formulation.
4.1 AIRFOIL SECTION AERODYNAMICS
This section describes a procedure that can be used to obtain the
geometric and aerodynamic section characteristics of virtually any user
defined airfoil section. Its incorporation into Digital. Datcom frees the
user from the labor of calculating those section parameters that were re-
quired inputs, yet allow him the flexibility to alter those parameters for
which he has data.
The Airfoil Section Module, will accept the following user inputs:
o The airfoil section designation
o Section upper and lower cartesian coorainates
o Section mean line'and thickness distribution
By these three methods,, many airfoil sections can be described' and the sec-
tion characteristics calculated.
-Since the Airfoil Section Module (ASN) use's the Mach and Reynolds number
inputs, they must ba defined' in namelist FLTC0N using MACH and RNNUB. How-,
ever, the ASH' uses the unit Reynolds number and 'by implication treats a
section one foot (or meter) in length.
This module. brings together the outstanding features of two separate
studies. -Kinsey ind Bowers (AFFDL-TR-71-87) have'. written a program that
calculates the airfoil coordinates of select NACA designations, then uses the
Weber technique to calculate the section aerodynamic characteristics.
Nieldling of McDonnell Aircraft has written a similar program using the Weber
method, then incorporates additional methods to refine the theoretical
67
_ _. '\
TABLE 5 AIRFOIL SECTION MODULE ROUTINE DESCRIPTION
PROGRAM/SUBROUTINE PURPOSE
M5002 (OVERLAY 50,0) MODULE EXECUTIVE PROGRAMINIZ INITIALIZE IOMSECI READ USER INPUTSSECO TRANSFER MODULE OUTPUTSCSLOPE CALCULATE VARIABLE SLOPE FOR SUPERSONIC AIRFOILSXYCORD CALCULATE AIRFOIL SECTION FROM USER INPUTSDELY CALCULATE DATCOM PARAMETER.AY
AIRFOL (OVERLAY (50,1)) MAIN PROGRAM FOR NACA DESIGNATION INPUTSDECODE READ USER INPUT NACA DESIGNATION, DECODECOORO4 CALCULATE 4-DIGIT NACA AIRFOILCOORD4M CALCULATE 4-DIGIT (MODIFIED) NACA AIRFOILCOORO5 CALCULATE 5-DIGIT NACA AIRFOILCOOR05M CALCULATE 5-DIGIT (MODIFIED) NACA AIRFOILCOOROl CALCULATE 1-SERIES NACA AIRFOILCOOROB CALCULATE 5-SERIES NACA AIRFOILCORDSP CALCULATE SUPERSONIC AIRFOIL COORDINATESSLED SIMULTANEOUS LINEAR EQUATION SOLVER
THEORY (OVERLAY (50,2)) MAIN PROGRAM FOR AIRFOIL AERODYNAMICSIDEAL CALCULATE SECTION IDEAL AERODYNAMICSSLOPE CALCULATE LIFT AND MOMENT SLOPESASMINT NON-LINEAR INTERPOLATION ROUTING
MAXCL (OVERLAY (50,3)) CALCULATE VARIABLE CLMAX FOR SECTION
68.
.v .-'CS
* C *.." -* C''
predictions. A cross of the two procedures (coordinates of NACA airfoils and
viscous correction from Kinsey and Bowers, and the aerodynamic methods of
Nieldling) yields a program that generates fairly accurate results.
The module is incorporated into Digital Datcom as Overlay 50, and
includes three secondary overlay programs. The routines use the IOM arrays
for data storage so that core size will be kept to a minimum. Table 5
describes each of the 22 module routines and the logic flow of the module. is
presented in Figurees 21 through 24.
4.1.1 Weber's Method
The calculation of the pressure distribution over the surface of
an airfoil in an incompressible inviscid flow is accomplished by use of
the method of singularities. Conformal transformations are used as an
intermediate step in deriving the methods for determining the distributions
of singularities from which the velocity distributions are calculated. The
routine inputs are the airfoil coordinates distributed in any fashion, the
angle of attack, and the Mach number. The airfoil shape is defined by curve
fitting the input coordinates to obtain the airfoil geometry at thirty-two
required points, i.e.; SX = 0.5 (COS e + 1)
e = vn/32 for o<v<32V _
The chord line is obtained by joining the leading and trailing edges
of the airfoil, where the leading edge is defined as the forward most point
so that all points on the airfoil surface have a positive x coordinate.
The airfoil is placed in a uniform stream V at an angle of attack0
relative to the chord line. The velocity V is resolved into compcnents0
parallel and normal to the chord line.
V - V cos aXo 0
V - V sin.zo 0
Combining the results for the parallel and normal flows, the velocity
distribution equation for a,symmetrical airfoil at angle' of attack is
V0 dzsr+J. ( dx'
V(x,z) C a +"2 1 L r dx' x - X
+ (dz/dx)21 [T T .Jx' X - d ]
0
+ sin + 2 z W) dx-'d, 1 - (1 - 2x')
69
pW,- -A '' :',,,. .. , 6
OVERLAY
CALL INIZ INITIALIZE I.O.M. ARRAYS TO BE USED
IN-0
FORIN =I.DOWING
IN - N +1IN = 2, 00 HORIZONTAL TAILIN=IN~1IN s3,DOVERTICALTAIL
I IN -4,O3OVENTRALFIN
ITIN>I ALSC IFI E
DEIE
TINFIAC
CSLL CALLE
FIUR 2 ARFILSETIN ODLE XECUTIV ROUTRLNG
(701
STAR CALULATLo m. NEXTXOV*
OVERLAY150,1)
=7 CORRS6
FIGUEL2 AIFI SETO ODUL CAAAEINAINLOTN
COOR14 NA O71.
--2* -5
CAL- CAL
CO04 .3 04C0 0
OVERLAY150,2)
CALCULATE IDEAL AERODYNAMICCALL PARAMETERSIDEAL aiJ ao. a OL, CLi., Cmc/4
CALLSLOPE CALCULATE Cl a @M=O
(M= 0.0)
I, ICALL MACH LOOP. CALCULATE.SLOPE Cl AT EACH MACH NUMBER INPUT
RETURN
FIGURE 23 AIRFOILSECTION MODULE - SECTION AERODYNAMICS ROUTINE
72 i
, \
OVERLAY
(50.3)
ClMAX FIGURE 4.1.1.4-5
(B~ASEIGR)411.-
A' A FIGURE 4.1.1.4-61
A2QIA FIGURE 4.1.1.4-7a
46 CIMAX NOT USED
CIMAX CIMAXBS+A +'A +'63
RETU RN
FIGURE 24 AIRFOIL SECTION MODULE -SECTION MAXIMUM LIFT ROUTINE'
V
In the Weber Method certain combinations of the above terms have been rede-
fined as follows:
S(x) W dz dx' (Function for Source Distri-- ~ X X x0 bution in Parallel Flow)
S ( 2 ) dz (Slope of Thickness
dx Distribution)
3 ) f (dz 2z(x') dx' (Functioa for Vortex Dirtri-
((x f 1 (xd x bution in Normal Flow, to
Account for a)
These functions are approximated by sums and products of the airfoil ordi-
nates and certain coeificients which are independent of the section shape
by
N-I N-i() ki() (2)1 (2)
(1) (x)= sw, Zs ( (x = s ZV=Iil
N-I(3) (3) (3)S(3 (x) sv z +sv
V=l' z2 Y-C
The effects of camber on the resulting velocity distribution are
obtained by assuming the camber to be small compared with the chord.
This results in the camber effect being accounted for in the parallel
flow V V cosc only.xo 0
The Vortex Distribution, V(X), 'on the chord line which produces a
given velocity normal to the chord 'line and which si zero at the trailing
edge is
Y(x (4) S(4)(x (Vortex Distribution due to2VxO ), =4z (x) Camber)2Vxo s z s
VV V
74 1.
-/ " I "No .4
The total velccity Vx(x,o) on the chord line for an airfoil with camber and
incidence is
V (x,O) = V eosa 1 + SM(x) + S(4)(x
+ V 0sin a ; -x [i + S(3)((x
with the + sign being for the upper surface and the - sign for the lower
surface.
The resulting velocity distribution at the airfoil surface is computed
using
dz (x)
S(5)(x) W x (Slope of Camber Line)dx
where V(x) cosa [1 + W;+lS(x) + S(4')(X sina/1 x i + (3) (xITo xa1 + (2)(x) + S(5)x1 2
which is the complete expression for an arbitrary airfoil at angle of attack
in an ideal flow. The S( 4 )(X) and S( 5 ) (X) terms are computed by approxima-
tion. The pressure coefficient is obtained by
(4) xx ]cos a + S (1)(x) + S((x ) s+ n 2 + S (3)(x
C 1l
1 + [S(2) (x) + (
75
,, _~~~'~ . ' • _ • : •. ' :• " . - - : - •• < .
The term I - S( 1 )(x) + S(4)(x) accounts for the vorticles beirig puL into
a flow with velocity V (1 ,+ S (x) + S()x)) instead of V * The term0 0
(1 + S( 3 )(x)) accounts tor the difterences in the vortex distribution between(1) (5) 2
the thick and thin wing. The term 1/ 11 + IS (x) + S (x)2 I is the cor-
rection between velocities on the chord l1ine and on the surface.
4.1.. Compressibility Correction and Integration
The effects of' compressibility are accoun,'.=A for in Weber's Method by
the application of compressibility factors to the Velocity distribution
contributions due to thickness and camber, respectively.
= - ) - + ( ) ) -
c 1 . (S-3 = :" 1 - C:•" ))o o P i
The velocity distribution in compressible flc- is then given by
S(I s(• ina S~i X1 -- - --
IAe compressible pressure coefficient from the compresible form of
Bernoulli's equation is
The airfoil lift, axia'l torce and pitching moment are computed froa thhe
compressible and incompressible solutions In'the following 2nner
Set Ix ,,,
"0 f
.where
f i
Therefore trapezoidal rule
ct, (:0 -- • I x sin 9. + Ix s.in O - x s n
)0 -CLC)r i.. Kl. 2 IL,
Similarly N v 2 iv]
( () (2)r) = : (")' (S (x) + S (x)) - c (00 (S W(x)
CA ('I) P (
.... ... ( ........ +r2 C'(M
4K11 I '2
77~ 2 L I-4.1.j Ideal Parameters
The ideal parameters are obtained from thirn atrtoil theory, which
in effect means results are obtained for tre meanline characteristics Inman
incompressibie inviscid flow. The ideal angle of attack '. is obtained fromI
l l-2x
r
However, at the leadi'ng and trailing edges the equation Is undefined and
increi~ents in the vicinity of the leading and trailing edges must be deter-
mined, in addition to the Integration over the interior piortion of the
iird.
77 ...
. . - ;#--'., L I I L
IT..
l% a -. 3739 z + 04745dzSIxx = .9619 1~
x - .9619 tox = 1.0
resulting in
Ai=57.3 + Aa. + A~iAti5x=7 to x=.0381 to x=.9619 to]x -. 0381 x-. 9 6 19 x=1.0
The angle of attack for zero lift is obtained in a similar manner1
01. = z If • (1-x)• l-] dx
with o
OL. -. 7834 7 + dzx
x-.9619 to x=.961d x-l.Ox1l.O
The total value is given by 0!. ]aOL - [aOL + a• , OL •01.
x-.9619 to x-O tox-1.0 x-.9619
The ideal lift coetficient is now simply
C 2 - [i + aOL57.3
The pitching moment about the quarter chord is
7r)
2os O + CSo QOL'C2, 90 57.3 2,, N u 72
78j
. . . . . . . . . .. '.
4.1.4 Crest Critical Mach Number
The crest critical Mach number is precisely defined as that free stream
Mach number for which local sonic flow is first reached at the airfoil
surface crest on the assumption of shock free flow. Its significance is
founded on its relation to the drag rise Mach number. Various empirical
studies have been aimed at finding the critical pressure ratio at the crest
which corresponds to a drag rise in the test data. Nitzberg (NACA KMA9G2U)
proposed a critical pressure ratio for drag rise of
PCREST/PTOTAL = U-5283
which corresponds to a crest Mach number of M 1.0. Sinnot (RAS TDM-b4U7)
proposed the ratio
PCREST/PTOTAL - . 515
which corresponds to a Mach number at the crest of M - 1.02 and which corre-
lates better with drag-rise data. Sinnot's value is used in the Airfoil
Section Module, thus the crest critical Mach number corresponds to a local
flow at Mach 1.02 at the crest rather than sonic conditions. The relation-
ship between the crest pressure and crest critical Mach number is
0.515(1 + 0.2 M 2 3
SO. 7 F M 2 c
cc
where
F - C + 1/2 (1 Pcc)Cl PCREST
M c CREST CRITICAl. MAC:;
C = INCO!,1PRESSIBLE VALUEPCREST
79
Rewritten so that MCC is a function of CpCREST, the relation is approxi-
mated by"Mcc- [12 .90 CpRT 414 CpRS • 1.061-
[1.023 - 9507 414 - 1506 CpaREST - .0212 Cp&RESTJ
The crest location for each angle of attack is determined by comparing
the airfoil surface slope for each x location to tangent a. The final
location is obtained by interpolating between the two'given x locations whose
airfoil slopes bracket the tangent a value. The CPCREST value is obtained
by interpolation of the Weber incompressible pressure distribution between
the two x values surrounding XCREST. The crest critical lift coefficient
is obtained using the' Karman-Tsien compressibility rule on the M = 0 Inte-
grated Weber lift coefficient.
C cc '
"cc CL(M)Ilc - I---
where, CL(M) = CL for M U.
No specific boundary layer correction is used. However, the Datcom
recommends a 5Z correction factor to bring the reaults in line with experi-
mental data, and the yiscous correction of section lift curve slope proposed
by Kinsey and Bowers (Appendix B, Volume ) has been incorporated.
80
- . . .7. . ... .. . .
4.2 TRANSONIC WING CL FAIRING, TRANSONIC WING X., FAIRING, and TRANSONIC
WING C1 FAIRING
Datcom wing methods in the transonic Mach regime calculate aerodynamic
parameters only at specific Mach numbers. Data at the requested Mach number
is then determined by interpolation. This approach is used for the wing
lift curve slope (CL ), wave drag (CD.), and aerodynamic center (Xac).
Nonlinear fairings for each of these parameters are discussed in the follow-
ing paragraphs.
4.2.1 Transonic Fairings of Wing. CI
Wing lift curve slope,, CL , is calculated in subroutine TRSONI, overlay
24. The. same methods are used for the horizontal tail in subroutine TRSONJ,
also in overlay 24.
Datcom section 4.1.3.2 defines the methods for calculation of CL at
five discrete Mach numbers from 0.b to 1.4. Values at Mach 0.6 and 1.4 ure
the subsonic and supersonic methods, respectively. The routine used to fair
this curve is a modified version of subroutine ASMINT used in the Airfoil'
Section Module, overlay 50. To ensure a smooth continuous interpolation, a
curve is constructed by fitting the points by a left-hand parabola joined to
a series of cubic curves, and finally a right-hand parabola. This technique
yields a function which has continuous derivatives everywhere. The slope
of the curve at subsonic Mach numbers is obtained by differentiating the
equation on Datccm page 4.1.3.2-49 with respect to Mach number. At Mach 1.4
th0 slope is found by calculating values at Mach 1.3, 1.4 and 1.5 and assum-
ing a curve of the form:
CL A + b/l + C/82
Subsonic methods are used to Mach 0.75, or 0.1 less than the force break
Mach nuwber (Mfb), whichever is smaller, and transonic fairings are initiated
at that point.
Subroutines TRANWG and TRANHT are used to calculate CL, at Mach 1.3,
1.4, and 1.5 and return CL, and its slope at Mach 1.4. Subroutines TRS0NI
and TRSONJ calculate CL using the subsonic equation if the Mach number
is less than 0.75 (or Mfb - 0.1), calculate the slope of the subsonic CL,
curve at Mach 0.75, and call the new fairing routine if the Mach number if
g:eater rhan 0.75.
81
4.2.2 Transonic Fairing of Wing CnW
The wing wave drag, CDw, is calculated in subroutines TRSONI and TRSONJ,
overlay 24, for the wing and horizontal tail, respectively. The method is
given in Datcom section 4.1.5.1.
Digital Datcom performs a linear interpolation of Datc.om Figure 4.1.5.1-
29 at fifteen discrete Mach numbers to determine the variation of C . Non-
linear interpolations of this curve are performed as required at te user
defined Mach numbers using the fairing routine developed for wing CL . Two
additional constraints were applied to perform this fairing.
a. If the linear slope to the left or right of a given point, except
the end points, is less than UNUSED, (10"60 on CDC computers), the
slope at that point is set to zero.
b. Any computed value less than zero is set to zero.
Within the fairing routine, the number of points in the curve is used to
discriminate between a fairing of CD and CL .
4.2.3 Transonic Fairings of Wing Aerodynamic Center
Aerodynamic center, Xac, is calculated in subroutine's TRANCM and
TRHTCM, overlay 25, for the wing and horizontal tail, respectively.
Dattom section 4.1.4.2 defines the method for calculation of X atac
six discrete Mach numbers from 0.6 to 1.4. Values at 0.6 and 1.4 are deter-
mined using the subsonic and supersonic methods, respectively; the remaining
four points are obtained from Datcom Figure 4.1.4.2-30 corrcsponding to
V - -2, -1, 0 and +1. If the thickness ratio is less than or equal to 7%,
these data are interpolated for the aerodynamic center. If the thickness
ratio is greater than 7%, the curve is defined using points which are a func-
tion of the force break Mach number, Mfb. An increment to the aerodynamic
center is found from Datcom Figure 4.1.4.2-33'and applied at the fifth point
(Mfb +0.07) and the resulting curve is then interpolated for the aerodynamic
center. The following table summarizes the interpolation table:
82
.....
Using Six Points Using Eight Pointst/c < 7% t/c > 7%
M1 0.60 0.60
M2 H for V - -2 (0. 6 0+Mfb)/ 2
M3 M for V --1 Mfb
M4 M for - 0 Mfb + 0.03
M5 M forV - +I Mfb + 0.07
M6 1.40 Mfb + 0.14
M7 - M for V -'+I
M8 - 1.4
The interpolation routine used is similar to the routine. used for CL and CD
(Sections 4.2.1 and 4.2.2).
4.3 TRANSONIC WING CL , TRANSONIC WING CD, TRANSONIC WING-BODY-TA LC ±4.NSNI TRANSONWIIC
TRANSONIC WING-BODY-TAIL C,_TRANSONIC NG C , and TRANSONIC WIN8-
BODY C
This section describes those methods used to compute the transonic con-
figuration aerodynamics using Second Level Methods, and are summarized in
Table 6. Additionally, the partial output is described.
4.3.1 Transonic Wing Lift Coefficient, C
The wing lift curve versus angle of attack id programmed in subroutine
WINGCL. The method described in Datcom section 4.143.3 is used as a guide to
produce trends and is not construed to be an exact methodof solution. Since
the method is an approximate 'one, the following procedure was employed to
produce the wing lift characteristics applicable io thin, low aspect ratio
wings:
1. The required experimental data inputs by tht user are a (zeroo
lift angle of attack) and a* (the angle of attack where the lift
becomes nonlinear).
2. The lift variation is assumed to 'be linear up to a*, and nonlinear
to a (maximum lift angle of attack).•CL
max
83
TABLE 6 PROGRAMMED TRANS3ONIC SECOND LEVEL METHODS SUMMARY
DATCOM AERODYNAMIC SUBROIl INE EXPERIMENTAL DATA PARTIAL OUTPUTSECTION PARAMETER CONFIGURATION PROGRAMMED INPUT REQUIRED AVAILABLE
4.1.3.3 CL WINGS WINGCL a.. a. a., a,
4.1.5.2 Crk WINGS WINGCL CL OR %, a. CDL/CL2
5.1.2.1 Cfý WINGS WINGCL CL OR %, a. CIO /CL
5.2.2.1 C WING-BODY WBCLB CL CI//CL
4.5.3.2 CD WING-BODY-TAIL COWBT CDWB (NONE)
CDH
cLH
q/q
C)oV OR CDoWBT*
4.5.3.1 CO0 WING-BODY-TAIL WBTCDO ITYPE (TYPE OF MDGENERAL CONFIGUR-ATIONi)
*CDoWBT IS AVAILABLE FROM THE SECOND LEVEL ROUTINE OF DA COM, SECTION 4.5.3.1,
SUBROUTINE WBTCDO.
84
Za:
3. The nonlinear lift region is modeled by a mathematical relationship
that satisfies the following conditions:
c L =c L at a CLmmax
C L = C L 0•,-• at •=•
dCCLL
= C
at "mI 1
* dCL
=0 atd ,i CLmax
A modified polynomial of the form
y A + B(X-X) + C(X-X )Ny0
is utilized to satisfy each of the boundary conditions and yield a cucve
somewhat parabolic in shape. This relationship has provided excellent
results in modeling the nonlinear lift range. Derivation of the unknowns A,
B, C and N is described in Section 4.3.7.
Two other user options are available from the routine; (a) the user
may input only a 0 or (b) the user inputs only a,. Since both a0 and a
are required to estimate the lift variation by the preceding technique, the
subroutine will provide an estimate for the missing parameter from a qua-
dratic expression. Specifically, a quadratic polynomial can be faired
through the nonlinear lift region if a* is an unknown. 'Applying the gener-
alized boundary conditions to a polynomial of order two, and solving for a*
will yield an estimate for this unknown. Conversely, if a is not input, it0
can be determined in a similar manner.
85
i C2I,- _t
The relationships used are as follows:
1. -a ,not inp';t CL
01 =a + 2[o -a C + max
Lmax max ot
2. ao not input
L ,- C
a o Cm a + 2 amax, L
If neither a 0 nor •, 'are user inputs, no solution is possible, but
the program calculated values for CL I CL and aC areci max L
available as partial output. max
4.3.2 Transonic Wing Drag due to Lift, C€L 2a
The programmed procedure for computing the ratio CD /CL is exactly asI' " L
described in Datcom section 4.1.5.2. The method does a three dimensional
table lookup for Figure 4.1.5.2-55a (A tan (ALE) 0) and for Figure
4.1.5.2-55b (A tan(ALE) - 3). Figure 4.1.5.2-55c shows a linear relation-
ship of the dependent variable (t/c)- 1 / 3 CDL/CL 2 as a function of the tran-
sonic similarity parameter A tan (ALE) for each value of the ratio (M2 -
)/(t/C)2/41; it was assumed that this linear relationship would hold for
all other taper ratios other than 0.50. Therefore, linear extrapolations on
all varibles would be performed if required.
This method was programmed in subroutine WINGCL with the calculation
,for wing CL. Since CL is required to calculate CDL, the calculation
of wing CL would enable the calculation of this parameter if CL is not
input as experimental data. The routine will not overwrite experimental data
input, and thus the user oriented, features are retained.
The ritio CDL/CL2 is available from the routine and will be output
for user reference if CDL cannot be calculated.
4.3.3 Transonic Wing Roll Derivative, Cq
Like the wing CDL calculation described, the method of Datcom Section
5.1.2.1 requires wing lift to calculate from the relationship C a/CL',
equation 5.1.2.1-c. Thus, this method is Also programmed in subroutine
WINGCL.. The calculated value f.;: C, will not overwrite any experimental
86
•-
data input. The ratio C2 /CL is provided if the calculation for C. cannot
be completed. No exceptions are taken for the Datcom method. The ratio.
C, /CL at Mach numbers 0.6 and 1.4 are obtained by calling the subsonic
and supersonic aerodynamic modules.
4.3.4 Transonic Wing-Body Roll Derivative, C
The derivative C, will be calculated by Datcom equation 5.2..2.1-d if
the wing-body lift coefficient variation with angle of attack is supplied, or
computed as described above. The ratio C /CL is given as partial output
if the lift variation is not sjx-cified. This method is implemented exactly
as described in Datcom and is programmed in subroutine WBCLB. Since Ct /
CL at Mfb and Mach 1.4 are required input items for this method, they are
calculated by calling the appropriate aerodynamic modules.
4.3.5 Transonic Wing-Body-Tail Drag Coefficient, CD
This method is a "method for all speeds" as described in Datcomm Section
4.5.3.2, and is incorporated in exactly the same manner as presently pro-
grammed for the subsonic solution. This method, as programmed in subroutine
CDWBT, require the following experimental data inputs:
1. CDwS vs angle of attack-. CD vs angle of attack
3. CLH vs angle of attack
4. q/qC vs angle of attack
5. f vs angle of attack
6. CDoV or CDowBT
If CDoV is not an experimental data input item, the program will
calculate it from the estimated CDowBT calculated as follows:
CDov CDowBT - CDowB - CDOHNo partial output is available from this method.
4.3.6 Transonic Wing-Body-Tail Zero Lift Drag Coefficient, CDo,
This method follows exactly the method of Datcom section 4.5.3.1,
and is programmed as subroutine WBTCDO; This routine does not require
experimental data input, although experimental data input is an optional
feature for this routine.
87
87,.i
...........................
Utilizing appropiate configuration description parameters the pro;3am
computes the drag divergence Mach number, MU, from Figure 4.5.3A1-19. The
experimental data input allows the user, at his option, to select ýhe type of
general configuration to be used in computing MD. The three options
are,:
o A - Straight wing designs without area rule.
o B - Swept wing designs without area rule.
o C - Swept wing designs incorporating transonic area rule theory.
The program default options are as follows:
"o No wing sweep - General Configuration A
"o Swept wing, configuration type not defined - General Configuration B
The general configuration types are defined by the parameter ITYPE,
where ITYPE=1 for. configuration type 'A, ITYPE=2 for configuration type
B, and ITYPE=3 for type C. In the case of configuration type C, the line
for type C, in Figuie 4.5.3.1-19, was linearly extrapolated and programmed.
All extrapolations in this figure, with the exception of thickness ratio, are
assumed to be linear; thickness ratio is extrapolated in a quadracic fashion.
With MD calculated from Figure 4.5.3.1-19, it is necessary to fair the
curve across the transonic Mach regime. The followiag criteria wasCDo
used to fair the curve:
dCDo1. ~j-=o, ooM=MD
dM MD2. CDo =CDoM=.7 e 002 @ M H
4., O C0= CDoM=1
d@ .3
A polynomial fairing of the same type as used for the wing nonlinear
lift coefficient is used here and has 'shown acceptable results.
The values of CD at Mach .7 and 1.1 for this method are obtained by
calling the subsonic and supersonic aerodynamic modules.
88
4.3.7 Data Fairing Technique
The 'data fairing technique used for computing the nonlinear lift region
of transonic wings and the transonic wing-body-tail zero lift drag co'.f-
ficient was chosen for its powerful features and ease of application.
The general fairing formula is a polynomial whose form is:
y A + B(X-Xo) + C(X-Xo)N
where A, H, C and N are, unknowns. Given the values of y and dy/dx at two
points, X 0 and XI, four simultaneous equations can be written. These
equations solved simultaneously for the four unknowns yield the following
results:
A-= y
B = d- @ '(=X'dx X0 "
Y [ YO a ' (Xl -xO )
Cdx x0 ( 1- 0
(X x- 0N
y ~y() Y dx )Y (XI - X0)
The -generalI equat ion reduces to
~' ~0 +dx X0 + 0 0 y x (X1 - 0 \X1 X0 x 0 10, xI
This equation is valid for X0 < X < XI and (dy/dx)x 0 • (dy/dx)Xl.
Neither of these conditions is violated in this application. The range of
values of X will always fall between X0 and X1 bepause of the program
logic, and in the nonlinear lift region the slopes at X0 and X1 will
never be equal. For the transonic wing-body-tail CD versus Mach0
fairing the Datecom relation (dCD /dM) 0.10 at M-MD.
89
4.4 SUBSONIC WING Cm, SUBSONIC AND SUPERSONIC WING AERODYNAMIC CENTER• SUB-
SONIC WING-BODY Cmand SUBSONIC WING-BODY-TAIL Cm
The subsonic wing pitching moment variation with angle of attack
follows Datcom Method I of Section 4.1.4.3, and is programmed in subroutine
CMALPH. The method is applicable to those configurations whose wing aspect
ratio satisfies the following criteriai
A f6 ("LOW ASPECT RATIO")(1+C 1 COS A LE
For "high aspect ratio" configurations, the default wing aerodynamic
center is either the quarter-chord of the wing mean aerodynamic chord,
or the user input value (variable name XAC in. the planform section charac-
teristics namelists). This value is used in computing pitching moment for
the wing tip to the angle of attack where the wing lift deviates by more than
7.5% from the linear value; at this point the method is no longer valid.
There are no methods in Datcom or Digital Datcom for supersonic wing
pitching moment, though the wing'XAC is estimated to be at the wing plan-
form centroid for unswept leading edges, and computed using the method and
design charts of Datcom section 4.1.4.2 for other surfaces. These supersonic
data are computed in subroutine SUPLNG.
There is no Datcom method for computing the wing-body pitching moment in
any Mach regime. Digital Datcom, however, computes the subsonic wing-body
pitching moment using the following formulation (programmed in subroutines
WBCMO and WBCM):
o Compute (Cmo)WB from regression formulation of Datcom Section
4.3.2.1, programmed in WBCMO. If the method is not applicable,
(Cmo)WB is computed from Method 1.
o Compute the wing-body aerodynamic center from Datcom Section 4.3.2.2
(WBCM), where Equation 4.3.2.2-a is used at all speeds.
o The wing-body C. curve is then computed as
SIB~~ CC+ 3CMW C OB+ C CL+ MCD
90
where CmCL is the pitching moment due to lift obtained by integr;-
ting the curve of XAC versus CL from CL - 0 and to CL at the desired
angle of attack, and CmC is the pitching moment due to wing-body drag
located at ZAC.
Subsonic wing-body-tail pitching moment versu- angle of attack is
computed by Digital Datcom in subroutine WBTAIL, though there is no Datcom
method for this parameter. The method formulation used is as follows:
CLj = CL - CLjiH j WBT j WB
C W Cmj) W + (q/q () a r ( C o (a)L
Cmj WBT (jWB(.)H+L H
+(cD) (q/q 00 )j SI N (a)] +(D( H L (q/ 0 ) COS(
r
-(C )L SIN (0)j
4.5 TRANSONIC BODY CL FAIRING AND TRANS NIC BODY CM FAIRING
The transonic CL, and Cm. derivat ves for the body alone configura-
ti.on is interpolated linearly between th subsonic (M - 0.60) and supersonic
(M - 1.40) Mach regimes in subrcutine B0D RT.
91
4.6 SUBSONIC ASYMMETRICAL BODY CL, SUBSONIC ASYMMERICAL BODY CMO
Cm, AND SUBSONIC ASYMMETRICAL BODY CDn, CD
Digital Datcom body solutions generally include lift, drag, and pitching
moment coefficients. In the transonic speed regime the solutions are re-
stricted to lift and pitching moment slopes, and drag coefficients.
4.6.1 Subsonic Bodies
Subsonic body analysis computes lift, drag, and pitching moment coef-
ficients for either axisymmetric or cambered bodies. Digital Datcom body
methods are identical to Datcom except for the base drag. Digital Datcom
calculates base drag using a minimum base area equal to 30% of the body
maximum cross-sectional area.
The cambered body pitching moment method is not defined in Datcom
and is therefore deqcribed in detail. For clarity, the lift method, which is
defined in Datcom, is also described. These body methods (subroutine
BODUPT) are executed when the parameters ZU and ZL are user specified
(namelist BODY). The method predicts the zero lift angle of attack,
zero lift pitching moment, and body lift and pitching moment versus angle of
attack. The Datcom drag methods are retained.
Zero lift angle of attack and pitching moment are calculated utilizing
conventional mean line theory. The equations are:
0O.95 1a -57.3 Z'0 = 7 d(X/T.), degrees
of L [(-X/L) [X/L - (X/L)21 1/2
C 0 2.0O Z [ 1[2.0 x X/L d (X/L)
0L X/L - (X/Q)2]1/2
92 •
These parameters are defined in Figure 25.
Lift and moment for asymmetric bodies are calculated by employing a
modified version of Polhamus's leading-edge suction analogy (References
2 and 3). Polhamus considers two components of lift, a potential flow
term, CLp, and a vortex-lift term CLV. Both of these terms are a
function of body aspect rAtio (A) and are defined as follows:
CL - CLp +. OV
CLp Kp sin a cosZ a
CLV = KV sin2 acos
- angle of- attack
Kp and KV are obtained from Figuee 26.
The Polhamus vortex lift equation ..ist be modified to make it applicable
to thick bodies because Lhe o-sC-L of vortex lift for such configurations is
not at zero angle of attack i it is with flat plate wings. The thick body
angle of attack for on!;et of vortex lift (av) can be correlated with the
fineness ratio (FR) ,-nd tae thickness ratio (TR) of the body as shown in
Figure 27a. 'The body thickness parameters are shown in Figure 27b. Experi-
mental data used in correlation are presented in References 4 through 7. The
redefired lift expressions for thick bodies are as follows:
CLp Kp sin a cos 2
C'LV 1 KV sin2 (' -•V) cos V)
C'L CLp + C'LV
The body pitching moment is obtained by estimating the center-of-
pressure locations of both the, potential- and vortex lift components.
The total pitching moment is equal to the sum of the moments produced
by the lift, forces acting at their respective center-of-pressure loca-
tions plus the zero lift pitching moment. The potential lift center-of-
pressure location employed stems from slender body theory and is presented inFigure 28 as a function of n. The equation for the powerla4 planform is of
the form R * Rmax (X/L)n. The program computes an exponent n that closelyapproximates the input planform area. The potential lift center-of-pressure
location is obtained from Figure 28 or the equation,
Xcp/L = 2n/(2n+l)
93
• , \\
LZ
Z*=ZNIOPOINT-ZCHMR
SIDE VIEW (Xi VALUES SHIFTED TO BODY NIOSE)
FIGURE 25 ASYMMETRIC BODY GEOMETRY INPUTS
1 2 3,4 10 1 .2 3 4A A
ASPECT RATIO' ASPECT RATIO
OATCOM FIGURE 4.2.1.2-38& OATCOM FIGURE 4.2LI.2-36b
FIGURE 26 POTENTIAL AND VORTEX LIFT COMPONENTS
94
20
uj
i I,--
0 5 111FINENESS RATIO - FR
0ATCOM FIGURE 4.2.1.2-37
FIGURE 27a CORRELATION OF aV
BODY PLANFORMl
LF
F INENE SS R ATIO - FRdTHINENESS RATIO - FR
ZRz
FIGURE 27b BODY THICKNESS PARAMETERS
95
Rmax POWER LAW PLANFORM
~~I-a ~ SLENDER BODY THEORY'-_________
0.6
.1.
POWER BODY EXPONENT -n
FIGURE 28 POTENTIAL LIFT CENTER OF PRESSURE
96
I,. _ _
Vortex lift center of pressure is assumed to be located at the total planform
centroid of area. The equation for the body pitching moment coefficient is:
Cm - CMO + Crp + CMV
Cmp %€p (xCG XCp)/L
CMv CNv (XCG - X)/L
where X is the location of the total planform center of area measured from
the body nose. The method.is applicable at angles of attack equal to or
greater than the wing maximum lift angle of attack.
4.b.2 Transonic Bodies
Digital Datcom body solutions are restricted to lift and pitching
moment'slopes, and drag coefficients in the transonic speed regime. These
data are computed.by performing a linear interpolation between the subsonic
(M - 0.60) and supersonic (M - 1.4) Mach regimes.
Subroutines that implement the transonic body methods are B0DYRT,
SUPBOD, TRSONI, and TRSONJ.
4.b.3 Supersonic Bodies
Supersonic body analysis provides solutions for lift, drag and pitching
moment coefficients. Datcom methods for lift, pitching moment slope,
and drag coefficient require the body to be synthesized from a combina-
tion of body components comprised of a nose, after-body, and/or taii seg-
ments. Digital Datcom requires synthesized body configurations to be either
nose alone, nose-after body, nose-after body-tail, or nose-tail segment
combinations.
Some of the Datcom body drag merhits in this speed regime have not been
implemented in Digital Datcom. The effects of blunted noses on drag are not
incorporated since the body lift and pitching moment methods do not ref lecc
the influences of this parameter. Some of the Datcom interference drag
methods are also deleted. In this case,.the methods were omitted because 'of
their limited range of applicability.
Calculation of wing-body, or horizontal tail-body, stability requires
the lift curve slope of the body ahead of the'wing or horizontal -tail. Body
CN methods are executed for the portion of the body ahead of the wing, if
the wing is present; the portion: of the body ahead of the horizontal tail, if
the horizontal tail is present; and entire body.
97
All methods are implemented by subroutine SUPB0D except for a portion
of the drag methods contained in subroutine FIG26.
4.b.4 Hypersonic Bodies
Hypersonic body analysis is performed at user designated. Mach numbers
that are equal or greater than 1.4. In this speed regime, Digital Datcom
stability solutions include lift, drag and pitching moment coefficients.
Hypersonic body analyses for lift and pitching moment slopes and drag
coefficients, like the supersonic body methods, require the body to be
synthesized from a combination of body segments. Hypersonic body analysis is
unlike the other Datcom hypersonic configuration analyses since the methods
are defined independent of the supersonic results. Body CN, for portions
of the body ahead of the wing and/or horizontal tail are also calculated.
The methods are implemented in subroutine HYPBOD. A small portion
of the drag methoas are found in subroutine FIG26.
.4.7 TRANSONIC WING-BODY CL
The transonic wing-body lift coefficient, if not input using name-
list EXPR-, is computed in subroutine WBCLB using the following equations:
C1" (C )( (a)
•WB [%(B),+KB(W) La 4 ,
L jW
SB(W)
+ [kW(B) + B(W)] CL,
98
In computing the transonic wing-body pitching moc .nt slope,. the center
of pressure of body-wing carryover is linearly interpolated between the
values obtained at Mach 0.60 and Mach 1.40 in subroutine TRANCM.
4.8 WING-BODY-TAIL MOVEABLE HORIZONTAL TAIL TRIM
Tne dil moveable horizontal tail incidence required to trim the vehicle
(CMC.G" - U) at angle of attack is calculated in subroutine TRIMR2. At
trim, the forces on the tail are CLH and CDH (trimmed lift an- drag),,
and are referenced to the local flow at a tail angle of attack of ( a- fH)-
Since these trimmed forces are located at the tail aerodynamic center, which
is known, the total body moments can be summed as follows:
"qH [AXAc AZAc ( )lC + C" " C - AC Cos (-x-C + H) sin (a-
MWB "OH q L H qX cH W;H
C ! [ZAC cos (a-) - sin (a-ek 00 H % H -
CDH can be expressed as
(CLH)2
CDH CDO + HA eH
Hence, the only unknown is CLH, the tail lift at trim, which can be
evaluated. From Sketch (a) note that
99 9
'.. y ' - f .4 4' L
M m'mn I I I "- "I I- l m u
a ACLtrim
Disneorme~.t nurer-hr on g. oiotLsaiie A
LAngllae defined yitreto of attacithkR (positive as shown)
with horizontal stabilizer above c.g.)
Sketch (a)
100
. . ...... .. .. ... ....
AX x
Aac XH
Thus,
A)ac Co ac AZac (-(eH) +-T. sinl aH)
- I Cos Q2 Cos (aE)+ sin ýi sin (i-;E H)l
cw
- H Cos a E EH)
cw
"'cCos (a~ac -~sin (a-E)
cw c w
[ H sin a co s cos cHsi (a-C H)]
s i X Hl ( z- + EH )
iOl
The moment equation reduces to
q H qH XHC- COSL( q + H)
(CLH) H H XHH 7ACD HAe AH q. W in ( - + LHI -0
Letting 6 = a- + cH and re-arranging yields a quadratic on CLH.
~ XH 6(CLH) 2qH XH sin 6q. C- rAHeH
wqH XH
Cos 6 (CLH)• = CwH
+ C sin6+C H 0ODOH qr¶ CW MW +CMoq
Simplifying,
.. tan .'6 (CL )2 C + C tan 6 + C MwB ; MOHC + CMoH
AHe H "H CLH CDOH qt' XH =x0•Cos
From the, quadratic formula,
q Hw[ iC + Hi
1 + [1- 4 ta 6!A 1C tand6 Mw CMO q.ir TH e H DI OH 9H XH
L JL ~ - Cos
102
In this form, the equation becomes invalid for - 0, and can be further
reduced to
q
H qHB + C MOHHcos
C 2 - H q H Cc:DOH ]a OHCCq
LH q H
F1 -4 tan6 MWB 'MOIH tanCo . Co
A plus sign in front of the radical is the valid solution, otherwise at
6 0 the solution is undefined. This result is similar to Datcom equation
4.5.3.2-e, with the exception of the term "CmOH qH/q=-"
Once the tail lift at trim (CLH) has been determined, a variation
of Datcom equation 4.5.1.2-a can be used to calculate the tail incidence
cH.
C L H q~ (K H(B) + KB (H))HH
+CL.. (a)[k H(B) k B(H)]
(H(b/2 " b*/) C '
+ IVB(H) raV (b/' 2 ) aL effH •H
where CLH is the pseudo lift-curve-slope of the horizontal tail in the
presence of the body,
CL* CL (KH(B) + KB(H))H aH
103
_ ___
CLU and CL. are the horizontal tail lift and lift curve slope at
(l - CH + ctOH)and aeff is the effective angle of attack of the horizontal tail in the
presence of the body .+
eff = "-CH + 'OH + 'lH(" KR•B) +
The incidence angle to trim can, then be solved directly, and becomes
CL \H(B) + KBH) L' + C' OH /2aLH HýH E( . ,~ H ]
(B(H) + k H(B))[L' + IVBH . /2 b/ ) C(L Ha H VB(H) U• H ' b72 t
Once the tail lift and drag at trim has been" computed the panel hinge
moment about the pivot point can also be computed. Since CL,, and CDH are
are referenced to the local flow, they must be computed relative to the
freestream flow. Relative to Voo, trim lift and drag are
CL = (CL Co's C- C sn )HTRIM HT HT
'2
CD H 0 , (C7LHeHTRIM HH
The pitching moment trimmed is
! H
CM C [ Cos ]+ CD sin siHTRIM H TRIM WH TR IM ;
The hinge moment about the pivot point is
CHM [CL Cos a + DHTRIM sin
104
4.9 WING-BODY-TAIL TRIM WITH CONTROL DEVICES
Configuration trim with wing or horizontal tail control devices is
performed in subroutine TRIMRT. The method programmed, which is not a
Datcom method, essentially does a table look-up of the control device
incremental pitching moment coefficient versus control deflection for
the deflection required to trim. The incremental lift coefficient and
drag coefficient ire then obtained by performing table look-ups for these
variables (which are a function of control deflection aagle) at the trimmed
control deflection.
4.10 STANDARD ATMOSPHERE MODEL
Incorpozation of a standard atmosphere model. (subrodtine ATMOS) into
Digital Datcom provides input and output flexibility for the user. The
program can operate on Mach number and altitude as separate independent,
variables. The addition of vehicle weight and flight path angle permit
calculation of equilibrium flight conditions.
The program allows the user to input either Mach number or velocity
as an independent variable for speed reference. If velocity is input,
the free stream static temperature must be available so that Mach number
can be calculated. The user will also have the option to. specify a flight
altitude, or static pressure and temperature, as an independent variable
defining the atmospheric conditions. If altitude is specified, pressure and
temperature will be found using the "U.S. Standard Atmosphere, 1962."
The user may input up to 20 Mach or velocity points. If Mach number is
input, the velocity will be calculated for each point where atmospheric data
are input. When velocity is input the Mach number will be calculated using
atmospheric conditions. If velocity is input instead of Mach numbers and
atmospheric conditions are not defined, an error message will be written and
Mach numbers will be calculated using a speed of sound of 1000 ft/sec.
The user may also input up to 20 atmospheric conditions. The atmosphere
may be defined by altitude, pressure and temperature, or Reynolds number. If
the altitude is given, pressure and temperature will be determined using the
105
• . , . * ..
- atmosphere model developed in Reference 9. The Reynolds number will be
calculated using the following equatior, (in the foot-pound-second system of
units):
RN/L - pV/- - 1.2527 X 106 PM (T + 198.6)/T 2
This equation was derived using the following relationships:
P = P/RT
- M 1R
V a 2.270 X 10- 8 T1 ' 5 /kT + 198.6)
If the Reynolds number is not input and cannot be calculated, an error mes-
sage will be written and the Reynolds number will be set to 5 x 10 6 /ft.
Given the vehicle weight, flighat path angle, and atmospheric condi-
tions, the equilibrium flight aerodynamic data can be determined. Equilib-
rium flight is achieved when the following relationship is satisfied.
Wr -(CL cOsS - CD sin6 ) qS
Along with the untrimmed aerodynamic output, the level flight (6 - 0)
lift coefficient will be output. Trim data output wi.llprovide an addi-
tional line of output at the equilibrium flight conditions (subroutine
FLTCL).
106
SECTION 5
SYSTEM RESOURCE REQUIREMENTS
Digital Datcom is a large and rather complex computer program which
requires specific computer resources to execute within a fixed core require-
ment. The program is written to conform to the American National Standards
Institute (ANSI) Standard Fortran IV. Certain computer resources must be
available to make the program operational without modifications These
resources are:
o Six disk files or scratch tapes are required for manipulation
and retrieval of input data. The logical 1/0 units used are 8, 9,
10,, 11, 12 and 13. These logical units are in addition to logical
unit 5 (read) and unit 6 (write).
o The system must have capability for primary and secondary overlay
structures.
"o The system must have a Fortran compiler which provides for NAMELIST
.input and output, and statement transfer when an end of file is
detected.
Each logical unit referenced by the program is reserved for a specific
purpose. The units referenced and their use in the program are listed
below:
Unit Program Usage
5 Standard system input (card reader)
6 Standard system output (printer)
8 Storage of experimental data namelists for the case being
executed
Storage of input namelists, dxcept experimental data, for the
case being executed'
10 Storage of experimental data namelists for a single Mach
number
11 Storage of all input data after processing by the input diagnos-
tic analysis module (CONERR)
12 Storage of extrapolation messages for processing by overlay 57
13 Storage of output data for use with the Plot Module as a post-
processing option
107
SECTION 6
PROGRAM CONVERSION MODIFICATIONS
6.1 GENERAL REMARKS
The program was written in Fortran IV for the CDC Cyber 175 computer
system. Several program modifications may be required to run under other
Fortran compilers or computer systems. It is recommended that users imple-
menting the program for their computer system become familiar with their
installation operatLng system and Fortran compiler requirements. Users are
forewarned that program core requirements and run times discussed in this
report may no longer be valid.
6.2 PROGRAM STRUCTURE
The program is composed of a root segment overlay (overlay 0), fifty-
seven primary overlays and twenty-eight secondary overlays. Table 7'shows
the overall program structure and lists those routines that are contained in
each overlay. In the CDC system, the first routine in an overlay is called a
"program" and subsequent routines "subroutines." Several subroutines appear
in more than one overlay. These subroutines are called "common decks" and
are listed in Table 8.
6.2.1 Calls to Overlay
All primary overlays are called by the root segment overlay, and
secondary overlays called by their respective primary overlay using the
calling sequence-
CALL OVERLAY (4LDATC, XX, YY, 6HRECALL)
where: DATC is the disc file where the overlay is located,,
XX is the primary overlay number in decimal, and
YY is the secondary overlay number in decimal.
Hence, each overlay is written to a disk file with the name "DATC."
Users should refer to the Fortran reference manual for their system and
determine the correct overlay calling procedure.
6. 2.2 Common Decks
Several subroutines are used in more than one overlay. The most commonly
used routines are located in the root segment for access by all overlay
programs.and subroutines. However, several decks are used by only a few
109
. . ......... ....
routines and placing them in the root segment would require an increase in
overall program core size. In order to maintain a low core requirement,
these common decks are located in each overlay in which it is referenced.
Warning - Not all systems allow two routines to have the same name even
though they are identical. If the user's system does not allow this option,
three alternatives are available as follows:
"o Rename each deck that is common, and change the calling sequence to
it.
natives are available as follows:
"o Place all common decks in the root segment (overlay 0) and re-
move the deck from each associated overlay. The user will increase
the overall program core requirement by using this technique, how-
ever, it is easier than the procedure outlined above.
o On some systems that have multiple region capability, these common
decks can be placed in a separate overlay region.,
6.2.3 "OVERLAY" and "PROGRAM" Cards.
Each primary and secondary overlay main program contains these two
cards. The CDC Fortran compiler requires all overlays to begin with an
"OVERLAY" card followed by a main program which begins with a "PROGRAM" card.
These must be replaced by corresponding code required by the operating system
and compiler being employed.
6.2.4 End of File Tests
Routines INPUT, CONERR and XPERNM utilize a transfer on end of file.
This statement must be modified for the Fortran compiler being used.
6.2.5 Use of 'I'.JJSED" and "KAND"
These cnstants are set in' BLOCK DATA. The value for "UNUSED" is
setin the program as 10-60. It is sometimes used as a program flag and is
used for initializing all variable arrays, to some number other than zero.
The value for "UNUSED" can be changed if desired and must be defined in BLOCK
DATA as a small positive number. The variable "KAND' defines the alphabetic
character used by the NAMELIST i-tputs. It is set to '$' for CDC systems.
110
- -~- ---- ---. ----
SECTION 7
PROGRAM DECK DESCRIPTION
This section contains a description of all routines in Digital Datcom.
Table 7 lists the decks by overlay, Table 8 lists those "common decks" in the
program, and Table 9 describes the purpose of each deck and the overlays
referenced. For convenience, Table 9 lists the routines in alphabetical
order. Table 10 discusses the use of *each of the variables in the Digital
Datcom control data olocks. The description of the plot module routines is
provided in Volume III of this report.
A complete program listing, which includes Digital Datcom and the
Piot Module, is provided as a microfiche supplement to this report..
Ill
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I-133
TABLE 8 PROGRAM COMMON DECKS
Deck Name Overlays R-ferenced
ALl 7, 10, 20, 28, 35ANGLES 2, 13, 15, 16, 18ARCCOS 12, 21, 41, 42, 50, 53ARGSIN 21, 41, 42, 44BODOWG 7, 10, 20, 28, 35CALCALC 31, 33.CALCAO 15, 16CDRAG 3, 5CLMXBS , 15, 16CLMXBl 24 (Both Secondary Overlays)CMALPH 31, 33DFLCON 41, 53DMPARY 11, 39, 42,46, 47, 49EQSPCE 4, 6EQSPCI 4, 6FIG53A 3, 5FIG68 21, 42GETMAX 4, 6, 29INFTGM 2, 21LIFTCF 15, 16PRSCID- 12, 39, 42, 46, 47SETUP1 2, 18SIMUL2 38,'42, 47SWRITE 12, 39TABLEC 7, 20, 25TABLES 7, 24TBSUB 7,. 24TBSUP 7, 24TBTRN 7, 24TEST 1,34TLIN4X 17, 25, 26, 52TLIPIX 43, 44, 45, 54TLIP2X 43, 44, 45, 54TLIP3X 43, 44, 45, 54TRANF 24 (Both Secondary Overlays)TRAPZ 4, 6, 9, 19,.23, 26,29, 37, 46, 47WBCDL 7, 24WBCMO j 7, 20, 25WBCM1 25 (Both Secondary Overlays)'WTGEOM 2, 18WTLIFT 15, 16YUP 43, 44, 45, 54ZERANG 1, 2, 13, 18
134
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rO d= a , e
6 -8- J
clL)JL LA-L
co (a z0 CD
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= w- =~v UI- co b.f ;=I-U u- U-~ Ln wU coLU( J
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CD <)D C.D, < < oc.JZ -~i0 I uLU 0/ WI- U. V) 0 IU)- CL)LV)LL I (nU CD U-U C)
= u ~ =u. z Ln cn F U 1&n'0 ..J OL. a. U. I1 U- C; V;~ *
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u) ..- J 'n-0 CDi w -I,
L)~U 0- QLa W J z 40 a~I.L ~ ~ ui
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U-LU L uj u V) U- 0 w
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<J V) -iU LU 0- " <. C o<D:c 3
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C9L L %O .u u U uu .W V
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L . -J -J U ~ In O%". c
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~ L~ CD u4 C-) U) " Q 0 4 ull 110-- Li<CI v -. .i fp 00 m C. M 0 D co U 00
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LUJ
CD I- L/3 4i LJ -LIP w. =) =J .a o c o
0D e 0 0 & OW I <~ u -a L. I-=& -4 LJ0 12 0. (A OL.)
0 Dc LJP .O U. CL F L A. Lu L=. - s- 4 *ý ". .. J( I.- Ln Ln O
U =. < . U.. _jL .L J Ln =- (0 1- -Cn ZA -4 u < = L 4 CD~ LA- 1= LL Ln <
o 5-x I U ) 4 C) =L 1-- 0 (DX = .C) LU Q6 I- C.) P.-~-0D 0iIE - cEi0=I.a -i L). >- ce -E mLL A
-LJ WD L6 w1) V)O 0 m L L~~V)- L)D) F-L LL L . zj
cc -. < r%4 V) Ln V) I.. - 1 -
0 00 Cn L- -1 J 0 0 0 0 0 C(m~ ~ a a: ce w5c<=-jA0" .J V)a.a.LLJAO tmP AJ Sa
ULOf -0Ln (A (A L- UC UJ -J OL)aLa lUJ L&J~ " ~ LUJ LLJ 14 Il j r-4 a-T< C
U.S '-J. X.S LU ceJZ ~ ~ . .. S .
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LiJ M' ~ CJ ~ ~ If ' n S U ) 4- en w m- 4- - 0< en
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139
l-4
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IA uULJL w I F- -4 <. 0 6.4 <Z Z~LAJ LJO0 Ln i < Z0 co L =
a-0U. Lj LA- < = 0 L.) 0-
x- 3:AO . 1 -J -J : e L : = " COL CD Z caJ C6 I-D CDA w Ln = C UZ
= -= (-) UU U Z .Jw nU3 LA < -j W :w =..J. = (A(A. - 0 Z 0
(A I--c ~i LL. < >. wd V) (n (A 4n ( -n LUi L A- LL Ia u w.O L 00 (A OLJ~
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0 C> = V I-i. w 0- ) A A( A A(L - i U w . < U'iJ (D LD i
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140
f.-I cc ) vi)
a- Ln
(A 1' 0 co5 LUJ 0 ) ..u -.=U
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F- Ln V -u
w.. . o CD Li Li O) (UL; .U- 4/) L"
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J =, LU = M- =U =A =/ =A D = = ,=
.U &U 0.) a& a Q I al r; a;Is
1 - c w.. >- >- >- >- 'o r - ~ .. - -
In Q J J - -J -J -J -J -.J -J _j. _UJ .J . jJ
uj .J wi. L . L L a Li. LL Li. Li~ w L U. wL wL LA. w L u. Lw wA
w- w w w LU LU LU LU"UL UJ LUL UL LU LU LU LU L
::w U.. C) LU LU L U L U L U'U L U L U L LU LU L
*J M W n .. 0 J-
VLU e ><u 0, (\J en -4 LO) to0 P% C Q ft ML -m L.Lem e
wL CD LU .n %o ~ I 10 !. 0 - ~ ~ ~ a r-. .
141
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(A >- clV A L A IL .) 0)L
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(A -i 'C> CO A Lj 1.) Li.Z) ... 0 C.) C.. >- .J .) -
LU 0Co . -i -J = = - .. J 5 cc- ;- LL> - < icI I.- ~ J Li
Oz Z =CJ I-I w :
>-CL :m <LI 0c) u -C C'
Ww a j 1LI-4 "' (A wi
LU U w
LU C-3 0 '-ý C) C.. a~ C> C). 0 C
3.. (A (A V) (A V) CD 0) 0 n C.A Ln wAO c 1 C -J CL.I-- = =A wA = ) L = = == =
cxCL CL 0. CCL CL a- CL cnC m
a. C..3 V) (A.( V) V) (A L - Ln (A -1 -3. V) Ln (A 0 U-CL Li..0A
q(AO C. -
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-L" L LL. L& L& LA. LU U.U LA. L 6 LUL LA.UU LU LU LU- W U.) L
LU L LU LU U.) LU LU LU LU LU L" u LU LU LaU I. La WU LU W
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x 1C :< X> K X X >
L" LU w L U L u LU 10 f%. eo c" LU L U LU C2 I LU 4U.L LU
L(AL
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C)-
xA -i U- C>uu
c U0 Li-
o (L w wa <L= w 0 >- uJ u
LU- C> cm <.J- -
a- m m CM >-w C5 at I CA Co) = m C
-cJ <. -cc < m=
U. f- -LLJ M0 I L u i -i wC
W P- 0 =- - 0<LUCCo =~ Co- 0D U K Cl <
- CA.. Cn a0 - Co~ = Q = U
CDI a. V ) - C 5 (5 = L.U ( 4 Co -
O ) Q.. (/ Q -) M < . (A cc. LU -
0J -0J -A 0 J -J -3 -j _ j
a 0 C C>a CA (D Cl LU CD Q Z~ (A- aA .a Q(ACýC
ao C a (Al CoU (D a CD a 0 CL Icfl U0 W (D 0CU. U. . . 0- . _. U. U. w w a. . " W-)
0% ~ ~ ~ > >- UJ 'U 0J UJ UL. w Ju Ju JU LU u u
C-)~~~~- ta a * a a a * * aL" U JL JU W L SW w U jU Uj oujcae uifL
0m 1C > . C :C 24 X X ý < x x x X 1--JU JU JU JU u aU JU J 6 U
kn .
-W L.J LU Ln Ln LU Ln Ln Ln LU to to L0 La %a LU LU LU .i
~L L LL h UU LL ULL
LU zUL I~ itL ULUULL LU LnJUU L Ln LU
LUL~ L U U U U UUJLULU .U U U UL143LUL
C-9J
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0 0 t-) CL L A0~ ~ LJ f ..A j
LA.1 (j ui Wp o t0 ~LAJ 4x
I.-LJ Lai ~ a l
L*4 .j -. L<L LLu a).. = =
4.jo _VLA LA. U
tJUJ L,& ce C L W LJ
LA.' ZE C_ jZ
W 0> cc jC. C
o 0 Ujeý0 ACu~1 ( a00I-- ~ ~ cJL & JL U. I --
cla .- L, C U.0= c
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LL-. - "
CL V
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Li rl cr CC Wi SI- -i ui LM
0. Ul 0- JM '-C> tn -n U- C> m
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Lii 1-J < -< 1- ...J Licm - < CA (5C <- L' V)0Jc
0< 0 ( = A =A wA m 0 <~ c-C
P -4 >- CA ELJ CJ-) CC 1--
0.-~4 1- L -jC CD -tc~ia ma~- - m < tn CA
L) CA LiC1-. 1
a) V) ý4 = Zl( LO CA Li X =
VO Q- >- u Z:C:i C> C= -4 UJ C) 00j UJ UJ J
w =L =- E-4C> W - >LD V) U- .V) tn-
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*CA 0 :I- 0U 00 LU W UJ U W W
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(n w.J. C) .__ -(D 0i C) ui a < 0 5 c a. < <~ <- 0 0 0 0 0<.U Ui .I) Ui 0) V. V). CA U Ul UL V- Ui U U CA CA C CA CA
wJ L iD Ln 0 0n 0; CA. CA 0.D CA CA CA CA C-U m~ m - i.J 1 0,nC
Li Lo M. Li CM L" tn Mi U.. U) Li V1 U,
=i u0. L qrL LiCD Li =V. 1-0 00 0. -j -. C.. uj < X: X - C < >
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LII
LLI-::I LI)
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0 <JC>~I cc < I-
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u C) 0A uJ :j
I- o L i >-~ 0>- - ui
Cl 0. E -i LIi U
LAJ CD 00 iz i C.. *0I-- r-4 r-4j ca c d F-
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cc m m ~ = ~= = >. -j -j::.
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ULt u u u )
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Lii Lii
oD LA -W c U') 'IJ V, C.J -W LO -c w e~CIA . % .~ . . cli~ "r w
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146
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LAJ Lm CA-e z u.
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REFERENCES
(1) Glauert, H., "The Elements of Airfoil and Airscrew Theory," Cambridge at
the University Press, 1948.
(2) Polhamus, Edward C., "Predictions of Vortex-Lift Characteristics Based
on a Leading-Edge Suction Analogy." AIAA Paper No. 69-1133, October
1969.
(3) Polhamus, Edward C., "A Concept of the Vortex Lift of Sharp-Edge Delta
Wings Based on a Leading-Edge-Suction Analogy." NASA TN D-3767,
December 1966.
(4) Stivcrs, Louis S., Jr. and Levy, Lionel. L., Jr., "Longitudinal Force and
Moment Data at Mach Numbers from 0.60 tr. 1.40 for a Family of Ellitic
Cones with Various Semiapex Angles." NASA TN D-1149, 1961.
(5) Spencer; Bernard, Jr. and Phillips, W. Pelham, "Effects of Cross-Section
Shape on the Low-Speed Aerodynamic Characteristics of a Low-Wave-Drag
Hypersonic Body." NASA TN D-196, 1963.
(6) Spencer, Bernard, Jr. and Phillips, W. Pelham, "Transonic Aerodynamic
Characteristics of a Series of Bodies Having Variations in Fineness
Ratio and Cross-Sectional Ellipticity." NASA TN D-2622, 1965.
(7) Spencer, Bernard, Jr., "Transonic Aerodynamic Characteristics, of a
'Series of Related Bodies with Cross-Sectional Ellipticity." NASA
TN D-3203, 1966.
I (8) McDonnell Douglas Corp.: USAF -tability and Control Datcom. Air Force
Flight Dyn. Lab., U.S. Air-Force, Oct. 1960. (Revised April 1976).
(9) Centry, A. E., Smyth, D. N., Oliver, W. L, "The' Mark IV Supersonic-
kypersonic Arbitrar Body Program." AFFDL-TR-73-i59, 1973.
'155
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