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THE

SEAWORTHINESS PROBL4 IN

HIGH -SPgED SMALL CRM2

BY

Seabury C. McGown

A paper for presentation at the January 21.,

1961

meeting of

the New York Metropolitan Section of the Society of Naval Architects and Marine Engineers.

The opinions or assertions contained

herein are the

private ones or

the writer and. are not to be construed. as official or reflecting the

views of the Navy Department or the naval service at large.

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The Seaworthiness Problem in High-Speed Smfl Craft

Abstract

One of the most challenging areas in small craft design today is 1.uiprovement of seaworthiness at high speed. Types of hull forms adapted for the optimum combination of high speed and good rough water performance at high speeds are discussed. The merits and limitations of the "round bottom form" and. the hard chine forni" are compared. It is contended that for speed/length ratios up to the range of

3.5

the "slender" round bilged form is generally superior providing the necessary speed potential with good seaworthiness. For speed/lçngth ratios in excess of -.O the hard

chine boat is favored for its lower resistance characteristics at these high

speeds. The limited seaworthiness of the hard chine boats at high speed in rough water is discussed and an analysis is made of the features of these craft which contribute to good and poor rough water performance. The lack of systematic comparative test data, either model or full scale, to clarify the effect of various features of hull form on behavior prohibits concrete conclusions, however a critique is niade of a number of high speed designs providing a background for further scientific investigation.

A. Seaworthiness of High-Speed all Craft.

1. Introduction.

Seaworthiness is the quality of a boat which allows it to perform its

design

task under adverse weather conditions with reasonable comfort and. safety. As used here it includes seakeeping and. seakindliness.

Great efforts have been made in the area of developing high-speed sm1 i craft. As a result many craft capable of very high speeds in caam water bave been developed. However Rh to)frequently rough water per-formance and. maneuverability have not been given sufficient consideration and the resulting craft have suffered to varying degrees from limYced seaworthiness.

The ship designer and to a lesser extent the boat designer has been aided in recent years by model basin testing. However for the most part this has only contributed to improvements in smooth water resistance. The improvements thüs made are helpful allowing either greater speed or a reduction in the power required. Some work has been done in model basins to assess seaworthiness of small craft in rough water. It is expensive and to date very little has been done. Although it will probably

eventnhly have a great influence on small craft design it has not yet become a significant factor. This has left the problems of seakeeping and

seaworthiness to be resolved for the most part by analysis of rough water trials of full scale craft. This has the major drawback of beIng slow and. in general not systematic. Very few custcrs wish to risk their money on

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novel hifll forms and. the desier is forced to be conservative and make

srll changes at a t1Tn He also has very few opportunities to make thorough evaluations of the changes he does make.

Thüs, even though the problema of seakeeping and seaworthiness have been with us for a long time, there is no thoroughly proven solution to this problem for the high speed boats of today. As the power/weight ratio of marine engines has increased, hul i desiges have been developed by trial and

error to utilize theni. There have been 3 basic approaches to this

develop-ment.

Evolutionary development of proven seaworthy low powered types to adapt them to more power and speed with a minini loss of seaworthiness. An example is the modern "Jersey" sea skiff which shows the result of evolutionary development from a double ended pulling surf boat to the high powered sport fisherman type of today.

Evolutionary development of proven high speed (low resistance) types to make them more seaworthy with a minimum reduction of speed in rough water. An example is the modern P.T. boat developed from high speed runabout forms originally desigeed for maximum speeds in protected waters.

Development of novel types using new approaches based upon application of devices desigeed to reduce resistance and increase

seaworthiness by lifting the craft free of the water. An exemple being hydrofoil supported craft which solve the resistance and seakeeping problem by supporting the craft above the water reducing the resistance to only that

of the hydrofoils and their struts.

This paper is centered upon developments in area (b).

2. Requirements.

First to take a look at our problem. 'wlhat is a seaworthy boat?

a. She should be dry, in respect to both green water and sprar.

b She should have moderate motions of pitch and roll. She must be stable but if possible not have a quick period. of roll such ai to throw passengers about.

c. She should pound and. slam as little as possible for the comfort

and safety of the passengers, and. to reduce the impact loads on the hull struc-ture, machinery and other equipment.

She should be able to maintain as high a speed as possible in rough water.

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e. She must be directionally stable with a mininum tendency

to yaw nd. broach, and yet she must also be maneuverable

at Rh speeds and in all

sas.

It can be said that there are boats which can fulfill

all the boye requirements, exce:pt perhaps speed, to

a satisfactory degree. Some of he slow heavy-displacement

types operating at mxi speed/length ratios f' 0.8 to 1.2 when prudently

handled come close to meeting all the require-ants, an example being the Navy's 26' motorvhaleboat, but difficulties rise when the desier is concerned with providing these

qwhities for igh speed craft.

Regardless of the type of hull foin used - the slender round ilged form., or the hard chine forni in either

case when driven at high speeds n rough water seaworthiness becomes a serious problem.

Excessive wetness can be a serious

hazard to vision, can cause alfunction of deck equipment,

cause leakage thru deck openings, and.

dis-omfort or at worst bodily harm to persons on deck.

Excessive motions can imkc .h i the functions of manning the raf t difficult.

In a case known to the author the helmsman of an

ir-sea rescue boat firmly braced himself holding the wheel in anticipationslam and tore the wheel d'

right off. Slamming and. pounding can cause ccessive hardship on the crew, the hull, the machinery and.

other quipment.

Compasses swing to violently to be read, and may be dislodged rom their housings. Fuel and. lub oil and hydraulic

lines break, shafts come ¡ni.sali-ied and at worst the hull structure may feil.

In following seas the danger of broaching is serious and is plicated. by the heisman's difficulty in maintaining constant control aile keeping his footing.

A long list of hair-raising tales can be told. of

the

brdships ' driving a high speedboat in rough water.

The one logical way to

leviate many of these hardships is to slow down and that is what is usually ne, increased resistance caused by rough seas will greatly reduce speed but ually the throttles are brought down also.

There is no doubt in my mind that much can be done to improve the aîorthiness characteristics of high speed small craft.

nhl

craft truly pable of operating at high speeds in rough water and exhibiting good

avorthiness qualities under all but the most sever conditions would be a eat asset for both naval

and cerc ial

snis1 1

craft and. would open up .ditional applications.

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3.

Approaches to Solutions.

Model testing: Ass quite common in the study of resistance and propulsion, model testing is a logical approach to examination of features which contribute toward seaworthiness. Recently facilities for thorough investigation have been made available for powering tests and maneuvering in rough water. This testing is somewhat limited since most waves artifically stimulated in model basins tend. to have a regularity not found at sea and the absence of wind makes proper study of wetness difficult. However rough water model tests are very useful for comparative studies and can be compared. with model test results of craft whose full scale performance is known.

Rough water model tests are expensive thus limiting the amount that has been done. As more rough water testing is done a.nd correlations of model vs. full scale are compiled it can be hoped that reasonable inter-pretation will be possible.

It would be

a

great help if more results of the work that has been done were made public. Much of what has been done to date is the confidential property of commercial designers or the Navy which limits the value of what has been learned.

pirical - Historical Approach: The scientific approach to small craft design should be applied more today than it is, however the economics of research for small craft design being what they are, trial and error is still the more prevalent approach. It is this which makes small craft design still an art. Thanks to the genius of some designers steady improvements have been made possible by a "seat-of-the-pants" approach. To make up for the lack of systematic scientific data a

constant drawing board attack is required; that i analysis of the lines plan in the light of known performance data. This is what I call the

empirical-historical approach. It is a sort of plagiarism since it is based upon assessing both ones own work and the work of others to ferret

out that which is good and. that which is poor. This is to a great

extent subjective since lacking the advantage of systematic variation one must makc his own determination of which features add. or detract to the

seaworthiness of a particular design. Another difficulty is that many

taies performance data must be

collected second-hind. and is based upon human estimates rather than mechanically recorded data.

B. Hull Forms for High Speeds.

An arbitrary definition of what is meant by high speeds for small craft would be approximately 20 knots or more which for boats up to 100 ft.

LWL

-hi meansY/-yof 2.0. Two basic types of hull forn are used, the hard bilged round bottom and. the hard. chine.

1. liard. Bilged Round Bottom, Semi-Plrn1-ng Type.

To use the historical approach, it is clear that in the development

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of high speed boats the asset of length has been appreciated for a long

time. If a boat does not depend upon planing principles

to

allow high speeds, the only alternative is to reduce the residn1 resistance. It is an important tool today and was even more important 0 years ago before the advent of fully planning boats. Since residual resistance is a direct function of the speed/length ratio and the displacement, the obvious solution is a low displacement/length ratio.

Long before the reasons for this were clearly understood, high speed boats were dèsied on this principle. Thus was produced the typical slender easily driven hull form of low wave-making resistance. .This type cannot be driven beyond a speed/length ratio (/fJ of l.5without special treathent of the afterbody providing a broad transom stern with flat buttock lines. Beyond a speed/length ratio of 2.0 this form will be in a

semi-planing condition and the hull must be desied to promote this planning, however the form will still be priimirily based upon producing a form of low residual resistance. The practical maxiinumV/Cis somewhat less than .0 depending upon how low a displacement/length ratio is used. A well known example of this type of boat are some IB types such as

shown in figure 1.

2. Fully Planing.Types..

The alternative to the use of length, i.e. low displacement/length ratio to reduce residual resistance, is to reduce the apparent displacement by dynamic lift thus reducing the residual resistance. At speed/length

ratios greater than 3.0 when considerable lift has been developed, thereby reducing the residual resistance, the frictional resistance

becomes a large percentage of the total, it is here that the "Vee" bottOEn chine hull shows its superiority. The hard chine hull is an effective planing surface and the angular chines and spray rails prevent the bow wave from wetting the hull sides. It can be seen that the fully planing boat depends upon the hard chine hull form which

will

promote an efficient

combination of J if t and trim reducing wetted surface and dynamic displace-ment. The basic prináiple is well illustrated by an acuaplane or water skis. A lift force is created by the downward moment imparted to the water which flows under the planing surfaces. The lift force thus produced is many times greater than the wtàtic buoyancy, the body is lifted to the water surface thus reducing residw1 resistance to a mînimi. The total resistance is then the total of the horizontal cponent of this lift force and the frictional resistance of the surface In prac SïIé flat plane

must be Improved upon to produce servicable hull forms.

Although the power requirements of a planing hull like the i

displacement type increases with displacement, specific resistance (')'A)

is

fairly insensitive to displacement and at high speeds specific resistance

will

reduce with increased, displacement. The p1n1 ng boat for the sake of

5

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32 B4-B

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63 F1 AB

FIGURE

2

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efficient aspect ratio is generally wider than a comparable displacement boat. From a resistance standpoint it is desirable, within limits, to decrease length/beam ratio with increases in speed. An example of a ty-pical planing boat is the USN - 63 ft. RB shown in figure 2.

3. Comparison between Types.

It is obvious from the above descriptions of the two basic types of high speed craft that there are fundamental differences between the types. A choice between the 2 types depends upon the specific requirements

of the individual design problem.

The usual arguments for the round bottom, semi-planing form are that although it may be limited in top speed in calm water it will out perform

nrd chine fully planing types in rough water and be more economical

at lower cruising speeds. There is considerable evidence to back this (t

up. On the basis of equal displacement and approximately equal cost,

the more slender semi-planing type can be built 20% to 30% longer than 'I i

the usual beamy fully planing type. As long as the displacement/length ratio is held at 150 or lass the semi-planing form can be economically driven to a speed/length ratio of 3.0 to 3.5, which is enough for many uses. The greater length of the semi-planing type aids in holding down the displacement/length ratio and allows a fine entrance for meeting head

seas. In rough water the slender hull designed for low residual resistance will usnlly slice through and result in a minimum of slaming and loss of

speed.

It is evident that comparisons can be made both on the basis of e displacement/length ratio or perhaps to do justice to the basic

differences in the types to compare them on the basis of equal displace- N ments with the proportions varied to suit the type.

Published data is available to compare the two types on the basis of equal displacement/length ratio. n one case the 2 boats have the wide proportions generally used for fully planing boats and in the other case the 2 boats have the slender proportions generally used for semi-planing types.

a. Wide Proportion Comparison.

References 1 and 2 report results of smooth water EHP tests for one rough bilge hull and 2 hard chine hulls.

6

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166.2 166.2 166.2

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Figure 3 is a comparison of smooth water EHP for these 3 models. It can be seen that the round bottom boat has less resistance below

of 3.0 - 3.5. Although these test only compare smooth water resistaxfce, I contend that in rough water the round bottom boat would be much more comfortable, easier to handle and result in less reduction in speed in rough water both due to resistance and the htnnan comfort element.

b. Slender Proportion Comparison.

Reference 3 reports a comparison of model tests in calm water for EHP and in waves for vertical accelerations in ahead seas arid for tendency to broach in following seas of one round bilge hull and 3

different types of hard chine huUs. For comparison the data for the narrowest chine boat is presented here.

COMPARISON OF MODELS

Hull A

Type Round Bilge Hard Chine, deep vee fwd.

LWL

117'

115'

BWL 19' 22.4'

LWL/BWL 6.16 5.127

Displacement 130 tons 130 tons

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81.17 85.5 7 // Hull CO1'1PARISON 0F NODT.S A

Type Round Chine Chine

LL

4.0.65' 40.651 40.65'

BX 10.26 Spray rail 9.52 at Chine 11.1 at Chine

L/BX 3.8 4.27 3.68

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FGL-Figures

4,5, & 6

simmiarize the test results. Figure

4

does not show the curves below 30 lmots however from the slope of the curves at 30 aiots it can be expected that the specific resistance of A is

considerably lees than B from O-30 kts.

The results of figures

4, 5, & 6

can speak for themselves. It can be noted that despite the narrow beam of the chine boat it shows

a definite calm water resistance advantage atV,/pgreater than

3.5.

Figures]

5 & 6

are important indicating that when the hard chine boat is given the1 i

slender proportions generally reserved for the round bIgtype, I

it can closely match the round bilge boat in flgl loadings and has superior anti-broaching characteristics. The advantage in this case of the chine boat in its tendency not to broach in the longer waves is probably attributable to the buoyancy and quick" lift features of the hard chine bow which allow it to ride over the longer waves.

-e. Comparison with Different Proportions.

A more realistic picture of general practice is to compare the two forms on the basis of eqii1 displacement with a chine boat of normal L/'B in the range of 3 to

4

and the round bottom boat with an L/B of approximately

5.

I regret that the only published data, Iaiown to the author, to document comparisons on the above basis is either

militarily classified or proprietary information of commercial designers, however it can be documented that in one case of full scale trials of

the two types (equal, round form 23% longer), that in state 3 seas and

above the semi-planing type was superior in both speed and seaworthiness. In another case ( equ1, round form 20% longer) of model testing in an artifical irregular wave pattern approximating a. state

4 to 5

sea,

the chine boat had 20% greater resistance at a speed/length ratio of

4.0.

d. Choice of Type.

On the basis of the above argument it is the opinion of this 'author that the semi-planing round bottom form should be used a great

deal more often than it is for medium speed range designs. A very large number of hard chine boats with max3inum speed/length ratios of approximately 3 to

4

sacrifice seaworthiness and speed in rough water for a small improvement in calm water speed. Another factor is that the estimated price of a boat is often measured by the length rather than by the more correct factor of displacement.

In favor of the fully planing boat is primarily its high speed potential and secondarily its capability to obtain high speeds even when heavily loaded. Low displacement/length ratios are an asset in any boat designed for high speeds, however in many instances low displacement/length ratios are a luxury which cannot be accepted. Thus the fully planing

boat is the only solution in many cases where a considerable load is to be carried. If truly high speeds are required in the range of of

4

to 10

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it is obvious that the fully planing type is the logical choice. Thus dispite Its drawhacks in the area of seaworthiness, there are good and sound ±easons why the hard chine type must be used for many designs and the seaworthiness problem must be accepted.

C. Development of the Hard Chine Type.

The fully planing boat is the only solution short of hydrofoils of piercing the so called "wave making resistance barrier" and it is therefore a necessity that its development be continually perfected until some

better alternative is found. The history ol' the design effort in planing boats has been a very well directed effort in producing a serviceable type

of hull which would be capable of these very high speeds. The fact is that there are now a number of variations of the hard chine planing boat which can with varying success make these high speeds.

The value of these developments cannot be overlooked however. it is the authorTs opinion that it is now time to give secondary consideration to improvements calculated solely to reduce calm water resistance and to give number one priority to improvements in the seaworthiness of fully planing type. It is important that the fully planing boat be improved in respect to its ability to maintain its speed in rough water and that it have reliable seaworthiness characteristics at high speed in rough water. This requires that the boat should have good directional stability combined with good maneuverability, a minimum of motions and. slam and be reasonably dry.

I cannot presume to set forth firm 'characteristics for the design of the perfect fully planing boat for rough.water service,

On the other hand an analysis of those forms which have been tried and those

showing current promise can provide guide lines for the search for the optimum type.

1. Variabl in Planing Boat Design.

As a first step in analyzing the various planing boat designs a

few of the variables need to be given individual

ttention. Assuming that displacement ïs fixed, or at least roughly fixed by the

power plant, its fuel and

the obher loads to

be carried

nil

other features become variable.

a. Beam.

Beam in planing boats is a factor which has been given

a great deal of study. The beam at the chines determines the aspect ratio of the planing surface and it has a definite effect on the loading and resistance. Some designers compare chine boats on the basis of speed/beam ratio

(-).

One popular loading coefficient is

where A is mean chine beam X projected length of chine, (for furhe' details see reference

4).

These

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and many other coefficients associated with chine boats attache a great deal of importance to the beam at the chines. From a purely resistance point of view this is correct since there is generally a particular

L/ which is optimum for a given speed. Optim beam will generally increaêe with speed until very high speeds are reached and then the

optimum beam reduces. The determination of optimum beoni for low resistance is important, however almost all the work to date has been based upon low resistance in calm water without due regard to the effect of beam on

seaworthiness. Contrary to the requirements for low calm water resistance, in rough water the beam should often be somewhat reduced to provide improved seaworthiness qil ities.

b. Deadrise.

Angle of deadrise is a factor which typlifies the give and take aspect in respect to resistance and seaworthiness. Starting with a

rectangle of zero deadrise as the best planing surface, the mininiinn refinement is to point the forward end and to give the forward sections some deadrise. From this meager start there are various refinements producing numerious practical hull forms incorporating a variety of

degrees of deadrise. The basic problem is that a fair waterline entrance and some deadrise is a minimum refinement necessary for running in broken water, however a fine entrance and deadrise reduce the planing efficiency. As a result there is a strong temptation to use a low chine and a low angle of deadrise to enhance the planing efficiency. Another factor is that dead.rise has a more adverse effect on calm water resistance at the higher speeds, where it is most desirable in its favorable effect on pounding. In practice the after hj1f of most chine boats has very little deadrise, but there is more variety in the treatment given to the forebody. This introduces the factors of twist and forefoot which will be treated separately below.

In summary it can be said that deídrise definitely has

an

adverse effect upon calm water resistance, however it is necessary for reduction of slam and combined with a pointed chine intersection is necessary to provide an acceptable bow. As a factor in reduction of

slam it is advantageous to use fairly high angles of de1rise of 200 to 350 in the slamming area. If the deadrise is carried through to a minimum of 150 at the transom, the effect on the lateral plane thus produced will greatly enhance the directional stability and banking in turns. The overall

benifical effect of liberal deadrise will generolly result in a boat which in all but the calmest water will out perform a boat of low deadrise.

c. Flam, Flare, Rake of Stem.

The shape of the sides above the chine has no effect on the

10

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calm water resistance and only a secondary effect upon rough water performance. However it can be seen that liberal flare and some(fl.i) will enchance the seakeeping of the boat and will provide greater buoyancy to lift the bow when plunging into an ahead or following sea. This will benefit dryness and help to aleviate the tendency to broach in the

following sea condition. Forefoot.

The characterof the forefoot can have an important influence on the maneuverability and handling of chine boat. As is the case with many features there are good and bad points about any one type of forefoot.

A deep forefoot is a help in close maneuvering at slow speeds since it holds the bow letting the flatter afterbody swing around.

When used with concave bow sections the deep forefoot slices nicely into seas and. lays a low bow wave contributing to dryness and will add a little buoyancy to make up for that lost by the concavity. Many very beautiful and clean riding boats use a fairly deep forefoot to

advantage. However, there is one important disadvantage which I feel rules out any pronounced forefoot on boats intended for all weather

use. It is that very same feature which assists slow speed

maneuvering. At high speeds if the forefoot takes charge it can cause broaching in a following sea or an overly quick turn, either of these is dangerous and to be avoided if at 11 possible. A very simple and ingenious solution which has been used at least by one designer is to use a chopped off forefoot for the safest high speed running combined with a small retractable centerboard placed well forward to provide the desirable forward lateral plane for close manauvering at slow speeds. This appears to be a very sensible way "tO have your cake arid eat it too".

Length, Loading.

Length is probably th most significant characteristic of any boat. Almost every seaworthiness feature is enchanced by using the

maximum economical length. The one feature which suffers is turning circle, in general turning circle is a function of boat length and in a very few cases where short turning circle is mandatory this must be taken into account. Although not so much a feature of seaworthiness it may be that to have a good aspect ratio for efficient planing the

maximi. economical length may not be used. However for good seaworthiness it can be iriade a good general practice to use the maximum, length

possible since the speed in rough water will be aided by the reduced and the lower trim resulting from the higher beam length ratio. As indicated above in figures 4., 5, & 6 the slender chine boat can provide

a good combination of the seaworthiness of the slender semi-planing round bottom type with the lower high speed resistance of the chine type.

(19)

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Js for minimum 8llowable length it is desirable to keep the displacement/length ratio below 200 if possible. The author has worked on designs with displacement/length ratios of over 300 but this is definitely not ari economical loading and far from desirable. The

corn-pansons shown in figures 7 and 8 (from reference 5) give a good idea of the advantages of length in reducing the slamming impacts iii rough water and the lower power required with lower loading.

f. Sections.

There are three general types of sections used for chine boats and they all have their virtues under certain circumstances. The

two basic types are concave and convex sections. The third is "bell" sections which are a combination of the first two, being round or convex on bottom and concave near the chine.

In general the concave sections are dry, throwing the bow wave clear of the boat, they also usually produce flater more efficient buttocks in the forebody. However they also are usually associated with pronounced forefoot which has been condemned above and the hardness of the bottom near the chine tends to create excessive pounding.

The main drawback of the convex section is that it is wetter and usually does not provide as fine an entrance for slicing through short waves. The wetness can us11y be effectively corrected by spray rails at the chine. The fullness of the bow although not as desirable in short waves will give desirable buoyancy to hold the bow from burying into

long

waves, particularly in following seas and will help combat broaching.

The "bell" bottom is an attempt to cbine the best features of both types and it definitely has merit in this respect. Its lack of popularity is robably attributable to the expense of this hull form

when constructed of wood, however with the advent of larger fiberglass hpllR it may find greater popularity.

In summary it is the author's experience that the reduced slamming of the convex section makes it the most desirable for rough water use.

g. Spray I.âils.

Spray rails are a useful and generally necessary device on any high speed boat. On hard chine types they are usu11y fitted at the

chine and run from the stem at least to midships and generally all the way to the transom.

In

some cases the spray rails may actually cause an

increase in resistance, but usuilly the resistance will be reduced. 12

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-I

They definitely contribute greatly to dryness and their use is desirable on all high speed boats. Reference 6 is an interesting report of com-parative model tests evaluating the use of spray rails on a number of small craft.

h. Skegs.

Skegs are sometimes used on high speed small craft. The usual.

purpose is to improve directional stability. They also may be used to counterbalance the effects of a deep forefoot to move the center of lateral plane aft of midships.

Although there are des igris which require skegs it is the author's opinion that good directional stability can be achieved by other means and there is no reason to penalize a boat with the increased resistance which is caused by a skeg.

j. Transom Width.

The arguments about transom width involve both resistance and seaworthiness. In favor of a relatively narrow transom is the fact that the narrower afterbody presents less wetted surface thus reducing

resistance, also the narrower afterbody will reduce the tendency to broach in a following sea since it will be less buoyant. On the other side of the coin is the dynamic transverse stabilizing effect of a broad stern particularly in the case of a warped bottom which carries its

twist 11 the way to t1 transom. The wide footing of a broad transom is also helpful at higher speed/length ratios where the boat is likely to

jump practicully clear of the water. In this case the broad footing will help hold the boat from rolling over on one side when the support is temporarily removed from the forward part of the bottoni.

On the basis of the above it is my contention that the broad transom of 80% to 90% of maximum chine beam should be used for smAller craft with speed/length ratios in excess of 5.0 and that the

narrower transom of. 65% to 80% should be reserved for the larger sizes which generally have lower speed/length ratios and less tendency to jump clear

of a wave.

j. Twist.

r..,1, . Some authorities place a great importance upon having a

-ìaximti of twist or warp in the after helf of the bottom which is the main plañing surface. The arguments are based upon lower calm water resistance.

Comparisons of a number of model test results seem to confirm that an aftorbody which is nearly a prismatic surface has the least resistance.

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Moro importanthowever, than low resistance1is the fact that

as argued

above it is desirable from a seaworthiness standpoint to

carry relatively

high deairise the full length of boat and this automatically

precludes

any appreciable twist in the afterbody planes.

k.

Wedges.

Transom wedges, hooked buttocks or transom flaps

are Fill

used to reduce dynamic trim.

Wedges are generally used as corrective

devices to help a heavily loaded boat over the resistance htrap at the

early planing speeds and to reduce trim at high speed

to reduce slamming.

Hooked buttocks or buttocks with

reverse in the last 10% of length are

simply premeditated wedges used for the

same purpose.

Transom flaps serve the same purposes but they have the

feature of being adjustable to suit the speed, loading

condition and

sea state.

The adjustable feature muces the transom

flap the most

useful of the three devices,

However it has the drawback of requiring

flat or nearly fJt deadrise at the transom.

This requirement runs

counter to the desirability of having good deadrise at

the transom.

The unpredictable affect of hooked buttocks

precludes their

use unless the subject lines are a redo of previous successful lines,

or the lines are model tested.

Adjustable transom flaps must be ruled

out if deadrise is to be used at the transom.

This leaves wedges as the

only practical device for most cases,and

their use is generally limited

to corrective measures rather than

ieatures of an original design.

2.

Analysis of Conventional Forms.

On the basis of the above discussion a critique can be made of the

effect of these features on some actiìl hull forms.

The following are some

conventional hull forais.

a.

Typical Developed Surface Type.

The typical developed surface type is used in

many pleasure

boats

to about 40 ft. LOA and some larger commercial

craft. It has

the very desirable feature of being adaptable to

easy forming with large

sheets of plywood, steel or aluminum.

Figure 9 represents a good

example of this type.

Reference 7 and figure 1 of reference U report the

resistance characteristics of this form and reference 8 reports the

resistance characteristics of a wider beam version including

a comparison

of the two.

(24)

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This type of form is very good for small craft operating in protected water. It combines good calm water resistance with limited rough water qualities. Its major drawback is low deadrise which causes

pounding in rough water. If trim is reduced to reduce pounding it becomés wet and is more difficult to steer since the full sections

forward being full and buoyant tend to be pushed first to one side and then the other when encountering head or following seas. A sub-stantial increase in deadrise would increase resistance but would do a lot to improve seaworthiness. For speed/length ratios under 5 a narrower transom could be used to advantage.

b. USN W II Elco P Ts.

Two examples of convention concave bottom planing boats are the 70 ft. Elco P T of early W II & t1improved 80 ft version which followed. The lines and principie dimensions of the two are shown in figures 10 and U.

Although the primary reason for the 80 ft. boat -was to have a bigger boat to carry a heavier load, a dimensionless comparison

shows the effects of the difference in length/beam ratio. Reference 9 reports the calm water resistance of the two at an equal dimensionless loading coefficient. The wider boat as would be expected has higher

specific resistance at the lower h1f of the speed range and lower specific resistance at higher speeds except at the highest speeds. The important point of this is that the calm water resistance is very much the same for the two. Thus at the designed speed the narrower boat with

greater deadrise does not lose much in calm water speed while it has improved seaworthiness characteristics having greater deadrise and narrower beam. Both boats are fairly dry due to the concave sections. The major drawback of both boats is that they do not have enough

deadrise.

The 70 ft. boat typlifies the earlier attemps to make large sea going boats patterned after smaller rimabout types which had been developed for high speeds on protected waters. The only noticeable

change from smaller types is the narrow transom. It has very low deadrise and the concave sections are very flat near the chines. This makes for severe pounding in rough water which in practice necessitated

substantial reductions in speed to safeguard both the boat and its crew. The 80 ft. boat was an improvement over the 70 ft. boat and although designed some 20 years ago, it is typical of many current vee bottoni designs, although for practical purposes most smaller boats do not have as narrow a transom. The raised height of the chine forward is helpful allowing greater deadrise without any pronounced forefoot, both of which are good. However this type of hull still

does not have as much deadrise as is desired for rough water service and it is not carried through to the transom which would improve directional

stability el-iminating any requirement for a skeg. 15

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c. Seaworthiness of convention forms.

The three designs discussed above are representative of the majority of planing craft in use today except that the P T Boats are

5roportionaUy narrower than sm lar smaller boats of the same type (see figure 12 and reference 2 for typical examples of concave bottoms for 40' LNL). All of the boats discussed do not have enough derrise

to effectively relieve pmmding, and all 3 would require skegs to give better directional stability. None of them have an viesirab1e forefoot. Of the three only the low chine 70' P T boat would be unreasonably wet, although the developed surface boat is dependent upon its spray rails to keep it dry.

3.

Analysis of Unconventional Forms.

There aie a number of unconventional forms which have been

designed to produce either improved resistance or better seaworthiness and handling. In a few cases a good job has been done on both scores. The following are same outstanding examples chosen to illustrate some of the poorer designs and some particularly promising ones.

a. Inverted - Vee Type.

Figure 13 shows a typical inverted - veo type planing hull. The resistance characteristics of this type are reported in reference 10 and figure 7 of reference II. From a resistance standpoint the only outstanding feature is low specific resistance at high displacement/length ratios and at high speed/length ratios. It was originally used for small ruabouts and its low resistance at high speed/length ratios made it a popular small boat.

The boat has some unusual features in respect to

maneuverability and seaworthiness. The inverted - vee bottom produces a very dry boat since it rides over its own bow wave. The fairly high dead-rise of the f ortiard sections satisfactorily dampens pounding in a short

chop and small waves. However in rough water and large waves this type pounds severely even at medii.0 speeds, this one drawback is enough to rule out this type for a boat intended for offshore use. Another serious drawback is the poor maneuvering characteristics of this type, it is hard to steer due to the large lateral plane of the vertical sides and takes an outboard roll on turns.

Figure 14 (from reference 5) presents some rough water trial results of a 55 foot inverted - vee bottom boat. The data in figure 14 when compared with figure 7, which reports conventional boats during the same trials, indicates the rough riding qualities of this type.

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In surmary the inverted-vee bottom is not adaptable for use offshore in rough water. This conclusion is fully doctuented by the full report of some rough water trials described in reference 5.

b. Deep-Forefoot, High Twist.

The forms shown in figures 15 and 16 are examples of a popular hifi form using a deep forefoot with concave sections

producing a large angle of deadrice in the slunnng area, twisting to flat sections at the transom.

This type of form may have slightly more resistance than one with less twist but it nevertheless is quite popular. The reasons for

its popularity are quite obvious. The fine bow sections slice nicely into seas, tl concave sections throw the bow wave clear giving

unusuiiy good dryness and the high death'ise in the s1anning area

cushions out pounding in ii but the roughest seas, and the flat sections aft produce lift to reduce trim at high speeds and thus aids in

re-ducing pounding. All these features tend to produce a fairly nice riding hurt form.

However this type of hpii form has its drawbacks also. First the coicavity of the sections near the chine, which is necessary

o encourage spray departure approaching the horizontal, is a cause

of severe impacts when alarming into really rough water. Second and more important is the problem of directional stability particularly in a

following sea. Any boat operating in waves has a tendency to yaw due to a variety of hifi and and propeller interactions with the buoyant and dynamic forces of the waves. This type of hull forni is particularly susceptible to yawing since the heeled shape of the hull, being

&syrmetricaJ. about the longitudinal centerline and radiciiy different in fullness fore arid aft, develops a transverse thrust causing a definite tendancy to yaw. This can be overcome to sane

extent by the use of a skeg fairly well aft but this of course reduce5 maneuverability and increases resistance arid even with a skeg constant ri.idder control is required to hold this type of boat on course. In rough going when the helmsman has a hard time just staying at the wheel this constant rudder control is hard to maintain.

Another detrimental feature of this type is that if the chine is raised relatively high and the forefoot is deep, the high angle of deadrise forward will fliow the boat to fall over on one side unless large re-entrant spray riis are used to produce concentrated lift at the

chines. This characteristic of rolling over on the chine is of course aggravated by a high center of gravity.

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-c. Nonoheth'on Forni.

The term inonohedron simply means a hull form using a

constant angle of deadrise over the main planing portioiof the bottoni. A particular hull of this type is a form advocated in in

reference 12. Figure 17 shows a typical form of this type. The ca]

water resistance characteristics are reported in references 13 and figure 8 of reference 11.

This form has better than average caJ..m water resistance

which can be expected from the long straight parallel run of the buttocks. The derrise at the stern gives good maneuverability combined with good directional stability. Unfortunately thia form has two rough water deficiencies. Ntnber one is wetness, the character of the forward

sections and the quick fr1] of the chine require very effective spray rails to throw dowii the bow wave. Ni.unber two is pounding, the abrupt decrease in deadrise from the stern to station 3 combined with

relatively low deadrise in the impact area produce high s1anndng accelerations in rough water.

This type of hull form has definite potential possibilities. The basic improvement required is an increase in deadrise which

would increase resistance and probably cause transverse instability unless accompanied by corrective devices. A number of variations of this type of form have been used, some of them incorporating an

improved bow to reduce wetness. But without any marked overall increase in deadrise or at least increase of deadrise ITA the impact area

between stations 2 and 5 no substantial improvement In pounding can be expected.

d. Clement Form.

This form is the product of a methodical analysis of the cauri water resistance characteristics of a variety of designEihich have been tested over the years at the David Taylor Model Basin. For lack of a better name I c1l it the 'C1ement Formit for the man who designed

it. Figure 1 shows the forni. In reference 14 Clement outlines hi procedure and reasoning and reports the resistance characteristics of his form. A comparison of figure 17 with figure 18, and figure 8 of reference U with figure 1 of reference 14 shows the similarity of the Clement form with the monohedron form. The basic differences are the low chine and wide convex sections of the bow of the Clement form.

1he-Clement form also has an unusually wide chine forward of amidships and an unusually xarrov' transom. It is essentially a development of the monobedron form, it ha very low specific resistance, slightly better than the monohedron at all speeds tested, and the bow on the Clement form is calculated to reduce the wetness problem of the form illustrated in figure 17.

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Unfortunately no full scale craft has ever, been built using the Clement form and the model has never been iested waves, therefore no data is available to evaluate the seaworthiness qia1ition of this form. However it must be recognized that this form was developed primarily for low caJ.m water resistance anddespite the designers allegatiar43 to the contrary,it is this author's opinion that this form would be

guite unsatisfactory in rough water. Nber one, for the sake of

planing efficiency it has very low deadrise in the slaxini..ng area of the bottom, and secondly the wide chine beam in the forward portion of the hull would aggravate slanning and would be wet and resistful when heading into a short sea.

This form indicates a serious attempt to use model basin techniques to produce a good fast boat but it does not seem to reflect a full appreciation of the primary need to reduce pounding in rough water. A substantial increase in deadrise compromising calm water resistance for better rough water resistance would go a long way toward inaid.ng this form a practical sea going design.

Constant Deadrise - Conventional Proportions.

The form shown in figure 19 is a development of the form in figure 9. It was designed to be used as a yardstick for comparative evaluation with figure 21 below. 18 ft. manned models of each have been built. The intention was to have a design of a conventional type with

the best rough water characteristiossib1e without any really novel or unconventional features.

It can be seen fran the lines plan that this form bears some resemblance to figures 17 and 18 above but that the form in figure 19 has a more seakindly bow and less beam than either of the others. The lack of pronounced forefoot and the constant deadrise of the afterbody lend themselves to good directioni1 stability, the deadrise at the transom is good for turning. The drawback of this form is that although the deadrise is liberal by conventional standards, it is still not enough to eJiixiinate seveipou.nding in rough water.

Hunter Form.

The Hunter Fm is namad for C. Ra'mond Huxt, the designer has perfected it. This form is a development of the constant dead-. riso types illustrated in figures 17, 18, and 19. This form is new and the designer has never allowed the lines to be published however figure 20

i thought to be a fairly correct representation of this form.

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This author has never ridden in a boat of this type but on the basis of the Lcwing reports in references 15a - 15g there is no doubt that this fi'Ii proven itself as an outstandin rough water performer. An analysis of t1 lines plan will explain the features which contribute to the seaworthiness of this type.

The Hunter has deep deadrise of 23° to 25° over the entire riding surface which provides a substantial reduction of slaning impact and gives good directional stability. Normally high deairise of this sort will cause transverse instability with a tendency to ride over on one side, unless the VC G is extrely low. Also a high

deadrise planing surface is not usiiy an efficient enough planing surface for a boat intended for very high speeds. However the Hunter form overcomes both of these drawbacks by the use of a rnnnber of

longitudinal spray strips on the bottom with a wedge shaped cross section giving a horizontal lower surface about 2 inches wide. These

longitudinal spray strips provide the necessarynanvc transverse stability and greatly increase the planing efficiency. They also give a high measure of dryness and reduce the wetted surface to a minimum. A comparison of trirfls of Hunter form boats with the model basin resistance

characteristics of the Clement form of figure 17 indicate that in respect to resistance t1 Hunter form is as good or better than the Clement form.

Another novel feature of the Hunter form is the extremely wide beam, the extension of the bottom surface will outboard of the static

waterline provide stable platform at rest and at low speeds which due to the high dead rise would not be true if the chine was at or below the static waterline. This wide planing surface also provides a good aspect ratio

for high speed/length ratios and the bottom spray stripireduce the drag

- of this surface at intermediate speeds.

Another interesting feature used on some boats of this form is a small retractable centerboard located forward to provide good low speed maneuverability. This makes up for the lack o± forefoot which as noted above is an undesirable feature at high speeds.

This high dendrise form has a large and long lateral plane thus making the bow centerboard a most desirable feature.

There is no doubt that the Hunter Form is an outstanding example of a boat

which

has proven itself of being both capable of high speed in rough water and exhibiting a high degree of seaworthiness un3er adverse conditions. Ou the othar hand the Hunter form certainly does not represent the ult-rnte in the development of seaworthy high speed craft

for off shore use. As reported in references l5d and 15e in really rough going the Hunter form leaves much to be desired in respect to

pounding, violent motions and ability to maintain high speed. It is,,

however one of the best rough water high speed hifi forms developed to date and being a recent development, further improvements of this type can

be expected.

20

(41)

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g.

Planing Catnran.

A rather novel approach to the high speed seaworthiness

problem is the planing catamaran.

There are a nimber of current designs,

all of th

quite recent, for p1ing catmans.

One promising Lype is

shown in figure 21.

As can be seen from the lines plan this particular design

consists basically of two rigidly connected slender hulls whose planing

siirfaces are similar to water skis.

The division of the planing surface

into 2 separate pieces

1low

the use of narrow flat planing surfaces which

although flat are slender enough when taken separately that

1 nmming

impacts are not too severe.

The slenderness of the individual hulls

allows them to slice through waves.

To date this type of hull form has been used only for rather

nll outboard runabouts and there is therefore not much to base a

judgement upon regarding the adaptability of this type for off shore use.

flowever the small boats of this type have done well in marathon races in

competition with conventional boats of the same size (see reference

15c).

Bascd upon trial comparisons of 18' manned modela of boats

to the lines of figure 21 and a figure 19, the resistance of figure 21 is

slightly less than figure 19.

This points up the efficiency of the

flat

laning surfaces.

In an 18" short chop the catamaran did not pound.

1hereas the more conventional boat of figure 19 would occasionally slam.

However the catrniran was constantly in motion bouncing along and

occasionally was momentarily lifted by aerodynamic lift on the tunnel

roof, and would then come down with a slight jolt.

This was a cyclical

sequence of motions and although the motions are

not severe, they are

constant.

Further impression based upon uxiconclusive testing indicates

that this type of catamaran requires rather low displacement/length ratio

and c.g. located well aft. In regard to a1aniiig it can be expected

that in really rough going the flat skis and perhaps the tt.mnel roof would

be subject to rather severe impacts and would produce objectionable

alarming.

In regard to inaneuveability, the catamaran does not bank.

The

lateral plane being effectively twice that of a conventional hull makes

steering by means of throttle differentil with twin screws desirable

in conjunction with conventionsl steering.

(43)

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g. Plum Boat.

Jill of the hull forms discussed above are of the stepless type, with continuous buttock lines. At higher planing speeds the stepless

type has a lPrge superfluous wetted area required only for proper long-itudinal support.

Stepped planing boats achieve a much greater reduction in wetted area by separating the water from a portion of the hull botttn aft of its

step. This type approaches ideal planing efficiency at high speeds, and is,

therefore, generally used for lightly-loaded racing boats. Attempts have been made to design stepped hulls which would carry significant payloads, but in general these have not been successftl, and the stepless type has, therefore, come to be preferred. The difficulty in designing a stepped hull for a hea'vy payload is that no single position of the rear planing surface is satisfactory for both low and high speeds.

A logical solution to the problem of designing a hull which would possess the advantages of the stepped type and obviate its disadvantages is a hull having a shnjlow main step and an adjustable rar

pinlg

surface. Such a design was developed during the period

1925-1935 by

John Plum, who has been employed by the David W. Taylor Basin since 1942. Previous load-carrying stepped hulls which were satisfactory at low speeds were found to be inefficient at high speeds, and those which were efficient at high speeds were wet and treacherous, and were inefficient at low speeds. Furthermore, the steps of previous designs have been of considerable

depth, which added to resistance at cruising speeds and also presented a difficult structural problem.

Mr. Plum's boat has a hull in plan view similar to the Clement shown in figure 18 above except that the transom is even narrower having chine beam at station 9 approximately one-half the maximum chine beam. The

naximum chine beam is at station 3. The main step in the form of a wedge is located just aft of station 5 and the buttocks aft of the wedge 1ise at about 40. The adjustable planing surface, or stabilizer, at the stern, is connected to a pneumatic piston in the hull in such a way that its

vertical position can be controlled by compressed air. At low speeds the stailizer is held close to the hull at an angle equal to that of the after body keel. At high speeds the stabilizer is lowered and its angle ehanged: athat it is approximately parallel to the forebody keel. At high speeds 'the boat planes on a small area forward of the main step and on the after portion of the stabilizer. The trim angle of the hull can be adjusted by the pilot

by

changing the vertical height of the stabilizer. l4hen lowered,

the stabilizer is free to rotate in an approxiate1y horizontal plane about the piston which connects it to the hull. This gives the stabilizer a caster

action which makes it trail whether the hull is on a straight course of turning.

22

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The model tests have shown that the Plum design has exceptionally low calm water resistance at high speeds, and that it efficiency is not

appreciably affected by changes in C.G. location. It is expected that the trim control made possible by the unique adjustable stern planing surface will pillow a reduction in pounding in rough water by lowering angle of attack of the main forward 1aning surface. This will not of course elim-i nate all slamming, but it should be an improvement.

The location of the engines in the Plum design is just forward of the step, in the region where the impact forces will occur at

high speeds. The presence of a large mass at the location of the wave impacts will, it is believed, result in lower angular accelerations and hull

stresses than are suffered by the conventional f orm. The Plum design should be safer than conventional designs at high speed in a following sea because of its narrow stern and longitudinal V, which give a higher, safer trim angle.

A 25 ft. manned model of a "Plum Boat" has been built to evaluate its full scale performance. Various mechanical deficiences have postponed trials of this boat. Until rough water trials of the manned model are run it is hard to predict how well the boat will actw3lly perform. However, the calm water model tests have already shown that this boat satisfactorily overce many of the deficiencies of previous attempts to design stepped planing boats for offshore use.

D. Conclusions and General Rmark.

1. Present State of the Art.

There are a number of uses today for high speed srn11 craft. The usefulness of these boats is unfortunately lmted by the lack of

seaworthiness of many boats designed for high speed. The factors

contributing to attainment of

high

speeds have beexi given a great deal of emphasis, but improvements in seaworthiness have not paralleled the im-provements in speed. There are certain conflicts between the requirenucs

for high speed and seaworthiness. To date most progress toward solution of these conflicts has been by trial and error on a case basis, which is by nature a slow evolution. The optiniu hull form has by no means been developed.

Model testing in rough water is a relatively new field and has not been done to any great extent. Comparative model tests under controlled conditions offer the possibility that the trial and error evolution of the r.ast can be accelerated.

(46)

Solutions Other Than

Hull

Form.

This paper has discussed hull form only. Outside of the general area of hull form two very promising developments hold great prnmse of

providing seaworthy high speed small craft. These are as follows: Hydrofoil support and air cushion, suDoot; Small seaworthy small craft capable of high speeds in open water have been developed using fully subnerged foil systems in conjunction with electronic flight control devices; and surface percing foil systems iing foil geometry as the primary flight control device. Both of these configurations have been sufficiently developed to the point where the technical feasibility and the superior rough water pformance are now proven facts. The one ajor drawback is expense and a minor drawback is that except for some retractable configuratiorithe draft and beam of the foils is not easily adaptable to many small boât facilities.

Air cushion support has not been developed for use on

rnall

craft to any great extent. It can be expected that as general developments are mañe in air support systems that adaptation for use on high speed

small craft will a logical application since the basic features of low water resistance and smooth motions are inherent to this type of support.

Future Prospects.

High speed small craft seaworthy enough to be classed as "all weather craft" will probably never be possible without employment of hydrofoil Support. But short of this there is a lot which can 'be done.

Applications such as navy patrol boats, oil±.g crew boats, passenger ferries, and private yachts all demand more speed and improved rough water

dependability. Small boats traditionally ha-v'è been economical solutions to many transport and naval requirements. Today when speed is no longer a ].uury but a necessity it is iAcubent upon small craft designers to develop

practical seaworthy boats keeping pace with modern developments in other fields.

24

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(47)

Rerences

Pournaras, U.

A.and Sherman, P; "Model test Results and Predicted

for a Round Bilge 40 ft. Aircraft Rescue Boat Design

from

Tests

of

Model 4525' DT

Report No.

1002, November 1955.

Eleftheriades, P. K.: "Model test Results and Predicated Eli? for two Designs for the MX 2 4.0 ft. AVR from Tests of

Models 4520 and 4543; DT Report No. 971, August

1955.

Du Cane, Peter; "Model Evaluation of Four High Speed Hifil Forms in Following and Head Sea Conditions"; Paper presented at "Symposium on

ehavior of Ships in a Seaway" held at the Netherlands Ship Model Basin, Wageningen; September 7th - 10th 1957.

Clement, E. P.; "Aialyzing the Stepless Planing Boat";

DTMB Report No. 1093, November 1956.

5.. Neyer, E. R.: "Results of

Standardization, Tactical, and Rough Water Trials on Five Aircraft Rescue Boats'1; Dfl

Report No. 1108, April 1957.

Ashton, Randolph; "Effect of Spray Strips

on Various Power-Boat Designs"; E. T. T. Technical

Memorandum No. 99, February 1949. Clement, E. P.:

"Experimental Boat-Hull Form Test Program, Basic Form, Model 4300, Resistance Characteristics"; DTNB Report No.

740,

November 1950.

Curry, J. H.: "Model

Test Results and Predicted EHP for Scheme "L", Experimental Boat. Hull Forni test program, from tests of Model

4312"; DTMB Report No. 757, March 1951.

Clement, E. P. and Kimon, P. M.: "Comparative Resistance Data for Four Planing Boat Designs"; DTMB Report No. 1113,

January 1957. Clement, E. P.: "Model

test Results and Predicted EHP for Scheme I, Experimental Boat-Thill

Form test Program, from tests of model 43O DThIB

Report No. 764, April 1951.

II. Clement, E. P. and Tate, C. W.: "Smooth Water

Resistance of a Number of Planing Boat Designs"; DTMB Report No. 1378.

12. Lord, Lindsay; "Naval

Architecture of Planing Hull , 'Revised Edition;

Cornell Maritime Press,

1954.

(48)

Curry, J. H.; "Experimental Boat-Hull Form test Program, Scheme "J" Model 4310, Resistance Characteristicstt; DTMB Report No.

738,

0ctob 1950.

Clement, E.P.; "Development and Model Tests of aix Efficient Planing Hull Design"; DT Report No. 1314, April

1959.

"Revolution Hunt Style"; The Skipper (agazine), July

1958.

i''hittier, Bob- "Boats and Boating"; pg

50-52,

The Salt Water Sportsman (Magazines, September

1958.

Bowen, Ezra; "Smooth Ride for Rough Seas"; pg

33-35,

Sports Illustrated (Magazine), January

26, 1959.

Mitchell, C.; "Glory Be To Power"; Sports Illustrated (magazine), April

25, 1960.

Bertram, R. not for the faint of heart"; pg

28-30

and

53, The

Skipper (Magazines, June

1960.

".A Redly Fast Fast Cruiser".; pg

341+ - 346,

The Motor Boat and Yachting (Magazine, British), July

1960.

"For High Speed in Rough Water" pg 63 and

105,

Yachting (Magazine), August

1960.

(49)

Bib1ioranhy

Du Cane, Peter; "High Speed SniaJ.1 Craft," second edition; Temple Press Ltd., London, 1956.

Phillips - Birt, D; "The Naval Architecture of Small Craft"; Philosophical Library, New York,

1957.

De Groot, B.; "Resistance and Propulsion of Motor Boats"; International Shipbuilding Progress, Vol. 2, No.

6,1955.

Nordstr6m, H. F.: "Some Tests with Modls of Small Vessels";

Publication of the Swedish State Shipbuilding Experimea1

Trnk,

Goteborg,

No. 19, 1951.

Murray, Allan B.; "The Hydrodynamics of Planing Hulls"; SNAME transactions vol

58 (1950) pg 658 - 692.

Du Cane, Peter; "The Planing Performance, Pressures, and Stresses in a High Speed Launch'; Institution of Naval Architects (British) -transactions, vol

98 (1956)

pg

469 - 490.

Cytaty

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