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NASA CR - 112229
A PARAMETRIC STUDY OF PLANFORM AND
AEROELASTIC EFFECTS ON AERODYNAMIC CENTER, a- AND q- STABlLW DERlVATIMS
APPENDIX A
A COMPUTER PROGRAM FOR CALCULATING
DRAG FCR THIN ELASTIC AER3PLANES AT SUBSONIC AND SUPERSONIC SPEEDS
U- AND 9- STABILITY DERIVATIVES AND INDUCE0
bY J. Roskom, C. Lon, and 5 . Mehrotm
Cctober 1972
SASA-CR-112229) A PA?AWZTRIC STUD? O?
STIIBILITT P E R I P d y V 5 S . A P P E K 3 I X 1: A (Kansas Univ . )
173-21897 PLAMPORR A I D IZPOELASTIC E z ' F P Z S CN AERODYlA3IC CENTER, A L P H b - AND 9-
U n c l a s 775 D AC $ 1 0 . 7 5 CSCL 01A ~ 3 ; 0 1 02002 w- t!:
Prepared under NASA Grant NGR !7-.N2 371 by The Flight Rtzxrch Labotc,. J
Deportment of Aerospace Engineer rng
The University of Kansas
Lawrence, Kansas 66044 for
Langley Research Center
National Aeronautics and Space Administration
https://ntrs.nasa.gov/search.jsp?R=19730013170 2018-07-01T08:19:00+00:00Z
Chapter
1 2 3
4 5 6 -. I
8 9
10
11
TABLE OF CONTENTS
Title - b age - Intduction .............................. 1 Table of Symbols. .......................... 4 Preparation ot Input Data ................... 10
3.1 Preparation of Planform Geometry Data ....................... 11
3.2 Prepmation of Moss Distribution Data ...................... 14
3.3 Preparation of Structural Data ................................ 14
Input Data Format ......................... 15 O\ryut Data Format ....................... 22 T a t Case 1 .............................. 26
TestCase 2 .............................. 38
Test Case 3 .............................. 59 Computer Program Listing ................... 72
Appendix .............................. 1 70 References .............................. 173
... Ill
1. INTRODUCTION - The computer program used t o determine the r i g i d and e las t i c s t z b i l i t y
der ivat ives presented i n the sumnary reoort (Ref. 1) i s l i s t e d i n t h i s appendix along w i th inst ruct ions f o r i t s use, sample input data and answers. represents the airplane a t subsonic and supersonic speeds as (a) t h i n surface9s) (without dihedral ) ca.posed of d iscrete panel s of constant pressure accordin the method of Woodward (Ref. 2) f o r the aerodynamic effects and slender b3am s) for the structural effects.
influence coef f i c ien t matr ix (PI and a st ructura l inf luence coef f i c ien t m t S * i x [C] by the methods specif ied above.
This pro r a m
‘i to
Given a set o f input data, the computer program calculates an aerodylamic
I n a d i f f e ren t opt ion (C] can be read i n frw tape.
The s tab i l i ty der ivat ives determined by t h i s program and the equations used i n t h e i r calculat ion are given i n Table 1. r i g i d s t a b i l i t y der ivat ives (as well as ACP) [A] i s needed, whereas f o r e las t i c s t a b i l i t y der ivat ives both (A] and [C] are required.
The program i s compatible w i th the geometry requirements and de f i n i t i ons of reference 3 , using assumptions defined I n the Appendix t o th is report.
Using the method of Reference 4 the program i s also capable o f computing CD+/CL* f o r r i g i d and e las t i c wings.
From the table i t can be seen tha t f o r
Stability Dcrivativcs for C) Rigid AitpIrincr
Ocr ivaf ives
C mQ
m C
q
For mu I as
Stability Derivat:ves for an Equivclent E
Zero mass
(constant
load factor)
Derivatives
C La-
E
ma- I
E C
m C q i
astic Airplane
Dimelision
Formulas
-1 rodion
-1 rad ion
-1 rad iar I
-1 tad ion
D imensim
radian - 1
-i radian
-1 radio,,
- 1 rad ion
Tablc 1 Lon!iiludinal Stobility Dcrivativcs for Rrgid and Elastic Airplnncs
2
- Stobil i t y Dcrivcitivcs for an Equivolcnt Elost ic Airplonc (cont iriucd)
Note:-
Inertial
(varying
load factor)
Dcrivativp;
b n
m
b n
bC -
C E
La
C E
Formulas
- 9 C t . wI
- 9 C m . wI
-' c acL 1 an -1 b-
'trim E ( 1 - -
D irncnsion --
non-dim.
non-dim.
2 se c
2 sec
2 - 1 sec ft
2 -1 sec ft
non-dim.
non-dim.
radian -' - 1
radion
Table -- 1 Longitudinal Stobilily'Dcrivativc!s for Rigid and - Elo:tic - - Airplancs (Concliirfcd) ----. -
3
2. TABLE OF SYMBOLS
The units used for the physical quantities defined in this paper are given both in the International System of Units (SI) and the U.S. Castornary Units.
Input Data
Symbo ls Dcscr ipt ion Dimension
ALT AI t i tude Feet (m .)
ALT NU M Number of altitude runs to be made
AM Mach Number
AMASS (I)
CCI
C.. 'J
Mass of panel "1" Structural influence md/lb. (rad/N .) cocff icient matrix
Structural influence coefficient , angle of attack induced on panel i due to a unit load on panel j
slugs (Kgm)
b (rad/N)
CLDES Desired I i f t coefficient
CPCWL
CPSWL
CRE F CSHT
KONl L
Constant percent chord- wise lines
Constant percent stream- wise lines
Reference Chord Feet (m .) Structural root chord of Feet (m .) thc horizontal tail
Structural root chord of Feet (m .) thc main wing
2 2 E l value of the i th elastic Ib- inch (N-m ) axis segment
GJ value of the Ith elastic Ib - incf 2 ax i s segment or Ib - f (N-m ) The Kth element of the array iASIGN and the number of an elastic axis end-point to which the Kth panel is attached
1 for fuselage geometry data
or Ib - ft2
= 2 for wing geometry data
= 3 for horizontal tail geometry data
= 4 for canard aeometry data
4
Symbols
LPNL (1)
LPNL (2)
LPNL (3)
LPNL (4)
M
MOVTEL
N
N1
NC
NCNTL NCONT
NCONTL
NCPl NCP2 NCP3 NCP4 NCPSWL
Description
Number of panels on front fuse I age
Number of panels on rear fuselage
Numbers of panels on main wing
Number of panels on horizontal ta i l
Maximum number of elastic axis end-points
= 0, Non-movable tail = 1, Movable tail
Total number of panels or, total number of unit loading points
Attachment point of horizontal ta i l elastic axis to rear fuselage elastic oxis, point number
Numbs of >ections of the aerodynamic surface
See Sec. 4 for complete description
= 0 i f geometr data are input
= 1 i f geometry data are prepared accordinq to Ref. 1 = 1 for front fuselage data
= 2 for rear fuselage data
= 3 for main wing data
= 4 for horizontal t - .I 4ata
Nurpber I of CPCWL on iuselage
Number of CPCWL on wing
Number of CPCWL on norkontal tail
Number of CPCWL on canard
Number of constant pe ient stream- wise lines
Number of elastic axis end-points
according to t b e present program
Dimension
NEA
s
NE1 GJ
RHO sos SREF TITLE W WDTHHT
WDTHMW
XCG (I)
XEA (I)
XREF
XXL (1)
XXL (2)
XXT (1)
X X T (2)
YCG (1)
YEA (I)
Description Dimension
= 0 if E1 and GJ values are in Ib-inch2
= 1 i f E 1 and GJ values are in
Air density
Speed of sound
Referenc- 0 area
Any tit le for computer run
Total weight of the airplane
One-half the width of the fuselage at the horizontal tail
One-half the width of the fuselage at the main wing
I b-ft2
x-coordinate of the loading point "I" x-coordinate of the elastic axis end-point "I" Attachment point of the main wing elastic axis to the fuselage elastic axis, x-coordinate
x-coordinate of the L.E. of inboard chord
x -coordinate of L .E. of outboard chord
x -coordinate of T .E. of inboard chord
X-coordinate of T .E. of outboard chord
y-coordinate of the loading point "I" y-coordinate of the elastic axis end-point "I" y-coordin l te of inboard chord
y-coordinate of outboard chord
Z-coordinate of the section under consideration
Sluss/ft3 (Kg/m3)
ft/sec. (m/sec)
f? (m2)
Ib. (N.) Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
6
Output Data -
Symbols Description
Aerodynamic inf hence coeff i matrix
a.. ‘J
ALTITUDE
AREA
CD
CDI
CL
CLALPA
CLALPE
CLALPR
CLI
CLQ
CLQEBR
CLQI
CiTDDI
CLTRIM
ient
Aerodynamic influence coefficient, load on panel i resulting from a unit angle of attack on panel j
AI t itude
Area of a panel
Total induced drag coefficient
Sectional induced drag coefficient $Li)
Total lift coefficient
C , Variation of l i f t coefticient with angle of attack f.x the elastic case with zero mass LaE
C , Variation of l i f t coefficient with angle of attack for the elastic case including mass effect
La E
C # Airplane l ift curve slope La
Sectional l i ft coefficient (C,)
cL
cL
CL
9
qE
41
C # L a I
C LTrirn
Variation of I ift coefficient wi th pitch rate
Variatior. of l i ft coefficient with pitch rate for the elastic case with zerc mass
Inertially induced variation of I ift coefficient with pitch rate
Inertially induced variation of lift coefficient with pitch angular acceieration
Dimension
2 -1 2 ft rad (rn rod-’)
2 -1 2 ft rad (rn rad-’)
Feet (m)
(Feet)2 (m2)
per rad.
per rad.
per rad.
per rad.
per rad.
2 sec .
7
Des cr id ion Dimension Symbols
CLWDl
CMALPA
CMALPE
CMALPR
CMQ
CMQE BR
CMQI
CMTDDI
CMWDI
CP
CT
DCLDN
C I Inertially induced variation of l i f t coefficient with rate of downwcrd velocity per- tur bat ion
'GI
C I Variation of pitching ma- moment coefficient with angle E of attack for the elastic case
with zero mass
Cm , Variation of pitching
of attack for the elastic case including mass effect
aE moment coefficient with angle
c # Variation of pitching moment ma coefficient with angle of attack
(i .e. I static longitudinal stability)
C Variation of pitching moment q coefficient with pitch rate
C
m
, Variation of pitching moment qE coefficient wi th pitch rate m
for the elastic case with zero mas,,
Cm I Inertially induced variation of pitching moment coefficievt with
91 pitch rate
c . . Inertially induced variation of
pitch angular cxelbrat ion "8, pitching moment coefficient with
- I Inertially induced variation of wI pitching moment coefficient with
rate of downward velocity ' perturbation
ACpr Change in pressure coefficient
Sectional leading edge thrust coaff icient
between upper and lower surfaces
8C /an I Variation of l i f t Coefficient with load factor I-
2 2
sec. per ft.
(set /m)
per rad.
per rad.
per rad.
per rad.
per rad.
2 sec.
2 sec. per f t
2 (sec . /m)
8
Symbols
DCMDN
GAMMA
1ASlGN (I)
MASS (I) REF. ARE A REF. CHORD REO sos VELOCITY
WEIGHT XCG (I)
XCP (I)
YEA (1)
Y
YCG (I)
YCP (I)
YEA (I)
ZCP (I)
Description
aC / an , Variation of pitching m moment coefficient wi th load factor
Dynamic pressure
E l Vu!ue for the I th elastic axis segment
Non-dimensional local circulation (C;,/Zb) GJ value for the Ith eiastic axis sesment
I un-ber of elastic axis end- point to which panel "I" i s attached
Mass of l th panel
Reference area
Reference chord
Air density
Speed of sound
= (Mach Number) x (speed of sound)
Weight of the airplane
-. v , coordinate of the centroid of l th panel or the lth unit loading point
x-coordinate of the control point of I th panel
x-coordinate of the Ith elastic axis end-point
Non-dimensional spanw ise locat ion
y-coordinate of the centroid of Ith panel or the Ith unit loading point
y-coordinate of the control point - j i Ith panel
-coordinate of the Ith elastic uxis end-point
z-coordinate of the control poiRt,. of Ith panel
Dimens ion -- - -
Ib per ft'(N/m 2 ) 2 2 Ib-ft (N-m )
2 2 Ib-ft (N-m )
Feet (m)
Slugs/ft3 (K9/n3)
ft. per. sec. (m/sec)
ft. per. see. (m/sec)
Ib. (N)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m)
Feet (m) 9
3. PREPARATION OF INPUT DATA
The preparation of input data for this computer program i s done in three steps:
Step 1 Step 2 Step 3 Preparation of structural data (Sec. 3.3)
Preparation of planform geometry data (Sec . 3.1 ) Preparation of mass distribution data (Sec. 3.2)
- - -
10
3.1 Preparation of Planform Geometry Data
The ground rules for defining the planform geometry and for dividing a planform
A general p!anform i s taken as an exomple. Its projxtions in the x-y plane and
The following paneling definitions should be observed.
into aerodynamic panels are described below.
the x-z plane are given in Figure 1 .
1 Break Lines
A break line on a planform i s a stream line which connects the leading and trailitkg edges and occurs when either the leuding - or trailing - edge has a slope discontinuity. Root and tip chords arealsa considered as break lines. A break line on one lifting surface creates a break line on the others. (See Figure 1 .)
Referrirlg to the x-y plane view of the planform, there are 14 break lines. Table 2 defines these break lines precisely.
TABLE 2
Break Line
1-1' 2-2' 3-3' 4 -4' 5-5' 6 -6' 7-7' 8-8' 9-9' 10-10' 11-11' 12-12' 13-13' 14-14'
2 Sections
Explanation
RoLt chord of fuselage Tip chord of fuselage Root chord of wing Due to fuselage-wi ng overlapping Due to break line 12-12' on horizontal tail Due to slope discontinuity at 6' Due to break line 14-14' on horizontal tail Due to slope discontinuity at 8 Tip chord of wing Root chord of horizontal tai I Due to horiiontal tai l-fuselage overlapping Due to slope discontinuity at 12 Due to break line 6-6' Tip chord of horizot+I tai!
A section i s a regiorr on !be configuration between two consecutiva break lines. For
The variable NC on inpui card 4 sets the ndmber of sections. the example planform of Fi9t"re 1 there are seen to 5e 11 sections.
3 Constant Percent Chordwise Lines. (CPCVUrL) ~
These are the lines which divide !he sections in the chordwise direction. In general there could be any number of CPCWL's in a section. In the current Frcqram i t i s limited to 35. These can be different or! different aerodynamic surfaces, The 0% and 109% lines are the leading and trailing edges of the section. For accurale values of C lines are se!ected by using the scheme given in Ref. 3. 4 Constant Percent Streamwise Lines. (CPSWL)
/ CL , these Di
These are the lines which divide the section in the streamwise direction. In general
1 1
HORfZONTAL TAIL \
X-2 PLANE VIEW
X-Y PLANE VIEW
Figure 1. Exampfc Planform
12
there could he any number of CPSWL's in a section. I n the current program it i s limited to 35. However, in case one section i s behind another section in the streomwise direction, or one section is directly above another section, i t is desirable to use the same CPSWL's. The L% and 100% lines are the inboard and outkJard chords of the section.
5 Pane; Numbers
board of the section and from the leading edge to the trailing edge. Panels are numbered in the increasing order of sxt ion numbers, from inboard to out-
6 Total Num5er of Panels (14)
The present computer program i s limited to 300 panels.
7 Control Point of a Panel
passes through the centroid of the panel. I n al l cases tke downwash control point i s located at 0.95 of the local chord which
?3
3.2 Prermration of Mass Distribution Data
In the wing-body-toil program there are three different types of mass distributions to be considered: wing moss, body mass and tail moss. A procedure for determining these masses cannot be given such that all types of airplanes are covered by it. For the family of parametric wings studied herex, a detailed procedure for the calculation of mass distribution i s included in Appendix D of the Summary Report (Ref. 5). It i s possible to develop such procedures for tails and fuselages of parametric families of oirplanes.
The user of this complete WBH program has the following options:
a)
b) read in a complete mass matrix from an external source.
use the procedure developed for the parametric family of wings in Ref. 1 to find the wing part of the mass matrix. Read in the other mass contributions irom an external source.
neglect the effect of mass and mass distribution. c)
Whether or not option c) is realistic depends on the type of airplane under study. In Ref. 1 it was shown that in many instances the effect of moss i s negligible. For transport type (low load-factor type) airplanes this i s definitely not so.
3.3 Preparation of Structural Data
Given an EI distribution for fuselage and EI and GJ distribution for wing and hori- zontal tail, !he rnefC13cl 3lvm in Appendix E of the Summary Report (Ref. 6). i s used to determine al l the input data for structural matrlx.
14
-c 0
-c .- 3
n
3 0.
6
c
d E !! 2 cn 0
YI Q) > .- c
9
c 0 0. 3
v) 0 3 Q
c
5 v .- L Q) -0
E 0 0
a
L
!2
N N
9 c c
c E 0 (v c
c Q Q, V X 9)
v) E 8 P
0 3
f c
0-
c c 2 a C I
P s P 8
0' 0
V P s f
U - 6
m c hl
15
E C 0 Q m C 1) (I 0
.-
-- - L .- C 3
0
0 0
3 C
0
Y
L
E
L
n - a, t 0 Q
0
9, 0
3 t
0 0 i-
cc
L
E
- &
n 0 > 0 >
.- +
f E 0
e C Q)
Q 9,
0
0, C
0 0 0 0 -0
0 Q
Q al 9 0
3
C
ul
E
f c
.- P
2
E
c c
n .-.
0 - h l m rt 0 -
II II :I II II II II
Q) m 0
Q) ur 3 rc C 0
Q) C Y)
.- - t 3 P .- 0 L U
C 9, U
9, Q
C 0
c 0 U
0
9, 5,
c
L
c
c m
Y
L
E i
0, c .- 3 C 0
0, C
Q)
m
.- - n .- 3 2 -f V
C 9,
P) a C 0
C 0 0
0
Q) 1)
.L
2 +
c n
%
L
E i
.- 0
0 C 0 -4
c - c
.- 5
-c C 0
9) C
9,
n
.- - n .- 3 P 0 3z 0
C 9,
9, Q
C 0
C
c
E c
c m
s cc 0
9, 1)
L
E 1
-2 0 C 0 U
C 0
9, C
Y)
.- - 9, VI .- 3 P 0 -t 0
C 9,
9, Q
C 0
C 0 L'
0
9,
c
2 c
c Y,
L
L.
n E 2
m 9, 0 0
3
0
0 C x 'D
9, 0 9,
.c L
Y)
.- E
I!
5 Lc. 0
C 0
0 9,
0
9, D
n
.- c
a LI-
L
E 1
I- z a * V t I - z z z w
4 0 v Z
C
-2 0 0 0 c
z II v c Z Z 0 V Z- &
v
Lc .- -0 a, c
n
2 n
-Y Y
2? v
3 's n C .- a,
- 9 c ! c
16
C 0
0 C 0
.- c - r"
0 c z
0 c
L. 9) 0 E
n n n n n n
c
h
L E ( 0 hl !Y Y
n
v!
c;t: 0 P
W
re C . -
v! 0 c LL CQ v
17
C 0
0 C 0
.- c
I
r"
. 8 E .- c
U Z
00
c
0 il lL
2 f u, 8 L
8 n v)
0 u- (v
c
Y
I c Z 0 V 'Z
- v! 0 u- c W
e . cn 0 c L L (v v
0 c
OI F c
18
. C 0
7J .- !?
. r! n Q)
5 C
Q) 0 0 - .
.Y 3 x u - 0
2 0
a, 3 0 >
m
- 0
P
z L 0 .I!
27i c 2 3
7 0
c m z - W
L Q) s I-
U C 0
C 0
0 C 0
.- c
- B
c Q) 9)
b b
C .- .-
Q) C 0 Q cc 0 .-
0 4- c
C a, U .- c c c c
0 0 0 0 - .- 0 c m w m v )
--c-
Q Q ) Q ) a , c c c c 0 0 0 0 Q Q Q Z
a, xl 0 >
-
8 Lcu-LcLc 0 0 0 0 'c, .E L b L l Q ) a , Q ) Q ) PP9xl E E E E 3 3 3 3 z z z z
'z)
2 .- m
i3 0-
II
. c
. c
't II II II
n
v! 0 u. a0
c
W
c 0
E u,
n
Q h v
/
L P, J) E
'D'
v 3 2
<v c
rn c
19
. .
4- e l 0 Ei 0 -i- W
LL
0 LL v)
c
Y
20
a, c 0 - !? .- 0
0
0 a 0
C
u-
c L
b
YI c
E" m Q, v)
v) .- X 0 0
0 P,
0
.- c v)
I
Lc
. z 'D C 0
c
21
5. OUTPUT DATA FCXMAT
The output data are divided into five sections.
1 . Geometry data
inputted. The format i s self-explanatory in the output printout. The output vari- ables are:
a) The number of sections into which the planform is divided.
b) For each section inboard and outboard chord coordinates are given along with the constant percent chordwise lines and constant percent streamwise lines for that section.
REF. AREA and REF. CHORD represent the reference area and the reference chord respectively.
The planform geometry data i s outputted exactly in the same way as i t was
c)
2. Rigid longitudinal derivatives' - Corn pu te r Var i ab 1 e
CLAL PR Explanation
cL a
CMAL P? C ma
CLQ
CMQ 9
cL
m C 4
3. Sectional Cdi/CI 2 and the total induced drag parameter CD/CL* for rigid cotit igura t ion
Computer Variable Explanation
Y
CDI
CLI Sectional l i f t coefficient (C,)
Non-dimens iona I spanwise I oca tion
Sectional induced drag coefficient (C,.J;)
GAMMA = C,C/2b where C = local chord
CT Sectional leading edge thrust
CDI/CL* * 2
CD/(CL ,. CL;
22
Total Induced Drag Coefficient
' 2 cL
4. ACp values for C L ~ ~ ~ o r a = 1 .O radians
Computer Variat l e
PANEL NUMBER
(XCP, YCP, ZCP)
(XCG, YCP = YCG)
AREA
CP
MASS
5. Panel assignment output
Computer Variable
I ' -
(XCG, YCG)
IAS IG N
6 . Elostic axis data
Computer Variable
I
(XEA, YEA)
E l
GJ
7. Elostic longitudional derivatives
Computer Variable
WEIGHT
RHO sos ALTITUDE
VELOClTY
Ex planat ion ~~
Panel number
Control point location
Panel centroid location
Panel area
CP Mass of the panel
Explanation
Panel number or unit loading point number
Panel centroid location or unit loading point location
Number of elastic axis end-point to which panel "1" i s attached.
Explanat ion
E1"rstic axis end-point number
Elastic oxis end-point location
E l wlue of the Ith elastic oxir segment.
GJ value of the Ith elastic axis segment.
Explanat ion
Total weight of the oirplane
Air density and speed of sound ot that altitude
= (Mach Number X Speed of sound)
23
DYNAMIC PRESSURE
CLT k IM
CLALPA
CMAL PA
CLQEBR
CMQEBR
CLQi
CMQ I
CLWDI
CLT D 0:
CMT GDI
DCLDN
DCMDN
CLALPE
CMALPE
Dynamic pressure
C h i m
E La
C
qE cL
m C 91
*I cL
C
C La E
rn C
24
8. Cp values for deformed shape
Computer Variables
PANEL NUMBER
Explanation -- Panel Number
THETA (E) &E, , . .a i
9. Sectional C,.,;/Cj - -n f igu rat ion. and the total induced drag parameter CDi/CI 2 for elastic
Computer Variables
Y
CDI
CL I
GAMMA
CDI/CL * * 2
CD/(CL * CL)
Explanation --- Non-dimensional spanwise location
Sectional induced drag coefficient (Cdi)
Sectional I:Tt coefficient (C y, )
= C,C/2b
Total Induced Drag Coefficient - - cL2
25
6. TESTCASE 1
This test case deok with Wing 5 of 2ef. 1 (see Fig. 2). An inpur dota cards listing i s given in Table 3. Output data fix this test case are presented in Table 4.
I '
A?= 3.0 A = 0.25 S = XIOSQFT (46.4SQM)
SCALE: 1CM = 2FT (.611M)
I I X
x \
Figure 2. Test Case 1 Planform
27
o . 4 0 Q ( C
0 .
o m c 0 9 \D
c o ....e.... . h'(C 0 0 0 0 0 0 0 0 0 0 c c c
P s 28
~ REPRODUCIBILITY OF THE ORIG1N1.4L PAGE 1s POOR. '
__ 5
OIOIOIOD 0 0 0 0 0 0 0 0 w w w w
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7. TOTCASE 2
This test case deals with a complete elastic wing, body and hor kontal tail configur- ation. Figure 3 defines the overoll geometry for this case. Figure 4 defines the elastic axis location. Input data cards are listed in Table 5. Output data listing for this case :s uiven in Table 6.
38
L t
4.160FT (1.268M)
/-
i
4 I
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- 5.824FT (1.778M)
4 8.925FT
I (2.720M)
1 8.90FT (5.761 M)
f 1 1
4
11 .‘02FT I (3.359M)
1 8.708FT (2.654M)
SCALE: 1CM = 5FT
Figurz 3. Test Case 2 Planform.
39
67 (20.
F i w e 4. Elastic A x i s End Points for Test Case 2.
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8. TEST C M E 3
I n this test case the geometry data of one of the examples given in Ref. 3 i s used. This geometry data i s reduced by the program to calculated rigid stability derivatives and A Cp values. Figure 5 gives the actual geometrical descl.iption and geometry assumed
by the program. Input data cards are listed in Table 7 and output data are listed in Table 8.
59
60
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71
9. COMPUTER PROGRAM LISTING
The computer progmm was originally written by members of the Flight Research
Labomtory at the University of Kansas for the Honeywell 635 computer system. The version listed in this document i s a revised version as optimized by Computer Sciences
Corporation of Hampton, Virginia for the CDC 6600 computer at NASA Longley Research Center .
72
Field length requid for problem
/CMROL/’, XCP, YCP, ZCP, XCG AREA, AMASS, XN, YN, ZN, BPRIM
FIGURE 6. FLOW CHART FOR MAIN LINE
73
FIGURE 6. (continued)
ALLOCATE COMMON FOR PROBLEM ARRAYS
COAMAON
OPE NMS 0 Open DISC Storage (TAPEZO)
Read CCMMON/CMROV From DISC
Read Problem INPUT From DISC, change DISC
MATRICES. *ndex key to store
8
74
FIGURE 6. (continued)
Initialize DISC index key for next case
75
OIGURE 6. (continued)
LlNKlL
AOICMX
(7) DELTCP a a DERlVR
Gew, ote Aerdynomic downwosh MATRUC (AW)
m = mi!-’
Compute pressure coefficients
Compute rigid Stability DER l VAT 1vf 5
Store A MATRIX on DISC
Compute leoding edge t hf\rlt emf fic ient, induced DRAC coefficient and (CD 1/CL)2 c j RETURN
76
FIGURE 6. (continued)
D U G CALL
NOR I ZO NT A L TAIL ONt
40 - HORIZONTAL TAIL TWO
Compute induced DRAG distribution
LEADING EDG THLUST I COEFFICIENT 4 INDUCED ORA CO EF F IC I E NJ ,
cj RETURN
77
FIGURE 6 . (cod inuc 4)
DERlV a DISMW,
DISMPY * (-)
MINV a MAT MPY * SETDRAG 0
Calculate elastic DER WAT I M S
(THETAE) = (CP)
Compu.2 LIFT DRAG PARAMETERS'
0 RETURN
78
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169
10. Appendix
Assumptions f o r Data Reduction from Reference 3 -
The present computer program i s valid only for thin elastic acroplones and therefore
requires the reduction of the anfiguration data of Reference 3 t o sat is fy the input data format. The following assumptions are made for data reduction . 1.
2.
3.
4.
5.
6 .
7.
a.
9.
10.
11.
12.
The "Y" locations of the chords in Ref. lines for the present program.
are assumed to be break
The height of the wing (ZAVWNG) is calculated by taking the average value of z - coordinates of a l l break lines. In other words, camber is !aken to be zero.
If the fuselage is not circular, it is modified to a circular s ' m p e by assuming a radius equal to the maximum y- coordinate at each station, the center of which is located at the omresponding z- coordinate.
The z- coordinate of the fuselage (ZAVFUS) i s found by taking average value of centers of circular section.
Half of t k fusokge width (FUSWTH) is calculated by taking the average radius of fuselage s=cticns at the root chord.
If IQAVFUS-ZAVWNG) 5 (FUSWTH/2), the wing i s assumed to be in the plane
mrd ina te of the root chord of the wing. of the fuselage, i.e., ZA ly 4NG = ZAVFUS and FUSWTH is replaced by the y-
lf the wing and Fuselage are not in the some plane, the wing is extended to the center line of the fuselage and the number of break lines for wing i s increased by one.
The portion of the fuselage ahead of the wing leading edge is replaced by a tropezoid having a width equal to FUSWTH and area equal to the projected area of the fuselage in the x-y plane between the nose and wing root leading edge (See Figure A1 ).
Assumption 8 i s also made for the portion of fuselage behind wing root trailing edge. (See Figure Al).
The y- coordinates of a horizontal tail and CI canard are assumed to be the y- coordinatcs of the break lines for the corresponding surfaces.
The heights of o horizontal tail by taking the avcrage value of surfaces
and a canard (ZAVHT(2)) are calculatad t- coordinates of the corresponding
Thc semi-width of ihc futelagc at the root chord of the horizontal tail (WDTHl) and the canard (WOTI-12) i s calculoted by taking the average radius of fuscloge sect ions Ixtwecn t Iic corresponding root chords .
1 70
13. If I(ZAVti1 ( I ) - ZAVFUS) I (WDTH 1/2), thc tail i s assumed to bc in the plane of the fusclogc i.e. ZAVHT I 1 ) = ZAVFS.
14. If thc tail i s not in the plane of the fuselage, thc tail i s extended to thc center line of the fuselage and the number of break lines of the tail ore increased by one.
15.
16.
Assumptions 13 and 14 are also applicable to a canara surface.
A break line on the wing induces a break line at the some y- location on the horizontal taif and on the canard and vice versa.
17. Between the two break lines on any aerodynamic surface the consiant percent streamwise lines are calculated such that they are at least (b/20) apart.
171
MODIFIED FUSELAGE
- ACTUAL FUSELAGE
Figure A . l . Futeloge Modification
172
11. REFERENCES
1. Roskam, J. , and Lan, C.; "A Parametric Study o f Planform and Aerrrelas- t i c Ef fects on Aerodynamic Center, - and q- S t a b i l i t y Der ivat ivest" Sumnary Report, NASA CR-2117; Prepared under NASA Grant NGR 17-002-071 by the F l i g h t Research Laboratory o f the Department o f Aero- space Engineering o f the Universi ty o f Kansas, October, 1373.
2. Woodward, F. A , , "Analysis and Design o f Wing-Body Combinaticm a t Subsonic and Supersonic Speeds," Journal of A i r c ra f t , Vol. 5, Na. 6, Nov.-Dec., 1968.
3. Craidon, C. B., "Description o f a D i g i t a l Computer PrGgram (P22?0) f o r A i r c r a f t Configuration Plots," NASA TM X-2074.
4. Lan, C. , Mehrotra, S. and Roskam, J., "Leading-Edge Force Features o f Aerodynamic F i n i t e Element Method ,'I CRINC-FRL Report F!o. 72-007, The Univers i ty o f Kansas, Ap r i l 1972.
5. Roskam, J., Hamler, F. R., and Reynolds, D.' "Procedures Used t o De- termine the Mass D is t r i bu t i on for Ideal ized Low Aspect Ratio Two Spar Fighter blirtys ," KKA CR-112232; Prepared under NPSA Grant NGR 17-002-071 by the F l i g h t Research Laboratory o f the Department o f Aerospace Engineering o f the Universi ty o f Kansas, October, 1972. Appendix D o f the Summary Report, NASA CR-2117.
6. Roskam, J., Lan, C., Smith, H., and Gibson, G.; "Procedures Used t o Determine the Structural Representation f o r Ideal i t e d Low Aspect Ratio Two Spar Fighter Wings," NASA CR-112233; Prepared under NASA Grant NGR 17-002-071 by the F l i g h t Research Laboratory o f the Department o f Aerospace Engineering o f the Universi ty o f Kansas, October, 1972. Appendix E o f the Summary Report, NASA CR-2117.
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