I I I i!IIAL
/D-t. ~-v:,p;!:; 5_~ ~ ·f-"L'-' :3 ~ . ~S~-4!N>#~7Y · \Joepartment of the Navy Bureau of Ordnance Contract No, NOrd 961:2
DRAG STUDIES IN WATER ENTRY
OF THE
\ MK 13~6 TORPEDO
Report No. E 12 .I July 1951
Hydrodynamics Laboratory California Institute of Tech no logy
CG:c: :Sill - a arb
Department of the Navy Bureau of Ordnance Contract NOrd-9612
DRAG STUDIES IN WATER ENTRY
0 F THE
MK 13-6 TORPEDO
by Genevieve M. Wilcox Research Engineer
Hydrodynamics Laboratory California Institute of Technology Pasadena, California
Report No. E 12 . 1 Joseph Levy Copy No. 9-9' Project Supervisor
'@! Gi 4 'IP- C snftd@ntial
TABLE OF CONTENTS
Page Abstract 1
Introduction 2 General Discussion of Water Entry 2 Purpose 2 Experimental Program 4 Models 4
Test Conditions 0 4 Determination of Drag. 4
Experimental Results . 5 Model and Prototype Drag Comparisons 5 Drag of the Standard Mk 13-6 Torpedo Model 5 Variation of Drag along the Trajectory 5 Effect of Initial Pitch o 5 Effect of Atmospheric Pre ssure 13 Effect of a Finer Nose Shape on the Mk 13-6 Torpedo Model 13 Sensitivity to Atmospheric Pressure 1 3 Sensitivity to Initial Pitch 18 Remarks 18
Conclusions 18
Appendix I 23 Apparatus 23 The Controlled Atmosphere Launching Tank 23 The Trajectory Analyzer 23 Models 23
Appendix II 27 Analysis of the Data 27 Reduction of the Photographic Data 27 The Distance vs. Time Curves 27 The Velocity-Time Curves 28 The Coefficie nt of Drag 28
Appendix III 3 1 Factors in Mode l Studies of W a ter Entry 3 l
Bibliography 33
@Rl!liidenhar ifjJ Iilide nh!f
The mode l of the stand a rd M k 13 -6 a ir c r aft t o rpe d o d u ring t h e cavity p h a s e of t h e und erwat er t rajectory
A BSTR A CT
An experimental investigation was made of are presented. A fixed trajectory angle of 19° t he drag characte ristic s of a 2-in. diameter was used in all tests. Prototype data from the model of the standard (He ad F) Mk 13-6 torpedo Naval Ordnance Test Station, Morris Dam, taken during the cavity phase of the underwater tra at a nominal trajectory angle of 19° with initial jec tory. The data used in this analysis were pitches between±. 1° were available for com available from a previously coompleted trajec parison. tory study. These data were sufficient to de termine the instantaneous velocity of the model Results from three tests of the Mk 13-6 tor along its trajecto ry 0 Hence, the deceleration and the instantaneous drag coefficient could be pedo model with the finer Dunn nose (Head I) determined. made at air pressures of 1, 1/ 11, and l/22 atm. are also presented. These runs were made with The model was dynamically and geometri a nominal trajectory angle of 20° and entry ve cally similar to the prototype; its entry velocity locity of 120 fps with initial pitches between + 0 0 of 120 fps was scaled from the prototype veloc - o 5 . There were no prototype data from ity of 406 fps in accordance with the Froude law. this shape suitable for drag analysis . Results from model runs made at nominal at mospheric pressures of 1, 1/ 2, 1/ 11, and l/22 The results of the investigation are summa atmospheres with initial pitches between±. 6° rized in the conclusions at the end of the report.
sol-5 1i&entia4; 2 ----
INTRODUCTION
An investigation of the water entry of small where: scale projectiles was undertaken at the Hydro dynamics Laboratory of the California Institute absolute static pressure in the of Technology in an effort to develop a satis undisturbed liquid factory modeling technique and to study the be absolute pressure within the havior of air-launched projectiles under a wide cavity range of entry conditions. This study was joint v velocity of the torpedo ly sponsored by the Bureau of Ordnance and the p density of water Office of Naval Research under Contract NOrd 9612. In order to fulfill the requirement of equal cavi tation numbers, the atmospheric pressures in General Discussion of Water Entry the model and prototype systems must be in the same ratio as the linear dimensions of the model When an air-launched torpeao strikes the and prototype. ::1:: water it creates a cavity which persists into the underwater trajectory. The analysis of the Much of the early work in the modeling of drag during the cavity stage is facilitated by water entry was done with models of the stand observing the orientation of the model as it ard Mk 13-6 aircraft torpedo launched in open moves along the trajectory. During the cavity tanks. These tests indicated that simple Froude phase the torpedo may do one of three things scaling was sufficient to reproduce the trajec (Fig. 1): ( 1) it may travel with only its nose in tory of that projectile. However, when the finer contact with the water, (2) it may travel with Dunn nose was substituted for the stan.dard head its nose in contact with the water and its after of the torpedo, the model followed a steeply div body oscillating between the top and bottom of ing trajectory in contrast to the level path of the the cavity, (3) or it may travel with both its prototype. It was necessary to reduce the air nose and afterbody in contact with the cavity pressure in the model system before the proto wall. If the first or second condition exists, type trajectory could be satisfactorily repro the mean trajectory is the straight line exten duced. 1, 2, 3'** Several nominal air pressures sion of the air path, The third condition, which were investigated with the fine nosed model. At most often occurs, produces a trajectory con l/11 atm., where the cavitation number was vex toward the side of the cavity in contact with equal in both model and prototype systems, the the tail. The drag will be lower when only the model trajectories fell within 5 calibers of the nose of the torpedo is in contact with the water. prototype trajectory for the first 70 calibers of When other portions of the torpedo in addition horizontal travel. At air pressures of 3/4. l/2, to the nose contact the cavity wall, the cavity 1/4, and l/22 atm., the model trajectories devi bulges at the point of contact causing the cross ated more widely from those of the prototype. section of the cavity and, hence, the drag to in Therefore, these results support the theoretical crease. In general, the drag on the torpedo e v idence that equal cavitation numbers should will be greater during the cavity phase than it be a criterion for valid mode ling. is when the torpedo is completely in contact with the water. Purpose
Froude scaling has been used in the modeling Modeling of trajectory implies but does not of water entry because the forces of gravity and prove that drag has been modeled as well. The inertia are of major importance during the cavi purpose of the investigation was to determine ty phase of the trajectory. This modeling sys whether drag was satisfactorily modeled by tem is not valid beyond the cavity phase because Froude scaling and to ascertain the effect of the viscous forces become significant after the atmospheric pressure upon the drag character cavity has been dissipated. Theoretical con istics of the model. Since the only prototype siderations further indicate that valid modeling data available were from the standard Mk 13-6 also requires equal cavitation numbers in the torpedo, a shape relatively insensitive to at model and prototype systems. The cavitation mospheric pressure at model size, the results nu1nber is defined as: *Appendix III includes a discussion of the im portant factors in modeling.
k = **Numbers in superscript refer to bibliogra phy at the end of this report. LiLT& A 3
WATER SURFACE
A. ONLY NOSE CONTACTING WATER
fMEAN TRAJECTORY
~ WATER SURFACE ~--,, ______:_:_:_:_----=-=-:..:.:.__ _
------~ ----:_-~ }~>
-~-=-~~
------':~~~' ~~ ---==:~-~~,' ... ~ 8 OSCILLATING IN CAVITY -----~~', - -,~,
~_., ""-TRAJECTOR~Y----~~~~~~~~------~ , WATER SURFACE ~
C. CONTACTING BOTTOM OF CAVITY D. CONTACTING TOP OF CAVITY
Fig. 1 - Orientation of the torpedo in the cavity.
c .08MHtential 4 ~
of this study could only establish the validity of Froude modeling and give some indication of the region in which the most satisfactory air pres sure might lie.
The model data taken at nominal air pres sures of 1, 1/2. 1/11, and 1/22 atm. were avail able from the previously completed trajectory study. The test results from two typical runs from each pressure condition were analyzed to determine the drag on the model. Both these and the prototype tests were made with initial pitches between±. 1°. Since it was hoped that this drag study could establish some trends in Fig. 2 -The Mk 13-6 torpedo model model behavior that would be of use in later (a) The model with the standard hemisphere work with more sensitive projectiles, the in and-cone nose (Head F) itial pitch range investigated at air pressures (b) The model with the finer Dunn nose (Head I) of 1 atm. and 1/11 atm. was extended from±. 1° where comparison with the prototype was pos sible to±. 6°. Data from the pressure sensi tive Dunn nose torpedo launched with essentially TABLE I. LAUNCHING CONDITIONS constant entry pitch and velocity, but with air Mk 13-6 TORPEDO MODELS pressures of 1, 1/11, and 1/22 atm., were also included even though prototype comparison was impossible. Standard Mk 13-6 Torpedo (Head F)
Experimental Program Tank Entry Entry Angles Models Run Air Pres. Velocity Pitch Traj. No. Std. Atms. fps 0 0 The two models used in these tests were of the Mk 13-6 torpedo. One was of the standard 9-1 0. 984 120.6 0. 1 F 18.9 Head F torpedo with the spherical-tip-and-cone 9 - 2 0.515 122. 1 o. 3 s 18. 3 nose, and the other was of the Head I torpedo, a 9-3 0.046 119. 9 0. 2F 18. 6 finer shape also known as the Dunn nose (Fig. 2). 9-4 0.035 120. 1 0. 6 s 19. 2 Both models were 2-in. in diameter, geometric 9-5 0.514 119. 2 1. 0 s 18. 5 ally and dynamically scaled from the 22. 42-in. 9 - 6 0.979 117. 9 1. l s 18.6 diameter "floater" torpedo used in the prototype 9-28 0. 977 120.9 2. 6 s 18. pt work. 4 The details of model construction and 9 - 30 0.978 119.2 6. 0 s 18.4 tolerances for the physical constants are giv en 9 - 32 0.089 115. 9 6. 4 s 19. 0* in Appendix I. 9-39 0.500 117. 2 2. 5 s 19. 5 9-40 0.045 119. 9 1. 7 s 19. 1 Test Conditions 9 - 41 0.089 119. 5 2. 0 s 18. 8 9 - 42 0.089 120.2 0. 8 s 18. 8 The models were launched at nominal a i r 9-43 0.089 117. 8 0. 1 s 18. 8 pressures of 1, 1/ 2, 1/11, and 1/22 atm. An air 9-51 0.967 121. 3 3 . OF 18. 3 pressure of 1/ 11 atm. will produce equal cavi 9-52 0.089 121. 3 3. 6F 18. 8 tation numbers in both model and prototype sys 9-53 0.975 121. 9 5. 2F 18. 6 tems. The entry velocities of the models varied 9-54 0 . 089 121. 2 5. 3 F 18. 7 between 116 and 122 fps; (120 fps corresponds to a Froude scaled prototype velocity of 406 fps). The tests were made with initial pitches ranging Mk 13-6 Torpedo with Dunn Nose (Hea d I) from 6. 4°S (S denotes steep or nose down with ../ respect to the trajectory) to 5. 3°F (F denot es Tank Entry Entry Angles flat or nose up with respect to the trajectory), Run Air Pres. Velocity Pitch Traj. at nominal trajectory angles of 19° for the stand No. Std. Atms . fps 0 0 ard torpedo and 20° for the Head I. The launch ing condit.ions of the individual runs are tabu 11 -14 o. 089 121. 6 0 . 2 s 20. 1 lated in Table I. 11-16 0.045 121. 5 0. 5 F 20. 5 11-23 0.978 120.4 o. 3 s 20. 3* Determination of Drag
Drag was determined from deceleration of *Possible error .±.0. 5°; all other trajectory the model along its trajectory. The methods angles correct to ±.0. 2°. cnc l ' tlllr 5
of calculation and the assumptions used in re mine the instantaneous drag coefficients. vVhen ducing the basic trajectory data are given in only the nose of the projectile was contacting Appendix II. The data used in this analysis are the cavity wall, 85o/o of the instantaneous drag from photographic records of the launchings coefficients were between 0.18 and 0. 30. The made in the Controlled Atmosphere Launching maximum and minimum values were 0. 36 and Tank.-* 0, 15, respectively. This coefficient should be comparable to that of the hemisphere at zero EXPERIMENTAL RESULTS cavitation number (Cd)O because the flow sepa rates on the hemispnerical portion of the nose Model and Prototype Drag Comparisons and the cavitation number is essentially zero. (The depth of submergence is small and t.he ve T:1e prototype data presented in this report locity high during this portion of the trajectory.) were taken at the Naval Ordnance Test Station The value of (Cd)O is approximately 0. 22~ and, at Morris Dam. The tests were made with the hence, in reasonable agreement with the meas "floater" version of the 22 , 42-in, Mk 13-6 air ured values. craft torpedo.4 This projectile is a full-scale buoyant model of the standard Mk 13-6 torpedo The first contact of the torpedo tail with the without engine or steering mechanism. cavity wall (tail slap) was always followed by an increase in drag coefficient, and after tail slap Instantaneous drag coefficients could not be the value of the drag coefficient fluctuated. Be determined from the prototype data. There tween tail slap and a distance of 50 calibers fore, comparison was made between the curves from entry, 80o/o of the instantaneous drag coef which resulted when the logarithm of the instan ficients were between 0. 28 and 0. 40. The maxi taneous velocity was plotted against the distance mum and minimum coefficients measured during from entry. The slope of these curves at any this portion of the trajectories were 0. 48 and point is proportional to the instantaneous drag 0, 23, respectively. The steady state drag coef coefficient (see Appendix II). Figures 3 and 4 ficients measured within a range of cavitation show the logarithm of the ratio of the instan numbers producing somewhat comparable cavi taneous velocity to the entry velocity plotted ties varied from 0. 30 to 0. 498 and, hence, are against the distance from entry in calibers. in fair agreement with the transient values ob Model data taken at air pressures of 1, 1/2, tained. Beyond a distance of 50 calibers from 1/11, and 1/22 atm are compared with the entry the measured drag coefficients varied prototype results,5, 6 These tests were made from 0. 14 to 0. 35. Unfortunately, it was not within an initial pitch range of±. 1°. The a possible to establish the end of the cavity phase. greement between model and prototype is good However, the data do show that the cavity was to a distance of about 50 calibers from entry. still present after the first 50 calibers of under Beyond 50 calibers the model was retarded water traveL mC!re rapidly than the prototy,e. The model data taken at 1/2 atm . and 1 11 atm. are in Figures 7 and 8 show the variation in drag closest agreement with the prototype results, coefficient with time from entry during' six typi indicating the best pressure for modeling to be cal tests. Tail slap and the approximate orien in this region. The results from the 1/22 atm. tation of the projectile in the cavity are indicated tests deviated most widely from those of the on the curves, prototype, Effect of Initial Pitch The curves whic1> resulted when the distance traveled from entry was plotted against time The path of the torpedo could be varied from . were also compared, as a greater distance trav broach to steep dive by changing the initial pitch . eled in a given time represents a lesser drag. The values of the critical pitch which separate Figures 5 and 6 show the distance from entry the upturning from diving trajectories are tabu in calibers plotted against prototype time. These lated in Table II. curves substantiate the trends in model behavior which were evident in the cur ves of Figs. 3 and vVhen the torpedo was launched with large 4. initial pitch, either flat or steep, tail slap oc curred as the afterbody crossed the surface of Drag of the Standard Mk 13-6 Torpedo Model 7 8 *Extrapolation of pressure distribution data ' Variation of Drag Along the Trajectory gives 0. 26 for the (Cd)O based upon the diameter of the hemisphere. This reduces to 0. 22 for the The model test data were sufficient to deter- torpedo because the diameter of the hemispheri cal nose is less than the maximum diameter of *see Appendix I for description of Launching the torpedo upon which the drag coefficient of Tank and Data Analyzer. the torpedo was based .
.c . ..] .... 4 ; 6
1.0 "" 0 .30S 0 .9 t-L~".--:::-::r:'-''Q.,..c--t--- PITCH O.I°F " TRAJ 18.9° 18 .3° 0.8 1 ---'~~...... ,---t _ --- ""' 6._ + VEL 120.6 FPS 117.9 FPS 0.7 ~~ I I 0.6 f----+--~~_""'k,*f::t.-+-, ------11-+~--+------+------+----+-----l------' +TI ~', 1/ 0.5~------~------~~~+"'~~,.~~~-....------~------~------+------+------4------~ .....>- 0 0>- 0.4 1------+----~--~~0 ~~~'~----4----4-----~----~----+--- ~t: >o ~',, (/)0 ~', :::>...J 0.3 r----4-----r------4-----+•~v~~~-----1------1------1------4------~ oLLI LLI> z ',
AIR PRESSURE IN MODEL SYSTEM I ATM ~~ 0.1 t------+----4---- 0.091------4------~~------4------~~------4------+------+------+------~ 0.080 10 20 30 40 50 60 70 80 90 DISTANCE FROM ENTRY MEASURED ALONG TRAJECTORY-CALIBRES
1.0 0.9 ', PITCH 0 .3°5 1.0°5 PROTOTYPE DATA ~i" TRAJ 18.9° 18.5 ° 0.8 RUN PITCH TRAJECTORY VELOCITY - + VEL 122.1 FPS 119.2 FPS NO. FPS 0.7 lo - 0 824 0.7F 20.4 397 0.6 ~'X, I I ""' X AVERAGE VALUES FROM 5 RUNS - '"'+~ 624 0.6F 19.7 393 ....._--~:-, 0.5 "· I 635 0 .6F 19.8 387 - .....>- 639 0 .9F 20.4 394 ~+~ 824 0.7F 20.4 397 0 ', 0 0.4 1195 OBS 20.3 418 ...J >- LLI ..... + AVERAGE VALUES FROM 5 RUNS > 0 AVERAGE VELOCITY : 402 F PS 0 ', (/) ...J 0.3 ~·+ ...... :::> LLI 0 > .... zI.U Fig. 3 - Velocity as a function of distance fr.om entry measured along the trajectory for the standard Mk 13-6 torpedo model and prototype C« 1.0 1 0 .9 ' ' PITCH 0 .8°S 0 .1°S ~+ TRAJ 18.8° 18.8° 0.8 + VEL 120} FPS 1)7.3 FPS 0 .7 ~~ 0.6 ~X L j_ ~ r:::,~ >- 0.5 L 1- ~~ <..:> 0 0.4 .....J >- w 1- > <..:> 0 en .....J 0.3 ~ :::::> w + 0 w > ' z <{ >- + 1- a:: z 1- 0.2 K+x z ~, + ~ w en ++ z f+- ~"' + AIR PRESSURE IN MODEL SYSTEM ~-- 1/11 ,ATM X 0 . 1 0 .09 0.08 0 10 20 30 40 50 60 70 80 90 DISTANCE FROM ENTRY MEASURED ALONG TRAJECTORY-CALIBRES 1.0 ,, 0.9 PITCH 0 .2°F o.6°S PROTOTYPE DATA \'~+ TRAJ 18.6° 19.2° 0 .8 .... RUN PITCH TRAJECTORY VELOCITY VEL 0 ,, + 119.9 FPS 120. 1 FPS NO. 0 FPS 0 .7 6 J I 0 824 0.7F 20.4 397 0 .6 ~X L v X AVERAGE VALUES FROM 5 RUN S 624 0.6F 19 .7 393 '~ )( >- · 0 .5 I 635 0 .6F 19.8 387 !:: 639 0.9F 20.4 394 <..:> ~:-~' X. 824 0 .7F 20.4 397 0 >- 0 .4 1195 o.as 20.3 418 .....J 1- '~ l+ w + AVERAGE VALUES FROM 5 RUN S > <..:> + AVERAGE VELOCITY : 402 FP S en 0 ~~X :::::> .....J 0 .3 0 w +~ w > + z <{ >- + + 1- a:: )(. z 1- 0.2 <{ z ~ u --+ - + 1- w (/) ++ z ~ .... "' + + ' + ' ' ' ...... , AIR PRESSURE IN MODEL SYSTEM ...... , 1/22 ATM ..... X 0 .1 ' - -' 0 .09 ...... 0 .080 ' ' 10 20 30 40 50 60 70 80 90 DISTANCE FROM ENTRY MEASURED ALONG TRAJECTORY-CALIBRES Fig. 4 - Velocity as a function of distance from entry measured along the trajectory for the standard Mk 13-6 torpedo model and prototype '·"'"":s1 a &eiiHdLhddi 8 (f) w 100 0::: ro AIR PRESSURE MODEL SYSTEM I ~~M I I I I ::J PITCH O. I°F I.I0 S o + &0 (f) ~ 1/ ---- - 0::: 30 1---- f-z w 20 , - - ~ - f-· 0 0::: l.L w 10 -- - 1----- (.) z ~ ~ 0 02 0.4 0.6 08 1.0 1.2 1.4 1.6 1.8 2 .0 2 .2 2.4 (f) w 100 0::: 1 I I ro AIR PRESSU~E IN MODEL SYSTEM ::J 1/2 ATM (9 ~ z 0 60 / _j PROTOTYPE DATA 0 626 0 .5F 20.3 406 (f) Fig. 5 - Distance from entry measured along the trajectory as a function of time for the standard Mk 13-6 torpedo model and prototype G@iih&C .tbial .-.n ?J aau 9 (/) w 100 a:: I I I I ro AIR PRESSURE IN MODEL SYSTEM 11 11 ATM ::J D + <1 JTCH J 8°S Jos 0 90 TRAJ. 18.8° 188° I VEL 120.2 FPS 117.3 FPS X a::>- 0 \ ~ '\ 1- 80 0 w J J?--v~ <1 a:: 70 1- v <.D z 0 60 / - f-- - _j <1 0 w 50 + '/ 1---- - a:: ::::> (/) <1 w 40 v ::2' >- a:: 30 6L 1- z I w ::2' 20 I - c- - - 0a:: LL f_ w 10 - - 0 z ;:! l (/) 00 0 0 .2 0.4 0 .6 0.8 1.0 1.2 14 1.6 1.8 20 2.2 24 (/) w 100 a:: 1 1 ro AIR PREssJRE IN ~ODEL sYsTEJ ::J 1/22 ATM D + <1 0 90 f-- I X >- a:: 0 t----- 1=2 80 - - "' c- 0 vv--- w J 6 v <1 a:: 70 t-- - t- r--- - 1- PITCH 0.2°F 0.6°S ~ -· <.D TRAJ. 18.6° 19.2° 0 z VEL. 1199 FPS 120.1FPS + 0 / v 0 60 _j PROTOTYPE DATA <1 v RUN PITCH TRAJECTORY VELOCITY \ 0 0 0 NO. FPS w 50 - + a:: "'? 0 624 0.5 F 20.3 406 ::::> 0 626 0 .5 F 20.3 406 (/) <1 X 634 1.1 F 20. 3 413 w 40 v 0 635 0 .5 F 20.3 407 ::2' D. 636 2.4F 20.4 399 >- + 637 0 .8F 20.3 402 a:: 30 6/ I-- lSI 824 0 .7F 20.4 397 1- z If w 0 AVERAGE VALUES FROM 5 RUNS RUN PITCH TRAJECTORY VELOCITY ::2' 20 I f------NO. 0 0 0 FPS a:: 624 0.6F 19.7 393 LL 635 0.6F 19.8 387 w 10 f - f-- 1-- 637 0 .9F 20.4 394 0 z 824 0.7F 20.4 397 <1 1195 0 .8S 20.3 418 1- 11 (/) 00 0 0 .2 0.4 0 .6 0 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 TIME FROM ENTRY- PROTOTYPE SECONDS Fig. 6 - Distance from entry measured along the trajectory as a function of time for the standard Mk 13-6 torpedo model and prototype 73ont±&EIIE±&r-.. 10 AIR PRESSURE I ATM 0.4 Q APPROXIMATELY 1/2 OF SHROUD RING <..> ON TAIL CONTACTING CAVITY WALL I ~ z 0.3 w <..> LAUNCHING CONDITIONS IL IL w 0 0. 2 VELOCITY 121.9 FPS <..> n. < IL (!) TRAJECTORY 1e .s• _J CONTACTING PORTI ON OF 0 SHROUD RING VARYING < (/) a:: BETWEEN 1/2 AND 5 /8 PITCH 5.2• F _J :::E 0 0 0 . 1 <( ~ PITCH FROM I- I- 0 CRITICAL 6 .9•F ID 0 .0 SHROUD RING ON TAIL ENTIRELY CONTACTING 0.4 CAVITY WALL Q <..> I ~z w 0 . 3 oOO <..> IL LAUNCHING CONDITIONS 0 IL w 0 0 <..> 0 .2 VELOCITY 117.9 FPS (!) TRAJECTORY 1e.s• ct a:: 0 PITCH I. I • S 0 . 1 PITCH FROM CRITICAL 0.6 • F 0 .0 0.01 0 . 1 1.0 TIME FROM ENTRY-SECONDS Fig. 7 - Instantaneous coefficient of drag as a function of t ime from entry for the sta ndard Mk 13-6 torpedo model CMHi I de h e+e.t 11 0.5 >- AIR PRESSURE t- 1/11 ATM 0...~ 0.4 ctO c ...Ju., 0 1/)0 I ...J::E t- -o z ~t- w 0 .3 t- 0 0 m u.. LAUNCHING CONDITIONS 0 u.. 0 w 0 0.2 0 VELOCITY 121.2 FPS (!) TRAJECTORY 18.7" a:: PITCH 5 . 3" F APPROXIMATELY 1/2 OF SHROUD RING a'"' ON TAIL CONTACTING CA VITY WALL 0 . 1 0 PITCH FROM 0 0 CRITICAL 8.0" F 0 .0 0 .4 APPROXIMATELY 1/6 OF SHROUD RING CAVITY WALL c r(ON TAIL CONTACTING 0 I zt- w 0 0 LAUNCHING CONDITIONS o oo o 0 itw 0 VELOCITY 119.5 FPS >- 0 t- ~ (!) TRAJECTORY 18 .8" ~0 ...J a::'"' PITCH 2.0° s 1/)u.. a 0.1 0 ...J-:::e PITCH FROM '"'o CRITICAL 0.7"F t-t- b 0.0 m >- RING t- ~APPROXIMATELY 3/4 OF SHROUD a.- ON TAIL CONTACT ING CAVITY WALL ...Jo 0 '"'~1/) 0.4 :::!~ -- c 0 t-a. '"' 0 I t- t- 0 z w 0 .3 0 0 0 LAUNCHING CONDITIONS u:: u.. w 0 0.2 VELOCITY 115.9 FPS 0 0 TRAJECTORY 19.0" (!) a::'"' 6 .4° s a 0 . 1 PITCH FROM CRITICAL 3 .7"5 0.01 0.1 TIME FROM ENTRY-SECONDS Fig. 8 - Instantaneous coefficient of drag as a function of time from entry for the standard Mk 13-6 torpedo model 12 0 .10 ::r: 0 .10 (.) ::r: (/) (/) (.) 0 1- 0 1::: z a: z u. 0 0 (.) .....J (.) .....J LJJ <( LJJ <( (/) 0 .08 (.) (/) 0.08 <..:> 1- I - I - t: a. 0::: a. <( (.) <( 0::: _J _J (.) (J') (/) _J _J 0.06 <( ~ 1- 0.06 0 0 z z <( <( 0 >- >- a::: a::: 1- 0.04 1- 0.04 z z LJJ LJJ z z LJJ 0 LJJ LJJ LJJ 3C 3C 1- 0.02 1- 0 .02 0 LJJ LJJ ID ID LJJ LJJ :::!! AIR PRESSURE 0 0 :::!! AIR PRESSURE 1- I ATM 1- 112 ATM 0 .0 8 6 4 2 0 2 4 6 6 4 2 0 2 4 6 STEEP FLAT STEEP FLAT INITIAL PITCH- DEGREES INITIAL PITCH-DEGREES 0.10 0 . 10 (/) 0 ::r: (/) (.) 0 ::r: z 1- (.) 0 z 1- (.) a:: 0 a:: LJJ 0 (/) .....J <( LJJ .....J (/) <( (.) I 0.08 0 .08 (.) a. I <( 1-- a. 1- _J 0::: <( 0::: (/) (.) _J (.) (/) _J _J <( - a::: 0 >- !- a::: z 0 .04 1-z 0 .04 LJJ LJJ z -- --- z LJJ 0 LJJ LJJ 0 LJJ p 3C 3C 1- 0.02 1- LJJ LJJ 0 .02 ID ID LJJ 0 ..... LJJ :::!! :::!! AIR PRESSURE 0 AIR PRESSURE i= 1- 1111 ATM 1122 ATM 0.0 0.0 8 6 4 2 0 2 4 6 8 6 4 2 0 2 4 6 STEEP FLAT STEEP FLAT INITIAL PITCH-DEGREES INITIAL PITCH-DEGREES Fig. 9 - Time from entry to tail slap as a function of initial pitch for the standard Mk 13-6 torpedo model j$ I H d@UU&'ir 13 the water. As the initial pitch approached criti TABLE II. CRITICAL PITCH% cal pitch, tail slap became progressively later STANDARD Mk 13-6 (Fig. 9). If tail slap did not occur at entry, the TORPEDO MODEL portion of the projectile in contact with the cavi ty wall after tail slap varied, causing the bubble Tank Critical configuration to fluctuate. At an initial pitch of Air Press. Pitch about 0° t h e entire shroud ring contacted the Std. Atm. 0 water at the cavity wall and then returned com pletely into the cavity. When tail slp.p occurred 1 l. 7 s at entry, the orientation of the projectile in the 1/2 2. 0 s cavity was relatively constant if the initial pitch 1/ 11 2. 7 s was flat. If the initial pitch was steep, the ori l/22 2. 3 s entation of the projectile was less stable. Since the torpedo contacts the top of the cavity when the initial pitch is steeper than critical, the %These values are from a pitch lesser stability may be caused by the force of sensitivity study currently in gravity pulling the projectile away from the progress in the launching tank. cavity wall. Figures 10 and 11 include sets of drag coefficient vs. time curves from runs with air pressures of 1 atm. and 1/11 atm. arranged with decrease in atmospheric pressure.%% This in order of increasingly steep initial pitch. Both is evident from Fig. 13 which shows the dis t he absolute initial pitches (pitch with respect to tance vs. time curves from runs made at air trajectory} and the initial pitches w ith respect pressures of l, l /2, 1/11, and 1/ 22 atm. The to critical pitch are noted on these curves. The curves become progressively lower as the at pitch with respect to critical should be used in mospheric pressure diminishes, indicating the comparing results from the two air pressures. increase in drag. These data show that the drag on the torpedo is similarly affected by change in initial pitch at The trajectories at 1/22 atm. differed some both air pressures. Further, these data also what in shape from those at the other pressures show that the fluctuation of the instantaneous (Fig. 14). Further, the variation of mean drag drag coefficient reflected the changing orienta as a function of time (or distance from entry) at tion of the projectile in the cav ity. (Also see l/22 atm. differed from that at other pressures . Figs. 7 and 8.} The drag coefficient was rela At l/22 atm. the mean drag coefficient increased tively constant after tail slap w hen the initial with time (Fig. 15). while at the other pressures pitch.was extremely flat. When the initial pitch the mean coefficient remained essentially con was steeper than critical, the drag coefficient stant from tail slap to the end of the cavity phase. increased at tail slap and then diminished, sug gesting that the projectile was falling away from Effect of a Finer Nose Shape on the Mk 13-6 the top of the cavity. At the intermediate initial Torpedo Mode 1 pitc he s the drag coefficient fluctuated after tail slap, reflecting the bouncing motion of the pro Sensitivity to Atmospheric Pressure jectile in the cavity. The drag o n the Head I model was lower than The average drag on the projectile was per that of the standard Head F model. This is evi ceptibly lower near critical pitch where the pro dent in Fig. 16, which shows the distance vs. jectile traveled longest with only its nose in con time data from both the Head F and Head I tor tact with the cavity wall. This is evident in Fig. pedoes. 12, which shows the distance vs. time data taken with an air pressure of 1/ ll atm . The curve The instantaneous drag coefficients measured from the run with an initial pitch close to criti on the Head I model ranged from 0. 10 to 0. 38, cal is perceptibly higher than the others, indi (Fig. 17). The variation of instantaneous drag cating the lesser drag. The same effect was coefficient with time was similar for both tor apparent at the other pressure conditions in pedoes. Further, the mean drag coefficient of vestigate d . the Head I model increased with time only at l /22 atm. (An increase in drag with decrease Effect of Atmospheric Pressure in pressure was also evident in the data taken with the Head F model.) However, the drag on The standard Mk 13-6 torpedo is r e lative ly the Head I model was extremely sensitive to insensitive to change in atmospheric pressure. change in atmospheric pressure, for the drag However, some slight but consistent differences were noted. Nithin an initial pitch range of.±. 1°, *±At the time of this analysis complete p re s the average drag on the projectile during the sure-sensitiv ity data were not available for the first 75 calibers of travel increased slightly extreme initial pitch conditions. ~ §o Lial ...... 0 5 0 .5 I AIR PRESSURE AIR PRESSURE I I ATM """ 0 I ATM (.) 0 (.) 0.4 I 0.4 i 1- ·.!- 0 z z LLJ LLJ ~ b ~ n J ;:; 03 LAUNCHING CONDITIONS 00.3 LAUNCHING CONDITIONS 0191 u.. 0 ;y ~!9 v« u. u.. VEL 121.9 FPS "~ u. VEL 117.9 FPS (9C ~~ LLJ 1\ LLJ Q_ loP' go2 TRAJ 18.6° go.2 TRAJ 18.6° ~ I PITCH 5.2"F Cl. Li.. PITCH I . I • S (l. <.!) <.!) Li.. 0 < 0 <( 0 (.)0 (.) 0.4 I 0 .4 I 1- 1- z z LLJ ~~ ~ ~ ~ ~0 . 3 LAUNCHING CONDITIONS \1 ~03 LAUNCHING CONDITIONS (.) :2Srtl '""'-"'t1" N: ~ u.. (l. tt~ ~ u.. VEL p E VEL 121.3 FPS LLJ 120.9 FPS <>- l:LJ ( ~ £ ih 00.2 TRAJ 18 .3" 8o.2 TRAJ 18 .1° "! 0 .5 v 7 ...J> (.) Cl.Li.. 10" 0 (.)00.4 )0.4 i I 1- w 1-z z jo ~~ 9%.. I n p ~ 0.3 LAUNCHING CONDITIONS 1---- ~ ~0.3 LAUNCH lNG CONDITIONS (.) (.) ib u. ~~ ~ ro< f-a u:: u. VEL 120.6 FPS u. VEL 119.2 FPS ~ p LLJ ,.(j Q 0 0.2 TRAJ 18.9° LLJ 0.2 TRAJ 18 .4° >- (.) ot."P" 1- Li.. 8 PITCH O. I"F (l. PITCH 6 .0• S < <.!) 0 e...J ~ u 0 0.4 ~z w _0 In b~ cfa. ° 0 0.3 LAUNCHING CONDITIONS ~ ~Q :~1,~-~'" ~-"~'1 ~ 11111111 c ,0~ I.Y" ltt ~'1 u: Ll.. Ll.. Ll.. p UJ VEL 121.2 FPS!l. u. VEL 120.2 FPS <>:0 UJ 0 0.2 r1\ 0 0.2 (.) TRAJ 18.7" TRAJ 18.8" ~ ,.. (.) ll. u. I 9 PITCH 5.3" F --' I\J (!) ~; (!) PITCH 0.8" S <>: 0 0 (.)0 0 I 0.4 (.) 0.4 -- I I 1- 1- z z UJ 0.3 ~;50 00 ~ 0.3 LAUNCHING CONDITIONS (.) 0 0 (.) u: jQS tt """"'"VEL 121.3 ""'"' FPS I 0 0 1111111 Ll.. VEL ~ UJ I 119.5 FPS 0 0.2 J1tttt+J R TRAJ 18.8" ~ 0.2 TRAJ 18.8° (.) lb (.) u. I ~ (!) PITCH 3.6 ° F PITCH 2 .0° s ll.o (!) <>: ,.. 0 0.4 o< o0.4 f (.) (.) I ~ 1- b~~ z z 0 0.3 ~ ~ 0.3I LAUNCHING CONDITIONS 0 2 (.) !? Ll.. '~""'" 00""'"' ~~ Ll.. Ll.. VEL 11 7.8 FPS Ll.. VEL 115 .9 FPS ~ 0.2 ~ 0.2 ~ ~-....o ~ TRAJ 18.8" TRAJ 19 .0" (.) (.) p' ,.. PITCH O. I"S Cl.u. PITCH Cl.l::: <>:0 (!) 6.4" s <>:> ~ _J ,.. <( _j for the standard Mk 13 -h torpedo model U1 16 90 I I AIR PRESSURE 1111 ATM 80 f-- I I / !?' c~ 70 ~ (f) w 0: (IJ _J <( 0 I ~ >- 0: 60 !J 0 f- 0 w A~ J <( 0: f- (.!) 50 r z ~ 0 _J <( 0 w 0: :::> (f) <( w 40 r- :::?! >- 0: , f- z w :::?! 0 30 0: LL. I w 0 @ z <( f- (f) Ci 20 J LAUNCHING CONDITIONS ABSOLUTE PITCH WITH RESPECT CURVES VELOCITY TRAJECTORY PITCH TO CRITICAL PITCH FPS 0 0 A 119.5 18.8° 2.o0 s 0.7"F 10 - B 115.9 19.0° 6.4°S 2 .7°S c 117.3 18 .8° 0.1 os 2 .6°F D 121 .2 18 .7" 5.3°F 8 .0°F E 12 1.3 18 .8° 3 .6° F 6 .3°F :/ I I I I I 0 .10 0 .20 0 .30 0.40 0.50 0 .60 0 .70 0.80 TIME FROM ENTRY -SECONDS Fig. 12 - Distance from entry m easured along trajectory as a function of time for the standard Mk 1 3 -6 torpedo model c c c :ttill1al CS!&i&CIIEidl 17 90 1 ATMOS \ 2 2 v +ATMO/} 80 L I ATMOS\ / -fr ATMOS ""\ 70 # v (f) lJJ 0::: f:Q __J LAUNCHING CONDITIONS AIR PRESSURE Pf"!;CH TRAJECTORY VELOCITY ATM 0 FPS 0 . 1° F 18 .9° 120.6 10 I I . 1° S 18 .6° II 7 .9 122 . I 1/2 0.3°S 18 . 3° 1.0°S 18 .5° 119 .2 08°S 18 . 8 ° 120 .2 1/11 0.1 °S 18.8 ° 117 .3 19 .2 ° 120 . I 1/22 0.2°F / 0.6°S 18 .5 ° 119 .2 0 0 0.10 0.20 0.30 0.40 0.50 0 .60 0.70 0.80 TIME FROM ENTRY-SECONDS Fig. 13 - Distance from entry measured along the trajectory as a function of time for the standard Mk 13-6 torpedo model ddHilcitmt 1 Confidential 18 coefficient increased about 80o/o when the air type drag characteristics. pressure was reduced from 1 atm. to 1/22 atm. This extreme sensitivity to pressure is not sur 1 prising because, as previously reported, the CONCLUSIONS trajectory of this mode 1 varied from a steep dive at an air pressure of 1 atm. to a broach The following conclusions were drawn from at a pressure of 1/22 atm. The photographs in the results of this analysis: Fig. 18 were reproduced from actual test data recorded during the launching of the Head I 1. Within an initial pitch range of± 1°, the model. at an air pressure of 1 atm. The photo drag on the standard (Head F) Mk 13-6 torpedo graphs show the instantaneous orientations of during the first 50 calibers of underwater travel the projectile and the cavity at successive points is modeled by Froude scaling to the accuracy of along the trajectory. the prototype data. However, the results from runs made at 1/2 atm. and 1 / ll atm. are in Sensitivity to Initial Pitch closest c o rrespondence with the bulk of the prototype data. No pitch sensitivity data were available when this analysis was made. However, later visual 2. Within an initial pitch range of±. l 0 , the observation indicated that the mo ~ 0 AIR PRESSURE I ATM a:: 1/22 ATM CD VELOCITY 120.6 FPS 120. 1 FPS TRAJECTORY 18 .9° _J 19.2 ° Fig. 14 -Effect of au pressure UIJOn the trajecto ry of the standard Mk 13-6 t o rpedo model Confidential 19 0.5 0 .4 Q oo (,) ....I z 0 ILl 0.3 00 0 CONTACTING AREA OF SHROUO ii: LAUNCHING CONDITIONS RING INCREASING FROM 1/2 TO 7/8 LA- PROJECTILE PITCHED ABOUT IO"F ~ >- c..> 1- 1APPROXIMATELY 1/4 OF SHROUg RING 0.2 VELOCITY 119 .9 FPS --- ON TAIL CONTACTING CAVITY WALL a:~ TRAJECTORY 18. 6° 0.0 APPROXIMATELY 5/ 8 OF SHROUD RING ON 0 . 4 1------+------t- TAlL CONTACTING CAVITY WALY Q c..> 00 1':)0/ I 1- z 0. 3 ILl 0 (,) LAUNCHING CONDITIONS ii: APPROXIMATELY~ LA- >- OF SHROUD RING ON ILl 0 0 0.2 VELOCITY 120. 1 FPS 1- 6~~~T$ ~ltP I N__G_ ___--\: ----=-=---1 (,) a_ ~ 00 0.4 Q (,) I 1- z 0.3 0 ILl (.) LAUNCHING CONDITIONS LA- AREA OF CONTACT BETWEEN LA- ILl PROJECTILE AND CAVITY WALL 0 0.2 VELOCITY 119.9 FPS ---+-..o>,u--~f.J..----- 1 > INCREASING (,) ---r- a._ 0 . 0 0 .00 1 0~ 1 ~I 1.0 TIME FROM ENTRY - SECONDS Fig. 15 - Instantaneous drag coeffic ient as a function of time from entry for the stan dard Mk 13-6 torpedo model ...... 7 20 6 A s · ntj.,r. 65 i--1/11 ATM 1\ 60 v v Cll w 55 ~ a: v "\..._1/22 ATM Ill ...J ~\II ATM ~ / \I ATM / (.) 50 ~ I ~ > a: 0 ~ I ATM / / ~ 1- 45 ~ d \_1/22 ATM (.) w -, ~ ~ a: § / 1- 40 IY ~ ~/ (.!) v ///' z HEAD I HEAD F 0 /hv ;;t 35 I /L 0 ~ LAUNCHING CONDITIONS w fY a: ~ AIR ::> 30 !J PRESSURE VELOCITY TRAJECTORY PITCH - Cll ATM FPS . w~ :I!; HEAD F 25 I ~ V~ I 115.9 19.0 6.4S- > a: 1-z 1/11 117.3 18.8 O.IS w 1122 120. 1 19.2 0.6S _ :::!: 20 II r/ 0 E7 ' a: HEAD I u.. I 120.4 20.3 0 .3S w 15 - (.) lfJ 1/11 121.6 20.1 0.2S z ~ 1122 121.5 20.5 0 .5F 1- C/l /; I I I I 0 10 v I I I I NOTE: THE RUNS USED FOR COMPARISON AT EACH 5 II PRESSURE CONDITION WERE CHOSEN ON THE - 1/ BASIS OF SIMILAR TRAJECTORIES 0 I I I I l 0 0.02 0 .04 0.06 0 .08 0 . 10 0.12 0.14 0.16 0 . 18 0.20 TIME FROM ENTRY- SECONDS Fig. 16 - Distance from entry measured along the trajectory as a function of time for the standard (Head F) and Dunn (Head I) models of the Mk 13-6 torpedo eolfifd@ liL¢' <\cirf 21 AIR PRESSURE I ATM .....> 0.4 ~------4------~~ ------+------1 0 ~u u ...JLL. I _o ..... APPROXIMATELY 3/4 OF SHROUD RING ;':a. ON TAIL CONTACTING CAVITY WALL z 0 .3 0 w I- u APPROXIMATELY 1/2 OF SHROUD RING LAUNCHING CONDITIONS ON TAIL CONTACTING CAVITY WALL LL. LL. w 0 0 :2 VELOCITY 120.4 FPS Q (.') TRAJECTORY 20.3" ct 0::: PITCH 0.3° s 0 0.1 > I- > ct u 0.4 r------+----- ~ LL. ...J 0 ~PPROXIMATEL Y OF SHROUD 0 Vl RING ON TAIL C b/2NTACTING u 0 ::IE CAVITY WALL I ...J 0 ...,----ENTIRE SHROUD RING I- - 1-- ,£ ON TAIL CONTACTING z ~ 1-- CAVITY WALL w 0.3 0 0 CD u: LAUNCHING CONDITIONS LL. w 0 0.2 u VELOCITY 121 .6 FPS (.') TRAJECTORY 20.1" ct '-CONTACTING AREA OF 0::: SHROUD RING DECREASIN 0 PITCH 0.2" s 0.1 TO APPROXIMATELY 1/2 > I- ~ APPROXIMATELY 5/8 OF SHROUD RING ON TAIL a. 0 0.4 r------+---- ct CONTACTING _C_A_V_I T~Y------=-~f_EtJI ~~I ~H~g ~ ~ A~t~~G CAVITY WALL 0 ~~ --?)ALL u ::IE - 0 0 I ...Jo 0 o I- ;[t z I-l- w 0 .3 0 - CDO u LAUNCHING CONDITIONS LL. u.. w 0 0.2 VELOCITY 121.5 FPS ______,,._ ____+------=::,__...LJ. A P P R 0 X I M ATE L Y 1/2 0 F SH RO U 0 u RING ON TAIL CONTACTING CAVITY WALL (.') TRAJECTORY 20.5 • ct 0::: PITCH o . 5" F 0 0.1 0.0~---~L--~~-~~-L~---~---L--L~~_L~~----L---L-~-L-L~~ 0.00 I 0 .01 0.1 1.0 TIME FROM ENTRY-SECONDS Fig. 17 - Instantaneous coefficient of drag as a function of time from entry for the Mk 13-6 torpedo model with the Dunn nose (Head I) ciHII ae II EI Jt • N N 1,..... Launching Conditions Air Pressure 1 atm. Velocity 120.4fps Trajectory Angle 20.3° Pitch 0.3° Total Elapsed Time 0. 084 sec Scale 1"=35" Fig. 18- A steeply diving trajectory of the Mk 13-6 torpedo model with Dunn nose. This composite photograph shows the instantaneous orientations of the projectile and cavity at successive roints along the trajectory. The images above the horizontal line are reflections from the underside of the water surface . rnfit 23 APPENDIX I Apparatus launching tank (Fig. 20}. It provides informa tion on the three linear and two angular compo 9 The Controlled Atmosphere Launching Tank nents of position. The launching tank was designed to study the The analyzer is essentially a half-size re hydrodynamic factors involved when a body trav production of the recording system with pro eling freely through a gas strikes and penetrates jectors taking the place of cameras and a half a liquid surface. The tank provides control of model on a movable screen replacing the model. launching velocity, pitch angle, trajectory angle The screen can be moved to any position that and atmospheric pressure. the model may assume. The components of mo tion are indicated by counters which supply nu The tank is a Koroseal lined, welded steel merical trajectory data for further analysis. pressure vessel 13 ft in diameter and 30 ft long with a smaller cylindrical bulge on one side All of the films from one run can be placed (Fig. 19). The launcher, which is of the cen in the projectors with the film strips synchron trifugal type, is mounted on the underside of a ized so that all frames taken simultaneously are large hatch cover on top of the tank. The model, projected simultaneously. A common drive op held in a chuck near the periphery of the wheel, erates the projectors so that the film strips re can be launched at any desired speed up to 120 main synchronized during the projection of the fps at any angle between horizontal and vertical. entire run . For each frame the scree)l is ma The angle of the model with respect to the se neuvered until the image falls on it. The coun lected path can be adjusted to any angle up to ter readings give the position and orientation + 10°. of the mode 1. During normal operation the water is about Each projector (Fig. 21) is equipped with a 10ft deep. The water is originally distilled and lens matched with the corresponding camera later maintained by constant filtration and ultra lens. The gate mechanism holds the film ex violet radiation. These precautions are neces actly in the focal plane. Temperature changes sary because the underwater light path for pho in the projector are kept low by use of low light tography is about 24 ft. intensity, a water cell between the light and the condensers, and a small cooling fan. The path of the model through the gas above the surface of the water and under the water is Models recorded by two groups of high speed 35 mm. motion picture cameras operated at constant The models used in the launching tank are speed by a synchronous motor. The film is made in three sections which are connected by spliced to form one continuous loop in each screw type joints. The nose and the afterbody camera magazine. In operation, the camera are of duraluminum, the center section and fins shaft is accelerated slowly to prevent film and shroud ring on the afterbody are of stain breakage. The cameras have no shutters. Ex less steel. The center section is grooved for posures are made by intermittent illumination fastening in the launching chuck. The groove of the interior of the tank w ith Edgerton type should have little effect on the trajectory during flash lamps housed in lucite tubes located in the the cavity stage, although it may have some ef bulge of the tank. The number of exposures can fect later. The internal construction of the stan be varied from 100 to 3,000 per second, and dard Mk 13-6 torpedo model is shown in Fig. 22. each flash is 2- to 3-millionths of a second in The Head I model is of similar construction. duration. The fields of view of adjacent cam Figure 23 shows the outlines of both torpedoes eras overlap to such an extent that the model is with the external dimensions given in calibers, photographed by at least two of them during each and Fig. 24 shows the outlines of the two noses exposure. This makes it possible to reproduce superimposed for comparison. the path of the model by stereoscopic observa tion of the projected images. The physical and dynamic characteristics of the models are listed in Table III together with The Trajectory Ana lyzer the prototype dimensions and the correlation tolerances. The contours of the he a ds and The trajectory analyze r is a device for re afterbodies of these models were ma c hined constructing the path of a mode l from the high undersize to allow for a coat of white lacquer speed motion picture records obtained in the about 0. 002 in. thick. au :· r 24 Fig. 19 25 Fig. 20 - Trajectory analyzer Fig. 21 -Close -up of projector RIMM!;R TRIMM!;R \../i;IG~T \J!;IG~T 3" 6-4 ~------B<~7() -" - - 1Ll . 3 6 o''_------ Fig. 22 - Sectional view of the standard (Head F) M i< 13 -6 torpedo model ~ ,. kiltl&i CoAU $" 26 .. _J STANDAR-D -+--- _ <( __ - MK.Io NOSE u --" 8 5 (a) ,;":'0 cii~ER ~ 8565 CAL. l------3 . 236 CAL.------•-+--·I - 1.535 CAL p~.~1 ~~~~T_H____ ~....J I 81 CAL I BE RS $ 1------7 . ------1 b= ~ CALIBER K= 3.43 _J -- <(------'---- u (b) f------:3.2.36 CAL.------+--:2.125 CAL.------t-o--1.82 CAL.----t f------7. I 81 CALl BE P.S ------~------1-t Fig. 23 - Outlines of the Mk 13-6 torpedo (a) The standard (Head F) torpedo (b) The torpedo with the finer Dunn (Head I) nose 5TANDAP.D NOSE. (HEAD'I=7 HEAD "I"_/'~ --l--+-l- Fig. 24 - Comparison of the Head F and Head I contours C~1·, h 27 TABLE III. SPECIFICATIONS FOR THE PRECISION Mk 13-6 TORPEDO Model Prototype Length Ratio = L 2 22.42 1/L . 50000 .04460 VL: 1.4142 4. 7343 1/fL . 7071 . 2112 Scale Factor = s 11.2100 1 1/.S . 08921 1 rs 3.3481 1 1/1[5 .29868 1 2.0000 in. 22.42 Diameter +0.020 ±0.0027 -0.010 14. 16 in. Length* 158.7 in. ±o.o8 ±.1. 0 1, 520 lb Total Weight l. 079 lb ±o.01 ±.15 Fresh Water l. 233 lb 1, 737 lb Displacement ±0.01 ±15 o. 154 lb Buoyancy 217 lb ±0 . 02 ±30 Distance of c. g. 6. 178 in. 69.25 in. from Nose* ±0.04 ±.0.50 Distance of c. b. 6. 234 69.88 in. from Nose* ±.0.04 ±0.50 Moment of Inertia 0. 1455 lb ftl 2. 57 X 104lb ft2 about Transverse ±.0.0018 ±.o. 03 x 104 Axis through c. g. :t Measured from tangent to hemisphere APPENDIX II Analysis of the Data carded. Coordinate positions were read to the nearest±. 0 . 01 diameter with an accuracy of Reduction of the Photographic Data ± 0. 05 diameter in most cases and to±. 0. 1 under the worst conditions. The experimental The data used in this analysis were photo ly determined trajectory angles are correct to graphic records of launchings made in the Con ± 0. 2°. During the air trajectory the inclina trolled Atmosphere Launching Tank. These tion of the model with respect to the horizontal photographs were taken at a rate of 500 expo is corre ct to±. 0. 1°. Since the initial pitch sures per second. angle is the differ e nce between the traj e ctory angle and the inclination of the model, the pos The film was analyzed to determine only the sible error in the initial pitch is±. 0. 3°. x and z coordinates of the model position and the inclination of the model axis with respect The Distance vs. Time Curves to the horizontal (Fig. 25). In some cases dis placements occurred in the y direction during The di s tance alo ng the tra jectory come s di the water travel. However, the yaw was ob r e ctly from the x a nd z coordinates measured vious from the divergence of data from adjacent with the analyzer. cameras. Therefore, any data with sufficient yaw to affect the x and z coordinates were dis- The distance increment between any t w o 1 <;onfj Qpt Q 28 z the trajectory where the original data were less reliable. However, the sudden changes in ve locity which resulted from tail slap and other changes in orientation could be separated from scatter in the data because the orientation of projectile and cavity were readily apparent in the original photographs. The times plotted with the v in Fig. 26 were determined by: n t + t m n t = INCLINATION avg 2 y The Coefficient of Drag Fig. 25 - Coordinate system The coefficient of drag is proportional to the slope of the curve that results when the loga points m and n along the trajectory: rithm of the instantaneous velocity is plotted against the distance traveled from water entry. 2 ~l/2 The force tangent to the trajectory can be writ S = X - X ) + (z - Z ) ten as: mn [ n m n m 2 mdv CdApv + g (m- p V ) sin Q The total distance along the trajectory s at F w any point n is the sum of the individual dista~ce dt 2 increments from entry to point n: (See Fig. 2 7) ( l) The gravity-buoyancy term g (m- pV ) sin Q, significant only at the low velocities b:Y,.ond the cavity phase, was not considered in either mod el or prototype work; nor was any virtual mass The intervals used were so small that approxi correction made. If the gravity-buoyancy term mating the curve of the trajectory within the is dropped, Eq. (1) may be rearranged and inte interval with a straight line did not introduce grated to give: appreciable error. The time tn plotted with the distance Sn was measured by the accurately known flash rate of the lights. The sample dis tance vs. time curve (Fig. 26) shows that these data were virtually without scatter. (2) 2m The frame designated as "one" in the original data was the frame in which the nose of the pro jectile first penetrated the water. The actual where S = distance from entry measured along entry of the nose occurred somewhere between the trajectory. 0 and -0.002 sec. No attempt was made to cor rec: for this. Whence: 2m ln v/v 3. 726 log v/v 2 2 The Velocity-Time Curves cd = (3) (52-Sl) The velocities came from the first differen tiation of the numerical distance -time data: The velocity-distance curves used to calcu s - s late the drag coefficient were plotted from the n m faired v elocity-time and distance-time curves. v n Figure 28 compares the velocity-distance curve t - t n m from the £aired velocity data with the points from actual computed velocities. Since the dis Overlapping intervals were u sed in the early tance-time data are virtually without scatter, portion of the trajectory where conditions were it is reasonable to assume that the velocity dis changing rapidly. There was some scatter in tance curves are not distorted in shape by the the velocities, particularly at the extremes of scatter in the velocity data. C? (" 1 I Q. l 29 )_ 84 r-- 0:: ~ 0 -0-""" I )..--<>" (.) ..-o- ...,w 72 v <( ,------' v 0:: I- v (!) z 60 g / v ---- <( / fi:l~48 / O::o:: ~'!! / <(_J v ~~36 / / /v p' I j II 0 .0 4 0.08 0 .12 0.16 0 .20 0 .24 0 .28 0 .32 0 .36 0.40 0 .44 0 .48 100 Lo o \ \ 90 '\ 80 1\ \ (f) 70 ~ a.. lL. I >- I- 60 \ (.) 0 _J w \ ' > [\ (f) 50 ::::> 0 \ w z ~ 4 0 I ~ LAUNCHING CO NDITIONS _ r-- z <( VELOCITY 120.6 FPS _ I- ~ - (f) z ~ TRAJECTORY 18 .9° 30 PITCH 0.1 •F - - ~ 0 r---. .___ 20 ...___ r---, ,______t-o.. 0 10 0 .0 4 0 .0 8 0.012 0. 16 0 .20 0 .2 4 0.28 0.32 0.36 0 .40 0.44 0 .48 TIME FROM ENTRY-SECONDS Fig. 26 -D istance f r o m e ntry m easured a l ong the trajector y a nd instantan eou s ve l ocity a s a function of time f or t h e standa r d Mk 13- 6 torpedo model c:., c 7 , t rr 30 WATER SUR =WETTED e VOLUME v= INSTANTANEOUS VELOCITY A= MAXIMUM CROSS SECTIONAL AREA OF TORPEDO ' MODE ~ AXIS , mg ~ Fig. 27 /50 X LAUNCHING CONDITIONS )( 100 AIR PRESSURE I ATM - VELOCITY 120.6 FPS _ 90 ~ - '1:~ TRAJECTORY 18.9' 80 -- PITCH 0.1' F - 70 60 ~ UJ " a.. "- I >- 50 ':::: 0 0 _j ~ 40 ~ ' ~ UJ :::> 0 "'z <{ 30 I- ~ z ~ ~ zUJ 20 ~'""" D---0--<) VELOCITIES FROM FAIRED VELOCITY VS TIME CURVE ~~ 15 f- X VELOCITIES FROM INDIVIDUAL POINTS ON VELOCITY VS TIME CURVE · ~~ X l( /0 I I I 0 10 20 30 4 0 50 60 70 BO 90 DISTANCE FROM ENTRY MEASURED ALONG TRAJECTORY-CALIBRES Fig. 28 - Instantaneous velocity as a function of distance from entry measured along the trajectory for the standard Mk 13-6 torpedo model Gs zt · d tta 'i'dr& 1 c 31 APPENDIX III Factors in Model Studies of Water Entry to produce similar cavities. The condition that the Froude numbers in the two systems be i In studying the behavior of free-flying bodies dentical requires that (v /v )2 =X., the ratio by means of scale models, the aim is to control of linear dimensions of th~ mbdel to the proto the variables which affect the motion so that the type. Substitution of this in the expression for model will follow a path which is geometrically the cavitation number shows that the ratio similar to that of the prototype and so that the - - = X.. (p 0 Pc)m/(p0 Pc) Since the hydrostatic scale ratio of the two paths will be the same as pressure is scaled in this ratio by the original the ratio between the linear dimensions of the requirement of geometrically similar trajec model and of the prototype. This requires that tories, it follows that the gas phase pressure the pressure distribution on the model be simi must also be scaled according to this linear lar to that on the prototype at corresponding scale ratio X.. points of the trajectories. If air is used in the model work, changing The phenomena associated with the water en the atmospheric pressure naturally changes the try of an aircraft torpedo are complex. Since density of the gas. Valid Froude modeling re only a limited number of the contributing fac quires that the atmospheric density be equal in tors can be modeled simultaneously, it is neces both systems. 1 Experimental investigations of sary to consider those most important to the the entry behavior of vertically launched pro projectile's behavior. jectiles indicate that the time until surface clos ure of the cavity increases as the atmospheric The forces of gravity and inertia are usually density diminishes. lV If closure is early, its of major importance in any hydrodynamic phe time and location are important to the subse nomena involving the free surface of a liquid. quent behavior of the projectile. If surface clo Hence these forces should be given primary sure is late, it does not significantly affect the consideration when attempting to model the projectile behavior . 1· 10 Photographic evidence cavity phase of an aircraft torpedo's flight. from the launching tank has indicated that sur Two geometrically similar systems will be dy face closure is sufficiently late to be neglected namically similar with respect to the gravita for the nose shapes, velocities, and entry angles tional and inertial forces if ·the ratio of these thus far investigated. However, when surface forces is the same in both ·systems. This ratio closure is late, the cavity may neck down at 1s known as the Froude number some distance behind the projectile and throttle 2 the flow of gas into the bubble. The pressure v Fr = drop due to throttling is not modeled unless the atmospheric densities are equal in both sys tems.l However, in studies using small scale where: v velocity of projectile models with reduced atmospheric pressure, the ..e a characteristic length total atmospheric pressure is small and any dif g the acceleration of gravity ference between that and cavity pressure due to the throttling would be of second order. There The size and shape of the cavity are deter fore, this effect of atmospheric density also has mined by the physical and dynamic character been neglected in the Controlled Atmosphere istics of the projectile, the orientation of the Launching Tank investigations. projectile in the cavity, and the cavitation num ber After the cavity has been shed, the viscous effects upon the projectile become important. Po-p~ In order to maintain similarity between these k = 2 effects, the ratio of the inertial to· the viscous 1/2 pv forces must be the same for both model and prototype. This ratio, known as Reynolds num- where: absolute static pressure in the ber, is undisturbed liquid absolute pressure within the Re = cavity v = velocity of the projectile p density of water where absolute viscosity of the liquid. Therefore, the cavitation number should be the same for model and prototype systems in order If the same liquid is used for both model and 32 prototype work, the velocity must be scaled as and any dependence of c upon V is neglected. >-,- 1 in order to satisfy the Reynolds criterion. The Mach criterion, which must be satisfied Obviously, Reynolds and Froude scaling cannot to maintain similarity of the elastic forces, be satisfied simultaneously if water is used in represents the ratio of inertial to elastic forces the model work. Wind and water tunnel tests M = V indicate that the lift and moment acting on sub c merged bodies are very nearly independent of viscous effects if the Reynolds number (based If the liquid is not changed, this mode ling la}IY upon length) is well above 10.6 Skin friction, requires equal velocities as opposed to the },.. 112 however, is a function of Reynolds number and scaling necessary in the Froude system. So long would cause greater deceleration in the Froude as water is used in the Froude-scaled model scaled model than in the prototype. Therefore, system, the impact forces pn the mode 1 will be similarity cannot be expected between the too small by a factor of >-,1(2. However, since Froude-scaled model and the prototype beyond the Mach number is low and the impact stage of the cavity stage. water entry very brief, l2 the unsealed elasticity of the water does not significantly affect the tra The forces occurring when the torpedo in jectory. On the basis of similar reasoning, the itially strikes the water surface depend upon elasticity of the model itself can be neglected as the elastic properties of the water, for the force well. upon the nose of the projectile is The effects of surface tension are insignifi F = pcVA cant compared with the forces of inertia and where gravity for all except extremely small-scaled, low-velocity work. Therefore, in this work of v = velocity normal to the water surfafe modeling, the cavity would be independent of surface tension. The surface closure of any c velocity of sound in water= (E/p)1 2 such cavity, however, might be affected, since A area of contact projected normal to V the inertia of the atmospheric gas and the sur E bulk modulus of water face tension are of the same order of magnitude. oil fdutie·l @ 't 33 BIBLIOGRAPHY 1. 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