NACA RESEARCH MEMORANDUM - NASAspeed of wave propagation (13.9 fps) for the 6-foot water depth of Langley tank no. 2. These experimental data are correlated with existing theory giving

Copy 1 RML51B13

NACA

RESEARCH MEMORANDUM

TEE EFFECT OF END PLATES, END STRUTS, AND DEPTH OF

SUBMERGENCE ON THE CHARACTERISTICS

CF C ISYFROFOIL

By Kermeth L. Wadlin, Rudolph E. Fontana, and Charles L. Shuford, Jr.

Langley Aeronautical Labo4atory Langley Field, Va.!

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

WASHINGTON A pril 12 1 1951

https://ntrs.nasa.gov/search.jsp?R=19930086498 2020-03-06T18:25:44+00:00Z

NACA RM L51B13

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

THE EFFECT OF ' END PLATES, END STRUTS, AND DEPTH OF

SUBMERGENCE ON THE CHARACTERISTICS

OF A HYDROFOIL

By Kenneth' L. Wadlin, Rudolph E. Fontana, and Charles L. Shuford, Jr.

SUMMARY

An investigation was made in Langley tank no. 2 of the effect of end plates and end-mounted struts on the lift-drag ratios of a hydrofoil. The hydrofoil had an aspect ratio of 14 The tests were made at various depths below the water surface at speeds from 15 to 35 feet per second

corresponding to Reynolds numbers fronf 0 .873 x 106 to 2.04 X 106. These speeds were all above the limiting speed of wave-propagation (13.9 fps) for the 6-foot water depth used and below the range at which cavitation occurs.

Only small improvements were found in the 'maximum lift-drag ratios by the addition of end plates and these improvements occurred only at low lift coefficients with small end plates. As the lift coefficient was increased above the value for maximum lift-drag ratio the optimum end-plate size increased; however, the absolute value of lift-drag ratio decreased. The detrimental effect of . the drag of the additional strut for a hydrofoil using end struts in contrast to a single central strut was greater than any beneficial effects due to the end-plate effect of the end struts. The ratio of the effective aspect ratio to the geometric aspect ratio varied with end-plate size approximately as predicted by aerodynamic theory (Von Karmn and Burgers). Although the hydrodynamic data obtained with the end plates were slightly higher than the theoreti-cal curve, the agreement was good when the accuracy to which such data could be . obtained is considered. An approximate theoretical solution of the effect of depth on the lift of a hydrofoil was developed. The agreement of the experimental results with the results given by this solution was good.

-p 'a

2 NACA EM L51B13

INTRODUCTION

The use of end plates as a means of increasing the effective aspect ratio of airfoils and thereby increasing lift-drag ratios has been inves-tigated at various times. In general, these investigations have not led to the use of end plates on airplane wings. End plates have been used on tail surfaces where the necessity for having two surfaces at right angles to each other enables the end plates to serve two functions. Because hydrofoils normally will be supported by one or more struts extending through the water surface, it is possible to use the struts for a dual purpose by placing them at the ends of the hydrofoil where they also serve as end plates. This possibility, together with other con-siderations, such as structural and stability considerations might result in the desirability of using end plates on hydrofoils has led to the present investigation of the effect of end plates and end struts on the lift and drag characteristics of a hydrofoil.

Another problem considered in the present investigation is that of determining the effect of depth of submergence below the water surface on the characteristics of a hydrofoil. There is a great amount of aero-dynamic data available for use in hydrofoil problems but, in general, these data are for a fluid without boundaries, whereas hydrofoils may operate close to the boundary formed by the water surface. In order to extend the usefulness of these existing data, an approximate theoretical solution for the effect of depth of submergence on the lift of a hydrofoil is developed.

Experimental data obtained with a hydrofoil of aspect ratio Ii- at various depths of submersion at speeds from 15 to 35 feet per second (Reynolds numbers from 0.873 x 10 6 to 2.04 x 106) and at angles of attack from _3•50 to Lo°, with and without end plates and end struts, are pre-sented. The investigation was conducted at speeds above the limiting speed of wave propagation (13.9 fps) for the 6-foot water depth of Langley tank no. 2. These experimental data are correlated with existing theory giving the effect of end plates on effective aspect ratio and with the developed theory giving the effect of depth of submergence on lift.

The .method for obtaining a theoretical solution of the effect of depth on lift was suggested by Mr. Thomas A. Toll of the Langley Stability Research Division.

SYMBOLS

L lift, pounds

D drag, pounds

- - NACA EM L51B13 3

CL lift coefficient (L/qS)

CD drag coefficient (D/qS)

CD1 induced drag coefficient

cd section drag coefficient 0

S area of hydrofoil, square feet

q free-stream dynamic pressure, pounds per square foot (v)

V velocity, feet per second -

P mass density, slugs per cubic foot

C l section lift coefficient at finite depth of hydrofoil submersion

C l section lift coefficient at infinite depth of hydrofoil o submersion

a angle of attack, degrees

CL - finite lift-curve slope at finite depth of hydrofoil a submersion

C l section lift-curve slope at finite depth of hydrofoil CL submergence

C l section-lift-curve slope at infinite depth of hydrofoil a0 submersion

L/D lift-drag ratio

(L/D)max maximum lift-drag ratio

CL(L/D)max lift coefficient for maximum lift-drag ratio

r circulation strength of vortex

downwash at three-quarter-chord point due to hydrofoil vortex, feet per second

downwash at three-quarter-chord point due to hydrofoil vortex image, feet per second

_r NACA RN

h depth of hydrofoil submersion below free water surface, feet

C chord of hydrofoil, feet

b span of hydrofoil, feet

h' area of one end plate, excluding hydrofoil section area, divided by chord of hydrofoil

R geometric aspect ratio (b2/S)

aspect-ratio correction factor for rectangular wings

Re effective aspect ratio

Ee effective edge-velocity correction factor for lift

DESCRIPTION OF MODEL

Various end plates and end-mounted struts were attached to an 8-inch-chord hydrofoil having an aspect ratio of 4. Photographs of all the configurations tested are shown in figure 1. The hydrofoil, struts, and end plates were made of stainless steel. They were polished to a smooth finish consistent with current wind-tunnel practice.

The sections for the hydrofoil and end struts were the same as those used in reference 1. The hydrofoil had an NACA 641A412 section which differs from the NACA 64 1-J+12 section Only by elimination of the trailing-edge cusp; the section characteristics of these two are essentially the same (see reference 2). The struts had an NACA 66 012 sec-tion. Figure 2 gives the ordinates for the hydrofoil and strut sections as computed from references 2 and 3.

The five end plates tested consisted of 1 -inch-thick flat plates

with elliptical edges. Three of the end plates were designed to cover various amounts of the two-dimensional pressure field about the hydrofoil computed at an angle of attack of 00, which was expected to be close to the angle for maximum lift-drag ratio. The coverage was such that the static pressure at the boundaries of the end plates would deviate approxi-mately 20, 10, and 5 percent from the free-stream static pressure. The details of these end plates are given in figure 3. The pressure fields were computed by the method used in reference 11 and are shown by the dashed lines In figure 3.

NACA RM L51B13 -- 5

The other end plates were rectangular and the details of these end plat--Z are given in figure 4.

APPARATUS AND PROCEDURE

The tests were made by using the main carriage of Langley tank no. 2. A sting support was used to reduce interference effects. Figure 5 shows a view of the test setup with the hydrofoil, supporting sting, and balance attached to the support structure on the carriage.

The details of the supporting-sting arrangement are shown in fig-ure 6. The sting was supported by an 8-inch-chord strut having an NACA 661-012 section. The spacing between the strut and the hydrofoil was such. (i.5 chords) that the influence of the strut on the-flow at the hydrofoil should be negligible (reference 5).

The hydrofoiiwas moved vertically by means of a motor-driven jacking screw which moved the balance and hydrofoil as a unit. Change in angle of attack was obtained at the plate attaching the strut to the balance.

Measurements of lift and drag were made by means of electrical strain gages. The force measurements were made at constant speed, angle of attack, and depth of submersion. The depth of submersion is defined as the distance from the water surface to the point of the hydrofoil nearest the water surface. A range of submersions from 0.5 chord (I in.) to 11 chords (32 in.), of speeds from 15 to 35 feet per second, and of angles of attack from _3.50 to 4•00 was covered. Submersions where the end. plates protruded through the water surface were omitted. The maximum angle of attack was limited. to 4.00 since the maximum lift-drag ratios were expected to occur below this angle of attack. The change in angle of attack due to structural deflection caused by the lift and drag forces on the hydrofoil was obtained during the calibration of the balance and the test data were adjusted accordingly.

The supporting sting and strut were run alone at the same range of speeds, depths, and angles as when the hydrofoil was installed. For these tests the end of the sting was fitted with a faired. cap. The tares thus obtained were deducted from the test data to give the net forces.

The net forces were converted to the usual aerodynamic lift and drag coefficients by using a measured value of p of 1.966 slugs per cubic foot corresponding to a water temperature during the tests of 70 0 F. All coefficients were based on the area of the hydrofoil, 1.78 square feet.

ORMN W_^ 0-

6 NACA RM L51B13

The correction for the ground effect of the bottom of the tank determined by the method described in reference 6 was only 0.7 percent of the induced drag at the maximum depth of submersion (4 chords) and 0.1 percent at the minimum depth (0.5 chord). The correction to the angle of attack was even less. The corrections therefore were considered negligible.

RESULTS AND DISCUSSION

The results of the tests are presented in figures 7 to 13. In these figures lift and drag are plotted against angle of attack with speed and depth as the parameters. The fairings appearing in these figures were made by using cross fairings against speed and depth so the data are faired as a whole and not for individual speeds or depths. This same method of fairing was carried out in all subsequent figures. The data, converted to coefficients, are presented in figures 14 to 20 in the usual form for aerodynamic data.

The present tests were made principally to investigate the effect of end plates, end struts, and depth of submergence on hydrofoil charac-teristics. The scope of the investigation was not sufficient to evaluate completely the effects of Froude number, Reynolds npmber, cavitation, and the possible effects of limiting speed of wave propagation in the towing tank. Care, therefore, must be taken in making specific applications of the results.

- Lift coefficient did not vary with speed but the drag coefficient decreased with increasing speed. The variation of drag coefficient with speed was, however, very small at the higher speeds. The slopes of the lift curves increased with increasing depth, but at depths greater than 2 chords the increase in slope was very small.

Lift-Drag Ratio

The variation of lift-drag ratio with lift coefficient for the hydrofoil with and without end plates is shown in figure 21 for a depth of 4 chords and a speed of 35 feet per second. It can be seen that the smallest end plate gave the highest maximum lift-drag ratio. Further increases in the size of the end plate reduced the maximum lift-drag ratio and increased the lift coefficient at which it occurred. Only a small increase in lift-drag ratio can be obtained in the region of maxi-mum lift-drag ratio and this increase can only be obtained with small end plates. However, at high lift coefficients even the larger end plates improve the lift-drag ratio, though at lower absolute values than

NACA BM L51B13 7

at the lower lift coefficients. As the lift cQefficient is increased above the value for maximum lift-drag ratio the optimum end-plate size increases.

Figure 22 shows the variation with depth and speed of the maximum lift-drag ratios and the lift coefficients at which they occur. With-out end plates the variation with depth was negligible at depths greater than 1.5 chords. As the size of the end plate was increased the effect of depth persisted to greater depths. As the speed was increased the maximum lift-drag ratio increased and the lift coefficient at which it occurred decreased; these effects of speed decreased with increasing speed. The effect of speed on the lift coefficient for maximum lift-drag ratio vaied with end-plate size. With no end plates the varia-tion with speed appeared to be negligible but it increased with end-plate size.

The variation of lift-drag ratio with lift coefficient for the hydrofoil with the end struts is shown in figure 23. These curves are for several depths and a speed of 35 feet per second. As the depth is increased the maximum lift-drag ratio decreased and the lift coefficient at which it occurred increased. Apparently the strut drag impaired the lift-drag ratio to a greater extent than the end-plate effect improved it.

The effect of end-plate size on the maximum lift-drag ratio and the lift coefficient at which it occurs are shown in figure 2+ for the range of depths and speeds covered. The parameter for end-plate size is h'/b where ht is the area of one end plate, excluding the hydrofoil section area, divided by the chord of the hydrofoil and b is the span of the hydrofoil. The increase in maximum lift-drag ratio by the addition of small end plates is again shown. This increase, however, disappears as the speed is decreased and indicates that the reduction in drag coeffi-cient due to the addition of end plates is of the same order as the reduction in profile drag coefficient obtained by increasing speed over this range.

Since the end struts provide for support of the hydrofoil and the end plates do not, a comparison of t'.e lift-drag ratios does not give an adequate measure of their relative merits for a practical application. Figure 25 shows the maximum lift-drag ratio that would be obtained if the drag of a single strut (from reference 1) were added to the hydro-foil alone, or to the hydrofoil-end-plate arrangement that gave the highest lift-drag ratio. The curve for the end-strut configuration is shown for comparison. Both the hydrofoil and hydrofoil-end-plate arrange-ment with a single strut had higher lift-drag ratios over the range of depths covered than the hydrofoil-end-strut arrangement.

7

8 NACA RM L51B13

Effective Aspect Ratio

Though the maximum lift-drag ratio was not improved to any great extent by the addition of end plates, the effect of the end plates in increasing the effective aspect ratio is 6f fundamental interest. The effective aspect ratio was obtained both from the slopes of the lift curves and, from the slopes of plots of drag coefficient against lift coefficient squared. By using the lift-curve slopes the effective aspect ratiowas obtained by using figure 26. This figure was calcu-lated from the formula

Rc CL =

a. 57.3c,

It

(see reference 7) where CL is the slope of the lift curve as deter-

mined in the tests, R is the aspect ratio, C l is the section lift-CX

curve slope, and Ee is an effective edge-velocity correction. Numeri-cal values of Ee are given in reference 8.

The section lift-curve slope for the hydrofoil of aspect ratio Ii. was obtained from the upper plot by using the finite lift-curve slope obtained in the tests. Since the finite slopes changed with depth, this change was reflected in the section slopes. For corresponding depths of submersion the finite slopes obtained at an aspect ratio of 10 (refer-ence 1) gave the same section slopes. In view of the agreement in sec-tion lift-curve slopes for the two hydrofoils at corresponding depths, it may then be assumed that the depth of submersion affects only the section lift-curve slope and not the relation between finite lift-curve slope and aspect ratio. (The lower plot is based on this assumption and was used to determine effective aspect ratios at the various depths of the configurations incorporating end plates and end struts. By using the drag data the slopes of the plot of the drag coefficient against the lift coefficient squared were considered to be 1/itRe(1 + ) where Re is the effective aspect ratio and a is a correction, derived by GIauert for rectangular wings, dependent on aspect ratio.

The effective aspect ratios obtained from both lift and drag data are shown in the upper plot of figure 27. The faired lines drawn in this figure are based primarily on the lift data because these data gave more consistent results than the drag data. The effective aspect ratio increased with increasing end-plate size and depth of submersion. The ratio of effective aspect ratio to the geometric aspect ratio Re/H

NACA BM L51B13

9

was obtained from this plot and are presented in the lower plot of the same figure. The ratio HeIR increased with end-plate size h'/b in much the same mariner as predicted by Von Krrnn and Burgers in refer-ence 9 though it was higher in the tank tests, the deviation being larger at the larger depths. Considering the accuracy to which such data can be obtained the agreement is good. The tank data for both the curved and rectangular end plates fell together, indicating no appreciable effect of end-plate shape for the shapes tested.

Also included in this figure is the variation of the ratio Re/H with h'/b where h t is the immersed depth of the end struts. The end struts were not as effective as the end plates in increasing the effective aspect ratio. This reduction in effectiveness could be expected since the effectiveness of the end plates was reduced as they approached the water surface and the end struts actually intersect this surface. In the case of the end struts the ratio Re/H was lower than that predicted in reference 9.

Wind-tunnel data for end. plates A. B, C, and D have been obtained In the Langley stability tunnel. The ratio Re/H obtained from both the wind-tunnel lift and drag data for end plates A. B, C, and D Is also presented in figure 27. The agreement between the tank and wind-tunnel data is good.

APPLICATION OF AERODYNAMIC DATA TO HYDROFOILS

For comparison with airfoil data, the drag coefficients for the hydrofoil alone were corrected to infinite aspect ratio by the usual equation

C 2 Cn. = -k-- (1 + a)

itR 1

where R is the aspect ratio and a is a correction for rectangular wings dependent on aspect ratio. For an aspect ratio of'4 the value of a is 0.032. The slope of the lift curve was corrected to Infinite aspect ratio by using the method previously discussed.

Figure 28 is a plot of the data at a speed of 35 feet per second

(Reynolds number of 2.04 < 106 ) after converting to infinite aspect ratio by this method. The aerodynamic data at a Reynolds number of 2.0 x 106 for the NACA 641_ 412 section (see reference 10) are also included in this figure. The slope of the lift curve increased with

10 NACA R1'I L51B13

increasing depth. At depths of 2 chords and greater the agreement with aerodynamic data is good. The drag coefficients fall slightly above the aerodynamic data for the smooth condition. The variation due to depth was very small compared to the possible effects due to roughness. During the tests the surface of the model was slightly pitted by the salt water in the tank and was possibly-rougher than in the aerodynamic tests.

There is a mass of aerodynamic data available on airfoils suitable for use as hydrofoils. The present tests together with those of refer-ence 1 show that at immersion depths of 2 chords and greater these aero-dynamic data are directly applicable to hydrofoils within the limitations imposed by Froude number, Reynolds number, cavitation effects, and the effects of the low limiting speed of wave propagation for the towing tank. At lesser depths the method of determining the induced drag Is apparently not strictly correct as evidenced by the large deviation at the depth of 0.5 chord (see fig. 28) from aerodynamic data. However, at the depths considered the drag data are applicable with an accuracy of the same order as the allowance that must be made for practical rough-ness of the hydrofoil surface. This error in determining the induced drag maybe-considerably larger at depths less than 0.5 chord.

At shallow depths it is, however, necessary to alter the aerodynamic lift coefficients to take into account the reduction caused by the prox-imity of the free water surface. One method is to establish the ratio of the lift-curve slopes at shallow depths to the slope at great depths.

Estimation of the Effect of Deth on Lift

A complete theoretical solution of the lift of a hydrofoil at various depths of submersion does not seem to have been obtained, although several approaches to the problem have been made (as examples, see refer-ences 11 and 12). The physical conditions that need, to be satisfied In such a solution are rather complex;. however, the phenomena can be at least partially understood by considering the similarity to the case of a wing placed near the jet boundary in an open-throat wind tunnel. The boundary condition to be satisfied Is that of . constant pressure along the boundary streamlines. If distortion of the boundary can be neglected (an assumption which on the basis of experimental observation seems per-missible, except possibly at very shallow depths), this boundary -condi-tion is essentially equivalent to that of constant longitudinal velocity and can be satisfied by introducing a system of vortices above the surface which have the same distribution and direction of rotation as those which represent the loading on the hydrofoil. As a first approximation to the two-dimensional problem, a single-image vortex can represent the load on the hydrofoil if located at a height above the fluid surface equal to the depth of the center of pressure of the hydrofoil.

NACA EM 151B13 ____ 11

The presence of the image vortex does not change the incidence of the flow relative to the hydrofoil chord, line in the vicinity of the center of pressure, but it does tend to curve the streamlines relative to the hydrofoil chord line and to introduce a forward component of fluid velocity at the hydrofoil. The curvature effect is equivalent to introducing camber of the hydrofoil in such a manner as to produce a negative lift increment. The significance of the forward component of fluid velocity due to the image vortex is not clear, although a first thought might be that this condition amounts to a reduction in dynamic pressure which should cause a reduction in lift in addition to the loss due to streamline curvature. This interpretation is, in fact, the proper one in the case of the biplane problem, as pointed out in reference 13. For the case of the hydrofoil approaching the planing condition, it is evident that, although the forward component of fluid velocity exists, this forward component results directly from the action of the lower hydrofoil surface, which tends to displace the fluid forward and downward. The reaction due to this displacement or acceleration of the fluid is responsible for the lift carried by the hydrofoil in the planing condition, and, as pointed out in reference 12, amounts to about .ne-half the lift carried by the hydrofoil at the same angle of attack but at infinite depth.

Since the arrangement of the streamlines of the flow below the planing hydrofoil probably is not greatly different from the arrangement of streamlines below the hydrofoil when at infinite depth, it would seem that a reasonably close approximation to the effect of depth could be obtained by simply evaluating the effect of streamline curvature. To accomplish this, a technique frequently used in approximate solutions of aerodynamic problems may be employed (see reference 14). This involves determination of the circulation 'r required to produce a down-wash velocity w1 + w2 at the three-quarter-chord location, which, when

Oombined with the free-stream velocity V produces a flow tangent to the mean camber line of the hydrofoil. Thus, if geometric camber is neglected, the hydrofoil angle of attack . a. is equal to the sum of the angles at the three-quarter-chord point induced by the hydrofoil vortex (assumed to be located at the quarter-chord point of the hydrofoil) and its image located at a distance 2h directly above the hydrofoil (see following sketch):

12

NACA RM L51B13

Wi + W2

that is (for small angles),

Wi W

V V

where

Wi = - cos a. tc -

and

Cos a

w22

2 /( +sina) 2 +Cos a)2(a+ sin a)2+(Cos a)2

The symbol c is the hydrofoil chord and h is the depth of submergence. Therefore,

r Cos aE i il+ itVc

(h \2 c

L +(_ COS ct)

NACA RM L51B13

13

where

cc r

211

The angle of attack a, which, when given in radian measure, is approxi-. mately equal to sin a, can be expressed..in terms of the lift coefficient at infinite depth; that is,

a. =2it

Therefore, by taking cos a = 1, the ratio of lift coefficient at finite depth to lift coefficient at infinite depth is,

f '2

+1 CI \ C 2itJ

CIOc\to +2

\C 2rrJ

For all practical purposes, the term c 1 1211 in this equation has an

insignificant effect on the results at all depths, and when this term is dropped, an equation, which can be interpreted as the ratio of lift-curve slope at finite depth to lift-curve slope at infinite depth, is obtained; that is

Cl =(+1

ciao ( )2 + 2

Comparison of Theory and Experiment

Results calculated by this method are compared in figure 29 with the present experimental results for a hydrofoil of aspect ratio II- and with the experimental results given in reference 1 for a hydrofoil of aspect ratio 10 after conversion of.both sets of data to infinite aspect

NACA RM L51B13

ratio by the method previously discussed. Results calculated by the method of reference 11 which shows a strong influence of speed (not indicated by the present tests or those of reference 1) also are shown in figure 29. No comparison has been made with results predicted by the method of reference 12, since that method suggests that the variation of lift coefficient with depth depends rather strongly on the value of the lift coefficient at great depth - an effect not noted in the experi-mental investigations. -

The agreement of the experimental results with results given by the equation develoed herein is good. Although the assumptions made in the derivation certainly do not allow a complete presentation of the known physical conditions, the simplicity of the final equation and the good agreement with experiment for aspect ratios of !i and 10 should justify use of the equation for certain applications. One possible application might be in connection with the calculation of the dynamic stability of hydrofoil systems. For such a problem, consideration may have to be given to possible variations with time of the depth of one or more members of the system, and it would, therefore, be convenient to express the variation of lift with depth by a' simple equation.

CONCLUSIONS

The results of the tank tests of the hydrofoil with aspect ratio 4 with and without end plates and end-mounted struts may be summarized as follows:

1. Only small improvements were found in the maximum lift-drag ratios by the addition of end plates. These improvements occurred only at low lift coefficients and with small end plates.

2. At values of lift coefficient above the value for maximum lift-drag ratio, optimum end-plate size increased with lift coefficient and considerable improvement was obtained.

3. The detrimental effect of the drag of the additional strut for a configuration having end struts in contrast to a single central strut was greater than the beneficial effects due to the end-plate effect of the end struts.

-i-. The ratio of the effective aspect ratio with end plates to the geometric aspect ratio varied with end-plate size approximately as pedicted by aerodynamic theory (Von Krmn and Burgers). Although the hydrodynamic data were slightly higher than the theoretical curve, the agreement was good when the accuracy to which such data could be obtained is considered,.

NACA RM L51B13 - 15

5. The agreement of the experimental results with the results given by the approximate theoretical equation developed. herein for the effect of depth on the lift of a hydrofoil was good.

Langley Aeronautical Laboratory National Advisory Committee for Aeronautics

Langley Field, Va.

16 NACA EM L51B13

REFERENCES

1. Wd.1in, Kenneth L., Rarnsen, John A., and McGehee, John R.: Tank Tests at Subcavitation Speeds of an Aspect-Ratio-10 Hydrofoil with a Single Strut. NACARM L9K14a, 1950.

2. Loftin, Laurence K., Jr.: Theoretical and Experimental Data for a Number of NACA 6A-Series Airfoil Sections. NACA Rep. 903, 1948.

3. Abbott, Ira H., Von Doenhoff, Albert E., and Stivers, Louis S., Jr.: Summary of Airfoil Data. NACA Rep. 824, 1945.

11. Daley, Bernard N., and Hanna, Lillian E.: Subsonic Two-Dimensional-Flow Conditions near an Airfoil Determined by Static Pressures Measured at the Tunnel Wall. NACA TN 1873, 1949.

5. Lindsey, W. F.: Effect of Mach Number on Position Error as Applied to a Pitot-Static Tube Located. 0 .55 Chord ahead of an Airplane Wing. NACA CB L4E29, 1944.

6. Reid, Elliott G.: Applied Wing Theory. First ed., McGraw-Hill Book Co., Inc., 1932, pp. 166-176.

1. Swanson, Robert S., and Crandall, Stewart M.: Lifting-Surface-Theory Aspect-Ratio Corrections to the Lift and Hinge-Moment Parameters for Full-Span Elevators on Horizontal Tail Surfaces. NACA Rep. 911, 1948.

8. Swanson, Robert S., and Priddy, E. LaVerne: Lifting-Surface-Theor? Values of the Damping in Roll and of the Parameter Used in Estimating Aileron Stick Forces. NACA ARE L5F23, 1945.

9. Von K 'rmn, Th., and Burgers, J. M.: General Aerodynamic Theory - Perfect Fluids. Airfoils and Airfoil Systems of Finite Span. Vol. II of Aerodynamic Theory; div. E, ch. IV, sec. 19, W. F. Durand., ed., Julius Springer (Berlin), 1935, pp. 211-212.

10. Loftin, Laurence K., Jr., and Smith, Hamilton A.: Aerodynamic Charac-teristics of 15 NACA Airfoil Sections at Seven Reynolds Numbers from 0.7 x 106 to 9.0 X 106. NACA TN 1911.5, 1949.

11. Keld.ish, M., and Lavrentiev, M.: The Motion of an Aerofoil below the Surface of a Heavy Fluid.. Transactions of the Conference on the Theory of Wave Resistance, U.S.S.R. (Moscow), 1937. British A.R.C., March 17, 1938. (Translated by A.I. (T), Air Ministry.)

NACA BM L51B13 17

12. Weinig, F.: On the Theory of Hydrofoils and Planing Surfaces. NACA TM 845, 1938.

13. Glauert, H.: The Elements of Aerofoil and Airscrew Theory. Second ed., Cambridge Univ. Press, 1948.

14. Wieghardt, Karl: Chordwise Load Distribution of a Simple Rectangular Wing. NACA TM 963, 1940.

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NACA RM L51.B13

SSP stream static pressure

percent

End plate A.

2:1 ellipse above hydrofoil chord line only

Filled in to contour of hydrofoil

End plate B. .LJ.J

Area of end plate A (excluding sectional area ofhydrofoil) 6.63 sq. in. Area of end plate B (excluding sectional area ofhydrofoil) 22.48 sq. in.

Sectional area of hydrofoil .12 sq. In.

Figure 3.- Details of pressure field end plates A. B. and C. All dimensions are in inches.

U'

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95 percent SSP

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NAPA RN L51B13. 27

SSP stream static pressure

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PIT percent

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1.984 8.000 l.076

11.060

End plate C.

Area of end plate (excluding sectional area of hydrofoil) 89.1 sq. in. Sectional area of hydrofoil = 5.12 sq. in.

Figure 3.- Concluded.

-:

28

NACA RN L51B13

Area of end plate D (excluding sectional area of hydrofoil) = 29.9 sq. in. Area of end plate E (excluding sectional area of hydrofoil) 66.48 sq. in.

Sectional area of hydrofoil 2 5.12 sq. in.

Figure ii-. - Details of end. plates D and E. All dimensions are in inches.

NACA RN L51B13 29

Figure 5.- Test setup showing hydrofoil suspended from balance attached to towing carriage.

Page intentionally. blank


NACA RN-L5]-B13 31

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60 NACA RM L51B13

.6- -------- .040Speed, .5 Depth, chords .035 fps

.00 4.00 1.88

15

0.50U .030 20 __

:50 . - - .025 35

4.

:2i,/'bD

:::

0 .010

-.1. I I I I •05 I I - I

4 -2 0 2 4 6 8 10 -.1 0 .1 .2 .3 .4 .5 .6 Angle of attack, a, deg Lift coefficient, CL

(a) Lift - all speeds.

.040

.035

'- .030 4) C

.025 a -I 'a

.020 0 a bo

.015

::r . . .

Lift coefficient, CL

(c) Drag - depth, 1.00 chord.

.040

.035

.030 4) C 0 .025 -

.020 ./ tzo

.015,-

.010 -

.005 • •' I

-.1. 0 .1 .2 .3 .4 .5 Lift coefficient, CL

(b) Drag - depth, 6.50 chord.

.040

.035

.030 4) - C

.025 C) -I 44

.020 0 C)

UD

:

.015

.010

I I I -.1 0 - .1 .2 .3 .4 .5 .6


(d) Drag - depth, 2.00 chords.

.040

.035

.030 4) C

.025 '-I 44

.020 0 0

bo cd .015

.010 ___7 I7'

J .005 6 -.1I I I I I

0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL

(e) Drag - depth, 3.00 chords. - - (f) Drag - depth, 4.00 chords.

Figure 14, Lift and drag coefficients of the hydrofoil without end plates. -

.010•

0 .1 .2 .3 .4 5 .6


NACA RN L51B1. 61

.6Depth, chords

.5 120 4 0.50

IAngle of attack, a, deg


.040Speed,fps

.035 -- 15 20 C, --25

.030 30

•.02535

.020 -

bD .015 -I .010

a.005 o 1 .2 .5 .4 .5 .6 -.1Lift coefficient, CL


.040

• 035

C,.030

4a S

.025

o .020

.010

.005 I I I I

- .1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL

(c) Drag - depth, 1.00 chord.

.040

.035 C,

.030 4, a a

.025 I .020

to Is

U

.015

.040

.035 C, C) .030 4, a

.025 /

.020

cs .015

.010

.005 L' I

-.1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL

(d) Drag - depth, 2.00 chords.

.040

.035

P

.030 4,

.025

.020 a IA bo

Ov 010

.0051 I1 I

-.1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL

(e) Drag - depth, 3.00 chords. (f) Drag - depth, 4.00 chords.

Figure 15.- Lift and drag coefficients of the hydrofoil with end plate A.

62 NACA RM 15lB13

.6Depth, chords

10 Angle of attack, a, dog


.040

.040 Speed,

.035fps

.035 ---20

: .030 35 I

e / .025 / - .025

0 01

bo to 015 w .015

.010 .010

1 00 1 0l 345 6

Lift coefficient, CL Lift coefficient, CL

(b) Drag - depth, 1.00 chord. (c) Drag - depth, 2.00 chords.

.040 .040

.035 .035

C .030 _ .030

.015 .015

.010 .010

.005 I I I I I .005LI

I I I -.10 .1 .2 .3 .4 .5 .6 -.1 0 .1 .2 .3 .4 .5 .6

Lift coefficient, C L Lift coefficient, CL

(d) Drag - depth, 3.00 chords. (e) Drag - depth, 4.00 chords.

Figure 16. - Lift and drag coefficients of the hydrofoil with end plate B.

NACA RN L51B13 -- 63

10

Depth, chords 4.00

.6

.5

C-)

• .4

.3 -4 c-I 4-I

.2 C,

4) 4-i 1

[!J

-.1-4 -2 0 2 4 6 8

Angle of attack, a, deg


.040

.0351-

o .030-4S I ID

.025 -4 •1

I

b c-I I

.020L o C) I -bo

.015

.040

Speed, .035 fps

--15

----20 7/ .030 -25

4) S

.025

.020 0 C)

to Cd .015

.010

.0051___ I

-L

-L

I -.1 0 .1 .2 .3 .4 .5

6 Lift coefficient, CL

(b) Drag - depth, 2.00 chords.

.040

.035

bo

.010 .010

•005 -' I I L I L -.1 0 .1 .2 .3 .4 .5


.0051 I I I I I

-.•1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL

(c) Drag = depth, 3.00 chords. (d) Drag - depth, 14.00 chords.

Figure 17.- Lift and drag coefficients of the hydrofoil with end plate C.

61i. V NACA RN L51B13

.6 Depth, ch'rds

0-/I..

L]

Angle of attack, a; dog


.040 .040 Speed,

.035fps .035

-----20 o 25

- .030 30 - .030

.025 .025

::.

cd

.010 .010

005 • I I oo.• I I I I

0 .1 .2 .3 .4 .5 .6 -.1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL Lift coefficient, CL

(b) Drag - depth, 1.00 chord. (c) Drag - depth, 2.00 chords.

.040 .040

.035 .035

.030 . 0.030.

.010 .010

00 I I I 005 I I I

-.1 0 .1 .2 .3 .4 .5 .6 ..1 0 .1 .2 .3 .4 .5 .6 Lift coefficient, CL Lift coefficient, CL


Figure 18.- Lift and drag coefficients of the hydrofoil with end plate D.

-. -;-

.040 r..rfh ,'hrn',i..

Speed, fps

- - 15 ---20

-25

bo.015

.035

C).030

4J-0 0

.025

.020

.6

.5

0. .4

.4.3

S 0

0

NACA RM L51B13

LJ

I I I I I -4 -2 0 2 4 6 8

Angle of attack, a, deg


.040

.035

.010

005L a I i i , 10 -.1 0 .1 .2 .3 .4 .5 .6


(b) Drag - depth, 2.00 chords.

.040

.035

::::4?

.020

to Cd .015

.010.

.005' • I I I I I I .005[ I I I _1 I I -.1 0 .1 .2 .3 .4 .5 .6 -.1 0 .1 .2 .3 .4 .5 .6

Lift coefficient, CL Lift coefficient, CL

(c) Drag - depth, 3.00 chords. (d) Drag - depth, 4.00 chords.

Figure 19.- Lift and drag coefficients of the hydrofoil with end plate E.

66 NACA RN L51B13

Depth, chords

.6

.5/::

-2 0 2 4 6 8 10 Angle of attack, a, deg


.040 .040 Speed,

fpe

.035 15 .035

I T" ( /IA4

.010 .010

.005 I I I I .005 -' I I

-.1 0 .1 .2 .3 .4 .5 .6 -.1 0 .1 .2 .3 .4 .5 .6 Lift coefficient. C1 Lift coefficient, CL


.035 /4V

.030

.025

.020 0

to 0

.015

.010

.005 I - I I -.1 0- .1 .2 .3 .4 .5 .6


(c) Drag - ' depth, 1.41 chords.

.040 / t,

.035 -

.030

.025

.020 0 0

to .015

.010

I I I I I .005 -.1 0 .1 .2 .3 .4 .5 .6



Figure 20.- Lift and drag coefficients of the - hydrofoil with end struts.

NACA RN L51B13 67

30 -

28 -

26 -

24 -

- End plate

c; 22-: None - CO

20-h

18• DJ.

16,E LJ

10 -

8- -

6 I I I

.1 .2 .3 .L . .6


Figure 21.- Variation of lift-drag ratio with lift coefficient for the hydrofoil with and without end plates. Speed, 35 feet per second; depth, .0 chords.

.6

0 cl-I

4.) 0

.I .1-I Cl O4 •rl

to 4-4Cl

C.)4)

Cl1.rl rlr All

speeds-

68 NACA RN L51-B13

2!

Speed, fps

22

•1

0

Cd

•r4 4.)

-' 20 bO Cl

4.) cl-I

i18

16

ThL 0 0. 5 1.0 11.5 2.0 2.5 3.0 3.5 h.o

I I I I

Depth, chords

0 0,5 1.0 l.S 2.0 2.5 3.0 3.5 1.0 Depth, chords

(a) No end. plates.

Figure 22. — Variation of maximum lift-drag ratio and lift coefficient at which it occur wLthd and speed.

NACA RM L51B13

214

22

tko Cd

j

16

1140

.6 r

Speed,

fps

15

0.5 110 1.5 2.0 2.5

3.0 3.5 14.0 Depth, chords

e' .14 Cd

G) 01j

.3

Speed, fps 15 20 25 30 35

I-0 0.5 3.0 3.5 •14.0 1.0 1.5 2.0 2.5

Depth, chords

(b) End. plate A.

Figure 22. - Continued.

70 NACA RN L51B13

21

22

0 •r4 4 20

Cd I..

18 '-I

16

41 I

Q 0.5

.6-

Speed, fps

- 35 - 30

- 2

- 20

- ].5

I I I,

1.0 1.5 2.0 2.5 3.0 3.5 Lo Depth, chords

-j.5 Cd

oO

4)0 •rI

W+) r4 Cd

Cd

0 C)4) 3

4. .H

Speed, fps 15

.2 1 I

0 0.5I I I I I

1.0 1.5 2.0 2.5 3.0 3.5 11.0 Depth, chords

(c) End. plate B.

Figure 22.- Continued.

22

I,

a' 0

•r4 4) Cd Si

bO Cd Si

18

-

fps

is

Speed,

NACA RN L51B13

71

21j r

.6

• 2.5 3.0 3.5 14.0 Depth, criorcis

Speed,

fps

LJ 01.) '4 'a 4)0

.

4bO

WSi 0 C)

4)CII

rtrl

.1 • .2 1 I I I

• 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 14.0 Depth, chords

(ci) End, plate C.

Figure 22. — Continued.

.6

J.

+). 0

..-4C1j

r1 'I

C)

4 .3 .- r4

o, C.-,Speed, fps

15 -20 -2

5

72 NACA RN L51B13

2r LJ Speed, fps

22 35

20M

16

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4 .0 Depth, chords

.2 I.. 0 0.5 1.0 1.5 2.0 2.5

Depth, chords

(e) End. p1.te D.

Figure 22.- Continued.

3.0 3.5 4.0

NACA RN L51B13

- 214

22

0 •r-1 4.)

CO k 20 1'.)O co

18

16

73

peed, fps 35 30 25

KIM

15

0 .0.5

1.0 1.5 2.0 2.5 3,0 3,5 14.0 Depth, chords

.6.- Speed, fps

.2I__ I

0 0.5

• w

I I 1 1.0 1.5 2.0 2.5 3.0 3.5 14.0

Depth, chords

(r) End. plate E.

Figure 22.- Concluded.

Jc o.)

44

.pO rI

..-cd

9-I

Cd

oi.3

30

28

26

2)4

o' 22 4.)

(ts I. to 20 Cd

4 18

16

14

12

10

8

6.1 .2 .3 .14 . .6


74 NACA RN L51B13

Figure 23.- Variation of lift-drag ratio with lift coefficient for the hydrofoil with end struts. Speed, 35 feet per second.

.10 .15 .20 .25 .30 .35 40 End-plate parameter,

22

0

1-' 20

Ii,

; 18

16

24

NACA RN L51B13 75

.6

c.-4

• .! Cd

CH Cd cIo

01j 0 .4)

'-I .-i H

2 u I I I I I

0 .05 .10 .15 .20 .2 .30 .35 .bO

End-plate parameter,

(a) Depth, 0.5 chord.

Figure 24. — Variation of maximum lift-drag ratio and the lift coefficient at which it occurs with speed and end-plate parameter h'/b.

76 NACA RM L51B13

21

22

a 0

".4 4)

20

18

16

114. .i.v ..L) .0 .5 .30 .35 .140


.6

4)0 "-I

..-4

'I

C)4)

.2015 .20 .25 .30 .35 .140


(b) Depth, 1.0 chord.


.05 .10 .15 .20 .25 .30 .35


0 -i 4) Ct .. 20

I..

'Ii,

18

a

16

22

24

NACA RN L51B13

77

j.5

ou

Cl-s Cl-I

.3

.2(.1

.6

.o, .10 .15 .20 025 .30 End-plate parameter, IL!.

(c) Depth, 2.0 chords.


.35 .)0

78 NACA RM L51B13

-j 22 a

0

4.) cd

20 Cd

4.)

18

16

x 5

. .,4 Cd

Cd

•rI 4o

0 U

4.) • CH .r

.05 .10 .15- ..20 .25 .30 .35 .40 End-plate parameter,

Speed,

.05 .10 .15 .20 .25 30 .35 .10 End-plate parameter,

(ci) Depth, 3.0 chords.

Figure 21._ Continued.

2

22

a 0

Cd 4)

Si 20

S..

Ii, 4)

;: 18

NACA RM L51B13 79

16

21

.6

x

FR

ilL: .2

C.,

.v, .10 .15 .20 .25 .30 .35 .140

End-plate parameter, h' Speed, fns

.10 .15 .20 .25 .30 .35. .140 End—plate parameter,

(e) Depth, 4.0 'chords.

Figure 24. - Concluded.

NA

CA

RN

L5

1B

13

coco

IiL//

rd

Qt\

H

/

Cd

tko

1 0C

c

Id rl

X P

4

JI II

I\\

c

'X

1)

Ic

U-'

II

II

I

c.'Jc'J c'J

C

_

c'Jf-I

i-ICs

tto r1

(7)'P

-4J

TI

.10 Section lift-curve slope, C1

.108

.106

.099

• 08I

Depth, chords

0 tj.08

0 H U)

a)

.0 C)

H

NACA RM L51B13

.10__ -

j .08

.o6

'-4

.oiL cz4

81

Section lift-curve slope,

_-___--- 0.12 -

0111

0.10

.02 I0 2 4 6 8

10

32

Aspect ratio, R

a).0)4

.

.02' I 1 I I I

2

4 6 8 10 12 Effective aspect ratio, Re

Figure 26.- Charts based on lifting-surface theory showing relation of - lift-cur'e slope and aspect ratio.

--

82 NACA RN L51313

111

Based on lift Based on drag measurements measurements -

12 0 Without end plate O El With end plate A O With end plate B

With end plate D 10 With end plate E

LN With end plate C-

8

Re:

2

I I

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ).0 4.5 5.0 Depth, chords

3.0

2.5

2.0.

Re

-, - - - - -

-- IT- - 1.5 .

R

0 0.50 depth, chords 0 1.00 depth, chords

1.0 0 2.00 depth, chords A 3.00 depth, chords

1.00 depth, chords

—0----- End struts

0.5 . Von Krmn & Burgers theory Lift data Langley stability

0 Drag dataf tunnel

0 I I I I I

0 .1 - .2 .3 .b .5 .6 .7 .8 .9 1.0

End-plate parameter, jI7'

Figure 27. - Variation of effective aspect ratio with end-plate parameter ht/b and depth of submersion.

NA

CA

RN

L5

1B

13

83

to

0 a

CM

Q)I I

'1 I

H

-1H

/ II

0 I

/U

) zt

U)

cdO

AlU

II

C

C'J

CC)-

010c

H

0

0 0

00

0 •

••

C)

0+

)

°P

'uato

jeoo 2

e.X

P U

Oj3

33

Q

r1

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•r-4•H

c-

•ca

C)

cii cii

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___________•r4 H

) 0

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C

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tto \\ \\_

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21.

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0 -

p a)

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NA

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-Langle

y- 4

-12-5

1- 2

50

Documents

NACA RESEARCH MEMORANDUM - NASAspeed of wave propagation (13.9 fps) for the 6-foot water depth of Langley tank no. 2. These experimental data are correlated with existing theory giving