AFFDL-TR-79-3032 • : ui.-" Volume T1 ADA0864 5 58 THE USAF STABILITY AND CONTROL DIGITAL DATCOM Volume HI. Implementation of Datcom Methods 416yo 7X7 .1350 MCDONNELL DOUGLAS ASTRONA UTICS COMPANY - ST. LOUIS DIVISION ST. LOUIS, MISSOURI 63166 Reproduced From APRIL 1979 Best Available Copy TECHNICAL REPORT AFFDL-TR- 79-3032. VOLUME II 1E C: 'E Final Report for Period 'August 1977 - November 1978 JUL 10 1980 A Approved for public release;distribution unlimited. 0. AIR FORCE FLIGHT DYNAMICS LABORATORY 0 AIR FORCE WRIGHT AERONAUTICAL LABORATORIES C-) AIR FORCE SYSTEMS COMMAND It' WRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433 SO 7 7 C38 X..=.
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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
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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
If your e dddzws has changed, if you wish to be rzwnved from our mauiling list,or if the addessee is no longer enployed by your, orgwmxaation pZea.. notiAA•WAL/PIC,, W-2AFB, 08 45433 to help us maintain a ournent nviting list.
Copies of this report should not be returned unzless retur is required bysecurity considerations, contrictuaZ obligations, or notioe on a speoifodocumn t.
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).
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.
• , , . , .1
- . . -, . i - .
44-)
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=A CA..
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Laf Liii S.. C
wj0 Q - 0
C- LU
z i-
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CD Q. QA CD CD C C.
= tA Ln ,.n (nC= (DLV) Ln
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w CJlCNJC% *- *C -j 4 (~4 -4 -
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=U La) 0,=L A n2 W i A=w.m co C . . l-d-CI~V I' Ii WV) V) V) 4 Ln ) (AV) 0
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:
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
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,
L" LU w L U L u LU 10 f%. eo c" LU L U LU C2 I LU 4U.L LU
L(AL
>1142
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
-J OLJ
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
-JC osA j L. 9 c
LuL&J
___ w__Ix I1.........--. C . .imaii)ii 1 ~~
LL-. - "
CL V
>- w
>- 4 0D U- ~CA co (n w
Li rl cr CC Wi SI- -i ui LM
0. Ul 0- JM '-C> tn -n U- C> m
P4 V)M <.lý C j ?5 C3- -Z
=D uA (A0 M -iCkaA 0 - L <X C-) - CD I- CL= U tn LiJ -) < Li S
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-
:2.~40~ c d0~ to CACAJCA o m wC..) .C~~ J CA 0 n CD A 1 1- C - Li i
0 C (A1- ~ i US 0. tn V)V C/0 (A
< Li 0J W.L ~ L 0. 0 - 0. 1~ < L/.)CA iW 0 CA -- ='0 - V)V n L CA C5- L ) 0 ) Ln V)(
*CA 0 :I- 0U 00 LU W UJ U W W
-j ~ tn 0) Li 0J u.J __ Iu Li Li -CC O 0 0 -- 1 4-2 -
(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 < >
E~~~> CA = -J, a. a. = -- ~- 4 . O - 4 i0 i0 L 0_Li <i 0 0 0 M0 C, C- V) CCL wC mC Ca.. I= V.) V) V-) CA V.) CA CV CA CA V-) CA (.C V-) Ln V) CA .)0 tn. V.) V.) %n.
14
LII
LLI-::I LI)
- U- LA-
>- (A 0n L
0 L)LI _j "
0 <JC>~I cc < I-
>- <- I LiJ Lu. .LU1( 0 0 0 0
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-
- 0 E 0= -i -i -i
u U 0 r-4 - r-.i r-oD c) ca>- (.D o LL- CD tD LL UJ (M -- biJ-
ULUJ 1 C3 = =0l = = DC I-*- = cI-0 CD 0 '-"k- CD0 C) *0Ln C UJ LAJ0 Q
cc m m ~ = ~= = >. -j -j::.
~~~C C~C.) C() () C . . ) a CD. a CDO a .. 0 a.
m - m0 0 0-0. 00 .u 0.00 .00 -0.00V- (f) (A V LI) V) I) C/) -i Cn V ) V) ) V) V )V n V
L/ (A) LI) LIVI ) $A) C ) . J L ) VI) ' Cl) L(A L ) C/) L ) (A) L(A L )I.--
uL) LI I LI) LI uI U.) u u C-)' uI uI u/ w u/ ul u/ /Lii Lix Li i i i i i Li Li Li L J. Li Li i i i i i
ULt u u u )
In= = = = 0= == =(A .).)(. UU.)..C) UCU U J
Lii Lii
oD LA -W c U') 'IJ V, C.J -W LO -c w e~CIA . % .~ . . cli~ "r w
0A a c== = = CY :m ===
V I) L) I) IA L) LI) I) LI) I) (A)CV) cl) V7) C) Cl) CI L) Cl) 4n) C)
146
oz
LAJ Lm CA-e z u.
= - U- IIJ 1-1 IU-z - V) LA - -A
0. >-. A(AC
_ (A .. JW -b 4 -P" LA U.. U-.>- w m- -i LU ClJ (
I -j -:r.- <~- <
I- ~ C - 2 1,- 1% toUL - a aJ
u F- w V iU
o- >. u0bJ ,, s Li .M: = w ( 0 A ( a( a U.1 U.1
(D 0 l 0::0I -~ b- LA. U-. = C i %..J w' 4:
cocaI- DU-U U- Q L .0 UJ = 4- '4- -4-.a a- a.C,. *n U. 40 0 L OW Lw . w. L ii cn l 11 11 if
oj ( 0 C-0 0C> 0L6 = 0Dta. w w OIxW >- >-U.1L Zj wZ LUL. 0 LiU.1 l tAm- I- C (A q ~ ~ i V)- ~ i~ x J C)=
0 a 0x - OZ~ 0 w w F-w w . w U
~- 1u uL -. V )(l)4 w Zu WZZZbZ * *V) (n (n UJ .4 I (ZW A~ =0L U 00P-0 0I.
0iU1 .~Z U -. L .L w UJ U 0.1u O 00.10
(A ~~~0 (AAi Zi (AZ UL i Z L1 -- 1111
=U Q U JL J Uu
C" Ln (n (A u V)( n I- ZZ Z
C5 Ln 1-W U C L0 i 4 L C.0
U, - u -(%Lfl LlU I
a a a
CJ cc CJ CJ 0.- u~I.% ~ I -% bD 4 ( O 0i i a aj aj
LU.
0.ON. .0 0 L A ( -( A L 4'4 ~0~~~ ~ 4 44 0. 0; 2n Ln U ~ .J. .j...j..
(A ( A( A ( Ii1 1 - 1 1 1 1-j R- - -W #-1 Wit
cli.4 N " C~ 147.
In~~ -oq
/j
V) -4
u 0ý
C> -i C, I
0L -) <(~
Zi E- C) d
o- 0oJ=I 1
0 uj co qt ~L) 0
-J 0 ~-J:3 LA UE ' -
w- V) 0j .r X UJL#
0 0 0E CO 0J 80 Ln I.-- - * C/
Lii~ LL U . .J
09 .2 0D Z 00 U- Z3 C)
I L.) M0 3,- F- r-J F- <- U ".J d
5- i 0 C ~ . C.0 Lo I-- -j -. iC 0m
0. U. L ii >. i V)i i -
I- V) C-) V) u ca)LJ a
In, (A)V V) w u I " 40 C3
0~ U-=
.) ) In In In VC..ul V) 0
-Li
w- w . w_ _ j - _ J i
< iC.)J-C.) LiZAJ- < < < < vi)
"i u i u
OLI C% .J jJ C C~j C 'j C. C~i w en) eni. mV c m) C' g C
148
LA.
-J L)0L
CL 0 C)caAL
uLij 00
-L 0n CD(Aý( <wA L
= LL c -j L iJ
C-cf.. - 0L.
0ý I =) ui
o -i
u-i ' ~-C 1- =A C)D fm I D1- w- cm 1z 31 1 2c (DL
cc . =- >- =LJ i -i .J 0- 1 0 4
Li 00 C. U L .
U L ) 0 =O ) _j _= 1-4 o c CD co' CD
Li = -i C.. cc: Li=Z ) -vi - V
1- ~ L L < > 0 ) =. co I- co coCC 93 w 0o 0 m V)l
Ll u u > L .>. 0 0 0 .41
LiN 0p I--<- -C I- I--D !Z C 0
1-. -C <) 0C 0ii -
CC ::C M CDC DZ 0 <D cC<D
0J -J -J Li J-i 0 -J -j -j - <- 3 _ - i <- 4
_j _j _j LiJ (A UJ -J (A I -J -J -J - J=i - 10 ;o=zo 0 _j _j
LCJ U (A L J U~ U A =j L>A ( U U
w C4
u< La.a)(A- (A (Aý( (A (A (A/Lf,(( (A (zA( (A Ln 0
Lil Li enL Li Li Li Li .Li .Li L: L L i Li Li l Lin i L L 4 L
uj -iIcU. U-
149
LiJ Lai
X-,
P-4
Li ~ (~DLL -4on C. tAL
Lhi w0') I ~ 4 Q
7' < r.a UJi
-4- CL V) .- L .~~- -
40.
-J I- LL ( LL&.
I---(
-~~ ~ a.~i .. JD D&.
-j -c L.(A ~LL.cc~ WL><iL J Li D-$(D
ccn-~~ w -I-- I)
r.i i L5 wA-w
~~b- -- 44 -
a W W .J
o. U--0.Di
0- 0. A. f-I.C
________
*..n~-
%0~- Lb-c-
Li 0
5 0o
C12 V) U LA-f44, I-- L
-cc
-j I-- Cflu I-s ;5
C'. Li. )- *i Li
.-o >4 m LiJt...Ji 64 -Z V)
V) a-O CDO~ =0 oxNe 0D U) >- -1 0. =i V) C
a. 0 u. i kn C). 0 ico X D u - en
0. UJ CDP Q-i~
a- U 0- CAiLa~l 0 -O a. U- ) (n = 0..
LM N4 < a ~ 0-Li w4 L.-i uJ X u V) ~ Li f Cn0.. 0
dZ ( J U ) L A . U .L n- i 4 i <
o2 = p f4 Z~-L0. . - L/&n U, tn. =) I--* 0 o: C~l >- >-U (n tn
CD 0 -I-0~J . a. L) -j 4x=i V- )..JUJ Li. ~ =44~ "*ICC <-< - i u.Ji c.D (nU)
oc VU) U i U)V) CD I-'- ý- (A %L Q . U Cý- < 0 -4 cn-L-.i Z l C i LAi P4 401-I- w i >- CD I >. L"~ (W u .-j
a. > J V)L W 44 V)...J V) u ( I i ..JLi CDLa U- 0- =~ =Z-~Z ýL. I =~ U- = x L6. ui
Li (..) Li w -O .4.. b C U
C, 0J 0- FS ~ w pd Li Li 0D L"..>- = - U.._. w -Ji .0L L C1 0. U- I 0
CC'- wi L U) M U) i-) U- P" Li2
W U) W. cn 4n . .. Zi 0
u- J
ca i uiQ L)4 I--J U
0C) ca w
151
I,-
LAJca
It e
M% M oJC
V) La.J 0J - z
M - W 0. -cc.
V) L~ 0 :E I ( l w w 0.z U. .
w- I m~ C-) :o =J LA L LAJ ým _ C
(/ 0e L < x x > D C L C LL.
LAS V) 1 " LiAh LU W Lh .1 L u - > -. 1.ýjLAJ Ul ix C.. >- (. * * (- '.
0 0 X ~ Ij. Li.. (D =i. LA.LA. CSL Li :cLL- < -A co4^ c -- c 1:5 - -
LO LL LiJ -ccLA >- V) Mi LiJ3 J Li
CC tm-j-Q
-JL
C) - 190 I - 1 0
ES Li
Lii
152
-j =D0
V) V) V) j LoL LAJ U, A-U
CK:~> U4 cc-----c
-AJ LIJ V) . -j L iJ 3c
co a.> L V)C n w &w ( x. >-. x- m. i.(-3V F- -- V) = :3.~ CL CL >. -)3c k == > Z a Q. 0 ". = :, tnU A .J ..C.)# *I1- A^ C.) , C.)C 40. 441 4001. 400 0) Ln ~ L L.
i. LL . LL.
cr.S
-j m- in c c.s V . Q-
CO I... I- - - n L V . tLA
-J 0. C) CL t.0 a.0. o CL~-.. C.AJL 0w = 0.C' 0 . ) 3 W Z a
U. 1 Z06 -- j .J I.- !fl Q,~. ( - 9
153
-J
LO
II.
(ajL-J
cr--
.1 =
0j -LJ LA. f
0) -I cc i0. J UzC.
= - kA LLJ =D LI- c L
a.0. )0 Mc
-i U. .LS
co Mi MU, -ý' I-Il U jT
o. w LA. w w
U.: Li
CO La Ij 2: C
Im:M t-L ~ U0. U, 0LL~ 2:~ Li : ECo
Li0.k LLi U. -i Z 0
IQ Z. U~0 V 2~ O W 002
15
~ U 0 . ~ 4 0 Ti 00
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-
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