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R-344

LABORATORY

REPORT SIT-DL-48-344NOVEMBER 1948

WAVE CONTOURS IN THE WAKEOF A10 DEADRISE PLANING SURFACE


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R-344

DAVIDSONLABORATORY




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R-344

DAVIDSONLABORATORY




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TECHNICAL REPORT SIT-DL-84-9-344NOVEMBER 1948

WAVE CONTOURS IN THE WAKEOF A10 DEADRISE PLANING SURFACEby

B.V. Korvin-Kroukovsky


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WAVE CONTOURS IN THE WAKEOF A

10 DEADRISE PLANING SURFACE

Prepared under sponsorship ofU . S . Navy

Office of Naval ResearchProject No. NR 062-012

(E.T.T. Project No. CC839)

Report No. 3hhby

B.V. Korvin-Kroukovsky


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TABLE OF CONTENTS

S U M M A R Y . 1I N T R O D U C T I O N 1S Y M B O L S 2M O D E L AND A P P A R A T U S 3T E S T P R O C E D U R E 3R E S U L T S AND D I S C U S S I O N UL o n g i t u d i n a l and T r a n s v e r s e S e c t i o n s T h r o u g h W a k e $C u r v e s for E s t i m a t i n g A f t e r b o d y W e t t e d A r e a 6

E f f e c t of D e a d r i s e A n g l e on C e n t e r l i n e P r o f i l e T h r o u g h W a k e 8C O N C L U D I N G R E M A R K S 9R E F E R E N C E S 10

T A B L E Is P L A N I N G T E S T R U N S OF 10 D E A D R I S E P L A N I N G S U R F A C E HP R I S M A T I C 10 D E A D R I S E P L A N I N G S U R F A C E 12D E T A I L E D L O C A T I O N OF M E A S U R I N G ROD P O S I T I O N S 13C H A R T S

R e l a t i o n b e t w e e n H e i g h t of L o n g i t u d i n a l ,


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SUMMARY

Model tests were made at the Experimental Towing Tank, StevensInstitute of Teclinology, to determine the shape of the wave contours inthe -wake of a 10 deadrise prismatic float planing with parts of thechines submerged. The tests were run at various forward speeds and load-i n g s , with trijns of k 8# and 12. Measurements of the water dis-placement relative to level water were made over an area in the wakeextending from the step to six beams aft, and for a distance of threebeams on each side of the planing surface centerline. These wake dataare presented in the form of transverse and longitudinal sections throughthe wake for each test run.

The longitudinal contours in the wake taken along the planingsurface centerline indicate a consistent variation with trim, speed, andaspect ratio. These contours are presented in a form that enables sea-plane designers tc readily estimate the contact area between the fore-body wake and afterbody bottom for a range of pertinent planing condi-t i o n s . The general shape and features of the wake of a 10 deadriseplaning surface are basically similar to those of a 20 deadrise plan-ing surface. A reduction in deadrise angle, however, slightly reducesthe height of the centerline profile but does not materially affect therelations between change in wave height and change in aspect ratio orload coefficient.

The study was made under the sponsorship of the Office of NavalResearch, Navy Department.


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indicate the effect of planing surface deadrise on the trailing w ake.All the tests w ere made under the auspices of the Office of Naval Re -search, Task Order IV, Contract N6onr 2l|.7*

The tests on the 10 deadrise planing surface were made over arange of velocities and test loadings that resulted in partial chinesubmergence in order to simulate the two-step planing stage of a landingor take-off. As in Ref. 1, the wake data are presented in the form oftransverse and longitudinal sections through the wake formations. Also,the longitudinal wave profiles along the planing surface centerline aresummarized in the form of plots w hich enable the seaplane desig ner toreadily estimate the afterbody planing area for various planing condi-tions. These longitudinal centerline profiles are compared with the20 deadrise profiles presented in Ref. 1.

SYMBOLS

The various terms and hydrodynamic coefficients used in this re-port are as follow s:C^ Load Coefficient = A/wb^O. Speed Coefficient = V / / g FLift Coefficient - A/ V 2b 2

Aspect Ratio = (L, + L ) /2b


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R - 3 U U- 3 -MODEL AND APPARATUS

The 10 deadrise planing surface was tested in Tank No. 3 of theExperimental Towing Tank (Ref. 2) . The model .was of laminated white pinehaving a beam of 0.U16 ft and a constant angle of deadrise over itsentire length. The principal lines and dimensions defining the size andshape of the model are shown on Fig . 1. Dark stripes, spaced at intervalsof 0.20 beams, were painted across the keel and chine from the step tothe bow in order to facilitate the measurement of the wetted keel andchine lengths.

The shape of the wave contours in the wake of the 10 deadriseplaning surface v/as obtained from underw ater photog raphs of streamlinedmeasuring rods w hich were towed in the wake behind the model. The shapeof the wake contours was determined by noting the intersection of thedisplaced water surface w ith the rodso A detailed description of thesliape and location of the measuring rods*, along w ith a description ofthe underwater photographic set-up and equipment used in these tests aregiven in Ref 1. The overall accuracy in measuring the displacement ofthe water surface w as estimated to be approximately 2 percent of thebeam.

TEST PROCEDURE


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at each test trim corresponds to approximately the shortest wetted lengthsat which the chines are initially submerged when the float model is towedin smooth water. The largest aspect ratio tested corresponds to approxi-mately the longest wetted lengths that occur in the region of the humpspeed for most conventional seaplanes. Several intermediate aspect ratioswere also investigated at each test trim. In order to investigate theeffect of velocity on the wake shape, the model was towed at a series ofplaning speeds at each test trim. The range of speed coefficients coveredin these tests corresponds to those just below and somewhat above typicalhump speeds for most seaplanes.

The shape of the wave contours in the wake is obtained from in-dividual underwater photographs of each of seven transverse rows ofmeasuring rods spaced at intervals of 1 beam length aft of the model.The detailed location of these measuring rods in the wake is g iven inFig. 2. The procedure involved in obtaining the underwater photographsof the wake intersection with the measuring rods is exactly similiar tothat used in the tests of the 20 deadrise planing surface described inRef. 1. The wetted keel and chine lengths, from which the test aspectratios of Table I are evaluated, were obtained from underwater photo-graphs of the wetted bottom area (see Fig. 6 of Ref. 1 ) .

RESULTS AND DISCUSSION

A summary of the planing test conditions for the 10 deadrise plan-


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- 5 -Longitudinal and Transverse Sections Throug h Vfake

The displacement of the w ater surface obtained from the underwaterphotographs of the measuring rods is plotted on Figs 16 through 3 9to determine the shape of the transverse and longitudinal contoursthrough the w ake For each test condition, transverse contours w eredraivn at each of the seven transverse stations at w hich rod measure-ments were made, and longitudinal contours were drawn through thearea between the planing surface centerline and 0 U0 beams outboardof the centerline. As w ith the 20 deadrise tests, the height of thewave contour at the long itudinal .centerline, and the height and lo -cation of the w ave crest were not directly measured,. However, by usingthe method of fairing described in Ref 1, these quantities were fairlyaccurately defined-

The shape of the transverse wave contour at the step station im-mediately adjacent to the sides of the planing surface (shown by ashort dashed line) w as veiy difficult to determine by the method ofmeasurement used in these testsj consequently, no reliable test dataconcerning the shape of this portion of the curve were obtainedo Thetheoretical results g iven in Fig. 2 of Kef. 3 for defining the shapeof the free streamline of the discontinuous flow past a submergedwedge w ere therefore utilized to calculate the shape of this regionof the transverse wave contours at the step. The calculated curvesfor the 10 deadrise model faired into the ex perimental curves verysatisfactorily for every planing test run.

In general,, the characteristics of the w ake contours for the 10deadrise planing surface are similar to those described for the 20deadrise bottom in Itef 1- That is,, the hollow,,, or troug h, formedimmediately aft of the planing surface first increases in depth andarea w ith increasing distance aft of the planing surface. Then, as


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R - 3 J U U- 6 -

b e a m s , and the maximum height of the wave crests is nearly 0.30 beams,usually occurring between 1 and 2 beams aft of the step. The height ofthe wave crests increases noticeably vdth increasing trim and aspectratio but increases only slightly as the speed increases. The angle be-tween the line drawn through the peaks of the wave crests and the plan-ing surface centerline, as seen in plan view, is large at small planingspeeds and low angles of trim but decreases as each of these parametersis increased. The planing speed has a major effect in changing thisangle and, at velocity coefficients of approximately 5 and larg er, theline of wave crests is almost' parallel to the float centerline.

T h u s , it is seen that reducing the planing surface deadrise anglefrom 20 to 10 does not have any pronounced effect upon the overallshape and general features of the trailing w ake. A comparison of theexperimental wake contours of the 20 deadrise planing surface g iven inF i g s . 18 through 38 of Ref. 1 with those of the 10 deadrise planingsurface presented on F i g s . 16 through 39 of this report shows that thewave contours for similar planing conditions are not very much different.Many of the differences that do exist are probably small enough to beobscured by the experimental scatter of the data. One distinction be-tween wave contours that was noticed, however, was that the longitudinalcenterline profiles for the 10 deadrise planing surface, plotted on thekeel axis extended aft, are slightly lower than those for the 20 dead-rise bottom. This difference will be discussed further in the sectionsthat follow.

Curves for Estimating Afterbody Wetted AreaThe longitudinal contours of the wake along the planing surfacecenterline are of primary importance in determining the size and positionof the afterbody wetted area. T h u s * the longitudinal centerline profiles


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R - 3 U U- 7 -in defining the centerline profile, both g roups are presented so that thesedata can be applicable w hen a forebody planing condition -is specifiedeither in terras of aspect ratio or load coefficient.

The summaries of the centerline profile curves show n on Figs. 5through 12 are quite comprehensive, illustrating the shape of these curvesover a range of aspect ratios and load coefficients at each of four sepa-rate speed coefficients. An examination of the planing test conditionslisted in Table I shows that an extensive investigation of the effect ofvariation in X and C^ w as made only at one speed coefficient; namely,Cy = 36S>. In order to establish the range of centerline profile curvesat other speed coefficients, a procedure exactly similar to that describedin Ref. 1 was employed: relations between change in wave height and changein aspect ratio or load coefficient w ere established from the test dataobtained at Cy - 36Q and then these same relations were assumed to ex istat other test speed coefficients. Thus, the height of the centerlineprofile curve obtained at a particular value of X or C A and at a testCy other than 3 , 6 9 was increased or decreased by the relations establishedat Cy = 3-&9 to derive the centerline profile heights corresponding tolarger or smaller values of X or C^ respectively. The detailed calcu-lations involved in this procedure are not presented in this report. How -ever, the relations between change in height of the centerline profile,at various distances aft of the step, and aspect ratio established atCy => 3 & 9 . are shown on Fig. 3 for each trim tested. The relations be -tween change in profile height and change in load coefficient also es-tablished at a Cy of 3 & 9 are shown on Fig. k * The test points plottedon these charts were obtained by transforming the test data g iven in thesection plots on Figs. 16 through 3 9 to the coordinate system, using theplaning surface keel, extended aft, as the abscissa. It w ill be seenthat a linear variation exists between the aspect ratio or load coef-ficient and the centerline profile height at any distance aft of the plan-ing surface. The wave height increases with increasing aspect ratio or '


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3 h k- 8 -trims, but decreases -with increasing planing speed.

In applying the curves on Figs. $ through 12, a linear variationmay be assumed to exist for all variables. Thus, by linearly interpo-lating between the appropriate curves, the shape of the centerline profilecurve may be obtained for most tw o-step planing conditions that may bespecified. Having thus determined the shape of the longitudinal center-line profile, superposition of these profile curves on the lines of theafterbody will indicate the size and position of the afterbody area incontact w ith solid water in the w ake. By combining the w etted area, localafterbody trim, and planing speed w ith appropriate planing force equations,an estimate of afterbody planing forces can be obtainede

Effect of Deadrise Ang le on Centerline Profile Through WakeA qualitative discussion of the effect of deadris(e on the over-all characteristics of the wake contours has been presented in the previ-ous sections. It has been shown that a reduction in planing surface dead-rise from 20 to 10 does not have any pronounced effect upon the g eneral

shape or features of the planing surface wake. Nevertheless, since thecenterline profile through the wake is of primary importance in determin-ing the area of the afterbody in contact with the w ake, a more detailedinvestigation of the effect of deadrise on the shape of this curve hasbeen made. A comparison of the centerline profile curves w as made at thefour test speed coefficients and at an aspect ratio of 3.00. This largeaspect ratio was used as a basis for illustration since the profile curvesare highest at the largest values of aspect ratio tested, a conditionw hich tends to minimize the effect of the experimental scatter of thedata.

Prior to investigating the actual centerline profile shapes, a


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- 9 -Fig. l ) . For the reasons previously presented, the comparison is madefor an aspect ratio of 3*00 at each test trim and speed. A similar com-parison plot is not presented for the centerline profile curves at equalload coefficients since it is believed that the effect of change in dead-rise angle will be the same at either a constant aspect ratio or a constantload coefficient. It is seen from Fig . 1$ that the shape of the profilecurves is generally similar for both deadrise surfaces and that most ofthe 20 deadrise curves are slightly higher than the 10 deadrise curves.Although the difference in wave profile heights is small, and might beconsidered by some observers to be within the experimental scatter ofthe data,the consistency of these results leads t6 a corroboration of theconclusion that reduction in deadrise angle will reduce, to some extent,the height of the centerline profile curves. For all practical purposes,however, the effect of change in deadrise from 20 to 10 can be re-garded as negligible.

CONCLUDING REMARKS

The 10 deadrise wake data, which are presented in the form oftransverse and longitudinal sections through the wake for each test run,indicate the following:1) The general shape and features of the wake of a 10 deadriseplaning surface are basically similar to those of a 20 dead-rise planing surface:


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R E F E R E N C E S

1 * K o r v i n - K r o u k o v s k y , B .V # S a v i t s k y , D a n i e l , a n d L e h m a n , W i l l i a m F . t" W a v e C o n t o u r s i n t h e W a k e o f a 2 0 D e a d r i s e P l a n i n g S u r f a c e " .S t e v e n s I n s t i t u t e o f T e c h n o l o g y , E x p e r i m e n t a l T o w i n g T a n k R e p o r tN o 3 3 7 , J u n e 1 9 1 * 8. S h e r m a n M . F a i r c h i l d P u b l i c a t i o n F u n d P a p e rN o . 1 6 8 , I n s t i t u t e o f t h e A e r o n a u t i c a l S c i e n c e s , N e w Y o r k .2 # F r i e d , W a l t e r t " T h e N o . 3 T a n k f o r M o d e l S e a p l a n e T e s t s " S t e v e n sI n s t i t u t e o f T e c h n o l o g y , E x p e r i m e n t a l T o w i n g T a n k R e p o r t N o 2 8 ,O c t o b e r i &

K o r v i n - K r o u k o v s k y , B . V ., a n d C h a b r o w , F a y e R #t " T h e D i s c o n t i n u o u sF l u i d F l o w P a s t a n I m m e r s e d W e d g e " * S t e v e n s I n s t i t u t e o f T e c h -n o l o g y , E x p e r i m e n t a l T o w i n g T a n k R e p o r t N o . 3 3 k , O c t o b e r 1 9 U 8 .S h e r m a n M F a i r c h i l d P u b l i c a t i o n F u n d P a p e r N o . 1 6 , I n s t i t u t eo f t h e A e r o n a u t i c a l S c i e n c e s , N e w Y o r k .


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R - 3 U U- 1 1 -

TABLE I

n No."123k567 .8

91 01 11 21 3Hi1 5

PLANING

, T x(deg.)kkkkkkkk8888888

TEST RUN> OF 1 0 (Beam = 0.X

0.8k0.861.231.321.362.292 . k l3.360.30O.kl1 .111.122.222.222.35.

A(lb.)1.253.20i.k51 .921 .063.252.323.20

k.k51.883.kkk.5k3.775-k37-16

DEADRISE P UNINGkl6 ft.)

V(ft./sec.)13.5019.99 '13.5015.5211 .0216.0213.5013.5019.9913.5013.5015.521 1 . 0 213.5015.5213.50

SURFACE

CV3.695-k73.69k.253.02k.393.693-&9

5.k73.693.69k.253-023-69k.253.69

CA0.280.710.32O.k3O.230.72O.52O.71

0.99O.k20.771 .010.8k1 . 2 11.591 .61

0 .0 .0 .d .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .

c LO klOk8Ok7Ok7052076076105,066, 061.DJ.2.112 1 8k.178.177.237


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R - 3 4 4- 1 2 - EXPERIMENTAL TOWING TANKSTEVENS INSTITUTE OF TECHNOLOGYHOBOKEN, NEW JERSEY

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EXPERIMENTAL TOWING TANKSTEVENS INSTITUTE OF TECHNOLOGY

HOBOKEN, NEW JERSEY-2.0

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4 BEAMS3 BEAMS"2 BEAMS1 BEAM

4 0

6 BEAMS

5 BEAMS

4 BEAMS

ASPECT RATIO (X) 4 0

10 OEAORISE20 OEADRISE

-< -

5 1 J

6 BEAMS

5 B EA M S^

4 BEAMS

2 BEAMS

IB EA M

FIGURE 13 COMPARISON OFRELATIONS BETWEEN fc PROFILE WAVEHEIGHT AND ASPECT RATIO FOR 10 AND 20DEADRISE PLANING SURFACE AT Cv = 3.69


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E X P E R I M E N T A L T OW ING T ANKSTEVENS INSTITUTE OF TECHNOLOGYHOBOKEN, NEW JERSEY10 DEAORISE20 DEAORISE

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.5 0 1.00 . 5 0 1.00 1.50.00 1.50 1.75 . 50LOAD COE FFICIENT, C AFIGU RE 14 COM PARISON OF RELA TIONS BETWE EN (fc. PRO FILE WAVE

HEIGH T AND LOAD COEFFICIENT FOR 10 AND 2 0 DEADRISE PLAN ING SURFACE AT C v = 3 . 6 9

2.00 2.50 2.75

4-


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R-344- 2 6 - EXPERIMENTAL TOW ING TANKSTEVENS INSTITUTE OF TECHNOLOGYHOBOKEN.NEW JERSEY

1.50

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DISTANCE AFT-BEAMS

= 4.25

10 DEADRISE20 DEADRISE

= 3.69

= 4 '

DISTANCE AFT-BEAMSiI 2 3 4 5 6

= 5.47


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TRANSVERSE CONTOURS LONGITUDINAL CONTOURS

M l I I I I . 1 1 I I3 2

DISTANCE FROM - IN BEAMS0 1 2 3 4 5 6HORIZONTAL DISTANCE AF T OF STEP - IN BEAMS

FIGURE 16 EXPERIMENTAL WAVE CONTOURS AFT OF STEP' T = 4 A * 1.25 CA = .28

V = 13.50 \ = . 8 4 Cv s 3.69RUN NO. I

m52

5 2 ovS

7


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TRANSVERSE CONTOURS O EXPERIMENTALA EXTRAPOLATED

I l l I I I I I I I I I

LONGITUDINAL CONTOURSi iLEVEL WATER ALONG

0.2 BEAM FROM

0.4 BEAM FROM

mxvm115im

ALONG WAVE CREST

DISTANCE FROM - IN BEAMS

FIGURE 17

I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I0 1 2 3 4 5 6HORIZONTAL DISTANCE A FT OF STEP - IN BEAM S

EXPERIMENTAL WAVE CONTOURS AFT OF STEPT = 4 A = 3.20 C A =.7 IV = 19.99 X = .8 6 Cv 5.47RUN NO. 2


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TRANSVERSE CONTO URS LONGITUDINAL C O N TO U R S

3 2 IDISTANCE FROM $_ - IN BEAMS

0 1 2 3 4 5 6HORIZONTAL DISTANCE AF T OF STEP - IN BEAMS

FIGURE 18 EXPERIMENTAL WAVE CONTOURS AFT OF STEPT = 4 A = 1.45 C& = .32V = 13.50 X = 1.23 Cv s 3.69

RUN NO. 3

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