Analyzing the stepless planing boat

A

_{0! ThE NAVY}

PRNC-TpiB-6u8 (Rev. 3-58)

tab. V.

rnsc

Deft

HYDROMECHANI CS ANALYZING THE STEPLESS PLANING BOAT

0 _S by AERODYNAMICS Eugene P. Clement 0 STRUCTURAL MECHANICS 0

RESEARCH AND DEVELOPMENT REPORT

APPLIED MATHEMATICS

ANALYZING THE STEPLESS PLANING BOAT

by

Eugene P.' Clement

November 1956 Report 1093

ii

NOTATION

Projected area bounded by chines and transom., .jnplan

view

B Breadth over chines at any point

BA Mean breadth over chines, A/L

BT Breadth. aver chines at transom

Maximum breadth over chines

t

Baseline

blip Engine brake hors?power

Centerline

CG Center of gravity

CHF Draft coefficient at rest, forward; equals draft at. 100% L (Measured from tangent to mean buttock at stern)

multiplied by A/'

CHA Draft coefficient at rests aft; equals draft at 0% L

(measured from tangent to mean buttock 'at stern)

multi-plied by A/v

ehp Effective horsepower

Fnv Froudé number based on volume,

v//g]/3

Acceleration due 'to gravity

Overall length of the area L, measured parallel to baseline

LCG Longitudinal center of ,gravty location:

R Total resistance,. lb

5' Wetted surrace, 'area of (includes 'side veited area at

low speeds)

- -

-iii

NOTATION (continued)

v

Speed

V

Speed, hots

-w Density of water (weight per unit volume)

-WLc Intersection of chine with solid water, forward of O%L, ft

WLK Wetted length of keel, forward' of L,, ft

WLp Intersection

of

chine wit-h spray,

Q.rward.Q-f ft

Linear ratio ship to model

Angle with horizontal of mean buttock-at, st-cm, dg-rees,

/3

Deadrise angle of hull bottom, degrees

-L

Displacement at rest, weight of

-'7 TrIm angle of hull 'with respect to tt:i,ude a d-ra

V Displacement

at

rests volume of

Subscripts:

M,m

Model

5, s Ship

ANALYZING TIlE STEFLESS PLANING BOAT*

By

Eugene P0 Clement

INTRODUCTI ON

During, recent years the David Taylor Model Basin has towed

a number of models of planing craft in smooth water to

deter-mine resistance, trim angle, wetted lengths and wetted surface. In most eases each of these models was considered to represent

a particular full-scale boat, and the data obtained were

pre-sented in dimensional form for specific boat dimensions and

displacements0 Each mode1however, can represent a boat of any

size. Therefore, when a new design is to be developed, all models of previous designs can be considered to represent boats

of the size of the new design, and the data on their performance

can be used for guidance0 In order to do this easily the desiner needs to have the information on the previous designs in suitable

form0 The purpose of this report is mainly to indicate appro-priate methods of presenting and utilizing the accumulated

information on hull forms and model test results for planing boats to guide the design of future boats0

In this report the important planing hull parameters are defined and a convenient method of combining them in a

hull-form characteristics

sheet is sh.own0

A plan for pre.snting

model test results 1fl .a d±mensionless form suitable for

com-parison and analysis is next given0 The hull-form

character-istics and model test results are at present being incorporated in a Taylor Model Basin design data sheet, an example of which

is given0 The effects on performance of variations in some of the primary parameters are then illustrated and discussed. Also, methods are proposed for improving the usefulness of

futur model tests for purposes of comparison and analysis.

Finally a step by step design method is proposed, ar data

are presented whici. it is believed will assist the designer in

making design dec1iOfl quickly arid with assurance of

correct-ness.

* This report combines, with some alterations, two papers

presented by the author t the Chesapeake Section of the

SNAII "The Analysis of Stepiess Planing Hulls" on

_{3 May 1951}

2

HULL FORN AND HULL LOADING PARAMETERS

The primary parameters affecting the performance of planing

hulls,' in the approximate order.of their importance, are as

follows:

(a) Ratio of length to beam.

This important ratio is

defined here as the ratio of the length L, of the hull bottom,

to the mean breadth'BA, of'.the'.chines (see Notation pg ii).

The chief reason for defining the length of a planing hull

in this way.is so that only one., value, of thelength' diniension

will be assigned to. each set of lines.. If the length

dimen-sionis defined.as the. length of the, load. 'wátrline., tien a.

given set of lines could conceivably, have various' lengths

assigned to it at different .times,. depending upon the

particu-lar displacement and center of gravity location of each Instance.

(1) Size-disPlacement, or area, coeffIcient

.

The

relation-'ship, between hull, size 'and grOss weight. an be. expressed in

'convenient dimensiobJ.ess form. by:'.the"ratio 'A/V"

,. where A. is

the projected area bOunded. by 'the'.. chines: and transom:, in plan

view, and

7

is the' volume of water displaced' at 'rest..

Since

thi,s coefficient is d±men'sio'nless it yields the' same..value for

geometrically similar boats of dif fe-rent.. size but of.

correspond-ing loadcorrespond-ing.

Lt'also'yieids. the. same. value1, for two. boats

which have different'length-beaifl ratios butthe'.same area,. A,

and the same displacement.

If two 'designs having. different.

ratios of length to.beam are .compaed on' the basis. of equal

values of A/-V"

' the comparison, will be 'avalid one.;

,for, to

a 'good first approximation

(assuming .the same, depth of hull

and similar, construction) the two.designs wIll'.then have equal

hull area

equal -hullvoiume9 and equal hull, structural weight.

It does not appear' possible .'to make. as plausible a case...

for any of the other coefficients which have been used 'to

characterize the' size-displacement relationship of planing boats.

The well known d1.splacemnt-iength ratio,

/(L/iOO)3.,.and t'he

load. coefficient,

/wB, are 'the. ones most cmmoni3r employed.

The unsatisfactory result of using".

./(L/iOO)

as the

size.-displacement 'critérionmay best 'be illustrated by 'ar'i example.

Suppose that'two'sets of lines, A & B,are under c'onsideration

for a boat of given displacement, and that design A has a :

higher ratio of length to beam than design B.

Coma,rison of

these two designs on the basis of equal

i/(L/lOO)i

will then

result in comparing the, two boats at the same length and

dis-placement.

Compared in this manner, however, design B has

and similar construction) more hull volume and more hufl structural weight than design A. These differences will clearly preclude a valId comparison. A similar confusion would result if he two designs were compared on the basis of equal /wBx

Cc) Longitudinal CG location, It is considered

appro-priate to define longitudinal CG Location as the distance of

the CG from the centroid of the area, A, expressed as a per-centage of the length L.

Cd) Deadrise., Deadrige angle of the hull bottom generally varies from a large angle near the how to an. angle of a Tew degrees at the transom0 The variation of this important anIe

throughout: the length of the boat can be indicated by approxl-mating eac,h section of the body plan by a straight iin& (see Figure' 1) and then plotting a curve of deadrise variation

versus boat length, Examples of this curve, for three different designs,: are shown in Figure 2. The variation of deadrise angle

with boat length eneral1y gives very nearly a straight. line for

the after half of the hull

length0

'Ce) Longitudinal curvature. The longitudinal curvature of the hull. bottom is shown by the shape of the buttock, lines.

For purposes of comparison and analysis it is desirable to

define an average, or mean buttock. This can be conveniently

don by Intersecting the straight' line approximations to .the

body plan sections by a buttock plane spaced at

.B/F

from the

centerline plane, as shown In Figure 1. Examples of the mean

buttock curves obtained by this method are shown in

dimension-less form in Figure 3a. The mean buttock lines shown in Figure

3a reflect the geneii practIce to have straight buttock lines

in. the after portion of planIng hull bottoms. Buttock lines

are generally straight.for at least the aft.er.30 pe.r cent of

the hull length. It is dfficu].t to mke further comparisons

of the buttock lines as they appear in Figure 3a, since their'

attitudes, and their heIghts from he horizontal axis, reflect

the arbitrary attitudes, and heights above the: baseline at

which the. corresponding lines were originally drawn. Comparison and analysis can be facilitated? therefore, by shifting each

mean buttock curve so that its after end.. is tangent to the'

horizontal axis of the grTaph. The mean bttock' lines of.

Figure3a, after being shifted in this. mariner, are shown in

Figure 3b. Inthe presentatlon.cf model test results in. this

report the angle of attack, or running trim of hull is

defined as the angle which the tangent to the xean buttock at

Plan view of chine. The significant features which

are determined by the shape of the chine line in plan view are the length/beam ratio of the: boat and the fore-and-aft distri-bution of breadth and of 'bottom.area0 Length/beam ratiohas

already been. adequately defined as the ratio L/BA. Therefore, it is desirable to reduce the plan vie'j of the chine line to a form which is independent of iength/beain'ratio," in order. to

compare relative fore-and-aft distribution o bottom area. This is accomplished by plotting the ratio of local chine

breadth to BA, against hull length, as shown in Figurec.-Each of the chine lnes in Figure + encloses the same area,

although the ratios L/BA of the hulls from which'they were derived are all different. Several dimensionless ratios

indicative Of- the relatve fore-and-aft distribution of breadth

are apparent in Figure +. First, the location of the point of

maximum chine breadth, as a. percentage 'of hull length from the

transQrn,iS apparent'. Also, the ratios of maximum breadth

and of traisom' breadth 'to. the mean breadth (BA) can be read

directly from the scale of the ordinate. An important criterion of the fore-and-aft distribution of the plan-view bottom area (area, A) is the location of the centroid of this area. This

dimensiois given.inFigu±e 1f for the different. designs.

pe' of section. Planitig boat sections generally fail

into one of the, following four categories:

1. Concave -, An example of ths type' of section is shown

- . 'in Figure 1..

2.. Convex . . The, use of developable surface will generally

result in this type of section.

3. Convex at keel' and concave at chine- This type is

exepl1fied by the B±it1h Vosper PT boat o World

Warli.

,. .

i. Concave at keel and convex atchine

Aliof the foregoing parameters of hull form 'and hull loading are incorporated in the' Taylor Model Basints design data sheet for'.planirig boats, an example of.whlch is shown in Figure

5.

Also- included in Figure ₅ are draft coefficients

'at 'bow, and stern for eaôh

of

the móde. test conditions. Drafts

at rest were measured up from the traight line which is

tangent to 'the mean buttock at the stern. The draft readings were .then converted to dimensionless coefficient form on the

5

basis of the following reasoning: Draft is proportional to

---Then, draft = (draft coefficient) x

Therefore, draft coefficient (CII) = draft x

The draft coefficient defined in this way is independent of differences in absolute size and of differences in length,' beam ratio. Also, by measuring the draft from the tangent to

the mean buttock, this draft coefficient is made relatively

independent of differences in eadrise angle. Accordingly,

the draft coefficients for a new design can be approximately

determined when draft coefficients are available from a pre vious similar design. The two designs should be similar in respect to A/V'21 , CG location, and longitudinal curvature.

Differehces in type of section and in plan form of chine should

cause only slight changes in the relative values of the draft coefficients.

PERFORMANCE CHARACTERISTICS

A performance characteristics sheet, which presents

model test results for planing hulls in a dimensionless form suitable for comparison and analysis, is included in the design

data sheet shown in Figure

_5,

Also included in tbe design

data sheet are the hull lines and other pertinent dimensions and coefficients0 It is the intention of the Taylor Model Basin to prepare such a design data sheet for each planing hull model

tested in the future, and also for a selected number of those

models previously tested.

Since displacement is a fundamental design quantity it is

desirable to compare hull forms on the basis of equal

displace-ment. This is facilitated in the performance characteristics sheet shown in Figure 5 by relating each of the variables,

speed, resistance and wetted surface, to displacement, _{y means} of the dimensionless ratios

v/V gY3

, R/A and

S/V

,

respectively.

Relating resistance to displacement as indicate.d here is

the isual practice in this country in dealing with planing

boats. Unfortunately however, it is not general practice to

o

is to compare the resistances: of planing huils by plotting the ratio of resistance to displacement a:;ainst speed-length ratio

(v/y9).

This method oftengives'an incorrect comparison, as

shown by the following example. SuTpose. tiat a 100,000 lb.,,

+0 knot boat is required. ;,.In Figure. 6 resistance, curves for

two models haviig different values of length-displacement

'con-stant (LtV") are potted in the usual manner*... Figure 6

gives the impression that a boat based on Model 2727 would

have higher resistance than ab0.a't,based on Model 27+2.. Such

is notthe case, however, because the use of V/(t as abscissa

does not bring the,,actual.ft.1 scale speeds into correspondence.

That 'is,, .,since 'the models hve. different values, of

length-dis,plc.ement constaxt (L/V'/ )., a given value, of 'V/IT does not

correspond t.othe same.fuli 'scale speed for,bothdesgns. For

Model '2727, expanded t.o .100,000 lbs.,displacejen.t, 1+0 knots

corresponds"to. ..a a1ue of V/ft

3.93,

while, for Model 27!2,

expanded to 100,000 lbs.: displacement,, 1+0 knots' corresponds to

.a. value. 'Of V/V 1+.95. Therefore, plotting R/ against

V/ramoi.thts, in this' case, 'to comparing the resistances of the two designs at entirely different speeds. What is required

is a plot of R/ versus a coefficient which

will

bring the full

scale speeds Into alignment'. ' The sp.eed.coèfficient is

correct for the purpose 'because it is derived from the

signifi-cant quantitiesof the design problem, i'e.: .speed and

dis-placement. 'in: Figure 7',' the data irom FiL:ure .6 have been

re-plotted onan 'abscissa 'of Fnv'. H'e, .th resistance curves are shoirintheir 'correct relatioisiIp, and, the order of super-iority is the' reverse of that Si'lOWII in Figure 6. The value of

'Fnv

3.5

corresponds to. 1+0knots :for both designs at '100,000

lbs displacement . More '.generally, 'a part;icular value of Fnv cqrrespondsto.thes'ame full :scale speed for both designs., for the same displacement. . ,. . '.

A, resistance cOmp.arion'made by plotting R/''versus

v/IT

will be incorre'Ot unless the length-ãisplacinent corstant

(L/VV3).is identi'ca1'for'ho.th.hulis and an identity of L/V'

will generally not. be the case. Confusion and error will also result from using the speed. coefficien v/V.gB (which is

some-times used. for,:planing boat analysis),tc conpare hulls of

,different proportions, except when the ratio B/VY3(or A'/wB3)

is the same for both boats.

* These values..are taken from the original data.for Reference 1. The .data for Model 2727 are froni the test at normal displacement

and 2 initial trim by stern. The data for Model 271+2 are from the test at nOrmal displacement and 00 initial trim. No correc-ti'on for 'the difference 'in the frictional resistance coefficients

of model and full size boat has been made, since that seemed

Wetted surface and tirn angle are included in the

perfor-mance. sheet because they are proportional, respectively, to the

frictional and wavemaking resistance of planing hulls. Ata

given speed the frictional resistance is almost directly prO-.

porti.onalto the wetted surface, so that for constant

displace-merit, which is the basis of th

present method of. comparison,

the frictiona1 resistance of two different designs. are

propor-tional to their respective values of the dimensionless quantity,

S/v

In the planing condition, the wavemaking resistance of a

prismatic planing

urf.ace equals the prOduct of the dUplàcernent

and. the tangent of the angle of attack of the bottom'(eqüals

tan o'-).

The planing area of the conventional planing boat

generally closely resembles a prismatic planing surface,, and

the angle o of the present paper is defined in such a way as

to represent approximately the effective angle of attack of

the planing area.

Therefore, the wavemaking resistances of

two designs which are beingcbrnpared on the basis. of equal

dispIacementare innear1y the same ratio as their respective .values

of. tan Oc

EFFECTS ON PERFORNANCE OF CHANGES IN AREA. COEFFICIENTS, LENGTH-BEAM RATIO AND LCG LOCATION

An aggregate of data suitable for analyzing the effects of

area coefficient and length-beam ratio on the résistance of

stepIess: planing boats is available from the tests0of EMB

Series 50 (Reference 1).

Th

original data, for 0

initial

trim only, was used for the present analysis.

The procedures

used for varying the model lcadixig and proportions in this

series, and for presenting the resistance data in Reference 1

are the same as those. used by Taylor for his standard series

of' ship forms.

The form in which the data are aailable will

be found disappointing by anyone who attempts to use them, for

determining the effects of the significant planing hull

para-meters on resistance, and a nei approach

therefore, seems

desirable.

When each. of the tests of E}'

Series 50 i's repiesented by

an x on a grid of A/V"3vs L/BA, the; reult is as shown in

Figure 8.

It can he seen that the tests fall into 'groups

corresponding to substantially constant values of L/BAe

Three

resistance curves from group D are plotted in Figure 9 to show

the effect of area coefficient on resistance for a constant

value o

L/BA (which is about +.25 inthis case).

The

seen to be superior to the resistance curve corresponding to either the higher or the lower value of area coefficient.

Resistance curves for all the 0 initial trim tests of

EMB Series 50 were compared by grOups of equal L/BA, and for

each value of L/BA it was possible to distinguish an optirnum

resistance curve corresponding to a particular value of area

coefficient. In Figure 8, the area coefficient for optimum

resistance for each of the values of length-beam ratio is

indicated by a circle around the appropriate x. It can be seen that the variation of optimum area coefficient :with

length-beam ratio can be represented with reasontblé accuracy

by a single straight line.

Resistance curves, for the three tests of Figure 8 Indicated by are plotted in Figure 10. This show the' effectof,

length-beam ratio on resistance for a constant value of A/V /3 (about

8.6). It can be seen that the high speed resistance decreases

markedly with decrease.of.léngth-beam ratiç, but that this is

accompanied by some increase in low speed resistance. Or,

looked at in a different fashion Figure .10 shows.that a

relatively long slender hull gives lower resistance at speeds

below = 2.3, while a relatively short wide hull gives lower

resistance at speeds above Fv 2.3.

Additional data showing the effects of a change in area coefficient on the performance of a planing hull are shown in

Figure 11. These data were obtained from tests of the same

model at two different displacements but apprOximatel the same

LCG location. The resistance data from both tests were corrected to 100,090 lb displacement (a äonvenient. average value for;boats

of the PT and AVR types) and are p1cttci in Figure 11 inthe

form of R/ versus F . Compared in tiis' manner the

resist-ance curves indicate he relativ,e resistance of two boats of

the same hull. form, same dispiacemen and Same center of gravity location, but:of different hull area. It can be seen that the smaller boat with area coefficient (A/V°1) equal to

+.93,

ha

a high resistance hump. This is evidently caused mainly by

wavemaking resistance since it corresponds a similar hump in

the trim angle curve. At the hump sped the lower vetted sur-face of the smaller boat apparently is relatve1y little

effect in reducing resistance. At hih speed the frictional

effect predominates, since the fritiona1 resistance is approxi-mately proportional to the wetted surface times the'quare of

the speed. Therefore, at high speed. be...aLse of her smaller

wetted area, the rl1 boat ns the lower net resistance, in

spite of the fact Gnat the trim angle curves indicate'that' she has the higher ,avemaking resistance0

9

The resistance curve for the small boat indicates that an

area coefficient of _+.93 is too low for most practical purposes.

One reason is that it would be difficult to provide adequate propeller thrust for such a high resistance hump; also,

resist-ance at cruising speed would be high; and, finally, the high trim angle would aggravate pounding in waves.

The effects on the performance of a planing boat of a

change in LCG location are shown in Figure 12. These data were obtained from tests of a model at two different LCG locations,

and the same displacement. As would be expected, moving the CG aft increases the trim angle of the boat and decreaâes the

wetted area. At low speeds, where the wavemaking resistance predominates, the CG forward condition produces the least

resistance because of the smaller trim angle. At high s.peeds

where the frictional resistance predominates, the CG aft cond

-tion produces the least resistance because of the smaller wett.ed area.

STANDARD MODEL TEST CONDITIONS

It was shown in the previous section that changes in the area coefficient and in LCG location have large effects on the

performance of planing boats. Therefore, in order to show the effects of other variables on performance, it is desirable in

any comparison to hold these two constant. Comparison would

evidently be greatly facilitated if future tests of planing boat models included one or more tests at "standard" conditions of

A/V"3 arid LCG location. Future designs could then be readily

compared without interpolation, without the necessity of search-ing for test conditions that happened to be similar, and without having significant performance differences unnecessarily

ob-scured by even srnalldifferences in. area coefficient and center of gravity location. The standard test conditions should, of

course, be selected. from consideration of the practical and

desirable region of planing boat design.

Figure 13 shows the values of A/V2hh/3and LCG location (with respect to the centroid of the area, A) corresponding

to the model test conditions for a number of boats. The after

limit in the practical range of center of gravity location is the point at which longitudinal instability (porpoising) occurs. The test condition for which one of the models porpolsed is

indicated by a tail on the corresponding symbol. Additional

points of instability, from other model tests, are also shown, in order to define more accurately the after limit of the

practical range of center of gravity location. Each of these

10

The standard test conditions decided upon for tests of

planing boat models at the Taylor Model Basin are

A/V'3

7,

and LCG location at 6 per cent L aft of the centroid of A.

Where :additional conditions are desired it is planned to select them from among the conditions indicated by the solid circles of Figure 13.

EFFECTS ON PERFORMANCE OF CHANGES

IN TWIST AND DEADRISE ANGLE

The effect of warp, or twist of the planing area, on the

performance of planing hulls is indicated by a comparison of

the World War II Elco and Higgins.PT designs. Figure 2 shows that the deadrise of the Elco design increases from 7 degrees at the transom to 18 degrees at midlength, giving a twist of the planing area of 11 degrees. The deadrise of the Higgins design increases frOm 2 degrees at the transom to 21 degrees at midlength, giving a twist of 19 degrees, or roughly twice as much as the Elco design. The mean planing deadrises for the two designs (average of deadrise at. mid-length and transom) are practically the same (i2 degrees for the Elco and

fl-degrees for the Higgins desigh). Figures 3b and indicate that the two designs are fairly similar with respect to mean buttock curvature and shape of chine in plan view. Performance of the two designs, from model tests, are compared in Figure 1+.

The resistance of the Higgins design is appreciably higher than

the. resistance of the Elco design, and the difference is con sidered to be chiefly attributable to the larger twist in the planing bottom of the Higgins design.

Data are not available to show how a planing boat with a low average deadrise angle compares in performance, throughout t.he speed range, with a boat having a high average dcadrise angle. The range of deadrise angles covered by the tests of EMB Series 50 was small, and deadrise angle was not varied

systematically. However, the effects of change in deadrise angle on performance at high speeds can be shon by means of data obtained from tests of prismatic planing surfaces.

Figure 15 shows the performance predicted from such data for

100,000 lb boat, of typical dimensons, for deadrise angles of

0, 10, and 20 degrees. These performance curves were calculated from the data of' Reference 2. It ciri he seen that. an increase

in deadrise angle from 0 degrees to 20 degrees increases the

wetted surface about 25 per cent, increases the trim angle 1 degree, and increases tie valne of R/ at high speeds by

ohout 0.0+0. For a prismatic planing bottom the anount of the increase in R/ caused by increased wavemaking resistance

11

is the same as the value of the increase in the tangent of the

trim angle. For the range of argles of interest here an

ii--crease in trim angle of 1 degree corresponds to an Inii--crease in

the tangent of approximately 0.018. Evidently then, of the increase in R/ of 0.0O, approximately -5 per cent (0.018) can be attributed to. increased wavemaking resistance and the

remaining 55 per cent to increased frictional resistance. In spite of the fact that a flat planing surface has

less resistance than one with deadrise, in practice adea.d.rise

angle at the tranwmof at, least 100 is desirable in' order to give a boat good directional stability, and in order that It

will have the desirable characteristic of banking Inboard on

turns.

Model data are not readily available to show the effects on resistance of longitudinal curvature, plan form of chine,

and type of section. It Is expected that this situation will be improved in the future, however, as models are tested at

.3tandard conditions and comparison and analysis are thereby facilitated.

DESIGN PROCEDURE

The coefficients and parameters presented in this report have been introduced with the intent that they should be useful

for design purposes. accordingly, in this section,a design procedure utilizing these coefficients and parameters will be

outlined. This report does not attempt to present a complete

design procedure. It would be necessary to include a

consider-able amount of additional information t accomplish that.

Among the information needed would be data on weights, engine particulars and propeller characteristics, all reduced to

conveniently usable form.

Tentatively, then, it is colasidered that an effective

design procedure would be to proceed somewhat as follows. First

the designer should obtain suffic1nty complete specifications as to payload, endurance, speed9 equipment, and crew to be

carried, so that a preliminary estimate cf gross weight, and a

preliminary arrangement plan can be madz. Ratio of length to

beam (L/BA) can then be selected,

In this cormection, Figure 10 shows that a low ratio of

L/BA is an attractive prospect with respect to high speed resist-ance. Experience indicates, however, that a low length-beam ratio can be utilized only for sheltered water boats, and that

12

for seaworthiness a relatively high value i..s necessary. Thus,

for stepless run-abouts the length-beam ratio is about

3.6,

while for the motor torpedo boats of World War II the ratio is

about

5.6.

A logical design procedure, then, is to select the

length-beam ratio of a new design from the proportions of

pre-vious successful boats of the same type. Figure 16 has been

prepared for this purpose. Having selected a value of L/BA, Fig.ure 8 can now be used to determine a good value for the area

coefficient,

/v13

. From the indicated value of A/V?L3 , and

the preliminary gross weight, the hull area A, can be calculated

as follows:

_; then, since w = 6-i-lb/ft3 for sea water.

v213 (

\2/3

2/3

-Then A

(A

\

2/3

y2/3,)

i

This value should be compared with the required hull area as

indicated by the preliminary arrangement plan.

Several considerations are involved in the decision as to the choice (or compromise) between the hull area indicated by the preliminary arrangement plan and the hull area indicated

by the area coefficient,

A/V/3

. If the arrangement-plan area

is very much less than the area indicated by Figure 8, then the

arrangement plan area will give a heavily loaded hull, and

conversely, if the arrangement-plan area is very much greater

than the area indicated by Figure 8, then the arrangement

plan area

will

give a lightly loaded hull. It should be pointed

out that the "optimum" line of Figure 8, from the nature of the

development is of limited significance0 Only one type of hull

lines and one LCG location are represented in this graph.

Furthermore, Figures 9 and 11 show that the optimum value of

area coefficient (value for minimum average resistance) is a

function of top speed as well as L/BA and that a relatively

low speed boat would have a low average resistance with a high

value of area coefficient (light loading), iihi1e a high speed

boat would have low average resistane with a more economical

arrangement plan and a low value of area coefficient (heavy

loading). Accordingly it would be desirable to recheck the

hull size selected, after the lines have been completed, by

making a model test to show the effects on performance of

would be to test a model ovr a widç range of disDiacements, calculate the resistane for the fuUsize design displacement from each of the tests, and compare the results in a graph of R/ versus The scale ratio between model and full size

boat will be. different for each model displacement, and can readily be calculated as follows:

'5

X SW/FW

13

For an accurate analysis the data should be. corrected for the

difference between the frictional resistance coefficients of

model and of full-size boat. The method of making this

correc-tionfor planing hulls is given in. Réference3. Figure 17 shows

theresults of a model test calculated and plotted in the

pro-posed manner. The model tested was a planing hull of normal

form, and the tests were originally made to determine the

resist-ance of a given size of hull for three different full-size

displacements. For the present purpose, however, the three tests are considered to represent tests of a partiu1ar set of

lines at three different scale ratios, each test co: responding to the same full si.ze displacement (100,000 Ib). Considered in this fashion, the following interpretation may be put upon the

data shown in Figure 17: A 100,000 1 boat built tO the lines

tested aM having a.length, L 58.0,anda mean beam,, BA =

will have the resistance given by curve A. If L = 63.1, end

= l2.' the resistance will be that given by curve B; and.

i L = 70.6', and BA, 13.9', the resistance will be that given by curve C. It is' clear from this figure that if the

anticipated top speed of the boat under consideration

corres-ponds to, a value of Of

35

or less., then the best boat of the three represented is that 'ccrrespondiñg to curve C. If the t'p speed of the boat corresponds'.to a value of Fnv of 1f.0 or greater, then a reduction in tep speed resistance would. result from

selecting boat dimensions' corresponding to

curves Aor B, instead of those

corresponding to

curve C; the

curves also show, however, that this seietion would be

accom-panied by substantial resistance penalties in the low and.

cruising speed ranges.

After selecting a value of A/V/3 (tentative, or otherwise.),

the next. step in the envisioned design procedure is for.the

designer to select suitable non-dimensional curves defining the

chine line in pran view, the deadrise variation', and the'

longi-tudinal curvature of the mean buttock. These curves are shown,

11+

design data sheets. It is anticipated that when a number of these sheets have been made available the designer will be

able o select the form characteristic curves for a new design

with the confidence of obtaining superior performance. The form characteristics presented in the design data sheets have all been derived with a view to the reverse

pro-cess, i.e. with the idea that the designer should be able to construct the complete hull lines for a new design from the

form characteristics selected.

- When the values ofL/BA and A have been obtained the valuE

of L andBA can be calculated asol1ows:

Since _BA

.,

then L2 A x L/BA. From thisL can be

L

calculated, and then, readily BA (equals A/L)g

The form characteristic curves of the design data sheets

are given in terms of L and B, so that when the values of the

two dinersions have been deterrined, and the form

criaracter-istic curves for the new design have been selected, the new

body plan, and subsequently the complete lines can he con-structed. Adescriptioii of the method of constructing one

section will indicate the essential features of the pxocess.

The process of constructing a section at 70 per cent of L

forward of the stern is indicated in Figure 18. The center-line is drawn and then a horizontal center-line representing that

waterline plane which is tangent to the mean buttock at the

stern. This plane is the primary horizontal reference plane

in the proposed design process.

A vertical line indicating the

buttock plane at BA/1+ outboard of the centerline is then drawn

and a baseline is drawn at any convenient location. Then, fro the selected' m?an buttock curve the height at 70 per cent L is

read (inper cent of L); this number is multiplied by L and th resulting dimension is plotted on the line representing the mean buttok plane, measuring up from the horizontal reference

plane. A straight line is then drawn thrbugh the point thus obtained.at the deadrise, angle for 70 per cent L, as indicated by the selected curve of deadrisé variation. From the selectec

curve of the chine in plan view the dimensionless ratio B/BA

for the 70 per cent point can be determined,

and multiplying

this by BA and dividing by 2 gives the half breadth of the

chine, at 70' per cent L. This dimension is 'then indicated on

the drawing. The type of section selectd is then sketched

in, using

the lines previously established for guidance. The

and the lines faired in all three views In the convent.ion1

manner. It is believed that by following such a design pro-cedure it will be possible toincorporate the desirable fea-tures of previous superior hull forms in a new design.

The waterline at which the boat will float can he

approxi-mated by means of the draft coefficient data presented. in the design data sheets. The.draft forward, for eampie., can be

estimated by deterthining the draft coefficient forward for a

previous similar design at values of A/VW3 and LCO location

corresponding to those for the new design. Multiplying the

draft coefficient value by V/A gives an approximatipn to the draft at 100 per cent L as mesu'red up from the horizontal

reference plane. The draft at the stern is determined in

similar fashiOn.

AI'ALYSIS OF FULL SCALE DATA

Resistance data from model tests are useful for

deter-mining the relative efficiencies of different designs and

also for estithating the ehp requirements of new designs.. The

information which the designer ultimately needs, however, is

the required engine brake horsepower, bhp. Some. data. are

avail-able on the weights, speeds and brake horsepowers of actual full

size boats. These deta can be reduced as follows to a dimension-less form similar to that in which resistance data are presented:

bh

P

550 :R'v

_éhp

550 .R

. v ehp

Brake horsepower, weight and. speed data for various type.s

of racing boats are given in Reference ii-. The data from this

reference on small vee-bottom motor boats are plotted in

dinien-sionless form in Figure l9 This figure can be used to make

rough estimates of the bhp requirements of new designs. It can

be readily seen that since differences in propellers, in hull form, and in hull loading are not considered here, the answers

obtained

will

only be very approximate0

Suppose that it is desired to estimate the bhp required to

propel a 5,000 lb boat at a speed of 25 knots. Then from Figure

.20 the corresponding value of F is

.3.6.

Entering Figure 19

with this value we obtain

a

valu of .R of

_Q.265.

We then

obtain bhp' as follows:. ehp

16

LV

bhp _ehp

₅₅₀

5000

21.689

bhp = 0.265

₅₅₀

102

In Reference 5 a large quantity of data on pre-war

American and foreign motor torpedo boats were compiled, These

data are plotted in Figure 21 in the form of bhp versus

ehp

F The data on German boats have been omitted, because of

t bad scatter. Data on stepped boats, and on unconventional

forms, have also been omitted. A. line has been drawn through the intermediate region of the remaining points. This line is

considered to be of some value as a criterion of good

perfor-mance, and for roughly estimating the bhp requirements of a

projected design.

If the published information on the performance of full

scale boats also included the center of gravity locations and

values of the average breadths and average dead rises in the planing condition, the total information would be extremely

valuable. The resistance of the boat in the planing condition could then be calculated from available planing surface data, and from this and the engine bhp data, values of propulsive coefficient could be obtained. Such data are p2.rticularly

necessary and desirable because it has not been possible here-tofore in thiscountry to self-propel models of high-powered

17

BEFERENCES

Davidson, Kenneth S. M. and Suarez, AnthQny, "Tests of Twenty Models of V-Bottom Motor Boats, EMB Series 50", David Taylor Model Basin Report R-7 (Revised Edition, March 1919).

Savitsky, Daniel, and Neldinger, Joseph W., "Wetted Area and Center of Pressure of Planing Surfaces at Very Low Speed Coefficients", Stevens Institute of Technology, Experimental

Towing Tank, Report No. }+93, (July 195'+), Sherman N. Fairchild

Publication Fund Paper No. FF-l1, Institute of the Aeronautical

Sciences, New York.

Murray, Allan B., "The Hydrodynamics of Planing Hulls", Transactions of The Society of Naval Architects and Marine

Engineers, Vol. 58 (1950), pp 658-692.

Nicolson, Daniel, "High Speed Motor Craft", North-East Coast Institute of Engineers and Shipbuilders, Transactions,

Vol. LIV (1937-1938).

5.

Hugh, W. C., "A Motor Torpedo Boat Comparison", Stevens

Institute of Technology, Experimental Towing Tank, Technical

Memorandum No. 5 (12 November l90).

BIBLIOGRAPHY

Du Cane, Peter, "High-Speed Small Craft", Temple Press

Limited, England (1951).

Lord, Lindsay,"Naval Architecture of Planing Hulls", Cornell Maritime Press, New York (196)

Phillips-Birt, Douglas, "Motor Yacht and Boat Design",

Straight line approximations to sections Mean buttock height Mean buttock plane O.57L

Figure 1 - Typical Planing Boat Body Plan with

Straight Line Approximations to Sections.

20

40

Figure 2 - Curves of Deadrise Angle vs Boat Length for Three PT Boats of World War II.

\0

Design Higgins Huckiris Elco

DTMB 3720 3721 3722 Model

-/ /

/7

/

-70 100

6 4 0

Design

DTMB Model cL 60 70 70 90

Figure

3

-Mean Buttock Cu

ës for Three PT Boats Of World War Ii..

90 100 l00

3720

Higgins

-

--.Huckiris

3721

Elco

3722

I0 Before (0) 20 30 40

shifting to horizontal axis

40

10

20

30

(b) After sftina to horIzosill

50

70

Figure 4 - Chine Offsets in Plan View, for Three PT Boats of World War II.

90

0

Design Higglzv3 Huckins Elco

DTMB Mode]. 3720

37?i

3722 of 47.2

484

CentrOid 43.55 A, %L chine (equals Distance breadth

42L

of position for fwd of Model of transom 3721) maximuxii

-:

-__

--z-_

---.225 (Hod e 1 3721) bk-=0.78 (Model 3722) I0 20

30

B BA 0. 0. 0. 0

3 PERFORMANCE CHARACTERISTICS 6 NO.

UUUE

M

ESTANCE ANO POWER CORRECT

TEB? NO. 4

FRETNCOOFIaENTSWHZERO

It

VAUtRU

PNttt iiit.iumut

.... titiuiuuu

: uuiuu

TEST NO.4

...1111i!!iiI!!fl

TEST NO.

RIIURt:tLBUIUU

2

U

dIIIIIIIIIIIIIIIII!o

IIIIIIIIIIIIIIIUI::

III!IIiiIIIIIIUI'::.

F5 a .10 06

ia')

2 A 8 .04 -As OWL

BASIN HIGH SPEED. SASIN BASIN SIZE

2968'x211'X(10'aM 16

DATE. OF TEST - 8 FEB 55 WATER TEMP

61°P

APPENDAGES

SPRAY STRIPS

TURSULENC

SlIM.

MODEL MATERIAL MODEL FINISH

TEST NO. 3. -10 MODEL DATA cT-BOT. KEEL 7372 -/TANGENT TO Efl'T AT STE 30

MO00 SCALE W FOES

fT

JUNE 1955

REMARKS:

He1ativ1F high

k.

ratio and narrow transo: give low resistance

characterjstjcs

at Fn?

<3.

Average resistance characteristics at

FnV> 3.

I TEST COIDITIONS

FORM CHARACTERISTICS

4

FULL SIZE A': 1009.8

sq ft La 76.39 ft s 13.22 ft

T2FNT-TO SEAN. AUTTOCATh AT STERN

70 S HORIZONTAL i-...JAT STATION 50.7 .219 CONSTANT SNOTION THROUGHOUT

E'YLARGEn CROSS- sTxTI0!r a? SPRAY SThIP

80'

90

L 1 8.489 FT.

Fgure '._-_Typical Design Data

Sheet9 TEST NO lb lb9 A V5 L

V"

F09 g e

ORAFT COEFF.. CO,,F.T

CENTROID LCG % L FWD AFT I 128 7 94,500 7 79 6 70 15°x - 1 300 1 795 0 762 2 1%!. 463 a 142.9 105,00G 7.25 6.47

Ox

- 0.60° 1.380 0.994 5.1%L. 43.3 3 148.0 1.1.0,960 7.00 . 6.36 O(x -0.35° 1o444 1.lfl 6.0%!. 42.4 4 121.1 90,790 8.00 6.80 Og'x -0.45° 1.409 0.982 6.0%!. 42.4 - -. R, WL WL9, WL., 3.89 6.97 8.22 . 7.50 8.18 4.87 11.12 .8.10' 6.95 7.84 5.85 13.46 8.00 . 6.48 7.53 6.81 15.10 ... .95 6.19 7.30 7.7.7 16.89 7.86 5.91 7.08 8.72 18.83 .7.75 5.58 6.60 -9.67 20.49 7.53 5.15 5.82 10.69 21.69 7.39 4.82 5.40 11.67 22.76 7.22 4.60 5.72 .12.60 24.24 7.19 4.38 '495 13.60 25.43 7.12 420 4.80 1.4.59 26.84 710-4.02 4.67 15.57 28.38 7.10 3.89 4.53 16.53 30.39 7.13 3.73 4.42 17.52' 32.10 7.16 3.65 4.40 18.51. 34.40 7.20 3.53 4.30 V1, RN, WLK. WL WL 3.88 5,58 8.20 7.20 8.02 -4.82 8.49 8.09 '16.72 1 7.80.5 .5 5.82 10.55 8O0 6.22 7.45 -6.79 12.08 7.92 5.98 : 7.22 7.75 13.78 79O 5.70 7.04 8.72 15.49 .7.80 5.41 -6.64 9.68 :17.02 7.63. 5.02 6.00 10.70 18.61 7.50 : 5.40 11.67 19.75 7o40 4.42 H s.io 12.59 21.25 7.35 4.22 4.90 13.60 22.73 7.29 4.02 4.70. 14.60 24.32 .7.24 .3.83 4.60 iSo60 26.22 7.27 :3.72 4.40 '16.56 28.28 7.28 3.60 4.40 17.49 30.45 7.30 . 3.8 4.30 18.51 33.02 .7.30 4.35 100 80

120:

:1

. 6c 30 ..

..

C

P-

SRPI'

--p _{1. I} 6OL/B: L/B B./B,° 5.78 4.74 .. , - ' -0651 CENTROID

20-22

PLANING BOAT DESIGN

DATA SHEET

DT

MODEL 3722

DAVID W. TAYLOR MODEL

BASIN DTMB MODEL 3722 1 SCALE 80 FT. ELCO PT BOAT 70 90 100 %L. 40 50 6G

NONE WOOD PAINT

TEST NO. 4 LINES. MODEL _{A: 12.466} sq ft. La 8.488 ft s 1.4-69 ft.

0.20 0.lo 4 Model L,Q'3

0

2727 8.93

-A

27i-2 5.62

Model data (no. friction

'resistance correction) Appendages: none

Figure

6

-Resistances of Two Models from EMB Series

50,

.28 .20 .10

Fnv

Figure

7

-Resistances of Two Models from EMB Series 50, Compared by a Correct

Method.

0

-0

/

A

0

8.93

5.62 friction

Model 2742 _correction) none

0

2727 _(no

-

Model resistance Appendages:

data -F

1.6

2.0

3.0

.

.

18 14 12 10

Model testy conditions for the EMB Series 50 Values of A/sl43for optimum resistance at approximátéiy constant L/BA Variation of A/v2'fbr optimum resistance with L/BA

0

LCG ç1.1L) aft of centroid of A (0 initial trim)

rLi

10

11

L/BA

Figure 8 - Variation of Area Coefficient for Optimum Resistance with Length/Beam Ratio,

.28 .20 10 0

V

V

/

V

V

V

ri

Legend

L/B=approx.. 4.2 Model data (no fr resistance correc

Appendages: none ictiona.1 'don) 1.0 2.0

5.0

4.0 3.0 Fnv Figure 9

-. Effect of Area Coefficient on. Resistance, with

.28 0 1.2 2.0

3.0

4.0

5.0

____

H.

H 1

_

--_

I. approx. 8.6

Model data (no fricticnai) resistance correction) _{Appendages: none}

Figure 10. - Effect of Length/Beam Ratio on Resistance, with Constant Area Coefficient.

.20 .10

Legend

A

Model resistance corrected to 100 000 lb using Scboenherr friction coetficLents wi

roughness allowance.

Appendages: spray strips only

-is placement, h zero 7.29 4.93 L/ 5.08; LCG is appoximately 3%L aft of centroid of A. .18 .16 .1 B/A .1 .1 08 .o6 2 F fl

Figure 11 - Effects on the Performance of a Typical Planing Boat Hull Form,

of a Variation in Area Coefficient.

28 0 5 Legend: A/ 5 4 3 2

10 6 18 .16 R/A .14 2 10 .08 .06 Lu 29

Fv

Fige 12 - Effects on the Performance of a Typical Planing Boat of a Variation in L.C.G.

10

A. 9

V2'3

Test condjt ions

model porpoised Selected standard.

test conditions

for which the

at

high Spe$S

Q

"/ NI - i i --*20 .

-'+-IO

--.'

--- 7

LCG at

of centroid of A, %L

Figure 13 - Area Coefficients & LCG. Locations Corresponding to Model Tests of Typical PT & Aircraft Rescue Boats..

-8

Design DTMB ?*ode1

o 70' VI

3626

177* _PT

₃₆₅₁

G78' .P

3720

z80' PT

3722

Q 90' AVR

4375

52' A.VR'

4377

s, -31.

I

11UUmaR

I

1111N11UU1

--JuiIIII

UUIUUUUIE

B Fnv

Figure 14 - Effects on Planing Boat Performance of Different Amounts of Twist in the à1

ttom. . .

-£

S/ Legend Deadrise Angle, Degrees 20 10 0 Beam 16.2' , L.C.G. fwd transom = 27.4'

Resistance calculated for 100,090 lb displacement, using Schoenherr friction co -efficients with zero rouginess allowance. No air drag ideluded.

Appendages: none

2

32

6

Figure 15 - Effecta on Planing Performance of Variation in th T)eadriee Angle of the Thill

Bottom, from Planing Surface. Data.

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20 0 10 30 40 5.0 60 80 100 200

Displacement at rest, thousand of pounds

Figure 16 - Variation of Length / Beam Ratio with Displacement.

400

600

1,000

R/A .20 .10 .00

9,

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---

I -0 1

L/BA Centroid of A is 57.8%L aft of bow. L.C.G. is approx. 3L aft of

centroid of A.

Model resistance corrected to 100,000

lb

displace-ment, using Schoenherr fri.ction

coefficients with

zero roughness allowance. _{Appendages: spray strips ohly}

-Figure 17 Effect of Size of Hull on Resistance for

Constant Displacement (100,000 ib)..

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-63.1'

12.4' 15.7' 5.83 70.6' 13.9' 17.6' 7.29

BA 4

Height of

mean buttock at 7OL

Arbitrary distance

Reference Plane

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Figure 18

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opies

17 C}3t]SIiIPS, Library (C cxo 312)

5 Tech

ibrcry

1 Tech Asst to Chief (106)

4 Prelim Des & Ship Pro (420)

1 Hull Des (440)

4 Boats & SDI

Craft (452)

2 Landing Ships & Craft,

Standard, Special, & Iisc. Boats (529)

1 Cit, Phi1e1phia Nay Slüpyd,

Attn: Des Supt

COIiIDT, U.S. Coast Gwrd,

Washington, D.C.

Chief, Hytho Div, Langley Aero Lab, Langley Field, Va. Chief, Marine Br, T±ansp Res &

Dcv Stn, Tranp Bd, Fort Eustis, Va.

1

Head, Dept

of NA2, MIT, Cambridge, Mass.

1

Head, Dept

of NA1E, Univ of

Michigan, Ann Arbor, Liich.

4 Dir, ETT, SIT, Hobokcn, N.J.

2 Webb Inst of Nay Arch, Long

Island, N.Y.

Attn:

a-of.

Tboas 1. Curran

1 Dir, T1est1am Sch of Yacht Des,

Montville, N.J.

1 Chris-Craft Corp, Algonac, Llich.

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mc, New Orleans, La.

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Fla.

1 Luders Marine Construction Co.,

Stam.ford, Conn..

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Electric

Boat Div, General Dyn

"Corp, Groton, Conn.

Attn: Lfr. Irwin Chase

INITIAL DISi:uhIoN

Copies

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