._ _ NASA Contractor Report 367 5 

An Aerodynamic Analysis Computer 

Program and Design Notes for 

Low Speed Wing Flap Systems 

Harry W. Carlson and 

CONTRACT NAS I- 16000 

MARCH 1983 

Kenneth .B. Walkley 
TECH LIBRARY KAFB, NM 

IlnlllIIUllil~l~~~

IlOb 

NASA Contractor Report 3 67 5 

An Aerodynamic Analysis Computer 

Program and Design Notes for 

Low Speed Wing Flap Systems 

Harry W. Carlson and Kenneth B. Walkley 

Kentron International, Inc. 

Hampton, Virginia 

Prepared for 

Langley Research Center 

under Contract NASl-16000 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1983 
- 

SUMMARY 

This report describes the expanded capabilities for analysis and design 

of low speed flap systems afforded by recent modifications of an existing 

computer program. The program provides for the simultaneous analysis of up 

to 25 pairs of leading-edge and trailing-edge flap deflection schedules. 

Among other new features of the program are a revised attainable 'thrust 

estimation method to provide more accurate predictions for low Mach numbers, 

and a choice of three options for estimation of leading-edge separation 

vortex flow effects. 

Comparison of program results with low speed experimental data for an 

arrow wing supersonic cruise configuration with leading-edge and 

trailing-edge flaps showed good agreement over most of the range of flap 

deflections. Other force data comparisons and an independent study of 

airfoil and wing pressure distributions indicated that wind-tunnel 

measurements of the aerodynamic performance of twisted and cambered wings and 

wings with leading-edge flaps can be very sensitive to Reynolds number 

effects. 
INTRODUCTION 

The low speed aerodynamic analysis method of reference 1 provides 

estimates of wing performance which include the effects of attainable 

leading-edge thrust and vortex lift. The method was shown to be particularly 

useful in the subsonic analysis of vehicles designed for supersonic cruise. 

In reference 2, the computer program described in reference 1 was used as an 

aid in the design of low speed leading-edge flaps for a candidate supersonic 

transport configuration. 

This report describes modifications and improvements to the original 

computer program to permit more convenient, more accurate, and more efficient 

treatment of simple leading and trailing-edge flap systems. In this improved 

program, there is provision for direct input of flap geometry. For the study 

of reference 2 it was necessary to make internal program modifications. In 

addition, the program is arranged so that, with little additional expense, 

solutions may be found for various combinations of leading and trailing-edge 

flap deflections. 

Another improvement incorporated in the present computer program is a 

revised attainable thrust algorithm which is more accurate at the low Mach 

numbers sometimes encountered in wind tunnel testing. A means of estimating 

the distribution of leading-edge separation vortex forces has also been 

provided. 

The applicability of the program results to the aerodynamic analysis of 

wings with flaps is demonstrated through correlations with experimental 

data. In addition, suggestions for use of the program in an iterative 

fashion for flap system design are given. 

2 
SYMBOLS 

AR 

b 

C 

z 

Cave 

CA 

CN 

ACN,v 

cn 

CR 

ct 

ct,F 

CA 

CN 

CD 

cD,O 

ACD 

CL 

cL,a 

cP 

Cp,lim 

ACP,V 

wing aspect ratio, b*/S 

wing span 

local wing chord 

mean aerodynamic chord 

average wing chord, S/b 

section axial force coefficient 

section normal force coefficient 

section normal force coefficient increment due to the leading 

edge separation vortex 

chord of wing section normal to local wing leading edge with 

maximum thickness at mid chord 

'n = sinh 

27l 

' LL(l+n)tanAL+ntanATJ+cosAL 

section resultant force coefficient 

theoretical section leading-edge thrust coefficient 

theoretical section leading-edge thrust coefficient for a flat wi'ng 

at lo angle of attack 

total axial force coefficient 

total normal force coefficient 

total drag coefficient 

drag coefficient at zero lift for a flat wing 

drag coefficient due to lift, CD-CD,0 

total lift coefficient 

total lift curve slope, per degree 

pressure coefficient 

limiting pressure coefficient used in definition of attainable 

thrust 

incremental pressure coefficient due to detached leading edge 

vortex 

3 
be 

k 

m 

M 

Mn 

R 

Rn 

r 

rf 

S 

sS 

S 

t 

t max 

LX 

AU 

X,Y,Z 

X’ 

Xi 9x; 

X’ 

V 

a 

exponents used in Cp,lim equation 

arbitrary constant 

flap deflection multiplier 

free-stream Mach number 

Mach number normal to local wing leading-edge sweep angle, 

Mn = M cos AL 

free-stream Reynolds number based on 2 

Reynolds number normal to local wing leading edge, 

Rn =R$ cosAL 

wing section leading-edge radius 

effective leading-edge radius for attainable thrust calculation 

wing reference area 

suction parameter, 

CL tan (CL/CL a) - AcD 

CL tan (CL/CL,a) I C,*/WW 

distance along section camber line 

airfoil section local thickness 

airfoil section Mximum thickness 

effective maximum thickness for attainable thrust calculations 

longitudinal perturbation velocity difference across the wing 

lifting surface as a fraction of the free stream velocity 

Cartesian coordinates 

distance in the x direction measured from the wing leading edge 

X’ values at leading edge and trailing edge of wing element at 

element semispan 

x' value for center of detached leading-edge vortex flow 

angle of attack of wing, in degrees 

4 
Aaft range of angle of attack for full theoretical thrust 

azt angle of attack of wing giving a theoretical leading-edge thrust 

of zero for a specified wing spanwise station 

B m 

Y ratio of specific heats 

n location of maximun wing section thickness as fraction of chord 

6 flap deflection angle in degrees 

A sweep angle 

Subscripts: 

L leading edge 

n measured normal to flap hinge line 

0 original or first value 

T trailing edge 

132 flap segment identifier 

des design condition 

zt zero thrust condition 

hl hinge line 

C cambered wing 

F flat wing 

5 
DEVELOPMENT OF COMPUTATIONAL SYSTEM 

Expanded capabilities for the analysis and design of low speed flap 

systems are offered by recent modifications of an existing computer program 

introduced in reference 1. The revised program provides for the simultaneous 

analysis of up to 25 pairs of leading-edge and trailing-edge flap deflection 

schedules. Among other new features are a revised attainable thrust estimation 

method to provide more accurate predictions for low Mach numbers, and a choice 

of three options for estimation of leading-edge separation vortex flow effects. 

The development of the basic computational system is covered in considerable detail in reference 1. That report describes numerical methods which have 

been incorporated into a computer program to permit the analysis of twisted and 

cambered wings of arbitrary planform with attainable thrust considerations 

taken into account. The computational system is based on a linearized theory 

lifting surface solution which provides a spanwise distribution of theoretical 

leading-edge thrust in addition to the surface distribution of perturbation 

velocities. In contrast to the commonly accepted practice of obtaining 

linearized theory results by simultaneous solution of a large set of equations, 

a solution by iteration is employed. The method also features a superposition 

of independent solutions for a cambered and twisted wing and a flat wing of the 

same planform to provide, at little additional expense, results for a large 

number of angles of attack or lift coefficients. A key feature of the superposition technique is the use of leading-edge thrust singularity parameters to 

identify and separate singular and nonsingular velocity distributions. This 

separation permits more accurate determination of leading-edge thrust and more 

accurate integration of pressure distributions for twisted and cambered wings 

of arbitrary planform. The following discussions will be concerned only with 

significant changes and improvements to the methods described in reference 1. 

6 
Leading-Edge and Trailing-Edge Flap Surfaces 

The leading-edge and trailing-edge devices that may be treated by the 

present method are limited to "simple" hinged flaps. There is no provision 

for additional slats or for any separation between the flaps and the main 

wing surface. 

In the revised program separate solutions for the longitudinal 

perturbation velocity distribution are made for both a leading-edge flap 

surface and a trailing-edge flap surface. These two additional surfaces 

cover the entire wing planform as do the two original surfaces for the flat 

and twisted and cambered wing. With this distinct separation of individual 

contributions to the overall wing loading distribution, it is a simple matter 

to combine loadings to cover not only a range of angles of attack but also a 

range of leading-edge and trailing-edge flap deflections. 

For input flap surfaces, described as a spanwise distribution of flap 

chord and streamwise deflection angle, values of surface slope for each of 

the wing elements are determined within the program. Solutions for the 

longitudinal perturbation velocities corresponding to these new surfaces are 

performed simultaneously with the solutions for the flat and cambered wing. 

Because an assumption of lifting pressures proportional to the sine of the 

deflection angle rather than the tangent (the surface slope) is more 

reasonable, the lifting pressures are defined as: 

cP 

= auF sfna for the flat wing 

tan lo 

sin6 

cP 

C 

= 2AUc Tandy = 2Auc COS 6c for the cambered surface 

7 
C 

sin6L 

P =a"LtangL= 2AUL cos &jL for the leading-edge flap 

cP 

sindT 

= 2AUT Tandy = 2AUT cos 6T for the trailing-edge flap 

For additional flap deflection angles, the user may specify factors mL 

and mT for the leading and trailing edges respectively: 

= tan 

% , 

-l 0-y tanSLlo) 

6T = tan (mT tan6T,o) 

where the subscript o indicates the original input flap deflections. In 

accordance with the assumption of lifting pressure proportional to the sine 

of the deflection angle, the flap induced lifting pressures are: 

C 

sinsL 

P = 2AuL tansL 

= 2 mL AUL,o cos(tan-l(mL tanbL o 

, )) for the leading-edge flap 

sins 

C T 

P = auT tansT 

= 2 mT AUT,O cos(tanB1(mT tansT o 9 )) 

for the trailing-edge flap 

Section force coefficients are found through the integration techniques 

described in reference 1. Now, however, the cambered wing coefficients include deflected flap as well as camber surface contributions. Both of these 

solutions are handled as described for the cambered surface in reference 1 

except that, for the flap contribution, additional cos 6L and cos 6T 

terms are introduced. The following sketches illustrate the necessity for 

this correction. As shown in sketch (a) an incremental force for the cambered 

8 
wing section may be defined as: 

dCN = dCBCOS 6 

= (Cp ds cos 6 

= /C, dx 

because dx = ds cos 6. 

But for the flap surface shown in 

sketch (b): 

dCN = dCB COS 6 

= JC, ds cos 6 

= IC, dx cos 6 

because dx = ds 

Sketch (a) 

Sketch (bl 

These refinements, which introduce a cos 6 term in both the lifting 

pressure and the normal force coefficients for deflected flap surfaces, were 

not used in the flap system study of reference 2. The cos 6 correction and 

the numerical method improvements afforded by the individualized treatment of 

the deflected flap surfaces (instead of handling by methods designed specifically for generalized camber surfaces) are expected to increase the accuracy 

of the program for application to flap systems. 

Attainable Leading-Edge Thrust 

The method for prediction of attainable leading-edge thrust described in 

reference 3 was incorporated in the computer program of reference 1. That 

method has been retained in the present revised program but has been modified 

somewhat to be more applicable at the low Mach numbers sometimes encountered 

in wind-tunnel testing. In general, the method described in reference 3 is 

9 
based on the use of simple sweep theory to permit a two-dimensional analysis, 

the use of theoretical airfoil programs to define thust dependence on local 

geometric characteristics, and the examination of experimental twodimensional airfoil data to define limitations imposed by local Mach numbers 

and Reynolds numbers. The following discussion is concerned with a reexamination of experimental two-dimensional airfoil data and a redefinition 

of limitations imposed by local Mach numbers and Reynolds numbers. For a 

detailed discussion of the method the reader should consult reference 3. 

In reference 3 limiting pressures, Cp,lim, were determined from correlations with two-dimensional airfoil experimental data covering Mach numbers 

from 0.3 to 0.9. To extend that range to lower Mach numbers, similar 

correlations for Mach numbers as low as 0.03 are shown in figure 1. Shown in 

figure l(a) are axial force data from reference 4 covering a range of 

Reynolds numbers for airfoils of three thickness ratios at a Mach number of 

0.061. The vertical dashed lines in figure l(a) indicate that for angles 

greater than those indicated there was a large but undeterminable increase in 

axial force. Figure l(b) gives data from reference 5 for two airfoils at 

various combinations of Mach numbers and Reynolds numbers. As in reference 

3, values Of Cp,lim were found by iteration. 

In figure 2(a), Cp,lim values from figure 1 are plotted as a function 

of Reynolds number. The dashed line fairing of the data is intended to 

provide data for Reynolds numbers of 1 million and 3 million that can be 

plotted as a function of Mach number. Similar data from the original 

correlations of reference 3 are shown in figure 2(b). -The arrows next to 

some of the data indicate that the Cp,lim might be more negative than shown 

because the data did not show a definite break from the full thrust curve at 

10 
the highest angle of attack available in the data. In spite of considerable 

scatter in the data, general levels of the limiting pressure can be established and a trend of increasing limiting pressure with increasing Reynolds number 

for the lower Mach numbers is observable. More complete two-dimensional data 

would be desirable. There is a particular need for coverage of a greater range 

of angles of attack and Reynolds numbers. 

Figure 3 shows Cp,lim as a function of Mach number for three Reynolds 

numbers. The empirical data was obtained from the dashed line fairing of the 

data in the previous two figures. The empirical equation is intended to represent the general nature of the data. It has the same form as the equation 

given in the original development -differing only in the exponent, e. For 

normal Mach numbers greater than 0.3 the values are essentially the same as 

those given by the original equation. 

The variation of Cp,lim, with Mach number and Reynolds number as given 

by the equation: 

-6 

[ I 

E 

C -2 Rnx10 

p,lim = - 2 

Y"n R,xIO-~+~O~ 

with E = a05 + -35 (l-Mn)' 

and e = 4-3 M, + 4 (1-Mn)15 

is shown in figure 4. Note that Cp,lim approaches the vacuum limit as the 

Reynolds number approaches infinity, and approaches zero as the Reynolds 

11 
number approaches zero. Because there is little data to provide guidance in 

selection of parameters for the equation below a normal Mach number of about 

0*05s Cp,l im is held constant at the Mn = 0.05 value from Mn = 0.0 to 

0.05. In the new program, this equation replaces the original derived in 

reference 3. 

Vortex Force Distribution 

The computer program of reference 1 accounts for a vortex force 

generated by detached leading-edge vortices which form when there is a failure 

to achieve full theoretical leading-edge thrust. In that program, the vortex 

force is assumed to act perpendicular to the wing reference plane at the wing 

leading edge and thus offers no contribution to wing axial force. That method 

is available to the program user as the default option, but there are two 

additional options in the present code. Both.of these new options give an 

estimate of the distribution of the vortex force and provide contributions to 

the axial force as well as the normal force. 

Option 1. For delta wings and delta wing derivatives, the vortex force 

center may be located through use of an empirical relationship derived with the 

aid of figure 5. In this figure, data from references 6 and 7 for uncambered 

delta wings with sharp leading edges are used to define, in an approximate 

fashion, the lateral location of the center of the vortex flow pressure field as 

a function of the wing local semispan (x cotn) and the angle of attack. The 

fairing of the data represented by the equation: 

yV 1 

x cotn = l+ J3iiTii 

should be applicable to a range of sweep angles from about 50 degrees to about 

80 degrees. As shown in sketch (c) it may be possible to provide an approximate 

12 
location of the center of the vortex pressure field even for wings with significant 

departures from the delta planform, and for 

wings which may employ twist and camber or 

deflected flaps. This 

use of the equations: 

may be accomplished by 

X’ 

V 

= 0.0 

x’= y V- cotAL 

/tan(a-azt-fmft) 

x’= y V- COtAL 

Jtan(aZt-Aaft-") 

Sketch (cl 

("zt -Aaft) < a < (azt+Aaft) 

a > (azt+Aaft) 

in which AL is the local leading-edge sweep angle, azt is the wing angle 

of attack for local leading-edge thrust of zero, and Aaft is the range of 

angle of attack for full thrust. This formulation locates the vortex center 

aft of the leading edge only when full thrust is not realized. However, it 

does not account for the initiation of leading-edge separation at points 

along the leading edge other than the apex of the superimposed delta wing. 

Option 2. An alternate and very simple means of locating the vortex 

force center is given by Lan in reference 8. When applied to the present 

numerical method the location of the vortex force center is: 

x’ = c V t 'ave 

13 
For both of the new options for 

vortex force location the distribution of 

the force is assumed to take the form 

shown in sketch (d). Mathematically this 

form can be expressed as: 

AC P3v 

= k( 

Over an element 

vortex is given 

*cp,v 

Sketch Id) 

l-COST 5) 

V 

chord (Xi to xi) the incremental normal force due to the 

by: 

ACN,~ = -i- Ixi Acp,v dx 

'ave xi 

X’ 

= k 

C 

(Xi - Xi) - + xi 

- sin 51- ) 

ave 

and over the entire interval from 0 to 2x' : 

V 

1 

“N,v = z 2kx; 

so that: 

k = ACN,~ 'ave 

2x; 

The k factor establishes the magnitude of the Ac~,~ distribution acting on 

the wing surface. Since the surface may be cambered and may include deflect14 
- 

ed flaps, there will be contributions to axial force as well as normal 

force. If the vortex center lies aft of the local chord midpoint, part of 

the vortex force will not affect the wing and will be lost. 

Only limited advice regarding the selection of the vortex options can be 

offered at this time. The first option, with the vortex force acting perpendicular to the wing reference plane at the wing leading edge, was used in the 

correlations with experimental data given in reference 1. At large angles of 

attack, that approach seemed to overestimate the vortex effect-probably 

because rruch of the vortex field was actually aft of the wing surface rather 

than at the leading edge. The correlations with experimental data given in 

this report have been made using the second option. However, as discussed 

previously, this option is appropriate only for highly swept wings with delta 

or modified delta planforms. The authors have had no experience with use of 

the third option, the method given by ban. 

Angle of Attack Range for Full Thrust 

As will be discussed in a later section of this report, it may be 

desirable for design purposes to know how rmch a local leading-edge flap 

deflection angle may be changed from the local flow alignment condition 

(presumed to be defined by azt) and still retain attached flow and full 

theoretical thrust. This angle of attack range may be found from the flat 

wing attainable leading-edge thrust calculations by setting the attainable 

thrust fraction Kt (defined by equation (9) in reference 3) equal to 1.0 

and solving for ct,n. Since Ct,n is related to ct (equation (5) in 

reference 3) and ct is dependent on a (equation (15) in reference l), the 

flat wing angle of attack at which thrust begins to be lost at any given span 

station may be calculated. 

15 
PROGRAM DESCRIPTION 

The following description of the revised program will cover the entire 

listing of input data and program results even though mrch of this 

information is repeated from reference 1. 

The computer program entitled "Aerodynamic Performance of Low Speed Wing 

Flap Systems" may be obtained for a fee from: 

Computer Software Management and 

Information Center (COSMIC) 

112 Barrow Hall 

University of Georgia 

Athens, GA 30602 

(404) 542-3265 

Request the program by the designation LAR 13116. This program is written in 

FORTRAN IV for use on the Control Data 6600 and Cyber series of computers. 

Data are input in namelist form under the code INPTl. 

The wing planform information is specified by a series of leading-edge 

and trailing-edge breakpoints. Up to 21 pairs of coordinates may be used to 

describe the leading edge and up to 21 pairs to describe the trailing edge. 

The planform input data in program terminology are: 

NLEY 

TBLEY 

TBLEX 

NTEY 

TBTEY 

TBTEX 

XMAX 

SREF 

CBAR 

16 

number of leading-edge breakpoints ,(limit of 21) 

table of leading-edge y-values in increasing order of y from wing 

root to wing tip 

table of leading-edge x-values corresponding to the TBLEY table 

number of trailing-edge breakpoints (limit of 21) 

table of trailing-edge y-values in increasing order of y from wing 

root to wing tip 

table of trailing-edge x-values corresponding to the TBTEY table 

largest x-ordinate occurring anywhere on the planform 

wing reference.area for use in aerodynamic force and moment 

coefficients 

wing reference chord for use in aerodynamic moment coefficients 

._____... . a. . . ...,,,-1 . . . . , m.-I... ., ., . , .* _.._ _.... -., ._.. . . _ ,__,,. ..-... . . . . . . ._ . . . . ..--.-- --. --.--.--. 
- 

XMC x-location of moment reference center 

ELAR desired element aspect ratio (for flat and mildly cambered wings 

without flaps an element aspect ratio approximately one-half the 

full wing aspect ratio is recommended, for small chord flaps it 

may be necessary to use a larger element aspect ratio to place at 

least two elements within the chord) 

The size of the wing in program dimensions is controlled by the entry: 

JBYMAX integer designating the number of elements in the spanwise 

direction (limit of 41) 

The necessary scaling is done within the program by use of a scale factor 

2(JBYMAX)/(SPAN x B). The number of complete wing elements N corresponding 

to a given JBYMAX may be approximated as 

N = 4 x JBYMAX' x 

ELAR 

wing aspect ratio 

The program has been written to accommodate 2000 right hand panel elements. 

Except in very special cases the JBYMAX integer will be much less than the 

limit of 41. The normal range is 10 to 20. Computational costs tend to 

increase as the square of the number of elements and the fourth power of 

JBYMAX. 

The wing section mean camber surface must be specified by exactly 26 

chordwise ordinates at up to 21 span stations. When fewer than 26 camber 

coordinates are used to define the sections, the ordinate tables must be 

filled with enough zeros to complete the list of 26. The necessary section 

information is: 

NYC number of spanwise stations at which chordwise sections are used 

to define the mean camber surface (limit of 21) 

TBYC table of y values for the chordwise camber surface sections, 

increasing order of y from root to tip 

17 
NPCTC number of chordwise stations used in mean camber surface definition 

(limit of 26) 

TBPCTC table of chordwise stations, in percent of chord, at which mean 

camber surface ordinates are defined; in increasing order from 

leading to trailing edge 

TZORDC table of mean camber surface z-ordinates corresponding to the 

TBPCTC table; the full 26 values for the root chord (including 

zeros for values in excess of NPCTC) are given first, followed 

by similar information for all spanwise stations in increasing 

order of y 

The TZORDC table may be rmltiplied by a scale factor TZSCALE if desired. 

This may be useful if the original tabulated ordinates are nondimensionalized 

with respect to a single measurement (the wing root chord, for example) or if 

it is necessary to evauate the effect of change in camber surface severity. 

The following wing section information is required for the calculation 

of attainable leading-edge thrust. 

NYR number of spanwise stations at which airfoil section information 

is supplied (limit of 21) 

TBYR table of y values for airfoil section information, increasing 

order of y values from root to tip 

TBTOC table of airfoil maximum thickness as a fraction of the chord 

TBETA table of the section location of maximum thickness as a fraction of 

the chord 

TBROC table of the l'eading-edge radius as a fraction of the chord 

The flight or test conditions are specified as: 

XM free-stream Mach number 

RN free-stream Reynolds number (based on c) in millions, R/lo6 

NALPHA number of angles of attack to be calculated (limit of 12) 

TALPHA table of angles of attack to be calculated 

NADRN number of additional Reynolds numbers 

18 
TADRN table of additional Reynolds numbers (based on c') in millions, 

R/lo6 (limit of 3) 

IVOROP vortex location option 

0 full vortex force acts normal to wing reference 

plane of the wing leading edge, does not contribute 

to axial force 

1 vortex center given by empirical relationships derived 

from delta wing experimental data 

2 vortex center given by the method of Lan (ref. 8) 

(program defaults to 0) 

The following information will permit the calculation of loadings and 

forces on deflected leading-edge and trailing-edge flaps. If flap data is 

not desired, simply omit these entries. 

NLEFY 

TBLEFY 

TBLEFC 

TBLEFD 

NADLEFD 

TXMLEFD 

LEFTYPE 

number of breakpoints in leading-edge flap chord distribution 

(limit of 20) 

table of y values at breakpoints in leading-edge flap chord 

distribution, in increasing order of y from wing root to wing tip 

table of leading-edge flap chords corresponding to the TBLEFY table 

table of.flap deflections in degrees (positive for leading -edge 

down) corresponding to the TBLEFY table 

number of leading-edge flap deflection multipliers, other than 

1.0 (limit of 4) 

table of leading-edge flap deflection multipliers (applied as a 

nultiplier of the tangents of the input flap deflections) 

type of leading-edge deflection 

f 

1 for linear 8- 

< 

2 for parabolic 

j - 

8< 

(program defaults to 1) 

19 
NTEFY 

TBTEFY 

TBTEFC 

TBTEFD 

NADTEFD 

TXMTEFD 

CLDES 

number of breakpoints in trailing-edge flap chord distribution 

(limit of 20) 

table of y values at breakpoints in trailing-edge flap chord 

distribution, in increasirig order of y from wing root to wing tip 

table of trailing-edge flap chords corresponding to the TBTEFY 

table 

table of flap deflections in degrees (positive for trailing edge 

down) corresponding to the TBTEFY table 

number of trailing-edge flap deflection multipliers, other than I.0 

(limit of 4) 

table of trailing-edge flap deflection rmltipliers (applied as a 

multiplier to the tangents of the input flap deflections) 

lift coefficient for which flap system aerodynamic performance is 

n with y = 0 and extend to y = b/2 (with chords 

. At spanwise positions where there are disSpanw ise tables mtst begi 

of 0 where there are no flaps) 

continuities in either flap chord or deflection, it will be necessary to make 

closely spaced tabular entries inboard and outboard of the discontinuity. 

The program requires flap deflection angles measured in the x-z plane. 

Flap deflection angles measured normal to the flap hinge line may be converted to program input angles by: 

6 = tan-l (COS Ah1 tan 6n) 

The program provides solutions for wing surfaces composed of all possible combinations of leading-edge and trailing-edge flap settings provided by 

the original deflections (TBLEFD and TBTEFD) and by the flap deflection 

multipliers (TXMLEFD and TXMTEFD). Up to 25 pairs of leading-edge and 

trailing-edge flap deflection schedules may thus be treated simultaneously. 

to be optimized. 

only for angles 0 f 

is specified. 

Program aerodynamic characteristics are given 

attack in the input TALPHA table unless CLDES 

20 
The program provides for a maximum of 50 iterations. If this number is 

reached without the convergence criteria being met, the results for the 

50th iteration will be printed with a warning of the failure to meet 

criteria. If desired, the maximum number of iterations may be increased or 

decreased by the entry: 

ITRMAX maximum number of iterations 

The program convergence criteria is met when, for all four wing surfaces and 

for two successive iterations, the average difference in perturbation 

velocity between iterations is less than one-half of one percent (0.005) of 

the average velocity over the wing. If the average velocity for the camber 

surface or either of the flap surfaces is less than the average velocity of 

the flat surface at lo angle of attack, the flat wing surface value will be 

used instead. In many instances this criteria may be more stringent than 

necessary. If desired the convergence criteria may be changed by an entry: 

CNVGTST convergence criteria 

The commonly accepted practice of performing subsonic calculations for a 

Mach number of 0.0 is not appropriate for this program. Realistic estimates 

of attainable thrust can be made only if both the Mach number and the 

Reynolds number correspond to actual conditions. In fact, the program will 

stop and write an error message to the user when XM = 0.0 is input. 

The printed program results include: 

(1) An iteration by iteration history of the convergence parameters. 

(2) A listing of theoretical pressure distributions for the camber surface at 0" angle of attack and for the flat surface at lo angle of attack. 

For each of the program spanwise stations (controlled by JBYMAX), 

21 
interpolated or extrapolated pressure coefficients are given for a set of 

chordwise stations. 

(3) A listing of the spanwise distribution of section normal, axial, 

and pitching moment coefficients for the cambered wing at 0" angle of attack 

and the flat wing at lo angle of attack. The interference axial force 

coefficient due to the flat surface loading acting on the camber surface and 

the theoretical thrust parameters Ct,F and azt are a?SO printed. 

(4) A listing of wing overall theoretical aerodynamic coefficients 

CR, CA, CM, CL, and CD with no thrust and with full theoretical 

thrust as a function of angle of attack. 

(5) A listing of the spanwise distribution of the flat wing angle of 

attack range for full theoretical leading-edge thrust. 

(6) A listing of wing overall estimated aerodynamic coefficients 

including CR, CA, and CM for the basic pressure loading; ACN and 

ACA for attainable thrust and vortex force increments; and finally CR, 

CA, CM, CL, CD, and S, for the total loading. 

Additional printed output data may be selected by use of the following 

print options: 

IPRCPD = 1 theoretical pressure distributions for each of the selected 

angles of attack 

IPRSLDT = 1 theoretical span load distributions of CN, CA, CM, CL, 

and CD with no thrust and with full theoretical thrust for 

each of the selected angles of attack 

IPRSLDA = 1 estimated span load distributions of CR, CA, CM, C , 

and CD with attainable thrust and vortex force e \ fects for 

each of the selected angles of attack 

22 
IPRALL = 1 the preceding print control options apply to only the first 

set of flap deflections. Select this option if the three 

preceding options are to apply to all of the flap 

deflection combinations. Selection of this option could 

result in a very large volume of printed output. 

PROGRAM APPLICATION 

Among the program application topics to be covered in the following 

discussions are correlation of program and experimental data, the influence 

of Reynolds number on aerodynamic performance, and suggestions for use of the 

program in an iterative fashion for flap system design. 

Correlation of Program and Experimental Data 

The correlations of program data and experimental data contained in this 

report are intended to serve two purposes. The first is to demonstrate the 

applicability of the programmed nunerical methods to the aerodynamic analysis 

of flap system test data obtained at a reasonably large Reynolds nunber. The 

second is to show the dependence of wing aerodynamic performance on Reynolds 

number conditions. 

No estimate of skin friction and form drag contributions to the coefficients have been made. For the corrparison with experimental data shown in 

this report, the sun of these two contributions, CD,O, has been set equal 

to the experimental zero lift drag coefficient for the flat wing version of 

the configuration. Separated vortex effects have been estimated by use of 

the second option (IVOROP=l) described in the "Program Description" section. 

Correlations of program results with unpublished experimental data for 

an uncambered arrow wing supersonic cruise configuration with leading-edge 

and trailing-edge flaps are shown in figure 6. These are the same data that 

were used in reference 2. A nunber of refinements in the present program 

23 
which were not considered in the calculations of that reference provide a 

better correlation with the experimental data. In particular, the axial force 

correlations are noticeably improved. The normal force prediction is also 

changed, but in such a way that there is only a sliqht improvement in the draq 

prediction for the lift coefficient range of interest. 

The data for the winq with no flap deflections show a slight underestimation of the leadinq-edge thrust achieved and some underestimation of 

the normal force. Generally, however, the method provides a reasonab1.y good 

prediction of the drag relative to the full and no thrust values. 

Fiqures 6(b) through 6(d) show data for a series of leadinq-edge flap 

deflections with the trailinq-edqe flaps at 10'. Notice, in particular, the 

behavior of the axial force data. The large neqative values of the axial 

force achieved in the experiment and generally well predicted b-y the program 

are responsible for the improved wing performance with increasinq flap 

deflection. Note the decreasing potential for leading-edge thrust (the 

difference between the no thrust and full thrust curves) as the leading-edge 

flap deflection is increased. The attainable thrust prediction method is 

seen to give a good estimate of the degree of thrust actually achieved. The 

proqram data indicate that increasing the flap deflection beyond 40" would 

produce some small additional performance qains. The experimental data, 

however, show little or no gain in performance for the 40' flaps compared to 

the 30" flaps. It is probable that linearized theor.y methods will qenera1l.y 

overestimate the benefits of large flap deflections. 

Figures 6(c), 6(e), 6(f), and 6(q) form a series in which the trailinqedge flap deflection varies while the leading-edge flap remains set at 30". 

Notice that in this set of data the axial force shows a considerable chanqe 

24 
in the general level but only a small change in shape. Generally, there is 

good agreement between the program prediction and the experimental.data up to 

30" flap deflection. At 40' the correlation is poor. The reason for this 

failure is evident in the normal force correlation; the trailing edge flap 

has lost effectiveness. The normal force generated at 40" is not appreciably 

greater than that generated at 30°. 

Experimental data from reference 9 shown in figures 7 and 8 point out 

the dependence on Reynolds number of wing aerodynamic performance. Data for 

a wing-body combination with an aspect ratio 4 flat delta wing with an NACA 

0005-63 section are shown in figure 7. The experimental data are compared 

with linearized theory program results for no leading-edge thrust and full 

leading-edge thrust as well as with present method data which include attainable thrust and vortex force estimates. The data for both Reynolds numbers 

show a reasonably good correlation of the program data, labeled present 

method, with experimental data at least up to about 10 degrees angle of 

attack or a lift coefficient of about 0.6. The effect of Reynolds number on 

axial force and drag appears to be predicted adequately by the present 

method. Correlations for the same configuration with a twisted and cambered 

wing instead of a flat wing are shown in figure 8. For this wing, 

predictions given by the present method are good only up to about 7.5 degrees 

or a lift coefficient of about 0.5 at the Tower Reynolds number, but are good 

up to about 10 degrees or a lift coefficient of 0.65 at the higher Reynolds 

number. The difference is most apparent in the axial force curve. At the 

higher Reynolds number the critically important axial force behavior is given 

quite well over an angle of attack range from about -8.0 to +lO.O degrees. 

25 
An example of the effect of Reynolds number on the pitching moment of 

these two wing-body models is given in figure 9. The flat wing pitching 

moment curve shows a break from the predicted curve at about 6 degrees for 

the lower Reynolds number. At the higher Reynolds number this break is 

delayed to about 8O. In contrast to this mild improvement, the cambered wing 

data show a dramatic improvement with the increase in Reynolds number. The 

break in the pitching moment curve has been delayed from about 6 degrees to 

12 degrees or higher. These data show that twisted and cambered wings are 

far more sensitive to Reynolds number effects than are flat wings. The good 

agreement between program results and experimental pitching moment data at 

the higher Reynolds number appears to be very promising. However, as of yet, 

few other pitching moment correlations have been made to test the general 

applicability of the method. 

Reynolds Number Limitations 

The experimental force data .examined in the preceding section of this 

report showed a greater effect of Reynolds number on twisted and cambered 

wing performance than on flat wing performance. An examination of pressure 

distributions and limitations on peak suction pressures shows that wings with 

leading-edge flaps as well as twisted and cambered wings can generally be 

expected to have a greater sensitivity to Reynolds number than flat or 

uncambered wings of the same planform. 

Figures 10 to 12 give examples of the effect of Reynolds number on 

achievable'peak pressures. In all of these figures, Cp is shown as a 

function of the square root of the x ordinate to chord ratio in order to 

accentuate the leading-edge region. These distributions are shown for a 

series of angles of attack so that the approach to a limiting pressure and 

26 
the subsequent collapse of the pressure peak may be observed. In addition, 

limiting pressures as defined by the empirical attainable leading-edge thrust 

technique are indicated. In figure 10, data for a two-dimensional airfoil 

from reference 10 are shown for Reynolds numbers from 0.1~10~ to 3.1~10~. 

These data show a strong dependence on Reynolds number of the magnitude of 

the peak pressures achievable. The negative pressure peak for the largest 

Reynolds number appears to be about two and one-half times greater than that 

for the lowest Reynolds number. Limiting pressures given by the attainable 

thrust prediction method of reference 3 are also shown on this figure. These 

limiting pressures serve merely as a device for accounting for thrust losses 

observed in experimental force data for two-dimensional airfoils. The 

attainable thrust limiting pressures actually account for two factors which 

limit thrust: the failure to attain theoretical peak suction pressures and 

also the tendency of these peaks to occur at a more rearward position on the 

airfoil. Thus, it is not surprising that the attainable thrust limiting 

pressures are less than the actual peak pressures. Even with this discrepancy, however, the attainable thrust limiting pressures should be valuable in 

prediction of trends due to changes in Mach number and Reynolds number. The 

data for a swept semispan wing (ref. 11) in figure 11 and the data for wingbody configuration (ref. 12) in figure 12 show similar trends and about the 

same relationship of actual pressure peaks to the attainable thrust limiting 

pressures. 

The performance of wings with sharp leading edges is generally believed 

to be insensitive to changes in Reynolds number. This appears to be true for 

flat highly swept delta wings, but the generalization may not hold for wings 

with sharp leading-edge flaps deflected so as to minimize separation. 

27 
Research data collected for use in the analysis of wind energy systems 

(reference 13) can be of use in a study of the problem. In that research, it 

is necessary to consider the behavior of airfoils in reversed as well as 

forward motion. Typical lift curve data for a range of Reynolds numbers are 

shown in figure 13. The airfoil in reversed flow, of course, has a very 

sharp leading edge. These data indicate that only above angles of attack of 

8 to 10 degrees is the sharp leading-edge airfoil CL appreciably less 

sensitive to Reynolds number changes than the rounded leading-edge airfoil 

CL* For smaller angles of attack, CL changes are actually larger for the 

sharp leading-edge section than for the rounded leading-edge section. Thus, 

within this Reynolds number range, there will be important Reynolds number 

sensitivities for sharp leading-edge flaps if the local angle of attack must 

be restricted to small values to prevent separation. For the rounded 

leading-edge airfoil there are likely to be further increases in CL.with 

increases in Reynolds number above 1.8 million (the lift curve slope for 

R=1.8 million is still below the potential.theory value). For the sharp 

leading-edge airfoil, increases in CL with increases in Reynolds number 

above 1.8 million are likely to occur only for angles above about 6" (up to 

this point the lift curve for R=1.8 million matches the potential plus vortex 

lift theory). There is a need for data covering a larger range of Reynolds 

numbers and for data applicable to airfoil sections with sharp trailing edges 

as well as sharp leading edges. Highly swept flat wings with sharp leading 

edges apparently are relatively insensitive to Reynolds number changes, even 

at low Reynolds numbers, because the large growth of upwash along the leading 

edge causes the outboard wing sections to operate at large effective angles 

of attack where Reynolds nunber effects are insignificant. 

28 
The special importance of Reynolds number effects 

twisted and cambered wings and wings with leading-edge 

trated with the aid of two sketches. In sketch (e) is 

flat wing with 

tributions for 

shaded portion 

and the shaded 

superimposed pressure distwo Reynolds numbers. The 

of the pressure loading 

Aon the performance of 

flaps may be illusshown a section of a 

force arrow represent the 

effect of an increase in Reynolds number. The force arrows at the right rep- Sketch (el 

resent the resultant pressure force on 

the section at the lower Reynolds number 

and the increase in this force due to the increase in Reynolds number. These 

two forces act in generally the same direction, normal to the wing surface, 

and thus there is only a small improvement in the lift-drag ratio due to the 

increase in Reynolds number. 

For a wing with a leading-edge flap (or a wing with leading-edge camber) 

the situation can be quite different as illustrated in sketch (f). For such 

a wing section to perform efficiently the 

flap rmst carry a significant load so as 

CL 

to produce a force with a thrust component. This loading will be similar to 

the loading on the forward portion of a 

flat wing. As shown by the shaded por- Sketch (f1 

J!? CD 

tion of the pressure distribution and the 

shaded force arrow, here too, Reynolds 

29 
number could have a substantial influence on the force generated. But as 

shown in the resultant pressure force vector s at the right, the additional 

force due to the increase in flap loading with Reynolds number, which acts 

normal to the flap surface, can have a relatively large effect 

ant drag and the lift drag ratio. 

From this discussion, it can be seen that there is a spec i 

on the resultal need for 

high Reynolds number testing of candidate flap systems. Inadequate Reynolds 

number test conditions could lead not only to poor prediction of flight performance but also could result in rejection of flap systems with excellent 

high Reynolds number performance but poor low Reynolds number performance. 

Unfortunately, results from the present study do not provide firm guidelines 

for acceptable test Reynolds nunbers. 

An effort to introduce pressure limiting based on the attainable thrust 

method into the present corrputer program was not successful. A severe deterrent to such measures is the sometimes drastic collapse of the pressure peak 

as illustrated in figure 14. The data from reference 5 show an extreme 

change in the shape and magnitude of the pressure distribution between the 

angles of attack of 9 and 10 degrees. 

Effective Thickness and Leading-Edge 

For any of the wide variety of NACA "standard" a 

thrust calculations are naturally based on the listed 

Radius 

irfoils the attainab 

values of airfoil 

le 

thickness and leading-edge radius. The attainable thrust method was 

calibrated with airfoils such as these. However, for nonstandard airfoils 

(for example, blunted circular arc sections) direct use of the geometric 

thickness and radius may lead to erroneous results. A method for obtaining 

the effective thickness and radius for these problem airfoils is outlined in 

the following discussion. 

30 
Airfoils on which the method is based have a family resemblance. The 

leading-edge radius and thickness interdependence may be approximated as: 

0.28 tmax 

2 

!l- - - C n c C 1 

t 

and the thickness distribution follows 

the general form shown in sketch (g) 

which with little error may be 

represented as: 

t 

- = 1.0 - t [ 

x’/c 1.5 

max 

1.0 - y- /I Sketch (g) 

The leading-edge radius is actually a measure of the rate of growth of 

thickness over much of the forward portion of 

localized leading-edge characteristic only. 

The preceding family relationships 

may be used to obtain effective thickness 

and radius values for arbitrary sections 

through the following steps illustrated 

in sketch (h). 

(1) Plot airfoil ordinates in the form 

t/t max vs / + 

(2) Fit a curve of the form 

the airfoil rather than a 

Sketch.(h) 

&ax It max 

t t* 

max 

t max 

= - { 1.0 - [l.O - by‘” } t IMX 

31 
by selecting a value of t:,, to match as closely as possible' the actual 

airfoil ordinates with particular emphasis on the forward half of the plot. 

(3) Use the effective thickness tiax to obtain an effective 

thickness ratio 

t* 

max = 

t* max 

t 

max 

C 5-G c 

and an effective leading-edge radius to chord ratio 

r* 2 t* 

c= q [ 1 

2 

max 

C 

Substitution of these effective values of thickness and radius for the pure 

geometrical quantities should result in more accurate estimation of 

attainable thrust. 

Special Handling of Small Span Flaps 

In the numerical solution for pressure loadings on deflected flap 

surfaces there may be a poor representation of the flap if the flap span 

covers only a few program element spans. Program surface slopes are assumed 

to be constant over any given program 

element with the value being determined 

Actual 

at the element mid semispan. For some 

cases, the program user may want to adjust input flap geometric inputs so that 

the program flap area will provide a better 

representation of the actual flap area. 

As shown in sketch (i) this may be accomplished by altering the location of flap 

chords to correspond to the program spanwise grid spacing b/E(JBYMAX) and changing the flap chords to preserve the area. 

Adjusted 

Sketch (i) 

32 
Flap System Design Notes 

The flap system design notes discussed herein are based on the concept 

that the primary purpose of the flaps is the generation of a specified lift 

with an aerodynamic efficiency comparable to that which could be attained by 

the flat wing with full theoretical leading-edge thrust. Properly designed 

leading-edge flaps can provide a substitute for the leading-edge thrust which 

often cannot actually be realized. This is accomplished by a loading of the 

deflected surface which produces a distributed rather than a concentrated 

thrust force. Trailing-edge flaps serve to reduce the angle of attack 

required to produce the specified lift and since they affect the span load 

distribution they may also influence the lifting efficiency. 

A supersonic cruise configuration illustrated in sketch (j) will be 

taken as an example to illustrate 

the application of design techniques 

made possible by features of the 

present computer program. This is a 

wing-fuselage configuration with a 

twisted and cambered wing designed Sketch (j) 

for CL=O.lO at M=2.7. Landing 

approach design conditions have been 

chosen at: 

M = 0.25 

R= 160 x lo6 

CL = 0.55 

a = 8O 

33 
The trailing-edge flaps on either side of the airplane (between the 

fuselage and the inboard engine, and between the inboard and the outboard 

engine)are fixed in planform but may be deflected as necessary. It is 

assumed for this example that trailing-edge devices for the remainder of the 

wing will be employed as ailerons for roll control and will be unavailable 

for use in generating lift. This configuration was previously used in the 

study reported in reference 2. As will be seen in the following discussions, 

corrections and refinements to the computational techniques alter to some 

degree the results of the previous study. 

Because the purpose of the leading-edge flaps is the restoration of 

performance benefits lost due to the failure to achieve leading-edge thrust, 

it is first necessary to estimate the extent of full thrust achievement for 

the basic wing. This may be done in the following manner. 

For the basic wing (which includes a distribution of twist and camber 

for a supersonic cruise design condition), the program provides an estimate 

of the spanwise distribution of the wing angle of attack for zero local 

leading-edge thrust as shown in sketch 

(k). At a given span station, this angle 10 

of attack is estimated to produce a azt Jeg 

stagnation point at or near the local 

airfoil origin. Local thrust will be 

generated only at angles of attack larger 

or smaller than the angle of attack for 

zero thrust. For a flat wing, azt will 

be zero at all s,pan stations. A well 

-10 1 

I 1 

0 .5 1.0 

Y 

b/2 

Sketch (k) 

designed twisted and cambered wing will have a nearly constant azt across 

the span at the design Mach number. 

34 
For a flat wing of the same planform, the program provides an estimate 

of the spanwise distribution of the range of angle of attack for full thrust 

as shown in sketch (1). For angles 

outside this range, the attainable thrust 20 

prediction method indicates attainable raft,deg 

10 

thrust less than the full theoretical 

values. 

A combination of basic wing azt 

and flat wing Aaft gives a plot of the b/2 

Sketch (II 

range of full thrust for the basic wing 

as shown in sketch (m). The shaded 

region indicates the total range of 

angles of attack that are estimated to 

result in full theore,tical thrust. 

Generally, as shown here, the range of 

full thrust will not cover the design 

angle of attack. For portions of the 

aAeg 

-- ades--‘-” 

b/2 

wing Sketch (m) semispan where the range of full 

thrust falls below the design angle of 

attack, leading-edge flaps will be required. As a rough guide, the product 

of the flap chord and the flap deflection angle should be proportional to the 

discrepancy between the upper limit of the full thrust range and the design 

angle of attack. This sketch indicates that leading-edge flaps are required 

for span stations beyond about the 0.15 semispan position. In contrast, th,e 

study of reference 2 indicated that the flaps were needed only beyond the 

0.30 semispan position. The difference is due to the newer and more accurate 

35 
method of estimating attainable thrust for low values of the 'Mach number 

normal to the leading edge. For the inboard wing panel of this example, 

normal Mach number is 0.071. 

The foregoing considerations led to selection of a candidate leading 

flap system shown in sketch (n). 

For the wing outer panel, flap 

the 

edge 

chords were constrained by structural considerations. Nominal streamwise deflection angles of 20" were 

chosen for both leading-edge and 

trailing-edge flaps. The computer 

program was used to estimate the 

Sketch (n) 

aerodynamic efficiency of the flap system as represented by the suction 

parameter, Ss. The results shown in figure 15 cover a range of leadingedge and trailing-edge flap settings from 0 to 40 degrees. The solid contour 

lines depict constant values of the suction parameter, and the dashed contour 

lines show the required angle of attack for the design lift coefficient. 

Subject to the design angle of attack of 8' restraint, the performance is 

estimated to optimize at a trailing-edge flap angle of about 22" and a 

leading-edge flap angle of about 24O. Linearized theory probably tends to 

overestimate the benefits of leading-edge flap deflection, so that the actual 

optimum deflection may be somewhat less than 24O-perhaps about 20'. 

As the design by iteration process is conducted, an occasional check of 

the span load distribution is warranted. A program estimate of the span load 

36 
distribution for the candidate flap system with 

20" deflections of both leading-edge and 

trailing-edge flaps is shown in sketch (0). 

This curve is compared with the well known 

1.0 

idealized elliptic span load distribution (the 

dashed line). The shape of the span load 

0 .5 1.0 

x-k 

Sketch (01 

distribution is controlled to a large degree by 

the wing planform, but trailing-edge flap deflections can provide some degree 

of modification. The idealized distribution could be approached more closely 

if trailing-edge flaps could be employed for the outer portion of the wing 

semispan, but this is not allowed by the design guidelines. The study of 

reference 2 showed a significant improvement in performance when this 

requirement was ignored to allow trailing-edge flaps to cover the entire 

span. 

The candidate leading-edge flap design based on attainable thrust considerations employs a constant deflection angle for the entire length of the 

flap. Figure 16 was prepared as a means of judging possible improvements 

with other deflection schedules. Section drag-due-to-lift factors have been 

plotted as a function of the leading-edge flap deflection. To eliminate the 

intermingling of curves that otherwise would occur, the drag due-to-lift 

factors shown are increments relative to the zero leading-edge deflection 

values. For the outer flap panel (outboard of the 0.726 station) the optimum 

deflection angles are generally less than for the inner panel. To explore 

the possibility of improved performance, the program was rerun with nominal 

deflection angles of 22.7O and 17.2' for the inboard and outboard panels 

respectively instead of the constant 20" angle. The results showed a very 

37 
slight decrease in performance rather than an increase. This perhaps indicates only the very complex nature of the interactions involved in camber 

surface design. Increased inboard flap deflections reduce the inboard lift 

and thus reduce the upwash field which the outboard flap utilizes for performance gains. A reversal of the deflection schedule to 17.2' inboard and 

22.7' outboard resulted in a slight gain in performance. But because this 

schedule would result in a gap between the edges of the inboard and outboard 

flap, the original constant 20" deflection was retained. It appears that 

section drag-due-to-lift factor patterns, such as those shown in figure 16, 

which enhance outboard flap performance, are a desired feature of good flap 

design. 

The previously discussed plots of the range of full thrust may be used 

to give some indication of the flap system flow separation characteristics as 

shown in figure 17. These plots are given for leading-edge flap deflections 

of O", ZOO, and 40°, and for a trailing-edge flap deflection of 20'. The 

program estimates cover flight conditions and representative wind-tunnel conditions. Angles of attack required to generate the design lift coefficient 

of 0.55 are shown by the dashed lines. For undeflected leading-edge flaps, 

the program data indicate that full thrust would be achieved only over the 

inboard 20 percent of the semispan at flight conditions. Thus, leading-edge 

flow separation and the formation of a detached leading-edge vortex system 

could be expected over the major portion of the wing. However, even with a 

large amount of detached flow the program can be expected to give good estimates of wing performance for flat wings, because the loss of leading-edge 

pressure peaks and the associated vortex formation have little effect on the 

direction of the resultant force. With leading-edge flap deflection increased 

38 
to 200, the separation point is estimated to move to about the midpoint of 

the wing semispan for flight conditions. At a 40' deflection, attached flow 

over the entire wing is indicated. However, the 40' deflection is well 

beyond the estimated optimum of about 24" given by the program (see figure 

15). A leading-edge flap deflection greater than that necessary to just 

bring the upper limit of the full thrust range to the design angle of attack 

is counter productive. At larger angles, the thrust will decrease and the 

axial force component of that thrust will also decrease. Furthermore, it is 

likely that the benefits of increased flap deflection will in actuality fall 

off more rapidly than program results predict. Thus, more attention should 

be given to deflection angles somewhat less than the program optimum. A 20' 

deflection angle might be a good compromise. Although some degree of flow 

separation is indicated for the 20" deflection, the effect on performance 

could be fairly small if the vortex induced pressures were to act for the 

most part on the deflected surface. This could happen in cases where there 

is a difference of only a few degrees between the upper limits of the full 

thrust region and the angle of attack for the design CL. The program gives 

an estimate of the distribution of the vortex pressure field (options 1 and 

2); but, unfortunately, this is one of the least reliable of the program 

features. Experimental evaluation also poses a dilemma. As indicated here 

and as d 

Reynolds 

sure way 

The 

is no 

iscussed previously, flow separation is very sensitive to the 

number. High test Reynolds numbers are required, but there 

of establishing an acceptable level. 

degree of leading-edge thrust achieved can be controlled by 

selection of airfoil parameters. Within limits imposed by other design 

requirements, the thrust can be increased by increasing the section thickness 

39 
and leading-edge radius. Conversely, the thrust can be minimized and the 

leading-edge separation vortex force maximized by introducing a sharp leading 

edge. A question that often arises in flap system design is: Under what 

circumstances should the leading edge be deliberately sharpened so as to 

create leading-edge separation vortex flow? The following discussion may 

provide a better understanding of the problem. 

Sketch (p) shows a deflected leading-edge flap and the axial force 

vectors that result from the attainable 

thrust and from the vortex force, provided 

that the vortex field remains totally on 

the deflected surface. The change in the 

section axial force coefficient due to a 

change in the attainable thrust may be 

expressed as: Sketch (p) 

sinsL 

dcA = -dct a cos 6L + dct a - 

, , COSAL 

or 

dcA siML 

= - - cos 6 

dct,a COsAL L 

Thus, there is no change in the axial force with a change in the attainable 

thrust when: 

6L = tan-l (coshL) 

If the deflection angle is measured normal to a hinge line which is parallel 

to the leading edge there is no change in the axial force with a change in 

the attainable thrust when: 

40 
6L,n = tan-l (tan dL/cos AL) = 45' 

For smaller deflection angles, axial force will be reduced by an increase in 

the attainable thrust. For larger deflection angles, axial force will be 

reduced by an increase in the 

streamwise deflection angle 

and the regions in which 

either an increase in the 

thrust or an increase in the 

vortex force will result in 

reduced axial force and 

improved aerodynamic performance. For wing sweep angles 

up to 50° or 60°, the critical streamwise flap deflection angle is quite large, 

and it is unlikely that sharp 

leading-edge flaps would 

offer any benefits. But, for 

vortex force. Sketch (q) shows the critical 

60 

increase vortex 

8L ,deg 

AL,deg 

Sketch (q) 

wing sweep angles of 60" to 70' and more, sharp edges may indeed offer 

performance benefits. As mentioned previously, this simple analysis is 

appropriate only if the separated vortex flow is confined to the deflected 

flap surface. A larger extent of separated flow would increase the critical 

angle and make leading-edge sharpness less attractive. Because the vortex 

center tends to move rapidly from the leading-edge as the angle of attack is 

increased (see figure 5), the incremental angle of attack (CCdes - azt) 

producing detached flow nust be limited to small values. On the other 

41 
hand, this simple analysis ignores the changes in the section normal force. 

Consideration of this factor would tend to reduce the critical angle and make 

sharp leading edges relatively more attractive. Thus the critical angle 

variati,zn shown as a line on sketch (q) should probably be a band separating 

the areas where an increase in thrust or an increase in vortex force will 

result in improved performance. In any case, this plot serves only as an 

indicator of the advisability of considering leading-edge changes. 

The inboard wing panel of the configuration used in the illustrative 

design problem has a leading-edge sweep angle of 73" and a critical flap 

deflection angle of 16.3O. Thus, it might appear that the wing performance 

could be improved by resorting to a sharp leading edge. However, according 

to the same criteria, the outer wing panel with its 60' sweep angle requires 

a rounded leading edge. Since the larger portion of the leading-edge flap 

performance gains are generated by the outer panel flap operating in a strong 

upwash field, it would seem that outer panel requirements should take 

precedence. Sharp edge induced flow separation on the inboard panel leading 

edges would tend to reduce the upwash at the outer panel leading edges. 

The computer program appears to be applicable to the analysis and design 

of wings with appreciable leading-edge radius over a large range of angles of 

attack and a large range of flap deflection angles, provided that the Reynolds number is large enough to insure attached flow over the major portion 

of the wing. For wings with sharp leading edges, the range of applicability 

may be more restricted. The program can be expected to give reasonably good 

predictions of aerodynamic characteristics for flat wings and wings with mild 

camber surfaces. But for sharp leading-edge wings with deflected flaps, good 

predictions can be expected only if the separated leading-edge flow reattaches 

42 
ahead of the leading-edge flap hinge line. Sketch (r) will help to explain 

the reason for this limitation. 

The sketch shows a typical section lifting 

pressure distribution given by the program 

for a twisted and cambered wing with deflected leading-edge and trailing-edge 

flaps. Note the strong singularities at 

the hinge lines of the leading-edge flap 

CP 

and the trailing-edge flap. If the real x '/c 

flow separates and does not reattach for- Sketch (rl 

ward of the hinge line, these loading 

peaks will not be realized. Thus with a 

strongly detached flow, both leading-edge and trailing-edge flaps will lose 

effectiveness. As discussed previously, an attertpt to introduce pressure 

limiting into the program was not successful. Thus, the program will tend to 

predict better aerodynamic performance than can actually be achieved under 

conditions which promote strong flow detachment. Fortunately, it also 

appears that the better the wing aerodynamic performance, the more likely it 

is that the program will be capable of predicting that performance. 

CONCLUDING REMARKS 

This report describes the recently expanded capabilities for analysis 

and design of 1~ speed flap systems afforded by a computer program introduced in reference 1. The present method provides for the simultaneous analysis 

of up to 25 pairs of leading-edge and trailing-edge flap deflection 

schedules. Among other new features of the program are a revised attainable 

43 
thrust estimation method to provide more accurate predictions for low Mach 

numbers, and a choice of three options for estimation of separated leading- ,-*! 

edge vortex flow effects. 

Comparison of program results with low speed experimental data for an 

arrow wing supersonic cruise configuration with leading-edge and trailingedge flaps shows good agreement over most of the range of flap deflections. 

Correlations of program and experimental data for a delta wing-body model 

employing twist and camber showed a significant effect on wing performance of 

an increase in test Reynolds number from 1.5 x lo6 to 8.0 x 106. At the 

higher Reynolds number the program provided good estimates of the aerodynamic 

lift, drag, and pitching moment characteristics. These force data 

comparisons as well as an independent study of the effects of Reynolds number 

on airfoil and wing pressure distributions show that the aerodynamic 

performance of twisted and cambered wings and wings with leading-edge flaps 

can be expected to be nuch more sensitive to Reynolds number effects than the 

aerodynamic performance of flat wings. Thus there is a special need for high 

Reynolds number testing of cand idate flap systems. Inadequate Reyno Ids 

number test conditions could lead not only to poor prediction of flight 

performance but also could result in rejection of flap systems with excellent 

high Reynolds number performance but poor low Reynolds number performance. 

Suggestions for use of the program in an iterative manner for the design 

of efficient leading-edge and trailing-edge flap systems have also been 

advanced. The design goal is the definition of flap systems which are no 

larger and no more complex than necessary to produce an aerodynamic 

efficiency comparable to that which could be attained with flat wing full 

theoretical leading-edge thrust if there were no Reynolds number limitations. 

44 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

REFERENCES 

Carlson, Harry W.; and Walkley, Kenneth B.: A Computer Program for Wing 

Subsonic Aerodynamic Performance Estimates Including Attainable Thrust 

and Vortex Lift Effects. NASA CR-3515, 1982. 

Carlson, Harry W.: Application of an Aerodynamic Analysis Method 

Including Attainable Thrust Estimates to Low Speed Leading-Edge Flap 

Design for Supersonic Cruise Vehicles. NASA CR-165843, 1982. 

Carlson, Harry W.; Mack, Robert J.; and Barger, Raymond L.: Estimation 

of Attainable Leading-Edge Thrust for Wings at Subsonic and Supersonic 

Speeds. NASA TP-1500, 1979. 

Jacobs, Eastman N.; and Sherman, Albert: Airfoil Section Characteristics as Affected by Variations of the Reynolds Number. NACA Report 586, 

1937. 

McCullough, George B.: The Effect of Reynolds Number on the Stalling 

Characteristics and Pressure Distributions of Four Moderately Thin 

Airfoil Sections. NASA TN-3524, 1955. 

Marsden, D. J.; Simpson, R. W.; and Rainbird, W. J.: An Investigation 

Into the Flow Over Delta Wings at Low Speeds With Leading Edge 

Separation. Rep. No. 114, The College of Aeronautics, Cranfield 

(England), February 1958. 

Wentz, W. H., Jr.: Effects of Leading-Edge Camber on Low-Speed Characteristics of Slender Delta Wings. NASA CR-2002, 1972. 

Lan, C. Edward; and Chang, Jen-Fu: Calculation of Vortex Lift Effect 

for Cambered Wings by the Suction Analogy. NASA CR-3449, 1981. 

Hall, Charles F.: Lift, Drag, and Pitching Moment of Low-Aspect-Ratio 

Wings at Subsonic and Supersonic Speeds. NACA RM A53A30, 1953. 

10. Pinkerton, Robert M.: The Variation with Reynolds Number of Pressure 

Distribution over an Airfoil Section. NACA Report No. 613, 1938. 

11. Tinling, Bruce E.; and Lopez, Armando E.: The Effects of Reynolds 

Number at Mach Numbers up to 0.94 on the Loading on a 35' Swept-Back 

Wing Having NACA 65 A012 Streamwise Sections. NACA RM A52B20, 1952. 

12. Fischetti, Thomas L.: Investigation at Mach Numbers From 0.80 to 1.43 

of Pressure and Load Distributions Over a Thin 45" Sweptback Highly 

Tapered Wing in Combination With Basic and Indented Bodies. NACA RM 

L57D29a, 1957. 

13. Jesch, L.F.; and Walton, D.: Reynolds Number Effects on the Aerodynamic 

Performance of a Vertical Axis Wind Turbine. Third International 

Symposium on Wind Energy Systems, Lyngby, Copenhagen, Denmark, August 

26-29, 1980. 

45 
0 Experiment, ref. 4 

---- Theory, full thrust 

- Attainable thrust, Cp,lim by iteration 

Rnz.4~ IO6 Rn= .8XI06 Rn=I.4xI06 Rn= I.9 ~10~ 

AcA ;m, k, , b, # b, NAzo1

. 

0 IO 20 0 IO 20 0 IO 20 0 IO 20 

Q, deg Q, deg Q, de9 Q, de9 

(a) Mnz.061 

Figure l.- Axial force characteristics of two-dimensional airfoils. 
o Experiment, ref. 5 

AcA 

Mn=.05, Rn=I.I x IO6 

-.12- \ \ \ 

-.I6 - Cp,lim’-4.1 ‘1, 

-.20L \ 

Mn=.03,Rn=.9xI06 Mn= .10, Rn= I.8 x IO6 

AcA 

-.20 - 

\ 

I J 

E 0 

Cp,lim=‘5.9 , 

L \ 

0 5 IO 

a,deg 

---- Theory, full thrust 

- Attainable thrust, Cp,lim by iteration 

0 

\ F \ \ \ \ 

Cp,lim=-4.9 ‘\, 

L -1 

0 5 IO 

a,deg 

( b) Mn as specified 

Mnz.22, Rnz4.1 x IO6 

\ \ 

- Cp,lim’-4.9’\, rl=.3 

\ L \ 

NACA 0006 

Mnz.17, Rn= 3.6 x lo6 

I I J 

0 5 IO 

a,deg 

NACA 0008 

3=.3 

Figure l.- Concluded. 
-6 

Cp,lim 

-4 

-2 

0 Data trom figure I 

e-w Fairing 

0 Data points trom tairing 

Reference 4 

Mn= -061 

Reference 5 

Mn as specified 

0 I I I I I I I I J 

0 1 2 3 4 0 I 2 3 4 

Rnx 10m6 R,x 1O-6 

(a) M,=.03 to .22 

Figure 2.- Limiting pressure coefficient variation with Reynolds number. 
-4r Mn z.6 

Cp,lim -3 1 

% 

-- ,a---- 4g 

-2 ,/ 

-I’ 

0' 

0 2 4 6 

Rnx IOB6 

0 

-cData from reference 3 

Fairing 

Data points from fairing 

I- Mnz.4 

r 

M,=.7 

I 

$3 

,,e-*-- --a- 0 

/’ 0 

L 

I I 1 

0 2 4 6 

Rnx low6 

r 

Mnz.5 

IM,=.8 

L- 

/@ 

% 

---* ---mm*- 

El 

0 2 4 6 

Rnx low6 

(bI Mnz.3 to .8 

Figure 2.- Concluded. 
Cp,l 

Data from figure 2 

R,xIO-~ 

0 I 

0 3 

0 5 

-6 

im 

-4 

- Empirical equation 

E 

Cp,lim Z-2 

YMn2 

E=.O5 +.35(1-Mnj2 

e=4-3M,+ 4[I-Mn)15 

01 0 .2 .4 .6 .8 1.0 

Mn 

Figure 3;- Limiting pressure coefficient,variation with Mach number. 
/- 

Vacuum 

-10 

-8 

-6 

Cp,lim 

-4 

-2 

lr \ \ \ I\ \:, \ \ 

. \\. dn x IOB6 

I-\ 

1 

-7- .I 

P 

0% 

0 .2 .4 .6 .8 1.0 

Mn 

.oT ------- Lwm 

"0 .2 .4 .6 .8 1.0 

Mn 

Figure-4.- Limiting pressure coefficient as given by the empirical formula. 
Experiment 

0 A = 70°, ref. 6 

0 A = SO’, ref. 6 

0 A = 7L”. ref. 7 

Empirical equation 

% 1 

xcotn.= ‘i7Kr 

I I I 

10 20 30 

%deg 

Figure 5.- Location of center of vortex pressure field as given by 

experimental data. 

52 
.04 

0 

cA 

-.04 

c 

, 

/ 

\ 

,/ 

\ 

\ 

.0 

.4 

CN 

0 

-.4 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.16 

cD 

.08 

-10 0 10 20 - 

Q, deg 

(a) BTn=09 SLn=OO 

1,. 1 . 

Figure 6.- Correlation of program data with experimental 

data for an arrpJ wing Eonfiguration. 

M= 0.28, R = 5.75 x 10 

53 
*T#n = %A” = %2,n 

*L,n= *L,l,n = sL.2.n 

.04r 

.8 

.I 

cN 

0 

-.4 

-10 0 10 20 

Q, deg 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

-24 c 

.I6 

cD 

.08 

(b) 6Tn’10q 6L n =20° * , 

Figure 6.- Continued. 

54 
‘T,n’ *T,l,n = ‘T,2,n 

*L,n’*L,l,n = ‘L.2,n 

.8 

.4 

CN 

0 

-.I 

-10 0 10 20 

a, deg 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.I6 

CD 

.08 

0 

k) 6T,n = loo, BL,, = 30’ 

Figure 6.- Continued. 

55 
'T,n' *T.l,n = %2,n 

sL,n=6L,l,n = ‘L.2.n 

.04 

0 

CA 

-.o 4 

.a 

.4 

CN 

0 

-.4 

oo;)\\ YL 

. 

/-% 

/ / 

/ 

7 , 

-10 0 10 20 

a, deg 

.24 

.l6 

cD 

.08 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

Id) ST,, = 10: 6L,, = 40’ 

Figure 6.- Continued. 

56 
GT,n’ST,l,n = %2,n 

‘L,n= ‘L,l,n = ‘L,2,n 

.04 

0 

cA 

-.04 

.8 

.4 

CN 

0 

-.4 

-10 0 10 20 

Q, deg 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.I6 

CD 

.08 

0 

\ 

t 

\ 

--. 

/ / 1% / / / 

J 

-.I 0 .4 .8 

cL 

(el 8T,n =20°, 8L,n = 30’ 

Figure 6.- Continued. 

57 
.04 

0 

cA 

-.04 

.0 

.4 

cN 

0 

-.4 

L 

L 

\ \ \ 

+ 

\ \ 

\ 

\ \ \ 

I \ 

/ 

/ 

0 

-10 0 10 20 

adeg 

%n%,n’ %2,n 

*L,n”L,l,n = ‘L,2,n 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.I6 

cD 

.08 

0 

-.4 0 .4 .8 

cL 

(f) sT,n=300, 8L,n= 30' 

Figure 6.- Continued. 
.08 

.04 

cA 

0 

-.04 

.8 

.4 

cN 

0 

-.4 

0 10 20 

a, deg 

*T,n’ ‘T,l,n = %2,n 

‘L,n”L,l,n = *L.2,n 

o Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.I6 

cD 

.08 

0 

-.4 0 .4 .8 

cL 

(g) 8T n=40°# 8L n= 3oo 

, , 

Figure 6.- Concluded. 

59 
3 

-.08 

a, deg 

0 

-.4 

(a) R =1.5x IO6 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.I6 

CD 

.08 

Figure 7.- Correlation of program data with experimental 

data for a flat delta wing configuration. 

M= 0.25. 

60 

I 
.04 

0 

CA 

-.04 

-.08 

.8 

.4 

CN 

0 

-.4 

B--D 

, 

7 I 

‘I 

--D-----B 

T ’ 0 \ 

8 

\ 

\ 

\ 

@ 

” 

0 10 20 

a, deg 

0 

-.4 0 .4 .8 

5 

(b) R = 8.0 x IO6 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.16 

cD 

.08 

L 

Figure 7.- Concluded. 

61 
.04 

0 

CA 

-.04 

-.08 

.8 

.4 

CN 

0 

-.4 

\ 

‘. \ 

/ / 

i 

7 

3 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

I I 

-10 0 10 20 

a, deg 

.24 

.16 

cD 

.08 

0 

ia) R = 1.5 x lo6 

-.4 0 .4 .8 

cL 

Figure 8.- Correlation of program data with experimental 

data for a twisted and cambered delta wing 

configuration. M = 0.25. 

62 
.04 

0 

cA 

-.04 

-.08 

.8 

\ \ \ \ \ 

+ i 

0 10 20 

a, deg 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

.24 

.16 

cD 

.08 

-.4 0 .4 -8 

(b) R = 8.0 x IO6 

Figure 8.- Concluded. 

63 
3 

0 

Cm 

-.04 

~08 

Flat wing Twisted and cambered 

0-o I”\ 0 \ 

\ \ 

\ \ 

II ,\ I 

-~08-10 0 10 20 

a, deg 

0 Experiment 

Theory 

------- No thrust 

--- Full thrust 

Present method 

R=1.5x106 

R=8.0x106 

%k% 

\ 

\ 

I ,\ J 

-10 0 10 20 

a, deg 

Figure 9.- An example of the effect of Reynolds number 

on pitching moment. 

64 
NACA 4412 airfoil 

- Experiment 

--- Cp,lim (attainable thrust 1 

a =12’ a= 16’ a=20° 

B-B 

b 

--- 

L 

~24~ 

--- L 

R=3.1x106 

R,= 1.9 x lo6 

cp -p p p - b ~ F?;w&l;;o6 

--II0 .5 1.0 0 .5 1.0 0 .5 1.0 0 .5 1.0 

J- x’k r- xl/c r x’/c n x’ c 

Figure lO.- Pressure distribution on an airfoil at 

three Reynolds numbers. M = 0.61. 
- Experiment 

--- Cp,lim (attainable thrust I 

Figure ll.- Pressure distribution on a semispan swept wing at three Reynolds 

numbers. M = 0.25. 
- Experiment 

( attainable thrust 1 

‘I 

0 .5 1.0 0 l.0 .5 0.5 1.0 o-l.0 

ST x’ c f- xk n-- x’ c n- x’ c 

Figure 12.- Pressure distribution on a wing-body combination at three span 

stations. M = 0.8. 
1.6 

1.2 

cL 

.8 

Rounded leading edge 

f-F%% 

/’ 

IL Potential theory 

! 

.8 

10 20 

a, deg 

Sharp leading edge 

I 

l’ 

‘L I 

/ 

Potential theory 

I + vortex lift 

10 20 

a, deg 

Figure 13.- Effect of Reynolds number on lift coefficient of wind energy 

airfoil. 
c -z 

NACA 0008 airfoil 

I J 

0 .5 1.0 

r- x’k 

- Experiment 

--- Cp,Lim (attainable thrust I 

a =gO 

I I 1 

0 .5 1.0 

$7- x’ c 

a ~10 

1 e-s 

I=- M,=.ll, R,= 2.4~ lo6 

L -- 

I=- M, =.17, R,= 3.6 x 10’ 

0 .5 1.0 

f- x’k 

Figure 14.- Illustration of a precipitous change in pressure distribution. 
__ ;; ;70, Suet ion -.. 

de!2 

sL= *L,l = SL,2 

‘T = *T,l = ‘T,2 

parameter, S, 

8T’deC.J 

Figure 15.- Flap deflection optimization data for a candidate flap system. 
= 8,j = 8T,2 = 20’ 

.4 

-.8 

-1.2 

Y b/2 

- .633 

- ,567 

I I I I I 

0 10 20 30 40 

Figure 16.- Variation of section drag-due-to-lfft 

factors with deflection of candidate 

leading-edge flaps. 

71 
M=.25 

a&g 

Flight 

M=.25 

R=160x106 

15 

10 Tunnel 

a,deg -a---- 

5 ------------ M=.20 

0 R=3.5 ~10~ 

-5 I J 1 I I L I I 

0 .5 1.0 0 .5 1.0 0 .5 1.0 

Y Y Y 

b/2 b/2 b/2 

Figure 17.- Program estimate of the range of full thrust for the candidate 

f'lap system. 
NASA CR-3675 

4. Title and Subtitle 

3. Recipient’s Catalog No. 

AN AERODYNAMIC ANALYSIS COMPUTER PROGRAM AND DESIGN 

NOTES FOR LOW SPEED WING FLAP SYSTEMS 

7. Author(s) 

Harry W. Carlson and Kenneth B. Walkley 

9. Performing Organization Name and Address 

Kentron International, Inc. 

Kentron Technical Center 

Hampton, VA 23666 

2. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, DC 20546 

8. Performing Organization Report No. 

__ 10. Work Unit No. 

11. Contract or Grant No. 

NASl-16000 

13. Type of Report and Period Covered 

Contractor Report 

14. Sponsoring Agency Code 

505-43-23-10 

5. Supplementary Notes 

Langley Technical Monitor: Barrett L. Shrout 

Final Report 

6. Abstract 

This report describes the expanded capabilities for analysis and design 

of low speed flap systems afforded by recent modifications of an existinq 

computer program. The program provides for the simultaneous analysis of up 

to 25 pairs of leading-edge and trailing-edge flap deflection schedules. 

Among other new features of the program are a revised attainable thrust 

estimation method to provide more accurate predictions for low Mach numbers, 

and a choice of three options for estimation of leading-edge separation 

vortex flow effects. 

Comparison of program results with low speed experimental data for an 

arrow wing supersonic cruise configuration with leading-edge and 

trailinq-edge flaps showed good agreement over most of the range of flap 

deflections. Other force data comparisons and an independent study of 

airfoil and wing pressure distributions indicated that wind-tunnel 

measurements of the aerodynamic performance of twisted and cambered wings and 

wings with leading-edge flaps can be very sensitive to Reynolds number 

effects. 

7. Key Words (Suggested by Author(s)) 

Subsonic aerodynamics 

19. Distribution Statement 

Numerical methods 

Leading-edge thrust FEDD Distribution 

Wing flaps Subject Category 01 

Vortex lift 

Linearized theorv 

9. Security Cfassif. (of this report1 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

Unclassified Unclassified 72 

Available: NASA's Industrial Applications Centers gASA-Langley. 1983