EB No. L5F15 t NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED July 19h^ as Eeetrlcted Bulletin L5F15 THEORETICAL AHD EIPERIMEaSTAL lOAMIC LOADS FOR A PRI31ATIC FLOAT HAVUSG AH AKGELE OF DEAD RISE OF 22 2^° '2 By Wlltur L. Mayo Langley Memorial Aeronautical Latoratory Langley Field, Va. t NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers orifinally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. ^ ■ ^° DOCUMENTS DEPARTMENT Digitized by the Internet Arclnive in 2011 witln funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/theoreticalexperOOIa NAG A RB NO. L5F15 NATIONAT, ADVISORY COMMITTEE FOR AERONAUTICS 3^^ RESTRICTED 31I[.LETIN THEORETIC yiL ^ND E^-^ERIMENT AL DYNjSMIC L^^ ADS FOR A PRISMATIC FLO^iT HMING AN 1° ANGLE OF DEAD RISE OF 222 By Wilbur L. Mayo SUMMARY An application of a modified hyarodynamic impact theory is presented. Plots are given from which the maxi- mum load^ the time to reach maxi.mium load, and the varia- tion of lead with time may be obteined for a orism.atic ]_0 "^ float of 22— angle of dead rise for different combinations of flight-path angle, trim, weight, velocity, and fluid density. The curves cover the range cf trim, flight-path angle, and weight-velocity 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. INTRODUCTION 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 An analysis (unpublished] of available treatments (references 1 to 8) was undertaken by the Langley Laboratory in order to determine the validity and possibilities of the theory.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 applicstion of a modified hydrodynam.ic impact theory is presented herein for the case of a rigid pris- lo matic float having an anrle of dead rise of 22— . The 2 validity of this thecrjT- is established experimentally by comparison with data f Lsjip:ley impact basin, directly applicrble to response of elastic ai variation of load v;ith by the structural el as verification of the ri in that it establishes dynamic theory which i vation of equations th history due to structu planned to include the on the loading; functic or a rigid flo The theoretic the calculati rframes, if it time is not s ticlty of the gid-bod;'- equat the validity s equally appl at involve mod ral elasticity effect of the n. NAG A R3 No. L5F15 at tested in the al solutions are on of the dynamic is assumed that the ubstantially affected body. Experimental ions is significant of a basic hydro- icable to the deri- Ification of the force Additional work is structural response A large number of force histories is given by three plots from which the maximum, load, the time to reach maxi- m^um load, end the variation of load with time may be obtained. The equations used in obtaining the results are given and the miethod cf solution is explained in an anoendix. SYMBOLS P T Y ^V V ^max m ^-iw max angle of dead rise, degrees trim, degrees flight-path angle, degrees weight of float resultant velocity at instant of first contact with water surface mass density cf fluid acceleration of gravity elapsed time between instant of first contact with water surface and Instant of maximum acceleration mass of float Impact load factor (maxim.um hydrodynamic load normal to water surface divided by VY ) N:\CA R3 NO. r,5Fl5 ".T".ere units are not given, any consistent system of units may be usee. RESISTS Comparison of Theory and Experiment Theoretical solutions made for a risid orismatic 1° ' float having an engle of dead rise of 22— were compared v;ith 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 sgreem.ent obtained in this comparison indicates that the theory can be applied to floats which do net differ from a prism more than the float in figure 1. Figure 2 shov.s the variation of the impact-load-f actor coefficient with flight-path an-^le for trims ranging from 5° to 12°. The equations, 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 arc negligible. In tank tests of seaplanes the ratio of the gravity forces to the inertia forces (Proude's number) is the criterion for determining the similarity of the flow for similar hulls of different size. The high speed associated v/ith an imoact tends to increase the inertia forces and to decrease the relative im.portance of the gravity forces; hov/ever, the tendency to design large airplanes to have landing speeds of the ssm.e 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 v/eight range above vtfhich the gravity forces may be of sub- stantial imoortance. Experimental 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 1100 pounds. Even the points obtained in low-speed teste, for which gravity forces are of greater im^portance than for high-speed tests, show rem.arkable agreement with com- putations made on the assumption that the gravity forces are negligible. For a full-scale landing speed of 70 miles per hour the experimental data represent airplanes weighing up to 160,000 pounds. For higher landing speeds, such as m.ay occur with military airplanes, the represented v/eight is even greater. These interpretations of the experimental check show that the theoretical computations presented es TIAC:\ R3 ITo . 15FI5 herein will give gcod results for all present-day air- planes. Pertinent data with regard to the weight-velocity relationships for equal ratios of the gravity forces to / / o \ 1 '^6 ^ the Inertia forces [equ5valent values of Mi—o\ ' 1 are included m figure d. . The fact that the curves in figure 2 intersect shov/s that the variation cf majrimum iiripact force with trim for large flight-nath angles is the reverse of the variation for small flirht-oath angles. For small flight-path angl 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 im.pact to be more severe than for small trim:. For large flight- path angles the increase of the virtual r^ass due to verti- cal velocity domiinates the impact force and, since the effect of increased trim is to lov/er the rate of increase of the virtual miass for a specific vertical velocity, lesser force for a specific draft, and consequently/ a less severe impact than for sr-.all trim, occurs. Figure 3 shows the variation of the time to reach maximum acceleration 'vith flight-path angle for trim.s ranging from 3° to 12°. The plot is slralar tc figure 2 and therefore does not require further explanation. Pigii.re I4. is a plot of scceleration ratio against time ratio for a wide range of flight-path angle and trim. The ratios ai-^e based on the acceleration and tim.e at any instant as compared with the maximum acceleration and the tim.e to reach m.aximum acceleration. By interoolating between the c'irves of figure '4. anci using the amplitude and time plots of figures 2 and 3 to define the maximum accel- eration and the tim.e to reach mr3ximum. acceleration, any number of time histories within the range of investigated conditions can be constructed. Because individual curves would be difficult to dls- tingu.ish if all the solutions of the equations given in the appendix were clotted, sone of the solutions have been grouped and the boundary lines for each group plotted in figure [|.. The solutions that lie between the boundary lines are tabulated in figure .'i. Although an approximate interpolation can be effected between the boundary lines of figure I4., the spacing is close enough to permit the use of a line centered between these boundaries for practical solutions. N,\Cr. R3 ITo. L5F15 5 The equations used to obtain figures 2 to 14. assurre that the beam of the float Is large enough to prevent -the chine from coming into firm contact v/ith the water. If the chine does come into contact with the water, a discon- tinuity occurs in the imoact orocess and the conditions specified by the equations of this report for the time of chine contact nust be taVen 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 imonersed; it should be noted that early immersion of the chines can cause only reduction of the maxim.um Iced and hence conservative load values. The variation of the Impact fcrce v/ith draft, which was obtained in the course of solving the equations of the appendix for the force-time variation, was used to determine the effects of beam loading, flight-path 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 -A'as indicated that the beam loadings of conventional American seaplanes and flying boats are sufficiently light to ensure that m.aximum load values given herein will not be unduly con- servative. Some Germ.an airplanes, and possibly some Am.ericsn flying boats with v/artlme overload, have high beain loadings, which may cause the Immersion of the chines to be significant for high trim.s and steep flight-path angles . For small angles of dead rise and for large trims the theory requires a different form.ula. Since the exact manner of the transformation from the condition requiring one form.ula 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 bov; of an actual flying boat; agreement between the data obtained and the theoi^etical computations for the prismatic float indicates that the effect of the bow is not Important for the conditions investigated. iT'iCA R3 ITo. LoF'lS Both the experimental data and the theoretic el csl- culations are for fixed-triin. impact and therefore do not indicate the ef:*^ect of angular rotation during imoact. Various design considerations tend to locate the center of grsvit:/ relative to the center of water pressure so as to ininimi7.e angular acceleration. Even when substantial angular accelerations are reached, the time to reach peak load is believed to be short enough and the aversge angu- lar velocity smsll enough to keep large angular disnlace- ment from being reached during this period. The experimental data used in the present report v;ere obtained in tests of the float shown in figure 1 with the afterbody removed. Although exact evaluation of the effects of afterbody 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 shielding, 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 carriage having a mass about three tim.es the m.ass of the float. This condition involves slight reduction of the speed during impact, whereas in the theoretical computations a constant hori- zontal speed is assum.ed. F^r observing the relative magni- tudes of the vertical and horizontal accelerations and velocities for an imosct and applying the laws of velocity dissipation, even in the case in which the float is entirely free in the crag direction, the reduction in horizontal speed during the imoact can be seen to be of small importance. By using different constants in the equations of the appendix, the reduction in horizontal speed can be incorporated; however, it is felt that the gain would be too slight to warrant the additional com- plication. The curves of the present report are for smooth-water impacts but they will give approximate results for roi;gh- weter impacts if the flight-path ejigle 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 Ig 'will affect the experimental results but the effect v;ill probably not be very large. NACn RB NO. L5P15 7 CONCLUSIONS Application of a modified hydrodynaniic i^nnect theory 1 o to a rigid prismatic float with angle of dead rise of 22— 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 flight-path angles is the reverse of that for small flight-path angles. This reversal is due to a change in the relative Importance of the planing and impact forces and shoves that both the forces must be considered. 2. The agreement between experiment and theory was good, and thus the theory was proved adequate for the conditions investigated. 3. Since hydroaynamic impact theory does not take into account the effect of the gravity forces on the fluid flow, the agreement of this theory with experiment for the ran^e of weight-velocity relationships for landing impacts of present-day airplanes indicated that the effect of gravity on the flow opttern is not important in impacts of such airplanes. ll. Consideration of the factors involved in applying the theoretical curves to actual airplanes indicated that such applications v;ill give good results. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. 8 MAC A RB NO. rSFl? ~N OJ 4J u c D- M u O <-< '0 O fo o -p G o ■ui_' IT! a Eh .H i>' j_> 3 X o E M p-' o P 'TJ o ^ K W f— 1 Ph •n •H fi^ t-1 <3; t3 -o ;=?; s w O 3 Ph (D i^ o & 1— i E-1 W <-f| CO k=^ <=£. r— i \A ;:5 K c C-< s:^ •rl! c s fciC •H o rH iH O Cm H O CO o + -p + H ni v- a OJ •H JJ OT o cq CO o o •H H wl CM j C m\ •H O W o ctj H 1 C •hI ^ w| •H ■ M I I f — l- 1 m o o >- i- a a 05 ros •rH +J f>- W u" r • >j CQ xC l- C\J CO CG I •>5 ct! -P O •>J CO o o •r-l (0 vO OJ o ^f^ I NACA RB No. L5P15 In equations (1) and (2) A = o.75Trp^|^ - i)^ + 0.79 --P- tan p B = 0.79 — ^ C = 1 - tan p tan T 2 tan p where p is measured in radians and. 7 draft of float at any instant Jq vertical velocity at contact y vertical velocity of float at any instant y vertical acceleration of float at any instsnt Formulas (1) snd (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 orocedure v/as 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 y-curves v;ith a minimum number of points . Ij.. plot the variation of l/y with y. For each point on this curve the acceleration is knov/n from the previous steps. The 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 l/y with y. Determine such time values for intervals that approximately define the acceleration- time curve. Repeat the process for such y 10 TIACA R3 Tlo. T^^FIS and y combinaticns as ai^e of greatest help in defining the more critical portions of this curve. The accuracj'' of the outlined method is dependent upon the nujr.ber of points for v/hich solutiors are inade in order to fair the various curves. \fter a certain amount of experience v.'ith these solutions, the accuracy of a specific solution may be approximated by estimating possible errors involved in fairing the curves through the limited num.ber of points. 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 computer in J or I4. hours. 1. von Karms'n, Th . : The Impact on Seaplane Floats during Landing. NAC^TNNo. 32l', I929. 2. ■^ahst, "'ilhel.m: Theory of the Landing Imoact of Seaolanes. ^^ACk TM No . 5&0, 1950. 2. Psbst, '.Vilhelm: Landing Impact of Seaplanes. NACA TM I-o. 62,^, 1931. I4.. 'Vagner, Herbert: Lsnding of Seaplanes. NACA TM No. 622, 1951. 5. ■'.'agner, Herbert: Tiber Stoss- und Gleltvorgange an der Oberflache von FlussiFkeiten. Z.f.a.M.M., Bd. 12, Heft 1+, Aug. 1952," pp. 195-215. 6. Schmieden, C.: Uber den Landestoss von Flugzeugschwimmern. Ing.-Archiv . , Bd. X, Heft 1, Feb. 1959, pp. 1-15. • • 7. Sydow, J.: I'l.er den Finfluss von Federung und Kielung auf den Landestoss. Jahrb. 1953 der deutschen Luf tf ahrtforschung, R. Oldenbourg (Munich), pp-. I 329 - I 558. (.Available as British 'Vir Ministry Translation No. 861 . ) 0. Kreps, R. L.: Fxnerimental Investigation of Imoact in Landing on -'ater. NACA TM No. 10l|6, lSk3' NACA RB lie. L5F15 11 C5 M ^ p o 1 s CO (U R ^ O -p bO ■H (0 -P ca > O ttO •H CD ^-3 (0 cJ o -_riCO r-i L'AC- cjN O rH rH i-H CV! 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