Hydrodynamic Design of Planing Hulls - Savitsky

The elemental hydrodynamic characteristics of prismatic planing surfaces are discussedand empirical planing equations are given which describe the lift, wetted area, center of pressure, and porpoising stability limits of planing surfaces as a function of speed, trim angle, deadrise angle, and loading. These results are combined to formulale simple computational procedures to predict the horsepower requirements running are trim, draft, and porpoising stability of prismatic planing hulls. Illustrative included to demonstrate the application of the computational procedures. l FUNDAMENTAL research on the hydrodynamics of planing surfaces has been actively pursued in both this country and abroad for well over 40 years. The VLL~ULCH ImpeljUS for this research was motivated by the of based aircraft and to a somewhat lesser of planing boats. In recent ever, research emphasis has been on with application to planing boats and 2 Numbers in brackets designate References Cf = friction-drag coefIicient V j 2Ab2 wide attention followed by Sedov [5 researchers describing the dead rise end of paper. D f cos f to gravity, distance between T (measured normal to Ib = lift coefficient, zero deadrise, = V 2b2 lift coefficient, deadrise surface, CL{3 V 2 b2 = Cp = dynamic component of lift coefficient hn,",ur,n+ component of lift coeffiOlS"LaIICe also D due where b Df = to rnc:1JlOml.1 D' COS'T 1:1 sin a keel, ft 'T 1964 Reprinted from MAR!NE TECHNOLOGY, Vol. 1( No.1, pp. 71-95 CG _)..b-- '---_~IP-"---V Fig. 1 \'7 ave rise on a flat planing surface LEVEL WATER SURFACE SPRAY THICKNESS u.s. of Stevens Institute of undertook of the a theoretical study .and phenomenon of planing. study produced 16 technical reports (listed in the Appendix), which consider planing-surface lift, drag, wetted area, pressure distribuspray tions, impact forces, wake dynamic stability, and parallel surfaces. 'Vhere possible the ONR sponsored utilized existing planing data and theoretical results but in many areas additional results and new theoretical were provided the Davidson In 1949, Korvin-Kroukovsky and lished a summary report on the then of lift, drag, and wetted utilized these results in deVelOrnng tational procedure for In Savitsky ONR study, developed an extensive \vhich increased the -,--"'-"'VV.LunJV STAGNATION LINE Fig. 2 Typical pressure distribution on Rat The planing coefficients used in the subsequent analysis are based on law of similitude and are the same as those used in the of waterbased aircraft and Each IS cally defined in the seetion on nomenclature. It ,vill be noted that the beam is the dimension i'ather than the considered the naval The USl:,mC;alJJlOn for this is that for of the boat varies with the wetted )J.la,HH.lF, UU,ll.lV.l.l0 Area of Planing Surfaces In The purpose of the suIts of the studies [9] to characteristics of faces and then to combine these results to computational to power requirements matic planing hulls. Some the material is repeated in this paper since had a limited distribution and is out of print. of Prismatic A knowledge of the elemental istics of simple planing surfaces the design of boats. In this section of the to the of characterIS , surconstant assumed to have constant beam and a constant trim for the wetted Variations from conditions will be the 72 surface "'""" ..HF,u,""vvu over water pressure is forward thrown spray this sense is .l Z o o w (j) « m 2 ~------------4-------------~---?L---------r-----------~ o « I- 2 A= 1..60 Al A Al and The + 0...0. Here A the mean 1vetted and Al the calm-1vater length-beam ratio length-beam ratio obtained horn the relation Al sinT) where d is the of the of the 1964 I A 1.30 wave-rise relation is (0 ~ Al ~ 1) (1 ~ Al ~ m form of ..9 Z W -. At very small values of trim the line and root line are coincident.30 AI (0< 0::: { :::?! (1~ + 0.surfaces at a short distance aft of the line.. As the trim creases) the line moves farther aft of the sprayroot line.60 A...l w > W -.-0..l o W lIW 3: o ~~~~~~~~~-L~~~~~~~~~~~~~~~~~~ o 4 3 2 WETTED LENGTH-BEAM RATIO BASED ON WAVE RISE Fig.30 « I) AI ~4) w m I :r: I<.. 3 A Wave-rise variation for flat .-----------~ w () « LL 0::: ::J (f) 0::: W ~ 3 ~------------~--------------+-------------~--~r-------~ -..30 0.4 ~------------~------------~--------------. .. data from all available SOurces are shmvn in the form of A versus Al in 3.. HINE 8 c ON 2-- .--_ _C~... 00 (J) :?! <! W ill 1.Lc versus trim and deadrise two equations since..J.lJ''.J . usually than duced to very = Al empirical wave-rise nr.J..00 r----. also As with all some bound must be range of applicability of discussions in [9] conclude that is in the trim range from 2 to CUfJIJUvCU11J1v 24 . 0.--y--.00.Y\ similar in form to was J. 6 Lk . 2. Wetted Pressure Area of Deadrise In the case of section of the bottom surface with Surfaces the inter- two oblique lines and 4.>.0.J.3. The location of the line is seen from underwater such as that shown in It is generconvex.---. SPRAY ROOT LINE 2. A :::.:-----..vater surface the spray root line ahead of line of calm water intersection.__j. :::.--------------.3. to a trim 15 deg there appears to be no nOtlc:eaOle of water at the keel line..00 1-----\-_+_4--Jr---l~-~:____+_--~.J.50 0 -l I ~ -l /. DEGREES Fig. 4."n+".60 :::. but found that the since the curvature is Thus the of a measured HJJ.---. For trim '-'~J''''H."" UJ.---- o 4 8 12 16 20 TRIM ANGLE.''''-' and indicate a water at the keeL Aft of the initial there is a rise of the . .01 Gv Gv Fig.7 Variation of shape of the transom to the The difference between the chine with of wetted area with speed coefficient. T = is defllled b T . in.Cv = Cv 2. .:' Wetted-Spray Area of Deadrise Planing Surfaces The total wetted bottom area of a surface is actually divided into two is aft of the spray-root to as the area and the other is forward of the e<"""O.UW1."' . 6. and nel:LQI'lSe [13].lv then the mean wetted fines the pressure area is d jJJlGLl1.J. This of 4 and at five values of The calcur = 17° It is seen at 3.1tvH. The flow directions in both wetted areas have been determined of tufts such 4 and 5 sketch of the flow direc8 of this Y'r'AT .U 1964 that the to break- where: measured in A 1 . To an observer located between these two planes. area contributes to but is not forward to support any of the load.:.'.66b.J1.. the passage of the prismatic Vee planing surface will identical· to the vertical of a the case.02 and the spray-root line is one continuous line and the value of with that com1.v1.Gb11.vU> . ment of the keel which would section with the bottom.U.vl.'I.. and found that actual wetted width of the was times the wetted width defined the calm-water intersection with the bottom. pnen1011'len. ..on is in evidence "".I'he wave rise in the spray-root area is accounted for the consideration...nT portion of the line is reduced.. 4°.'l1JlGbtJ. the wave rise for a two-dimensional a fluid surface vertically.V1J1. the sprayroot formation to break down for a deadrise. 6°.1..1Jl.:. This indicates a and water full of the deadrise surfaces of 10 <._.UC.1l1'>..0.. The root line forward to tween the keel and spray of the bottom is tan <I> llla .J1.:JAjJvJl..~~r"~ l. IvQ'Ul. and the difference between wetted keel length and chine length for a surface is given by b 7r tanT It is seen that this is a factor times the corresponding length defined the level-water intersection with the Vee planing surface.l1. It for = 1.0. the wave-rise factor is applicable.0. than those breakdown of the spray-root evidence for 30deg deadrise surfaces similar effects except at = 1.. Since the wetted keel defined in terms of the draft of the aft end of 1. A.UJ.>.. A of this is given in Fig.0.-vUl.va. the trim is reduced to a value such that theoretical value of to 1.Hv at = 1. the a broken line forward ~A ·.0. which de- b evidence indicates that for deadrise and trim combinations coefficient is than 2. the formation breaks down when T ::::..J.0 and T ::::. The motion of deadrise surface can be represented as a the water flow between two of of the planing surface.'O..1. = 1. ferred to as the The pressure area) has been defined sections of this is the load-carrying area of the bottom. be recalled that the fluid-flow directions over PA""''''O area of a combination UU~UH~~J flow across both ..'l.HF1 run) it is to intersection and the the chine.J.JUJ.:".JlJ. total along the Lift of Flat Surfaces projected on a plane 1 4 tan<p In making visual observations of the wetted chine 1-'H"'U~.TAND:: TAN q) COS f3 TANT TAN a:: TAN f3 FLOW DIRECTIONS' SPRAY LINES SPRAY EDGE LK VIEW OF BOTTOM ON PLANE PAR ALLEL TO KEEL Flow direction along planing prism and extent of spray area and The. 9 illustrates It is seen that the of the u.UW'U Lift of Planing Surfaces discussions \vill first surfaces and to account 78 and static effects. /."" ..1 power.Characteristic features of vee-bottom surface. b) mean wetted of trim r can be written (11) that (A C011- OCTOBER. Hence for a normal low lift can be in the form CD) = AT + tanr If the difference between tanr and r1..U"" Sottorf's analysis of. ~"""+. B-transom. .. G-spray-root region DAn For surfaces of very small span A the flow is in a transverse direction and lift is r.. C-keel.l<-<>UJ."'..lll.1 is rll::. D-chine."""·:C' 1 hydrostatic term is HV:F-.lit:.-. The form of jJ. 1964 0. H.::.F-. nr"n""rl lift and is The constants and n are the formula to the collection of pH111lng data contained in the literature. spray.c.... The of lift for a flat A....Ll5. Hl~'U-.l V .I. I-Ienee 1J.U by r to the 1.·I. The mechanics of this evaluation are described As a result of this the for a where is a constant to be determined.. edge.rj can be written BT2 For the range of A-values to the second term takes the of a srnall correction to the first term and it is found that can be VA.llll''. trim the varied as to be of the form: + there are several ways lift.60 :::.iQ. 50 14 18. 10 3.t---t----+--+----Tt----:.".0 Fig.35 10 12.I 2 2.18 13 16."u>uU"6 surface.0120 2 ) + 0.0.01 T 1. coefficient for three The solid curves since this is the range of between the load is limited to of .r<-i:------.03 - TI.87 12 15.14 9 II. {3 is in a wide range of this at a fixed value of ~ contribution to lift is surface at very low 2.67 \-----j------t--------.98 4 4. 21 3 3.59 II 5 5.0 Lift coefficient of a flat planing surface.1 (0.59 13.85 15 19..23 8 9.39 6 7.J 0.04 0.80 7 8. "" o U .7""--1 f-.05 TO TO 0.0 4.0055 o ~~~~----~----~------~----~----~----~----~ 1.0 0° the resultant lift and that corstatic lift !-. LlJ.06 CL 1 OCTOBER. GAI.4 0.c----l 0.-L 0. 0.00.----..01 1------+- 0.. approaches zero.---.05 1--------+---+-----+---+-----+---+--"fIL--~-_"tif!.07 I__----+---~----J----L---~-----+-----+_- =c La -0.----..----..L---l 0.----.. it is lated load should 0.08 Lift of Deadrise Surfaces trim and mean wetted In(3reaS]nQ' the deadrise IS .2 0..!---=- 0..5 0..... the motion of the surface reduces the lift below the value whjch would be on a purely basis.-0.03 I------+----+----+---_f----"L----+-"r£---.4£~.1 0.£-:::-b.~--+-------+-----l u 0.. bottom increases mcreases.. 0.5 .09 .f---I_---I 0.3 0..!£----.0.yhat similar to vessels at low load is load.LA 0.----+---I---.----.---.3 1----I----+---J---:T~Sf_:."'H.02 0.10 a Lift coefficient of a deadrise planing surface that the calcuload.60 ~ ~ 1.2 1------+---+--.----. It is 12 that in the range 0..--..-L-----l 0.02 I-----+----I--.F.4 i------t----+---l---+--yL.-----+----I--"r£--f--:.1 0..06 I__----+----r----.-------.. This effect is some'.----.-------. reaction of the fluid as the on the 1-'H...0065 (3c La __I__~-+~L-~ 0.08 I----+---.60 0.04 0.------...JGvUGu. l. A) and as U.30) TANT 0.._--'=_-'-_.0120 \ 1/2 Cv 3 2 ] + 0. at the same .--TOTAL PLANING LOAD=6/1/2Pg ::: T 1.20 0.1 [ .1 o 2 3 Fig.50 1."s=.. For convenience in use) 11.~· T.80 0.0055 2 b=(\-0.00 2.40 0.40 0.20 2. of a deadrise the lift coefficient of a Vee was with that of a flat It was found in of r. .30 0...60 1.lU>'JV where 82 2 Planing load versus calculated displacement load for a flat planing surface at various velocity coefficients creases so that full pressures are no developed. N "- ""<J o '----1_--1.l(.EQUIVALENT DISPLACEMENT LOAD=l}.~\J'-' is m .. A.20 0.lUv >JLli._--1.80 1.11I2 0. and lift of a dead rise surface can be ref)re:se11tE~ci (3 00 lift coefficient for a dead rise deadrise ".. the presence of causes the line to be aft and leads to a lift reduction not unlike that on a swenL-r)~WK To formulate an the U~U'UH.~.~"n+.40 0..80 0..00 0. hence the lift is reduced.-"evU.. In effect then. 12 o ~~--~--~--~~--~ o 2 3 ULU.60 1.20 0.40 f'I) -0 en Q.70 lAO 2.10 0.60 0.~. .-1..1....+... between the free-stream conditions and the '"'~/"'...".. TANr l':!.-.. 13 load on the bottom is The (21) The average Pd pressure is 'Ab 2 cos T Applying Bernoulli's A.due to · to the bottom the resistance 13 to be pressure forces is shown in ~ tanT to the bottom 13 to be vVhen the viscous the total IS ~ D tanT + COST [9 J to be com- The friction C01llDon ient the 0) FRICTIONLESS FLUID where Schoenherr [14] turbulent friction coefficient = average bottom velocity The bottom D=l':!.. 1964 FLUI D Drag components on a planing surface r .O'-' b) VISCOUS Fig. TANr from was based the case of a zero tribution to lift is to be U"""..''''f' and conditions on the bottom of for!3 = 0° The average bottom is in an coefficient for deadrise surfaces The ratios have been for four dead rise and the results are 14 in a convenient form for use the It will be used in IS OCTOBER... ... there was appr<)Xlm2~tel values combination. If is defined to exist when the fluid breaks the transom and Cer)tlo'n of can be > 4° and at = 2°.2'1Jl1-Dlea:m and comAs for T stant when was suIts of this corl1nlLlta.. 1\1ean wetted len..... J:'H.rl 84 has been used to the ratio 10° and 20° deadrise surfaces at trim and 8 0. At T > 2° and at > 1..where is plotted in turbulent-friction cO(~rnClent.nn' the second term of the for T12b2 results 111 D L1 tanT + variations in curve for of A and I t is each test trim over also seen = 1 there is a very rapid increase the ratio for all test trims.U~~UJ.... defined.r\11T of five different VV"HVJ. Each "0.\JUU age.'.tlO the effect of lift ratio. It is evident from 16 that for any there is an trim for lowest ratios of Small decreases in trim below the ontm1UIl1 . and Cf is the Schoenherr The number is js the kinematic UlC.'·nT'. 1.~"UUb occurs when the rlrd...nr.00 the of flow from is force is increased and hence the ratio until complete flmv has occurred chines and transom. For more exact values it is recommended that detailed evaluations of be carried out for specific cases. of the fluid from the chines and at :::. the ratio stant for any combination of For T = 2°.the curve of constant value for ratios of The above variations of can be associated with observed of the flow conditions around the It vvas found at > 2.C.o.t-u An exact definition of the The Drag-lift Ratio of Planing Surfaces From surface can be calculated as D tan ratio of a + T rtnr1E'".0 there Qt:n-.. l..I. is assumed to be 33 are These distances are. foregoing trends in resistance variation with trim and deadrise have been shown by in cross plots of their specific test data.90 >- /3 0.""U..00 1. of course. the results of computations and includes a of the fact that Dill ratios -for a trim essentially independent of various combinations Ix providing that ~ 2 for T = 2°.T" >J~'~""'"' limits is defined as the combined oscillations of a and in of sustained or . A between and actual test data is 17 of reference Excellent the formula and data..00 2.l.00 in the this paper..r.90 T= !----==--~""'-----_+_----+_---___1 /3= 20 0 2. .80 1./\'.d. 964 3.v. and force '-"'-'\. . 0..co·.rl of the transom.Tr. the 1l10ments taken about transom for each cornp(ments of the total load and then rinnri'.'o.nO' .. The center taken to be at of pressure of the 75 percent of the mean wetted forward of the transom..21 Ix 2 + 2.r\'Y'c.. while the center of pressure of the force forward of the transom.00 3.U.h..00 1.. . 0.-"'oc'c>n't.39 where is the ratio of the distance from the transom to the center of pressure divided the mean wetted length...'" +rn'nu". ...-' UU..00 A Fig.VI AVERAGE BOTTOM VELOCITY V FORWARD PLANING VELOCITY T > "'-. '>'"""'. the tan r and the curves due to viscous that at low trim the total friction pressure for f3 = 0 is one pressure and one friction drag. coefficient are value determined from this chart.00 T= "'>-. and for T ~ 4° Center of Pressure of Surfaces It has been shown in [9] that the resultant center of pressure of planing surfaces can be evaluated considerations of the and force of the lift.... 1 5. OCTOBER.r\Y) for the distance . 14 A Magnitude of average botton velocity for a planing surface tan r which is the The difference .. . 17 of this paper.Ll...V _U. 30 T=6°· f-- 0.60 T=2° 040 {J =20 0 OIl:.0 CV 0.0 4. 15 Variation of drag-lift ratio with speed coefficient of certain be obtained 36 derivatives which could In the eXT)erllmEmtli.0 I ! 2.lm!~ntal1} .0 3.! eXl)er. f-- 0. r- I I VI I 0 I 1.0.30 - T= 4° 0.0 Fig./0 0 Vr T=15° ( ~/ f--L OIl:.10 0 i / T=IO° '-- -I V I I VI I l I I 0.20 0. b= 9" 0.20 OIl:.20 4. to avoid ... DEGREES Variation of drag-lift ratio for prismatic planing surfaces of tests of constant deadrise to determine The . .. as the lift coefficient is rlPI"l'p>1c:...0.. is to move If this cannot be and if the addition of a small transverse bottom at the transom 'will Imver the a small cost in added resistance.0 Method for Prismatic ..h'":rr. DEGREE S Fig.04 PRESSURE DRAG PRESSURE DRAG 2. It was shown 16 that a trim of 4° to 5° reDOrD()ls]~ng limits In as 1 ° to 2° to achieve boat. combinations of which the limit curves indicate stable operation while those above the line indicate the existence of porpoising.~'rj loaded hull T inertias.0 TRI M ANGLE. as a guide hulls.0 8.-. :::::i 0.'"\<:". It is seen that. "". . because of the boat at an n. which surfaces.20 0.16 <J '- 0 0.12 I VI SCOUS DRAG f- lJ. 16 6.'.08 I t9 TANT TANT « 0::: 0 0..vith the trim results in minimum resistance. It may of this compare 1964 4..0 TRI M ANGLE. No consideratiori was to the effect of propeller thrust on the hull lift and moment and. the pressure is much DuCane tions of the hull at a of location. ft For Vertical1CJu"IhIA..Q1"l 88 s1nr COSr = 0 .OILH moment is the viscous can be assumed the center of of EoebePs are included in this paper. "'. since porpoising information was time availlimits were not defined. The Dl'!eSEmt.LUI D.to speed ranges and for al'biand inclinations of the shaft line relative to the center of of the In [8] a procedure for which was based on the elemental available at reference (7].ed in this paper on much lower speed coefficients and. a DTIVIB. Clement of boats " " T n .Ib a = distance between and CG ea~3lU'ed normal to ft j = distance between T and CG .\A normal to shaft ft c = distance between and CG -'U'-''-''''-''~U'-''--' nonnal to ft fJ deadrise ft b € ili..U. mornents and center shows the where T= D.A thrust.ed In the perare similar in conditions those transom to spray root ft tral1sorn.. in addition. lb = CG = inclination of line relative to resultant of pressure forces to bottiom.-.. There are in the literature test results on related series of planing boats which provide excellent informa-tion on families of specific hull Davidson and Suarez present the results for Series 50. method involves the determination and \vhich will for TH'lQn-.-. '" n·"o"n+"n presEmt. lb of boat.o Forces: = Slnr For Horizontal Forces: T J11oments: a - Performance Prediction of a it be a mernber of a tested series.. 5 10.85 . I 10 at Transom d = Lk sinTe = 55.340 5. 1: .069 5 = 1115 hp 6_7 _. (10) /cOH 2094 7340 __ ..760 11 tan.60) 10 = 3.0 FT ':0.000 89 4600 336 600 .8304) 10 D = 9095lb "'0.1 Cf T 'T I Wette.85 67.89 29 Dda .1392 .2. 2.00232 7.d Chine length .73 645. Figure II Draft of Keel 0.86 66.0524 13 14 co'!'!' ·2~ ___ .1045 9964 .70 'leG - I 24 (23) (cofr) 25 f sin.9 X tan 2.0185 2.85 . (25) (a .3° d == 2.b/v Schoenherr ATlC Stands'd 6.(3.60 1. _----::c-::- Equilibrium Mean Wetted length-Beam Ratio 3 At = 3.085 (2) / (1) .59 5.000 L8 b :: 14FT (AVERAGE) j3 :: 10° V :40 KNOTS (67. 35 (24) . Cf (]) (8) pl~b2( :f + 6 :f) 2 CO'l/3 3..70 18.6 23.0349 .085 .00224 .500 5.53 332.l 1:1.1 ft = 0.001]4 40 . Horizontal Drag Force 3 ::60.9986 3144 5160 tllln.00184 108 1.00214 . Of/COS'!' 0 (14) + (15) 94J 8304 7948 17 Cp Figure 17 . ..(9434 .616 616 616 (20) 1. ]0 CLa Clo/'!' 1.9976 4188 3760 15 16 f}.3~t .. .0004 .0349 -2.085 315 .1219 (12) (22) .14 . Source .960 0174 0352 .. 4 5 b I tv Quant 3 Wetted Keel length Lk Row c LeG .f .0524 .0 3.0698 .990) -2.5 FT/SEC) V=40 KNOTS (AVERAGE) D = 9424 .50FT PORPOISING LIMIT VCG"2.0698 12 lIn. 39 1.8 19 20 21 OCTOBER.(25) 27 28 6. Flqure 10 Figure 14 Vm 6 II!! 7 Cf 9 Cf -LCI Vrrl.2 -2.0345 1 / 2 1: .0 FT €" 4° fj.Table 1 drodynamic Planing Hull REQUIRED: EQUILIBRIUM TRIM (Tt ) at which (30) = 0 line AR interpolation' between and T = 3° Osl39FT POWER REQUIREMENT LCG=29.(18) (b/4)tanB II 22 $ln('T+~) 23 I .0397 .025<4 ).000 10.89 3350 __ 648350 .61 x 108 .46 10.59 .3~ I .24 ft "'.65 18 Cpi--b 31.6 -156.5 .6 66.s n'T sln('T + c) .f) (10) (28) 6540 .9964 .f) (21) ..0349 .6 5.1Q (27) + (29) Eq 35 149. ..7) .160 ..2 108 2.29 = Aeb + ::---- Lc = Aeb - b tan = 36..00192 .42 .186 It 59 2.. 22 x 10 8 . 9 10 A.b 2 II Re Cf 12 13 14 vn.039 8 l::J. .069 Row 1 2 3 4 Quantity CLa 'pI A.5 FT/SEC) =0.07 2. the tional as follows: It can be shown that 90 Spurce Figure 11 LCG/b 2 f3 6670 6670 .1 5 6 Value .23' 7 tan.00177 .00217 l::J.f) 15 Of 16 17 Of/COST D (8) + (17) 9010 18 19 EHP Ox V/550 1100 JCLf1~ 20 7 pO'poising procedure is recommended. Cf Schoenherr ATTC Standard l:l"""nhn<>"<it (12) + (13) p"~b2(f 66.45 (1)/(4) 2.340 0) b 2 ~. 'f Cf + lJ.1+2 1" 2.186 FIgure 18 «4.085 Igure 19 Figure 19 3.\Jtan.000 LB LCG = 29.0 FT POWER REQUIREMENT PORPOISING STABILITY VCG= 2.9 3.5 0 COSE LlL~tHVl10 = are cos E =1 ./! 675 Figure 14 Vrrf'-b/v l::J.Table 2 Computational Procedure Hydrodynamic Performance of Prismatic PlanHull When all Forces Pass Through CG) !J.0 F T = 14FT (AVERAGE) b /3 V = 10° (AVERAGE) = 40 KNOTS a = c= f:::: E =0 V= 40 KNOTS (67. 2. . 60. CLoh 1• 1 '11.0004 . ... C =0....u E) that ·LtctLJIVLl....75.......' . ..80 II 0.20 1---- .. .t .1.21 +2.......' ...\Vhen T) c) and in equilibrium and the are then evaluated. ...........39 0.....L o 0:: W lZ W U 0. { ... .1~l~C the shaft axis is is assumed that E o can Case When Thrust Axis and Viscous Force Coincide and Pass General Case Through Center of to achieve and care OCTOBEP......... sinT + condition in their The moment c. 1964 I t is assumed ..COST the conditions of O...... There are wherein these o .+ .r .40 l...P 5.l . . U 0...'>"=Lm/b N= RESULTANT OF NORMAL BOTTOM PRESSURES o 4 3 2 5 N 6 7 8 9 VELOCITY COEFFICI Center of pressure of planing surfaces 17 N SO COST + 6... COST and into 6..00 .... f = c Performance Prediction etnlods--U:::>moultatilonal Procedures Case }Vhen Thrust Axis is Pm'aZZel to Keel U.. ...60 0..v")...' .. and Columns 3.'lULi>. for estimatDraft of keel (d) boat. The last line of this tabulation contains the of L1 value of for each of the trim Propeller shaft line location E) between the and Center of location c.urrled trim b) Dimensions and lines of boat angles. 4 Given: 5 are the computed value each of three as~.lnple is worked out. Required: calculate Running trim area.35 Porpoising lImits for prismatic planing hulls by a mathematical foril1ulation or initial information is ". The Power the Porpoising stability limit The detailed computational the values is trim co 111eX~l.30 0. is obtained results Speed of boat. w .25 0..:::: It will be conditions for force and moment value of trim angle that makes Case When Thrust Axis is ParaJfet to Keel zero is the required solution... resistance and power vVetted length Total resistance "'Y'r'l'ln. The ~la.. Column 1 in Table 1 is the this Oolumn 2 is the source 92 .---------r--------~------~--------~ 10 REGIME OF PORPOIS ING U) w 8 W 0:: (!) W 0 ' .rl the plots contained in this . 18 0. boat is is to assume several values carried out for the entire the restriction that . IS the The to be evaluated..rll1"-C.10 0.15 Fig..r..12 r--------..J 6 (!) Z « ::2E a:: I- 4 REGIME OF STABLE PLANING 2 0.r..20 0. 1964 ~l liLI Jlll 7 8 II IIII 9 ...8 .6 2.0 P/b:: I- 3.6 2. 19 Nomogram for equilibrium conditions when all forces act through CG Case When Thrust Axis and Viscous Force Coincide and Pass Through Center of Gravity For this condition the emwetted area.0 - "E 1.2 3. OCTOBER.'C.2.l"'·j"\rl.f>C\r.2 .0 . and center into one such a '\vhich is as 19 of this paper.J II --< f: o r~~ T' tIll ~~I I I I! ILl I I I 11 o 2 I III 3 I ! LIL~ ~~Li ~~~ III 4 5 I I I I 1 I 11 IIt I 6 Cv=VI Fig.1.8 2. From this the trim and wetted area are obtained without the for between assumed values of Table 2 the for the . on Bottom 1934. 14 "Uniform Procedure for tional Resistance and the Data to Full Size. 1943. tion in the Stevens Institute of. 5 L.u. ((The PlanTwo Prismatic Surfaces of Deadrise of 20° and 40°. of the and to Vee-Planing Surfaces. and Center of Pressure of Low 1954.lslng.-"". S. Froude No.". 2876." Bulletin No.u..·. The trim should be average of the keel and chine buttock lines. i (The Phenomena of " NACA translation Jr. 22 F.bearn should be taken as average in the area of the hull.. "Tank Tests to Show the Effect of Rivet Heads on the vVater Performance of a . research 10 11 H.lU>. F. 94 "The Effect of Deadrise t'Oll'Dc." Stevens Institute of Davidson Laboratory 1950. for Sea Surface "Tank of Flat and VeeNACA TN November 1947. Care should be taken to assure that the calculated and wetted do not result in wetted areas extendbow sections of the hull. relations are not for "\vhere there are extrerne variand buttock lines.L. Pierson S. on 1932. Parkinson.l-n(H'lij~LLLL ~~~'.lmn Relation February 1942. VV. I. S..ia>VVJ. UDtm. R. 13 J." NACA TN No.)) N ACA .V'VU. 15 J. B. 1-2 of 1948.v'C~!-.U'v JJ NACA TN 1938. 6 -. 16 F. In a ations in deadrise necessary area of research is to define the forces on bow forms over a range of trim These data will be of particular importance in the of hulls for hydrofoil-boat ""fJfJllv'''''u~v. 1953. S.U... 4 A.-. VV. References 1 G. of Davidson . The author is indebted Office of Naval surface research at interest in and support The many Stevens Stevens Institute of staff members who contributed Institute of too numerous to mention indito this to Prof."'~V 1952. £.U'VL 17 D. D. E." NACAReport 1355. )J Technology.'-"\.. 10. Institute of the Aeronautical New York. 1964 J O?.A 'v" . Including Test Data on a " Stevens Institute of Tank No. Institute of the Aeronautical Sciences.i.. 6 B. June 1948. L. 4 John D. Institute Publication Fund of the Aeronautical DClelJlCe. Shern1an 1\11:.:rnal 95 . John "On Penetration of a Fluid " Stevens Institute of Tank No. New York. 29 1(.. and J. {(Resistance Tests of a Series of Hull " No. and Loads )) Stevens Institute t!. Sherman Tank Report No. Ii How to Planing Hulls. New York. Publication Fund Institute of the Aeronautical 1-<"''''f'>')'1:" '-'V1\. 1\11. Tank No." vol. Sherman l\1. 382. G. Clement and D.of Cross Section and Plan Form.iXpel:mllental Towing Tank Report No. Davidson and A. David OCTOBER.-.1Vi. l::iet)telnbler Publication Fund No.-. 2 Pierson. and vVilliam F. and ('The Discontinuous Fluid Flow Past an Stevens Institute of October 1948. B. 169.-". l\1. 8 John D.. Fairchild Publication Fund No.. John D. Daniel and Interference Effects between Two Parallel to Each Other at tute of Published in -. 381.)) DT1V1B Report 1VIarch 1949. V. Stolz. 336. AIotor Ideal Series. Institute of the Aeronautical New York.. 1958. Koelbel. No. 1G8. presented at the Annual vember 19G3 of TRANS. of the Fluid Flow in the Regions of l?lat » Stevens Institute of Technology. "Sonle 1950./LlV'-'0. Jr. Sherman N1:. V. {i No. pp. dinger. Sur- Sciences.. '-''-'H:.Y) in Readers' AeTlYnautical June 1951. Blount. ilLift of Institute of Published in Readers' Forum Section . Publication l?und Paper No. D. November tion Fund Sherman 170. S. J.'. B. \Villiam Surface..un. Octo bel' 1948. P.S. Joseph A Chines-Dry Planing Body. 3 for a vVedge Institute of No. Publication Fund No.0. 28 J. and Leshnover. Institute of the Aeronautical and Lehman.. VV1Hi'-'iV. Tank No. Daniel.. 337.Ll\A:.'-". nautical Sciences. uvVave Contours in the Vvake of a 20 0 Deadrise Stevens Institute of Technology. "Test of Related 1Hodels of V-Bottom l\iotor Boats50. 10 Reports and Papers on Planing Published Stevens Institute of Technology Under ONR Contract 1 Korvin-Kroukovsky. 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