public domain aeronautical software (pdas) · nasa cr - 112229 a parametric study of planform and...

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

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 chordwise lines

Constant percent streamwise 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 streamwise 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 horizontal 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

. .

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 variables 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

OI0mDoI

O I * . - r c r \ 0 0 1 O I O O 4 0 0 0 0 0 0 0 w w w w

....

c

c - 0 c-

. *

!

i

!

0 0 0

. o 0

0 0 0 0 0 0

O E 0 - r.

- -

0 0 - - 0 0 N - 00 -4 0

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7. TOTCASE 2

This test case deals with a complete elastic wing, body and hor kontal tail configuration. 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 I I

I

- 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

x t

62

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k : I- 0 (3 w

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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


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


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

0

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167

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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