1、NASA TECHNICAL NOTE NASA .- TJ D-4897 e,- i LOAN COPY: RETURN TO KIRTLAND AFB, N MEX AFWL (WLIL-2) PREDICTION OF LIFT AND DRAG FOR SLENDER SHARP-EDGE DELTA WINGS IN GROUND PROXIMITY by Churles H. Fox, Jr. Lungley Reseurch Center LungZy Station, Humpton, Vd. NATIONAL AERONAUTICS AND SPACE ADMINISTRAT
2、ION WASHINGTON, D. C. JANUARY 1969 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- TECH LIBRARY KAFB, NM PREDICTION OF LIFT AND DRAG FOR SLENDER SHARP-EDGE DELTA WINGS IN GROUND PROXIMITY By Charles H. Fox, Jr. Langley Research Center Langley Statio
3、n, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTl price $3.00 “ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by
4、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PREDICTION OF LIFT AND DRAG FOR SLENDER SHARP-EDGE DELTA WINGS IN GROUND PROXIMITY By Charles H. Fox, Jr. Langley Research Center SUMMARY A method of predicting the lift and drag of slender planar sharp-edge delta
5、 wings in ground proximity is described, and the results are compared with experimental data. The method utilizes a vortex-lattice computer program incorporating an image technique to compute the potential-flow normal-force and axial-force characteristics of delta wings in ground proximity. A recent
6、ly published vortex-lift concept in free air based on a leading- edge-suction analogy is utilized, and a method is presented for combining it with the results of the potential-flow theory in ground proximity. A comparison of the theoretical and experimental lift and drag for delta wings with a wide
7、range of aspect ratios is pre- sented at selected angles of attack. The comparison indicates that this method provides a reasonably good prediction of the lift and drag in ground proximity for aspect ratios less than 2.0 in the angle-of-attack range from 5 to 16. INTRODUCTION In the design of aircra
8、ft, consideration of the effect of ground proximity on the aero- dynamic characteristics of the aircraft is always important. If not considered, ground effect may produce large unexpected alterations in the characteristics of the aircraft during landing and take-off. Therefore, methods for the accur
9、ate prediction of the aero- dynamic characteristics of low-aspect-ratio delta wings in ground proximity are neces- sary to the aircraft designer. The present study is concerned with delta-wing planforms for which the proximity of the ground considerably alters the aerodynamic characteris- tics of th
10、e aircraft. (See ref. 1.) The results are only applicable to aircraft having delta wings with sharp leading edges, low aspect ratios, and slender planar airfoil sections. In this study, only the isolated wing is considered. Classical potential-flow theory as implemented by lifting-line and horseshoe
11、-vortex methods (for example, see ref. 2) has proven inadequate to predict the lift and drag of the low-aspect-ratio sharp-leading-edge delta-wing planform irrespective of the presence of the ground. One reason for this inadequacy is the failure of these methods to treat the chordwise variation of l
12、ift. Lifting-surface theory implemented by vortex-lattice methods Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(for example, refs. 3 and 4) was developed in order to include the chordwise lift distribu- tions; however, even this technique is inade
13、quate to treat the present planform. The basic reason for these inadequacies is that classical potential-flow theory assumes com- pletely attached flow whereas, in reality, the flow separates from the leading edges and forms spiral vortices which result in a loss of leading-edge suction and an incre
14、ase in lift. Reference 5 presents a new concept for the calculation of the vortex lift of planar sharp-leading-edge delta wings based on a leading-edge-suction analogy. This concept provides a reasonably accurate method of predicting the total lift of planar sharp- leading-edge delta wings in free a
15、ir. The present study employs a vortex-lattice potential-flow-theory lifting- surface method incorporating an image technique to represent the wing in ground proximity; a method is also introduced for combining the potential-flow theory with the free-air vortex-lift concept. The resulting theory yie
16、lds a reasonably good prediction of the total lift and drag of planar sharp-edge delta wings in ground proximity. The method is not applicable to the prediction of pitching moment, which is not considered herein. SYMBOLS Longitudinal data are presented about the stability axes. 4 b CA CA,der CD cL C
17、N K aspect ratio, b2/S total wing span, feet (meters) axial-force coefficient, positive direction is toward trailing edge, Axial force qs axial-force coefficient derived from CN lat, CA, and aCDi 7 aC2L.lat drag coefficient, qs lift coefficient, - Lift qs normal-force coefficient, positive direction
18、 is away from ground plane, Normal force qs a free-air proportional correction to vortex-lattice axial-force coefficient defined as CA,der CA,lat dynamic pressure, pounds/foot2 (newtons/meter2) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-S wing r
19、eference area, feet2 (meters21 hE/4 normalized height parameter, height of local quarter-chord point of mean aerodynamic chord above ground divided by mean aerodynamic chord E e induced-drag factor a! angle of attack, degrees A leading-edge sweep angle, degrees Subscripts: lat results of potential-f
20、low theory vortex-lattice computer program potential-flow theory using CA,der t total METHOD OF ANALYSIS A vortex-lattice method of calculating the potential-flow aerodynamic characteris- tics of delta wings was programed for solution on a high-speed computer. In this method, the wing is subdivided
21、in both the spanwise and chordwise directions into a number of ele- mental areas. In the present study, six spanwise and six chordwise divisions were used on each half of the wing. The local chord was divided into six equal increments whereas the spanwise divisions placed trailing-vortex legs at 0,
22、14, 28, 42, 56, 70, and 100 percent of the semispan. Each elemental area is represented by a horseshoe vortex with the bound portion lying along the local quarter-chord line of the element. The boundary con- dition that the flow be tangential to the wing surface is then satisfied for each element at
23、 a point on the lateral midpoint of the local three-quarter-chord line of the element. The proximity of the ground is represented in the computer program by a mirror image of the vortex-lattice system of the wing across the ground plane. The system com- posed of the vortex lattice representing the w
24、ing and the vortex lattice representing the image wing is used to compute the aerodynamic characteristics of the wing in ground proximity. In the vortex-lattice program, the induced velocity at a given point is related to the circulation strength of a given horseshoe vortex through a geometric-influ
25、ence coeffi- cient given by the Biot-Savart law. (See ref. 6, pp. 126- 128.) In this program, the geometric-influence coefficients are computed, the boundary condition is applied, and the 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-circulation
26、strengths are calculated. These circulation strengths are used to obtain the total velocities at the midpoints of the vortex-line segments. The total velocities are then used to compute the normal and axial forces acting on the wing. The computer program provides the potential-flow-theory normal and
27、 axial forces corresponding to selected conditions of ground height and angle of attack for the specified wing planform. The results are presented in this paper as a function of a nondimensional height param- eter, given as the height of the quarter-mean-aerodynamic-chord point above the ground divi
28、ded by the mean aerodynamic chord. The computer program used herein was designed for wings of arbitrary planform. At the present time, however, this program has only been verified for computing CN lat, A, lat and for delta-planform wings. Therefore, the complete program is not described in detail he
29、rein, and it is not available for release at this time. However, a brief description of the equations used in this computer program is included in the appendix. aCDi 7 2C2 L,lat An axial-force coefficient cA,lat can be calculated by using the vortex-lattice method as implemented herein since the tot
30、al velocities used to compute the forces on the vortex lines were calculated at the midpoint of each vortex segment rather than at the control point where the boundary condition was applied. However, the values obtained are somewhat inaccurate because of the discrete nature of the vortex-lattice for
31、mulation of the problem. The first task is, therefore, the correction of the axial-force coefficient. The method used herein relies on the fact that the vortex-lattice span load distribution in free air can be used to compute an accurate value of the induced-drag factor acDi aCL,lat 2- The accuracy
32、of this calculation has been checked by independent methods. (See ref. 7.) Thus, a better approximation of the free-air axial-force coefficient, valid for large angles of attack in potential flow, is obtained from the solution of -CA,der = cL,lat sin a - ac2 L, lat J The corrected axial-force coeffi
33、cient in free air may be written in terms of the vortex- lattice axial-force coefficient as 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Equation (2) defines K, the fractional correction to the axial-force coefficient in free air. For a given wi
34、ng planform, K is assumed to be a function of angle of attack but not a function of height above the ground. The lift and drag coefficients are obtained by resolving the normal- and axial-force coefficients in directions perpendicular and parallel to the free stream. If the results of the vortex-lat
35、tice program are used directly, the lift and drag coefficients are The effect of introducing K is to replace equations (3) by In this paper, equations (3) are referred to as the vortex-lattice theory, and equations (4) are referred to as the potential theory. The vortex-lift concept developed in ref
36、erence 5 for planar sharp-leading-edge delta wings is based on a leading-edge-suction analogy. For a planar sharp-leading- edge delta wing, the leading-edge suction is lost, and a leading-edge spiral vortex is formed. (See ref. 5.) In addition, the equilibrium force required to maintain the spiral v
37、ortex adds an increment to the normal force which is identical in magnitude to the lost leading-edge suction. By using the vortex-lattice method to account for the effect of the ground on the leading-edge suction, the total lift coefficient can be expressed as K A, latv cN,lat + cos A cos a! Since t
38、he leading edge is sharp, no leading-edge suction is developed (that is, no force is developed in the axial direction); therefore, the total free-air drag coefficient is CD,t = CL,t tan a! Equations (5) are referred to herein as the present theory. RESULTS AND DISCUSSION Several features of the anal
39、ysis should be noted. First, the existence of the spiral vortices emanating from the leading edge implies a redistribution of vorticity in the wing 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-and wake. This redistribution is not accounted for w
40、ith respect to the image wing below the ground plane, even though the results of reference 5 have been used to correct for this effect at the real wing. Secondly, the choice of the coordinate system used in the vortex-lattice program described in the appendix leads to a wake which, at positive angle
41、s of attack, intersects and passes through the ground plane. Finally, since the present approach uses the method of reference 5, which does not predict the distribution of forces over the wing, this approach cannot be used to calculate pitching moment. In view of the assumptions used in developing t
42、he present theory, the justification for its use must rest primarily upon a comparison with experimental data. One of the most complete experimental studies of ground effect for sharp-edged delta wings is that of reference 8, in which a series of wings with leading-edge sweep angles of 75O, 70, 600,
43、 and 50 (aspect ratios of 1.072, 1.456, 2.309, and 3.356, respectively) were tested. These wings were tested by using both the fixed-ground-board and image-model test methods at a free-stream velocity of 114.8 ft/sec (35.0 m/sec) mounted on a strut support. Certain unexplained nonlinearities existed
44、 at low angles of attack in the data of reference 8; how- ever, the data were self-consistent. Corresponding with the assumptions of the theory, the wings were isolated; that is, there was no fuselage or tail. The experimental data are presented in terms of the height parameter used in the present s
45、tudy. The lift and drag characteristics of the wings as functions of normalized ground height are presented in figure 1 for a! = 10 and in figure 2 for a! = 15. The drag coef- ficients presented in these figures do not include the friction-drag component which has been removed by subtracting the min
46、imum drag coefficients from the data of reference 8. (The values subtracted were 0.008, 0.010, 0.011, and 0.012 for wings with leading-edge sweeps of 75“, 70, 60, and 50, respectively.) An examination of figures 1 and 2 reveals that when either the potential theory or the present theory is able to p
47、redict the free-air lift coefficients, it can also be used to predict the effect of ground proximity reasonably well. For aspect ratios less than 2.0, where the leading-edge vortex is well developed, the present theory (eqs. (5) accurately predicts the lift. As the aspect ratio increases and the eff
48、ects of the leading-edge vortex become less pronounced, the accuracy of the potential-theory lift predictions (eqs. (4) becomes progressively better and that of the present-theory predictions becomes worse. In general, the present theory yields a better drag prediction than the potential theory. The
49、se effects can also be seen in figures 3 and 4 which summarize the lift and drag char- acteristics as functions of aspect ratio for selected ground heights. In order to examine the effects of angle of attack over a larger range, the data of reference 9 were used. Reference 9 presents tabulated lift and drag data as functions of angle of atta
