The Performance of 60º Delta Wings: The Effects of Leading Edge Radius on Vortex Flaps and the Wing

Cranfield

College of Aeronautics Report No. 9004

March 1990

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The Performance of 60 Delta Wings:

The Effects of Leading Edge Radius on Vortex Flaps and the Wing.

B K Hu and Prof J L StoUery

The Department of Aerodynamics

College of Aeronautics

Cranfield Institute of Technology

Cranfield. Bedford MK43 OAL. England

College of Aeronautics Report No. 9004

March 1990

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The Performance of 60 Delta Wings:

The Effects of Leading Edge Radius on Vortex Flaps and the Wing.

B K Hu and Prof J L StoUery

The Department of Aerodynamics

College of Aeronautics

Cranfield Institute of Technology

Cranfield. Bedford MK43 OAL. England

ISBN 1 871564 05 0

£8.00

'The views expressed therein are those of the authors alone and do not

necessarily represent those of the Institute"

SUMMARY

Low-speed wind tiinnel tests were conducted on 60 delta wings. The wings were tested with well rounded and sharp leading edge vortex flaps to estimate the effects of leading edge radius on the aerodynamic performance. The Reynolds number based on root chord was approximately 0.8 x 10 .

Results indicate that leading edge radius has little effect on

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the contribution of the vortex flap to lift/drag ratio on the 60 delta wing. The 60 delta wing with a well rounded leading edge and no vortex flap deflection has a higher lift/drag ratio over almost the entire lift coefficient range tested.

AR

C

C D

c

Di ^L NOTATION Aspect ratio Wing chord Drag coefficient

Lift induced drag coefficient

Lift coefficient

c - c

Lift induced drag factor (K = )

L HL Hinge 1 ine L. Lift Drag /_, /_, ratio D ' Drag

Re Reynolds number (based on wing centreline chord)

R Leading edge radius

a Wing angle of attack

a Zero lift angle of attack

LEVF Leading edge vortex flap

5 Leading edge vortex flap deflection measured normal to the hinge line

S Area of delta 1 with LEVF-1

1

S Area of delta 1 with LEVF-2

2

-INTRODUCTION

On most highly swept and delta wings designed for supersonic cruise the leading edge radius is not sufficiently large to prevent flow separation along the leading edge at high angles of attack (e.g., take off, landing, and manoeuvre). This separation results in the formation of a vortex on the upper surface of the wing as shown in Fig.l. The strength of the leading edge vortex is normally sufficient to result in flow reattachment over the wing's upper surface. Furthermore, the low static pressure at the core of the vortex considerably modifies the spanwise pressure distribution and generates a non-linear vortex lift component of the overall lift produced by the wing (Fig. 1). However, it also contributes a drag force due to the rearward

inclination of the resulting force vector (Fig. 2A). The loss of attached flow leading edge suction due to the separation along the leading edge further aggravates the drag. The drag penalty associated with the leading edge vortex flow can be reduced in a number of ways.

Increased aerofoil nose radius has a very powerful effect on retarding the development of the leading edge vortex. The leading edge of the wing is well rounded in order to maintain attached leading edge flow and thus to prevent vortex formation.

It recovers leading edge suction and results in large reduction in the lift induced drag. But the high zero lift drag penalty caused by a rounded leading edge at supersonic speeds is usually unacceptable.

An alternative solution is to add leading edge camber to the wing by use of conventional leading edge flap (Fig. 2B). It is effective in preventing vortex formation and promoting attached

flow conditions. With this configuration lift induced drag is

reduced because of the absence of the vortex and because of the leading edge suction resulting from flow acceleration around the flap. However, some lift is lost with the absence of the low pressure under the vortex core. There may also be a reduction in

overall supersonic performance of the aircraft due to the added

weight of a complex flap system.

A leading edge vortex flap (LEVF) can substantially reduce the lift induced drag by 'capturing' the leading edge vortex along a forward facing deflected surface. The vortex suction acting on the surface can develop a thrust. When the flow reattaches at the LEVF hinge line, an attached lifting flow is provided over the upper surface of the wing. This concept is illustrated in Fig. 2C where the flap angle must be such that the flow separates at the edge of the flap and a vortex results. The size of the flap must be sufficient to give reattachment near the LEVF hinge line.

The primary purpose of this paper is:

a) to estimate the effects of leading edge radius on the

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aerodynamic performance of a LEVF on a 60 delta wing

b) to estimate the effects of leading edge shape on the aerodynamic performance of 60 delta wings.

A series of tests were made in the Cranfield lA open-jet, low-speed wind tunnel using 60 delta wings made from wood.

2^ EXPERIMENTAL DETAILS

Details of the models are given in Fig. 3. The models tested have

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a leading edge sweep angle of 60 and no camber. The delta 1 model (Fig. 3a) having a symmetric aerofoil section has a

thickness/chord ratio of 10% which occurs at 35% C and a well rounded leading edge, R = 0.69% C. The spanwise thickness distribution varies linearly from root to tip. The model incorporated a LEVF-1 hinge line running along a ray from the

apex to the 75% semispan station at the trailing edge (Fig. 3b).

Adding the thin strip to the leading edge of LEVF-1 made a sharp leading edge LEVF-2 (Fig. 3c). The delta 2 model (Fig. 3d) is a

-5-flat delta wing with sharp leading and trailing edges to enhance flow separation. The model also incorporated a LEVF hinge line running along a ray from the apex to the 75% semispan station at the trailing edge (Fig. 3e). All the LEVF deflections were 30° measured in the plan normal to the hinge line.

Measurements of lift and drag were made in the 40" x 27" low-speed open-Jet wind tunnel, using a T.E.M. three component wind tvinnel balance. All the tests were conducted at a tunnel speed of about 28m/s. The angle of attack range was from -6 to

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+ 40 to include the stall. The Reynolds numbers based on centreline chord were 0.735 x 10 (delta 1 model) and 0.853 x 10

(delta 2 model).

The model was mounted on twin shielded struts with a tallsting for angle of attack control (Fig. 4).

Prior to testing, the T.E.M. balance was calibrated. Corrections to the collected data were applied as follows:

A correction to the measured angles of attack due to the constraint of the working section boundaries. This is known as the lift effect and is calculated using the method of images (see Ref. 1).

Owing to the angle of attack correction, the lift vector is inclined and so a correction to the measured drag is also required.

Interference between the twin shielded struts and the wing was assumed negligible.

All the force data have been reduced to coefficient form. These coefficients are based on total plan area. Measured angles of attack, lift and drag coefficients along with the corrected values are presented in tables 1 - 5 .

RESULTS AND DISCUSSION

According to NACA Langley fully-scale wind tunnel tests on a German Glider in 1946 (see Ref. 9 ) , the vortex lift on a delta

wing with thick, blunt leading edges can be significantly

increased by forcing separation at the leading edge by adding a

thin spanwise leading edge strip.

Lift

The C - a curves are plotted in Figs. 5a and 6a.

Fig. 5a shows that at all angles of attack tested the delta 1 produces markedly higher values of C than the delta 1 with LEVFs

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deflected 30 . The delta 1 stalls at an angles of attack of 30 , while the delta 1 with both LEVF-1 and LEVF-2 do not stall until

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an angle of attack of 36.6 .

The C - a curve also shows a reduced slope for delta 1 with LEVFs deflected 30 . This is due to three effects, a reduction in the projected planform area (whereas the C plotted is based on the constant total plan area), a reduction in the effective aspect ratio and a increase in zero lift angles of attack

(a = 6 ° , 6.8° for the delta 1 with LEVF-1 and with LEVF-2

0

respectively).

Fig. 6a shows that the LEVFs deflected 30° on both delta 1 and delta 2 reduce lift. The flat sharp edge delta 2 with LEVF deflected 30 produces higher values of C and lift curve slope

than the delta 1 with LEVFs deflected 30°.

Drag

The C - a curves are plotted in Figs. 5b and 6b.

Fig. 5b shows that when the LEVF-1 and the LEVF-2 are deflected 30° the angle of attack at which the drag is a minimum will

-7-increase. It moves from about 0.4 to about 8 . At a < 6 the delta 1 with LEVFs deflected 30° produce higher drag than the delta 1. This is because at low angles of attack with the flaps deflected a vortex will form on the lower surface of the flaps. The suction acting on the underside of the flaps will produce negative lift and increased drag. For a > 6° deflecting the LEVFs markedly reduces drag.

Fig. 5b also shows that at 4 < a < 18 the drag for a given angle of attack is the same for the delta 1 with either LEVF-1 or LEVF-2 deflected 30°. The well rounded leading edge LEVF-1 probably maintains attached leading edge flow. According to Ref. 2 as the wing angles of attack is increased, a value is reached for which the flow comes smoothly onto the leading edge of the

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LEVF-2 deflected 30 . There is attached leading edge flow and no flow separation. At a > 18 the LEVF-1 probably continues to maintain attached leading edge flow and leading edge suction acting on LEVF-1 develops a thrust. But the thin leading edge strip of LEVF-2 forces leading edge separation and forms a vortex which spills off the LEVF-2 and is shed over the wing. So the LEVF-2 produces higher drag than the LEVF-1 for the range of angles of attack.

Fig. 6b shows that the delta 1 produces lower drag than the sharp leading edge delta 2 at all angles of attack below 34 This is because the delta 1 with a well rounded leading edge recovers

leading edge suction resulting from flow acceleration around the leading edge.

Fig. 6b also shows that the delta 2 with LEVF deflected 30° produces higher drag than the delta 1 with LEVFs deflected 30 .

The C - C curves are plotted in Figs. 5c and 6c.

Fig. 5c shows that the delta 1 with LEVF-1 deflected 30° produces lower lift induced drag than the delta 1 with LEVF-2 deflected 30° at C < 0.95.

Fig. 5c also shows that the delta 1 with deflected LEVFs produce higher lift induced drag than the delta 1 over almost the entire C range tested. This is because although the delta 1 with deflected LEVFs produces lower drag at any given angle of attack,

it needs higher angles of attack than the delta 1 to obtain a given amount of lift.

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Fig. 6c shows that the delta 2 with LEVF deflected 30 produces lower lift induced drag than both delta 1 with LEVF-1 deflected 30° at C < 0.8 and delta 1 with LEVF-2 deflected 30° over C

L L range tested.

Fig. 6c also shows that well rounded leading edge delta 1 produces the lowest lift induced drag over almost the entire C range.

Lift induced drag factors K for all the configurations tested are plotted in Fig. 7.

Lift/ „ .. /„ Ratio ^Drag

lift

The / ratio is used as a basic aerodynamic performance parameter.

L , o Figs. 8a and 8b illustrate /_^ versus C on the basic 60 delta

wings, the wings with LEVFs configurations tested and the effects

of leading edge shape on /^.

Fig. 8a shows that the delta 1 with deflected LEVFs has lower lift

/, ratios than the basic delta 1 over almost the entire C

' drag L range tested. Deflecting the LEVFs reduces both lift and drag.

Fig. 8a also shows that the delta 1 with LEVF-1 deflected 30 has

11 ft

slightly higher / , ratio at 0.15 < Cs 0.6 and markedly

11 ft drag L higher /^ ratio at 0.6 < C < 0.95 than the delta 1 with

^ ' drag L LEVF-2 deflected 30°

Fig. 8b shows that the delta 1 with the leading edge radius R _ = 0.69% C has the highest ^ ^ ^ V ^ ratio for all the

LE => / drag

configurations tested over almost the entire C range. The delta

2 with LEVF deflected 30° has higher ^^^^/^ ratio than the

flat delta 2. Deflecting the LEVF reduces both lift and drag but the drag reduction is the more significant on the sharp edged flat 60° delta wing.

4. CONCLUSIONS

It must be remembered that all these tests were made at the modest Reynolds number of 0.8 x 10 based on root chord. The effect of Reynolds number on round leading edge delta wings is known to be large.

1. Deflecting the round nose of delta wing 1 reduced both the lift and the drag at a given incidence. Unfortunately the L/D ratio was also reduced.

2. Sharpening the leading edge flap by fitting a thin strip protruding horizontally from the round leading edge had little effect, the performance changes were very similar to those obtained by deflecting the round nose flap.

3. The sequence in which the tests were made has so far precluded tests on the delta 1 wing with the leading edge sharpened but undeflected.

4. Delta wing 2, which had sharp leading edges but a different aerofoil section, was tested. Deflecting the leading edge of

lift

this model decreased C and C but increased the /, L D ' drag ratio.

5. Of all the configurations tested the best L/D ratios were measured on the round nosed delta 1 model with no flap deflection.

REFERENCES

1. Parkhurst, R.C., and Holder, D.W. Wind tunnel technique: an account of experimental methods in low- and high-speed wind tunnels. PITMAN, 1952.

2. StoUery, J.L. , and Ellis, D.G. The behaviour and performance of vortex flaps. College of Aeronautics Report No. NFP8914, November 1989.

3. Ellis, D.G. The behaviour and performance of leading edge vortex flaps. College of Aeronautics Report No. 8601, 1986.

4. Jones, R. , Miles, C.J.W., and Pursey, P.S. Experiments in the compressed air tunnel on swept-back wings including two delta wings. A.R.C. Technical Report R & M No. 2871, 1954.

5. Kulfan, R.M. Wing geometry effects on leading edge vortices. AIAA 79-1872. August 20-22, 1979.

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6. Hu, B.K. and StoUery, J.L. The performance of 60 delta wings: the effects of leading edge radius and vortex flaps. College of Aeronautics Report No. 9002, November 1989.

7. Paul L.Coe, Jr., Jarrett K. Huffman, and James W.Fenbert. Leading-edge deflection optimization for a highly swept arrow-wing configuration. NASA TP 1777, December 1980.

8. Pau L.Coe, Jr., and Robert P.Weston. Effects of wing leading-edge deflection on low-speed aerodynamic characteristics of a low-aspect-ratio highly swept arrow-wing configuration. NASA TP 1434. June 1979.

9. Herbert A.Wilson, Jr., and J.Calvin Lovell. Full-scale investigation of the maximum lift and flow characteristics of an airplane having approximately triangular plan form. NACA RM NO.L6K20, February 12, 1947.

-11-10. W.Elliott Schoonover, Jr. Wind-tunnel investigation of vortex flaps on a highly swept interceptor configuration. ICAS-82-6.7.3.

Date: 20/9/89 p.m.

TABLE 1

Incidence, lift coefficient, drag coefficient (both corrected and uncorrected) and lift/drag ratio for Delta 1.

NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 0 21 2 2 2 3 2 4 o a ' ^ ( U ) - 6 - 4 - 2 0 2 4 6 8 10 12 14 16 18 2 0 2 2 2 4 2 6 2 8 3 0 3 2 3 4 3 6 3 8 40 " ( C , - 5.630 - 3.756 - 1.890 - 0.009 1.855 3.708 ( 5 . 5 0 8 ) 5.580 7.382 9.270 11.151 13.033 14.924 16.833 18.762 2 0 . 6 5 2 2 2 . 5 4 3 2 4 . 4 3 4 26.351 2 8 . 3 1 8 30.300 3 2 . 3 3 4 3 4 . 3 6 1 3 6 . 4 7 7 3 8 . 6 3 1 C L

c

L ( U ) - 0.248 - 0.164 - 0.074 0.006 0.097 0.196 ( 0 . 3 3 ) 0.282 0 . 4 1 5 0.490 0.570 0.649 0.722 0 . 7 8 3 0.831 0.905 0.978 1.051 1.107 1.129 1.141 1.118 1.100 1.022 0.919 ^ 1 . ( 0 - 0.248 - 0.164 - 0.074 0.006 0.097 0.196 ( 0 . 3 3 ) 0.282 0.415 0.490 0.571 0.650 0 . 7 2 3 0.784 0.832 0.906 0.979 1.052 1.108 1.130 1.142 1.119 1.101 1.023 0.920 C D C D ( U ) 0.045 0.035 0.021 0.018 0.020 0.022 ( 0 . 0 3 3 ) 0.032 0.046 0 . 0 6 3 0.088 0.117 0.153 0.206 0.252 0.301 0.356 0.407 0.466 0.535 0 . 5 8 3 0.625 0.646 0.656 0.638 C D ( C ) 0 . 0 4 3 0.034 0.021 0.018 0.020 0.021 ( 0 . 0 3 ) 0.030 0.042 0.057 0.080 0.106 0.140 0.190 0.234 0.280 0.331 0.379 0.435 0.502 0.550 0 . 5 9 3 0 . 6 1 5 0.629 0.617 D ( C ) -0 . 3 3 3 4 . 8 5 0 9 . 3 3 3 ( 1 1 . 0 0 0 ) 9.400 9.881 8.596 7.138 6.132 5.164 4.126 3.556 3.236 2 . 9 5 8 2.776 2 . 5 4 7 2 . 2 5 1 2.076 1.887 1.790 1.626 1.491

-13-Date: 19/9/89 p.m.

TABLE 2

Incidence, lift coefficient, drag coefficient (both corrected and uncorrected) and lift/drag ratio for Delta 2.

NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 O a « ( Ü ) -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 «(C) - 5.587 - 3.774 - 1.940 - 0.109 1.741 3.569 5.427 7.258 9.073 10.851 12.738 14.568 16.436 18.303 20.179 22.031 23.986 25.898 27.836 29.859 31.939 34.165 36.385 38.453 ^L

c

L(U) - 0.212 - 0.116 - 0.031 0.056 0.133 0.221 0.294 0.381 0.476 0.590 0.648 0.735 0.803 0.871 0.935 1.011 1.034 1.079 1.111 1.099 1.058 0.942 0.829 0.794 C L(C) - 0.212 - 0.116 - 0.031 0.056 0.133 0.221 0.294 0.381 0.476 0.591 0.649 0.736 0.804 0.872 0.936 1.012 1.035 1.080 1.112 1.100 1.059 0.943 0.830 0.795 C D C D(U) 0.060 0.048 0.034 0.028 0.029 0.032 0.039 0.055 0.075 0.114 0.149 0.186 0.231 0.283 0.343 0.414 0.463 0.528 0.580 0.634 0.665 0.658 0.601 0.597 C D{C) 0.059 0.048 0.034 0.028 0.028 0.030 0.036 0.050 0.067 0.102 0.135 0.168 0.209 0.257 0.314 0.380 0.427 0.499 0.539 0.594 0.628 0.628 0.578 0.576 D(C) -2.000 4.750 7.367 8.167 7.620 7.104 5.794 4.807 4.381 3.847 3.393 2.981 2.663 2.424 2.163 2.063 1.852 1.686 1.502 1.436 1.380

Date: 27/9/89 p.m.

TABL] Incidence, lift coefficient, drag uncorrected) and lift/drag ratio for

NO. o a « ( U , " ( C ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 1 22 2 3 2 4 - 6 - 4 - 2 0 2 4 6 8 10 12 14 16 18 2 0 22 2 4 2 6 2 8 3 0 32 3 4 36 3 8 4 0 - 5.482 - 3.634 - 1.776 0.084 1.940 3.776 5.649 7.494 9.347 11.223 13.082 14.940 16.788 18.646 2 0 . 5 1 6 2 2 . 3 7 9 2 4 . 2 4 1 26.130 28.060 3 0 . 0 0 3 3 2 . 0 1 3 3 4 . 0 2 3 3 6 . 1 0 1 3 8 . 1 7 5 - 0.266 - 0.188 - 0.115 - 0 . 0 4 3 0.031 0.115 0.180 0.260 0 . 3 3 5 0.399 0.471 0.544 0.622 0.695 0.762 0.832 0 . 9 0 3 0.960 0.996 1.025 1.020 1.015 0.975 0.937 3

coefficient (both corrected and Delta 2 with LEVF. 5 = 3 0 ° .

LEVF

c

D

c

D ( U )

c

D ( C ) D ( C ) 0.266 0.188 0.115 0 . 0 4 3 0.031 0.115 0.180 0.260 0.335 0.399 0.471 0.545 0 . 6 2 3 0.696 0 . 7 6 3 0 . 8 3 3 0.904 0.961 0.997 1.026 1.021 1.016 0.976 0.938 0.069 0.051 0.039 0 . 0 3 3 0.025 0.027 0.031 0.037 0.044 0.051 0.066 0.088 0.115 0.164 0.209 0.258 0.306 0.362 0.432 0.496 0 . 5 5 3 0.576 0.622 0.608 0.067 0.050 0.039 0 . 0 3 3 0.025 0.027 0.030 0.035 0.040 0.044 0.059 0.078 0.102 0.148 0.189 0.235 0.278 0.331 0.399 0.461 0.518 0.542 0.590 0.579 -1.240 4.259 6.000 7.429 8.375 9.068 7 . 9 8 3 6.987 6.108 4 . 7 0 3 4 . 0 3 7 3 . 5 4 5 3.252 2 . 9 0 3 2 . 4 9 9 2.226 1.971 1.875 1.654 1.620

-15-Date: 18/1/90 a.m.

TABLE 4

Incidence, lift coefficient, drag coefficient (both corrected and uncorrected) and lift/drag ratio for Delta 1 with LEVF-1, 5 = 30° LEVF NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 o a " ( U ) -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 "(C) - 5.332 - 3.449 - 1.569 0.317 2.317 4.095 5.985 7.875 9.799 11.702 13.607 15.525 17.438 19.362 21.289 23.209 25.119 27.039 28.963 30.753 32.702 34.637 36.574 38.671 ^L

c

L(U) - 0.448 - 0.370 - 0.289 - 0.213 - 0.142 - 0.064 0.010 0.084 0.135 0.200 0.264 0.319 0.377 0.428 0.477 0.531 0.591 0.645 0.696 0.785 0.871 0.915 0.957 0.950

c

L(C) - 0.448 - 0.370 - 0.289 - 0.213 - 0.142 - 0.064 0.010 0.084 0.135 0.200 0.264 0.319 0.377 0.428 0.477 0.532 0.592 0.646 0.697 0.786 0.872 0.916 0.958 0.951 C D C D(U) 0.092 0.074 0.057 0.042 0.031 0.023 0.021 0.021 0.023 0.027 0.033 0.039 0.049 0.061 0.073 0.094 0.121 0.151 0.184 0.216 0.242 0.294 0.349 0.397 C D(C) 0.087 0.071 0.055 0.041 0.031 0.023 0.021 0.021 0.023 0.026 0.031 0.036 0.045 0.056 0.067 0.087 0.112 0.140 0.172 0.200 0.223 0.273 0.326 0.377 D(C) -0.476 4.000 5.870 7.692 8.516 8.861 8.378 7.643 7.119 6.115 5.286 4.614 4.052 3.930 3.910 3.355 2.939 2.523

Date: 8/3/90 p.m.

TABLE 5

Incidence, lift coefficient, drag coefficient (both corrected and uncorrected) and lift/drag ratio for Delta 1 with LEVF-2 6 = 30° LEVF NO. 1 2 3 4 5 6 7 8 9 10 11 12 1 3 14 15 16 17 18 19 2 0 2 1 2 2 2 3 2 4 o a " ( U ) - 6 - 4 - 2 0 2 4 6 8 10 12 14 16 18 20 2 2 2 4 2 6 2 8 3 0 3 2 3 4 3 6 3 8 40 " ( C ) - 5.244 - 3.291 - 1.421 0.460 2.331 4 . 1 7 7 6.028 7.928 9.808 11.702 13.597 15.493 17.388 19.278 21.139 2 3 . 0 3 9 24.947 26.831 28.741 30.626 32.549 3 4 . 5 0 2 36.440 3 8 . 4 4 3 ^L

c

L ( U ) - 0.452 - 0.424 - 0.346 - 0.275 - 0.198 - 0.106 - 0.017 0 . 0 4 3 0.115 0.178 0.241 0 . 3 0 3 0.366 0.432 0.515 0 . 5 7 5 0.630 0.699 0 . 7 5 3 0.822 0.868 0.896 0 . 9 3 3 0.931 ^ L ( C ) - 0.452 - 0.424 - 0.346 - 0.275 - 0.198 - 0.106 - 0.017 0 . 0 4 3 0.115 0.178 0.241 0 . 3 0 3 0.366 0.432 0.516 0.576 0.631 0.700 0.754 0 . 8 2 3 0.869 0.897 0.934 0.932 C D

c

D ( U ) 1 0.107 0.090 0 . 0 7 3 0.055 0.038 0.026 0.019 0.018 0.022 0.026 0 . 0 3 3 0.038 0.050 0.065 0.090 0.114 0.153 0.189 0 . 2 3 3 0.297 0 . 3 5 3 0.396 0.441 0.476 C D ( C ) 0.101 0.085 0.070 0 . 0 5 3 0.037 0.026 0.019 0.018 0.022 0.025 0.031 0 . 0 3 5 0.046 0.060 0.082 0 . 1 0 5 0.142 0 . 1 7 5 0.217 0.278 0.332 0 . 3 7 3 0.416 0.451 D ( C ) -2 . 3 8 9 5.227 7.120 7.774 8.657 7.957 7.216 6 . 2 9 3 5.486 4 . 4 4 4 4 . 0 0 0 3 . 4 7 5 2 . 9 6 0 2 . 6 1 7 2 . 4 0 5 2 . 2 4 5 2 . 0 6 7

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B: FORCE ON CAMBERED LEADING EDGE

C: FORCE ON VORTEX FLAP

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-19-/k.^2.Sl

Ordinates of Wing Section in Terms of Chord

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Distance from leading edge 0 0 0 0 5 00075 0 0 1 2 5 0 0 2 5 0 0 5 0 . 0 0 7 5 0 1 0 0 C I S 0-20 0-25 {)'M 0-35 Height above chord X 100 0 0-825 1-008 1-300 1-821 2-53 3 0 4 3-44s 4-05 4-47s 4-76 4-934 5-00 Distance from leading edge 0-40 0-45 0-50 0-55 0-60 0-65 0-70 0-75 0-8(» 0-85 0-90 0-95 1-0 Nose radius = Height above chord X 100 4-96 4-77 4-49 4-15 3-75 3-32 2-86 2-39 1-92 l - 4 3 j 0-95 0-48 0 0-0069 X chord

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Figure 3b. Delta 1 with LEVF-1 model details

-21-x-x

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Figure 3d. Delta 2 model detail<

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6 = 30° LEVF

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P = Cos e 8

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Figure 4. Model mounting and balance

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The effect of leading edge radius on C VS C

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U id

with LEVF-2 models

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: Delta 1,60 d e l t a wing with a e r o f o i l , R = 0.69% C