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MA(IL7O NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAllRTIME REPORT ORIGINALLY ISSUED July 1945 as Restricted Bulletin LF15 THEORETICAL AND EPERDMENTAL DYNAMIC LOAIS FOR A PRISmatIC FLOAT HAVING AN ANGE OF DEAD RISE OF 2A2 By Wilbur L. Mwyo Langley Memorial Aeronautical Laboratory Langley Field, Va. NACA WASHINGTON !;ACA WA.RTIME REPORTS are reprints of papersorginallUy issued to prc.vide rapid distributicn of aoivance research results to an authorized group requiring them for the war effort. They were pre '.i usly held under a security status Lut are now unclassified. Some of these reports were not tech nial', .*dited. All have been reproduced without change In order to expedite general distribution. L 70 DOCU1JMENTS DEPARTMENT RB No. L5F15 Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/theoreticalexper001a NACA RB No. L5F15 NATIONAL ADVISORY COMIiTTER FOR AERONAUTICS RESTRICTED BULLLT II' THEORETICAL AND EY~ERIMENTAL DYNA"IC LO ADS FOR A PRISMATIC FLOAT HAVING AN 10 At3LE OF DEAD RISE OF 22 By Wilbur L. Mayo SUITM, ARY An application of a modified hydrodynamic impact theory is presented. Plots are given fr.cr. which the maxi mum load, the time to reach maximum load, and the varia tion of Icad with time may be obtained for a prismatic lo float of 22 angle cf dead rise for different combinations 2 of fli:htpath angle, trin, weight, velocity, and fluid density. The curves cover the renge of trim, flightpath angle, and weightvelocity relationship for conventional airplanes. Test data obtained in the Langley impact basin are presented and are used to establish the validity of the theoretical curves. INTROC"CT 10'T During the past 15 yesrs numerous reports have been written on hydrodynamic theory for the landing impact of seaplane floats but none of these treatments has been accepted for design purposes. An analysis (unpublished) of available treatments (references 1 to 8) was undertaken by the Langley Laboratory in order to determine the validity and possibilities of the theory. This analysis showed that the previous treatments did not properly take into account certain hydrodynamic forces, particularly those associated with planing action. An application of a modified hydrodynamic innact theory is presented herein for the case of a rigid pris 10 matic float having an angle of dead rise of 22 The 2 validity of this theory is established experimentally by NACA R3 No. L5F15 comparison with data for a rigid float tested in the Langley impact basin. The theoretical solutions are directly applicable to the calculation of the dynamic response of elastic airframes, if it is assumed that the variation of load vith time is not substantially affected by the structural elasticity of the body. Experimental verification of the rigidbody equations is significant in that it establishes the validity of a basic hydro dynamic theory which is equally applicable to the deri vation of equations that involve modification of the force history due to structural elasticity. Additional work is planned to include the effect of the structural response on the loading function. A large number of force histories is given by three plots from which the maximum load, the time to reach maxi mum load, end the variation of load with time may be obtained. The equations used in obtaining the results are given and the method cf solution is explained in an appendix. p angle of dead rise, degrees T trim, degrees y flightpeth angle, degrees "T weight of float V resultant velocity at instant of first contact with water surface p mass density of fluid g acceleration of gravity tam elapsed time between instant of first contact with amax water surface and instant of maximum acceleration m mass of float ni,,, impact load factor (maximum hydrodynamic load "v ax normal to water surface divided by W) NICA R3B No. 15F15 5 ".T.ere units are not given, any consistent system of units may be used. RESULTS Comparison of Theory and Experiment Theoretical solutions made for a rigid Drismatic float having an angle of dead rise of 22 were compared 2 with data obtained from tests of a float having the form of the forebody shown in figure 1 and the offsets given in table I. The agreement obtained in this commarison indicates that the theory can be applied to floats which do not differ from a prism more then the float in figure 1. Figure 2 sho,'.s the variation of the impactloadfctor coefficient :with flihtpath angrle for trims ranging from o0 to 120. The eauations, from which the curves were obtained, were derived on the assumption that the ratios of fluid compressibility, viscous forces, and gravity forces to inertia forces are r.>i ible. In tank tests of seaplanes the ratio of the gravity forces to the inertia forces (Froude's number) is the criterion for determining the sirmilarity of the flow for similar hulls of different size. The high speed associated with an impact tends to increase the inertia forces and to decrease the relative importance of the gravity forces; however, the tendency to design lare airoplnes to have landing speeds of the same order as small airplanes results in lesser acceler ation for the larger weights and greater importance of the gravity forces. For a specific landing speed there is a wei7rt range above which the gravity forces may be of sub stantial importance. Z:y.erimental data are included in figure 2 for the two boundary values of trim investigated. The data were obtained at widely different speeds for a float weighing 110C pounds. Even the points obtained in lowspeed tests, for which gravity forces are of greater importance than for highspeed tests, show remarkable agreement with com putations made on the assii'ition that the gravity forces are negligible. For a fullscale lending speed of 70 miles oer hour the experimental data represent airplanes weighing up to 160,000 pounds. For higher lndinfc speeds, such as may occur with military airplanes, the represented weight is even greater. These interpretations of the experimental check show that the theoretical computations presented ITAC\ RB io. 15F15 herein will give gcod results for all presentday air planes. Pertinent data with regard to the weightvelocity relationships for equal ratios of the gravity forces to the inertia forces equivalent values of V T 1/6NT ) are included in figure 2. The fact that the curves in figure 2 intersect shows that the variation cf maximum impact force with trim for large flightnath angles is the reverse of the variation for small flightoath angles. For small flightpath angles the planing forces predominate and, since the effect of increased trim is to increase the downwash angle of the deflected stream, the resulting increase of the resultant force for a specific draft at the step causes the impact to be more severe than for small trim. For large flight path angles the increase of the virtual mass due to verti cal velocity dominates the impact force and, since the effect of increased trim is to lower the rate of increase of the virtual mass for a specific vertical velocity, lesser force for a specific draft, and consequently a less severe impact than for small trim, occurs. Figure 5 shows the variation of the time to reach maximum acceleration with flightpsth angle for trims ranging from 30 to 120. The plot is similar to figure 2 and therefore does not require further explanation. Figure 4 is a plot of cceleraticn ratio against time ratio for a widee range of flihtoath angle and trim. The ratios are based on the acceleration and time at any instant as compared with the maximum acceleration and the time to reach maximum acceleration. By interoolating bet.' een the curves of figure 1+ an!d using the amolitude and time plots of figures 2 and 3 to define the maximum accel eration and the time to reach rnximum acceleration, snr number of time histories within the range of investigated conditions can be constructed. Because individual curves would be difficult to dis tinguish If all the solutions of the equations given in thb appendix were clotted, so e of the solutions have been grouped and the boundary linas for ech :.:.) plotted in figure 4. The solutions that lie between the boundary lins are tabulated in figure .t Although an approximate interpolation can be affected between the boundary lines of fi ;1r l., the spacing is close enough to oprmit the use of a line centered between those boundaries for practical solutions. N1[CA RB ITO. L5F15 The equations used to obtain figures 2 to L assume that the beam of the float is large enough to prevent'the chine from coming into firm contact with the water. If the chine does come into contact with the water, a discon tinuity occurs in the impact orocess and the conditions specified by the equations of this report for the time of chine contact must be taken as the initial conditions for a different equation for the case of immersed chines. It is planned that a later program will deal with such calculations. Applicability to Flight Impact The load values given herein are based on the assump tion that the chines do not become immersed; it should be noted that early immersion of the chines can cause only reduction of the maximum lead and hence conservative load values. The variation of the impact force with draft, which was obtained in the course of solving the equations of the appendix for the forcetime variation, was used to determine the effects of beam loading, flightpath angle, and trim on chine immersion. A comparison of the data obtained in this study with available data for a number of different airplanes was made. It was indicated that the beam loadings of conventional American seaplanes end flying boats are sufficiently light to ensure that maximum load values given herein will not be unduly con servative. Some German airplanes, and possibly some American flying boats with wartime overload, have high beam loadings, which may cause the immersion of the chines to be significant for high trims and steep flightpath angles. For small angles of dead rise and for large trims the theory requires a different formula. Since the exact manner of the transformation from the condition requiring one formula to the condition requiring another formula is not known, the formulas of the appendix should not be applied indiscriminately. The equations presented are for the absence of pulled up bow. The bow of the float tested is representative of the bow of an actual flying boat; greement between the data obtained and the theoretical computations for the prismatic float indicates that the effect of the bow is not important for the conditions investigated. E:iCA. R3 To. L5,15 Both the experimental data and the theoretical cal culations are for fixedtrim impact and therefore do not indicate the effect of angular rotation during impact. Various design considerations tend to locate the center of gravity relative to the center of water pressure so as to minimize angular acceleration. Even when substantial angular accelerations are reached, the time to reach peak load is believed to be short enough and the aver~g' angu lar velocity small enough to keep large angular displace ment from being reached during this period. The experimental data used in the present report were obtained in tests of the flost shown in figure 1 with the afterbody removed. Although exact evaluation of the effects of afterbodyT leads is not possible at this time, various design considerations ensure that actual airplanes will have sufficient depth of the step and reduced trim at the afterbody to be effective in promoting the shieldin:, at impact speed, of the afterbody by the forebody and in causing thereby the loads on the afterbody to be of rela tively small importance. The experimental data used herein were obtained with a float attached to a coasting carrice having a mass about three times the mass of the float. This condition involves slight reduction of the speed during impact, whereas in the theoretical computations a constant hori zontal seed is assumed. By observing the relative magni tudes of the vertical and horizontal accelerations and velocities for an impact and applying the laws of velocity dissipation, even in the case in which the float is entirely free in the drag direction, the reduction in horizontal seed during the impact can be seen to be of small 1. ortance. By using different constants in the equations of the appendix, the reduction in horizontal seed can be incorporated; however, it is felt that the gain would be toc slight to warrant the additional com plication. The curves of the present report are for smoothwater impacts but they will give approximate results for rough water impacts if the flightpath nle and the trim are defined relative to the wave surface rather than relative to the horizontal. The equations in the appendix are based on the assump tion that the float is weightless (Ig wing lift). Devia tion of the wing lift of the actual airplane from lg will affect the experimental results but the effect will probably not be very lar:0. NACA RB No. L5F15 CONCLUSIONS Application of a modified hydrodvnsmric impact theory to a rigid prismatic float with angle of dead rise of 22 2 and an analysis of data made to determine the validity of the theory indicate the following conclusions: 1. The effect of trim on load for large flightpath angles is the reverse of that for small flightpath angles. This reversal is due to a change in the relative importance of the plening and impact forces and shows that both the forces must be considered. 2. Tle agreement between experiment and theory was good, and thus the theory was proved adequate for the conditions investigated. 3. Since hydrodynamic impact theory does not take into account the effect of the gravity forces on the fluid flow, the arement of this theory with experiment for the range of weightvelocity relationships for landing impacts of presentday airplanes indicated that the effect of gravity on the flow pattern is not important in impacts of such airplanes. L4. Consideration of the factors involved in applying the theoretical curves to actual airplanes indicated that such Epplications will give good results. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. NIACA RB No. L5F15 C4 OJ 0 0 O 0 CQ FI I Io S0 EI ',I I 0 0  P , 4 0 f CI) ^ ( NACA RB No. L5F15 In equations (1) and (2) A = 0.7p( 2 + 0.79  S23. tan p B = 0.79  tan p C =1 tan 2 tan p where p is measured in radians and y draft of float at any instant yo vertical velocity at contact y vertical velocity of float at any instant y vertical acceleration of float at any instant Formulas (1) and (2) are not applicable when y is negative, that is, after the float has rebounded from the water surface. These solutions, which can be readily obtained from equation (2), lie in the region where y is negative. Efforts to obtain a solution giving the dis placement explicitly as a function of the time have not been successful and, consequently, the following procedure was used to calculate the curves presented herein: 1. Substitute arbitrary values of y in equation (1) and solve for the corresponding values of y. 2. Substitute corresponding values of y and y in equation (2) and calculate the corresponding values of y. 5. Repeat process for values of y selected to define adequately the ycurves with a minimum number of points. 4. Plot the variation of l/y with y. For each point on this curve the acceleration is known from the previous steps. Th: time for each combination of y, y, and y can be obtained by integrating the area beneath and to the left of a particular point on the curve showing the variation of 1/y with y. Determine such time values for intervals that approximately define the accelerationtime curve. Repeat the process for such y NXCA RT3 No. T F15 and y combinations as ae of greatest help in defining the more critical portions of this curve. The accuracy of the outlined method is dependent upon the number of points for which solutions are made in order to fair the various curves. After a certain amount of experience with these solutions, the accuracy of a specific solution may be approximated :v estimating possible errors involved in fairing the curves through the limited number of 2oirts. It has been found that after the constants for equations (1) and (2) are computed curves giving the relations between acceleration, velocity, and draft within an accuracy of the order of 1 percent can be obtained by one c'iputer in 3 or + hours. PA ,r 7 " 1 77.NC > 1. von TKarmsn, Th.: The Impact on Sonplane loats during Landing. 'TAYC TN 1o. 21, 1929. 2. Past, "ilhel m: Theory of the Landing Imoact of Se ilans. 'CT A TM No. 580, 1950. 2. Pabst, ;ilhelrr: Landing Impact of Seaplanes. 'ACA 7"1 Io. 624, 1931. 1. 'Wagner, Herbert: Landing of Seaplanes. NACA TM No. 622, 1l. 5. "/agner, Herbert: Tber Stoss und Gleitvortr'.ge an der Oberflache von Flu'ssihkeiten. Z.f.a.M.M., ?:1. 12, Heft 4, Aug. 1952, pp. 195215. 6. Schmieden, C.: TUber den Landestoss von '1Pugaei chwirmmern. Ing.Archiv., Bd. X, Heft 1, Feb. 1959, pp. 115. 7. Sydo:, J.: Iber den Einfluss von Federung und Kielung auf den Landestos.L. Jahrb. 1953 der deutschen Luftfahrtforschunp, R. 01]dcnbourg (Munich), pp. I 29 I 3558. (Available as British Air ""':stry Translation No. 861.) 8. .'rs, R. T.: ExDcrimental Investigation of Tmonct in Landing on afterr NACA TM T'. 10146, 1945. NACA RB :c. L5F15 NM KvC' t^o (t1N'iococc o o irW It N" rcv {o H z o ri (IQ (0 \ L' CM NON C) 0 0 o o C o ro oM N\ H Hl (\J CM CM) C'. tCi'r\N fl\< fK C rJ r J CM CM CH1 r LflK.NO OCN'L\ 0 LCS rH "\ H ri Ht ON' . Lt" C' ' NN M CMC,0 'C t..r...N C.NO,cru",._(J o C)...O oG H 4 r o C)w ZN. C N Cr c' .\'. iLfd r H H HrA H H ,.C ") ,M 0 K^.O 0) LCN J ON mtoC C, C; C) H; , N~ NM K'C\ WIN"~>\1 ONC, ,,O ,O UC.O N'r4  H4 1Jr4CO a "_JTC Oc,CUrx ii ,M NN'L H CM '0 1, \ o O\ N ON Lp,.O H (c H M 'L ",)4 i^ Ckl'K^^ a C*ICO L, c c r'cI 7 c  ! (\) 0 rQtJi C,i r ri ON 1 r r ri rN  ON i.O, iPC4O .t"\J Co! 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XVCU4 ) ',walf/J%,Lao ^w Fig. 3 Fig. 4 NACA RB No. L5F15 C 1 0 tI <... 1 ^ a I o 1 2 cz.   ^  ^    (Q^'CO ^ ^ t0 'E __ __ __ : : ^ ^ __ __ __I Q UIo/1DJ1/azf2 Xvw //1uOqJa/d2,v UNIVERSITY OF FLORIDA 3 1262 08105 014 7 ':rY OF FLORIDA ' '.Fr : TS DEPA RTP'.1NT l .F Gil701t1 USA 