Correlation of resistance test results from fixed- and free-to-trim methods for a dynamic-lift craft (Model 4667)

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11//111111111111111111111111

DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

BETHESDA, MD. 20034

CORRELATION OF RESISTANCE TEST RESULTS FROM FIXED- AND FREE-TO-TRIM

METHODS FOR A DYNAMIC-LIFT CRAFT (MODEL 4667)

by

Nadine Hubble

APPROVED FOR PUBLIC RELEASE:

DISTRIBUTION UNLIMITED

Apri 1 1972

REPRODUCED BY:

NT.§,

u.s. Department of Commerce National Technicallnfonnation Service

Springfield, Virginia 22161

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DOCUMENT CONTROL DATA·

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S"ClIrltr (li1s."i(;c"tlrlnof title, hnd\ (If<lostructHtldItHll'x;",! ,1f/notatiun-nllI .... ' 1J('etlterf>d when 'he overallTeport ; .... cliJ ... sified)

1 ("l~I\.., I NAT IN l> A e l l VI T Y (('otpllrate ,iJllthor) 2D.REPORT SECURITY CLASSIFI<:AlION

~aval

_{Ship Research and Development Center}

_UNCLASSIFIED

Bethesda,

~Iaryland

20034

20. GROUP

,

REPORT TITLE

CORRELATIO~

_{OF RESISTANCE TEST RESULTS FRm1 FIXED- AND FREE-TO-TRIM METHODS FOR}

_A

DY!\MlIC-LIrT CRArT

(~IODEL

4667)

4 (lESCR1PTIVENOTES(Type of report and inclusive dates)

5 AU THQRtSl(FIr/it name, middle ;nitial, last name)

E. Nadine Hubble

6 REPORT DATE 78. TOTAL NO. OF PAGES

r

b

'6

NO OF REFS

April 1972

₉₇

BB. CONTRACT DR GRANT NO 98. ORIGINATOR'S REPORT NUMBER(S.

b. PROJEC T NO

Subproject SS4606

3544

c.

Task 1707

9b. OTHER REPORT NotS) (Anyother numbers thatmay beassigned

this report)

d.

10 DISTRIBUTION STATEMENT

APPROVED FOR PUBLIC RELEASE:

DISTRIBUTION UNLHIITED

I I SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

Naval Ship Systems Command

"

ABSTRACT

Customary methods are discussed for determining the resistance

characteristics in smooth water of hulls of planing and hydrofoil

craft.

Results are presented and compctred for a hull, with possible

application to either type of craft, which has been tested by both

the fixed-trim method, generally used for hydrofoil craft, and the

free-to-trim method, generally used for planing craft.

Recommenda-tions are made for conducting future resistance tests of

dynamic-lift craft,

i.

e., both planing and hydrofoil hulls

J

in the fixed-trim

mode as well as for converting the data to the form of free-to-trim

test data to facilitate general design studies for both types of

craft .

SIN 0101.807·6801

(PAGE 1)

UNCLASSIFIED

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Page

ABSTRACT

.•• . • • • • • • • • • • • • • • • . . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

1 ADMINISTRATIVE INFORMATION

•• • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • •

1 INTRODUCT ION

.• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

1 TEST PROCEDURES

• . • . • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

3 TYPE A TESTS

• • . • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

3 TYPE B TESTS

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

4 TYPE C TESTS

.. • • . • • . • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

4 CRITERIA FOR COMPARISON

•..• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

5 MODEL DESCRIPTION

• . • • . • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • •

5 BASIC FIXED-TRIM DATA

••••.••..•.••••••••.••••.•••••••••••••••••

5

FREE-TO-TRI~l

DATA

.••....••..•••.••••.•.•••••••••••••••••.••••••

6 RESISTANCE STANDARDIZATION

• . . • • . • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • •

6 DATA CONVERSION

•.•••.•••••..••••••.••.••••.••• • • • . • • • • • • . • • • • . •

6 COMPARISON OF RESULTS

...• • . • • • . • • . • • • • • . • • • • • • • • • • • • • • • • • • • • • • • . • •

8 CONCLUDING

RE~lARKS

. • . • • • . • . • . . . . • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • •

9 APPENDIX A - PROCEDURE FOR

DE~IVING

RISE IN CENTER

OF GRAVITY

..••..••••••••••••••••••••••••••••.••••••••

23 APPENDIX B - FORCES AND EQUILIBRIUM EQUATIONS FOR THREE

TYPES OF R2SISTANCE TESTS

•.•••••••••••••••••••.••••••

25 APPENDIX C - TABLES AND GRAPHS OF BASIC FIXED-TRIM

RESISTANCE DATA FOR MODEL 4667

•• • • • • • • • • • • • • • • • • • • • • •

43 APPENDIX D - TABLES OF CORReLATED DATA FROM

FIXED-AND

F~EE-TO-TRIM

TESTS

•••••••••••••••••••••••••••••••

71

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11

12 I

Page

Figure 1 - Wetted Area of Planing Craft

...••..•..•...•..••.•..

Figure 2 - Body Plans and Form Characteristics of

Models 4667 and 4667-1

...•..••...

Figure 3 - Comparison of Trim and

Resistance-to~Lift

Ratio for a lOO,OOO-Pound Boat, Derived

from Fixed- and Free-to-Trim Testing

Techniques

. . . .

13 TABLE 1 - CONDITIONS FOR COMPARISON OF PLANING-HULL

FORMS, BASED ON PATTERN OF SERIES 62

•....•..••...•.

7

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CG

d

g

LCG

L

c

o

S

v

VCG

w

NOTATION

Projected planing-bottom area, excluding area of external

spray strips, in square feet

Hull loading coefficient

Breadth or beam over chines, excluding external spray

strips, in feet

Mean breadth over chines Ap/L p in feet

Breadth over chines at transom in feet

Maximum breadth over chines in feet

Center of gravity

Vertical depth of 0 below level water surface in feet

Speed-displacement coefficient

V/~Vl/3,

also referred to

as Froude number based on volume

Acceleration due to gravity in feet per square second

Longitudinal center of gravity, i.e., x-coordinate of CG

in the hull coordinate system, in feet

Projected wetted chine length, excluding spray, in feet

Projected wetted keel length in feet

Projected chine length in feet

Origin of coordinate system for dynamic-lift hulls

Wetted surface area of hull underway, including area of

sides wetted at low speeds and wetted bottom of spray

strips but excluding area wetted by spray, in square feet

Speed of boat in feet per second, unless otherwise specified

Vertical center of gravity, i.e., z-coordinate of CG in the

hull coordinate system, in feet

Water density in pounds per cubic foot

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x,

y,

z

x',y',z'

\)

p

Body axes and Cartesian coordinates for dynamic-lift

hulls.

The y-z plane with x

=

0 passes through

inter-section of transom and chines.

The x-y plane with z

=

0 is the baseline of the hull as drawn.

The x-z plane with

y

=

0 is the longitudinal centerplane of hull.

Note that

the origin 0 is at the intersection of the keel and transom

if, and only if, the keel coincides with the baseline, and

the transom is perpendicular to the keel.

Fixed axes and Cartesian coordinates relative to the earth

but with same 0 as the hull coordinate system

Deadrise angle at transom

Displacement at rest in pounds

Shaft inclination from x-axis

Trim angle, i.e., angle between the level water surface

and x-axis (baseline of hull as drawn)

Kinematic viscosity of water in square feet per second

Mass density of water wig in slugs per cubic foot

Volume of water displaced at rest 6/w in cubic feet

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Customary methods are discussed for determining the

resistance characteristics in smooth water of hulls of planing

and hydrofoil craft.

Results are presented and compared for a

hull, with possible application to either type of craft, which

has been tested by both the fixed-trim method, generally used

for hydrofoil craft, and the free-to-trim method, generally

used for planing craft.

Recommendations are made for

conduct-ing future resistance tests of dynamic-lift craft, i.e., both

planing and hydrofoil hulls, in the fixed-trim mode as well as

for converting the data to the form of free-to-trim test data

to facilitate general design studies for both types of craft.

ADMINISTRATIVE INFORMATION

This project was authorized and funded under Naval Ship Systems

Command Subproject SS 4606, Task 1707, and the General Hydromechanics

Research Program.

INTRODUCTION

It is customary at many towing tanks, including those of the Naval

Ship Research and Development Center, to determine the smooth water

resist-ance characteristics of planing craft by free-to-trim model tests.

The

hull is constrained only in yaw and sway, and the trim and draft of the

hull vary with speed as dynamic lift is developed.

The model is ballasted

to a prescribed displacement at rest

~

and initial-trim

T

condition and is

o

then towed at varying speeds over a prescribed range.

With free-to-trim

tests, it has been the general policy to tow the model in either the actual

shaft line or an arbitrary shaft line for preliminary designs in an attempt

to simulate trimming characteristics representative of the hull when it is

self-propelled.

This method is referred to as a Type A test in this report.

If the thrust along the shaft line were the only force arising from a

pro-peller, this method of towing would likely give good agreement in trim with

the self-propelled condition.

However, there is a force normal to the

thrust, generated by a propeller in inclined flow, as well as pressure

forces, induced on the planing surface from propeller loading, which may

also have a significant effect upon trim.

Towing at an angle

(£

+

T)

to

the horizontal applies a vertical lift component to the hull in addition to

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the horizontal drag component so that the effective lift of the hull, i.e.,

the resultant of the buoyant lift and the dynamic lift, is less than the

gross weight of the model.

This lift from the tow force may be as much as

15 percent of the gross weight.

An alternate procedure for free-to-trim resistance tests is to tow

the model horizontally at the center of gravity CG.

This method is referred

to as a Type B test in this report.

In this case the effective lift is

equal to the gross weight of the model.

Data from this form of test can

be used to predict self-propelled characteristics for the boat with shafts

at any inclination or with systems such as the right-angle drive where the

propellers are normal to the flow, using the method developed by Hadler. I

The resistance of hydrofoil boat hulls, which have characteristics

similar to planing craft, is normally obtained by a fixed-trim technique,

referred to in this report as a Type C test.

With this method the model is

restrained in pitch (trim) as well as yaw and sway, and the towing force is

applied horizontally.

Since the hull lift and drag forces have to be

com-bined with the lift and drag of the hydrofoils to predict the hull attitude

and drag during takeoff, tests of this kind are conducted at numerous trim

angles and displacements to obtain the necessary matrix of hull-performance

data for takeoff studies.

Consequently, the data resulting from a set of

fixed-trim tests are also sufficient for predicting the hull performance in

the planing regime for a matrix of initial displacement and trim conditions.

The major objectives of this report are (1) to show that the

resist-ance characteristics for a planing craft at a particular initial

displace-ment and trim condition can be derived from a matrix of fixed-trim test

data, using the equilibrium equations, and (2) to correlate the results for

planing hull Model 4667, which has been tested by Types A and C methods.

Results from both Types A and C tests have been converted to the form of

Type B test data for comparison.

IHadler,

J. B., "The Prediction of Power Performance of Planing Craft,"

Vol. 74, Transactions of The Society of Naval Architects and Marine

Engineers (1966).

(13)

The model resistance tests of dynamic-lift craft described herein

are for a straight course in smooth water; hence, we are concerned only

with motion about the y-axis.

The yaw is always constrained to a zero

angle, and the roll, although not immobilized, is set to zero with the

hull at rest and should not vary under normal conditions.

An exact description of the testing apparatus is not presented here,

since these types of tests may be conducted at several different facilities

where the equipment is not identical.

Indeed, some of the data, especially

the trim and heave, may be measured or derived in a variety of ways at the

discretion of the test engineer.

The basic towing gear for both fixed- and

free-to-trim tests used at the Langley Field Facility of the Center are

described in Reference 2.

Wetted keel L

k

and wetted chine L

c

lengths are generally measured

visually from markings on the hull, and in some cases photographs are taken

to verify the measurements.

These lengths are projected to and measured

along the x-axis and define the area wetted by solid water; see Figure 1.

Wetted surface areas are approximated for each test condition by a series

of rectangles and triangles, including side areas wetted at low speeds and

the wetted bottom of the spray strips.

The area wetted by spray is not

included.

Heave for planing craft is normally reported as a rise in CG.

The

CG rise may be computed from hull depth d and trim angle

T

measurements

according to the method presented in Appendix A.

TYPE A TESTS

A Type A test is setup so that the model is free to pitch (change

trim) and heave (rise or sink), and the towing force is applied at an angle

£

with the x-axis, where

£

is the propeller shaft inclination.

Before

20lson,

R. E. and W. F. Brownell, "Facilities and Research Capabilities,

High Speed Phenomena Division, David Taylor Model Basin, Langley Field,

Va.," David Taylor Model Basin Report 1809 (Apr 1964).

(14)

testing, the hull is ballasted to a required displacement

~

and to either

a specified static trim angle

T

or a specified longitudinal CG (LCG)

o

position--either one determining the other.

At any given speed, the

magni-tude of the hydrodynamic resistance of the hull is equivalent to the

hori-zontal component of the towing force; whereas, the magnitude of the

hydro-dynamic lift is equivalent to the static displacement minus the vertical

component of the towing force.

TYPE B TESTS

A Type B test is similar to Type A in that the model is free to

pitch and heave and is ballasted to a specified

~

and

T

or LCG condition.

o

For Type B tests, however, the towing force is applied horizontally at the

center of gravity.

Since the towing force in this case has no vertical

component, the hydrodynamic resistance is equal in magnitude to the towing

force, and the hydrodyanrnic lift is equal in magnitude to the static

dis-placement, or gross weight, of the model.

TYPE C TESTS

A Type C test employs a fixed-trim technique.

The model is attached

to a towed gate at a fixed attitude

T;

the gate is suspended at two

posi-tions by tapes in which the tension can be measured.

The rigid system of

towing gate plus model is allowed freedom to heave.

At each required

speed V, the rigid system is towed with the hull lowered in the water to

various depths at which the net loads, i.e., total weight of the system

minus the lift provided by a counterbalance, are equal to the various hull

displacements 6 required.

Since the system is towed horizontally, the

hydrodynamic resistance of the hull for a particular V, 6,

T

condition is

equal in magnitude to the force required to tow the system at that

condi-tion minus the force required to tow the gate alone at the same speed.

The magnitude of the hydrodynamic lift is equal to the hull displacement.

Moment arms from the origin of the hull coordinate system to the towing

force and the applied lift forces must be measured for each fixed-trim

position so that the trimming moments

~

may be computed.

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of tests is presented in Appendix B together with sketches showing the

applied and hydrodynamic forces involved in each case.

CRITERIA FOR COMPARISON

MODEL DESCRIPTION

Model 4667 is a hard-chine, stepless planing-boat design of

compara-tively low resistance, tentacompara-tively chosen as a parent form for the systematic

series of planing hulls designated Series 62.

3 The final parent, Model

4667-1, was changed in the bow only to make a form consisting entirely of

developed surfaces.

The resistance and trimming characteristics of both

models in the planing regime have previously been found to be essentially

the same, so that, for the purposes of this report, the hulls may be

con-sidered to be identical.

Body plans of Models 4667 and 4667-1 and other model particulars are

given in Figure 2.

_{Both hulls have a projected chine length Lp of 8 ft.}

BASIC FIXED-TRIM DATA

Model 4667 was tested by the Type C technique at Langley Tank 1 in

July 1970 at six fixed-trim positions ranging from 0 to 7 1/2 deg,

displace-ments ranging from 51.0 to 229.7 lb, and speeds as high as 11.9 knots.

The

2/3

speed range for a load of 221 lb (Ap/V

=

5.55) was extended to 20 knots

especially for this comparison.

The basic fixed-trim data of Model 4667 are presented in Appendix C

since they have not been published elsewhere.

Trimming moments and effective

LCG locations were derived as outlined in Appendix B.

Computations were

performed by a digital computer with the output printed in the form of

tables for the report.

The graphic work was done by a computer-controlled

3Clement, E. P. and D. L. Blount, "Resistance Tests of a Systematic

Series of Planing Hull Forms," Vol. 71, Transactions of the Society of

Naval Architects and Marine Engineers (1963).

(16)

plotter.

Each table lists the seven variables--Mr, R, S, d, L

c

' Lk, and

LCG'--for a constant

T

and

~

at the various speeds tested.

The variables

are plotted as a function of

T

for each test condition of

~

and V.

FREE-TO-TRIM DATA

Models 4667-1 and 4667 have both been tested previously in the

free-to-trim mode, Type A technique, and the results have been reported in

References 3 and 4, respectively.

Since the performance of both models

was found to be essentially the same, the basic 4667-1 free-to-trim data

as tabulated in Reference 3, and already available on IBM cards, was chosen

for comparison with the 4667 fixed-trim results.

RESISTANCE STANDARDIZATION

The model resistance and loads from both testing methods were

cor-rected to a standard water density and viscosity so that the results would

be comparable.

Resistance data in the form of resistance-to-lift ratio for a

lOO,OOO-lb boat have been derived from both sets of data.

The full-scale

resistance R was computed by standard Center procedure, using the

Schoenherr friction line, zero roughness allowance, and the density and

viscosity of sea water at 59 F.

DATA CONVERSION

To compare. the results from different types of tests, it was necessary

to convert the data to some common format.

In this case both the Model

4667-1 Type A and the Model 4667 Type C data were converted to the Type B

format.

Both original sets of data were interpolated at the load, LCG

conditions specified in Table 1, corresponding to the initial-load, LCG

conditions at which all the Series 62 hulls were tested.

It must be noted

4Clement, E. P., "Development and Model Tests of an Efficient Planing

Hull Design," David Taylor Model Basin Report 1314 (Apr 1959).

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effective load varies with speed due to the lift provided by the towing

force; whereas, Type B data apply to a constant load throughout the speed

range, which is the gross weight of the boat.

TABLE 1 - CONDITIONS FOR COMPARISON OF PLANING-HULL

FORMS, BASED ON PATTERN OF SERIES 62

Loads:

A

/,v

2/ 3

₌

5.5 P

A /V 2/ 3

₌

7.0 P

A /V 2/ 3

₌

8.5 P

LCG Locations at Each Load:

12 percent of Lp aft of centroid of Ap

8 _{percent of Lp aft of centroid of Ap}

6 _{percent of Lp aft of centroid of Ap}

4 _{percent of Lp aft of centroid of Ap}

0 _{percent of Lp aft of centroid of Ap}

The basic test data were converted, using a digital computer to

interpolate the resistance and other parameters at the required matrix of

loads, LCG's, and speeds.

The method used in the computer routine was

based on the Lagrange interpolation formula of the third degree.

It

essentially fits a cubic curve through the four test points closest to the

desired independent variable on this curve.

A quadratic fit is used if

only three points are available.

In cases where less than three points

are available or the desired variable is outside the range of values

tested, the computer routine returns a value of -0, since the results of

straight-line interpolation and extrapolation may be misleading.

Three-way interpolation for a particular LCG, load, and speed is accomplished by

applying the procedure to one variable at a time.

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The data were interpolated at the load, LCG conditions specified in

Table 1 and at speeds corresponding to F

nV

in increments of 0.25.

A

mini-mum value of F

nV

=

1.0 was set for the interpolated data since the lower

speeds are not in the planing regime.

Model 4667-1 was tested at speeds

as high as FnV:::!::: 6.

The fixed-trim tests of Model 4667, however, were

limited to

FnV~

_{3, with the exception of one loading condition Ap/V}

2 /

3 =

5.55,

which was tested at speeds as high as FnV:::!:::

5. Consequently, this

load was added to those shown in Table 1 so that the data from the two

types of tests could be compared at higher speeds.

COMPARISON OF RESULTS

Model-scale values of the following parameters derived from testing

techniques A and C are tabulated in Appendix

0 at comparable lift, LCG, and

speed conditions

1. Trim angle

T

2. Resistance R

3. Wetted surface S

4. Wetted chine leneth L

c

5. Wetted keel length L

k

6. Center of gravity rise

To show the correlation more clearly, graphs of trim angle and

resistance-to-lift ratio for a 100,000-lb boat are presented in Figures 3a through

3r.

The following points should be considered when comparing the

resul ts:

1. None of the information was faired in the usual sense; it was

interpolated from the normal scatter of test spots.

2. The two tests were conducted at different towing tanks, Model

4667-1 at Carderock and Model 4667 at Langley, over an interval of

approxi-mately 8

yr.

3. The measurements for any given resistance test are considered

to be accurate within a ±2-percent range, and some data may be even less

accurate, such as the wetted surface and CG rise, derived from more than

one basic measurement.

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identical for this study, there was some variation in the hulls forward of

Station 3, which could have had a minor effect upon performance in the

displacement regime with the LCG far enough forward to result in an initial

trim by the bow.

In view of these factors, the correlation between the results of the

two sets of data seems fairly reasonable.

There is no appreciable

differ-ence in trim, except at Ap/V

2 /

3 of 5.5 and 5.55 with the 4-percent LCG

location.

At this condition the trim reported for Model 4667-1 at

F

nV

=

2.0 is about 1 deg higher than that obtained for Model 4667.

There

is obviously an error in the original Model 4667-1 data, since the Model

4667 data fit in more reasonably with the family of trim curves.

The

agreement in resistance is very good for the aftermost LCG position at all

loadings.

With the LCG moved forward, the resistance of Model 4667-1 tends

to be higher with a maximum difference of approximately 10 percent.

CONCLUDING REMARKS

The difference in resistance obtained from the Type A tests of

Model 4667-1 and the Type C tests of Model 4667 was greater than expected

at some conditions; whereas, at other conditions, the agreement was quite

good.

Therefore, additional tests are needed under more stringent

condi-tions to eliminate such factors as towing tank and hull differences which

exist in this case.

Assuming that a good correlation can be obtained between the

fixed-and free-to-trim methods, it would seem desirable that most towing tanks

conduct resistance tests of dynamic-lift craft in the fixed-trim mode,

which is the simpler of the two testing techniques.

However, the matrix

of test conditions must be carefully selected to include all possible

attitudes the hull might assume for the range of load, LCG, and speed

conditions at which the craft could operate.*

This permits prediction of

*If the matrix of test conditions is not sufficient, gaps may occur in

the converted data; see Appendix D conditions where Model 4667 would trim

at angles <0 or >7.5 deg, i.e., outside the range of trims tested.

(20)

resistance, trim, and heave to be made for any load, LeG condition within

the test matrix, using the existing computer routines to convert the data,

and also facilitate propulsion studies for the craft, utilizing the methods

described in References 1 and 5.

It is anticipated that the resistance data for Series 65, which is

a group of 25 related hulls developed for hydrofoil craft design studies,6

will be converted to the conditions outlined in Table I, so that the

tre-mendous amount of information resulting from that project may also be of

use in planing-craft design.

Specifically, this converted data can be used

directly for propulsion predictions for Series 65, utilizing the methods

outlined in References 1 and 5.

SHadIer, J. B. and E. N. Hubble, "Prediction of the Power Performance

of the Series 62 Planing Hull Forms," Vol. 79, Transactions of the

Society of Naval Architects and Marine Engineers (1971).

6Savitsky, D. and J.

K. Roper, "Development of an Integrated Program of

Research on Hydrofoil Hulls,"

Stevens Institute of Technology, Davidson

Laboratory Report 1230 (Jul 1967).

(21)

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.... :::::::::::::::'0h

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y-AXIS

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SIDE VIEW

LEGEND

mmmmm~~

AREA HETTED BY SPRAY

~AREA

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~;;:~~~

AREA OF SIDE HETTED BY SOUP WATER

...

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-~~r~r'

•• • 0 • • • : : : : : : : : : : : : :

=::::::

!~... ~ll" o' ~i';;"'"" • • • • 0 • • • •

••• , .,

L

e

-I

~I

L

k

-L

p

-I

K~'.~

... ::::::

. " I

1"'111111I11It1

tt7:::::::~::::

; ''''''''''''"

~I

..

1 . . - -

Le

L

k

:

V')

...

><

c:( I N

J.J

₁

L

~ 0 V')

z

~

...

lJ..

...

0 ~

:c

c.!l

...

1.LJ

:c

a

1.LJ ~ ~ 1.LJ

::=

(22)

_ '" s,ro,St,.Hor_ _"'"-010 5".4, '01... Ooodr. . . _ _ 4 .... 5,Fol_UIlo0 1 _ '.... 510.5 .. SIo.IO

Lp

=

8.00 ft

_Lp/BpA

₌

5.00 Ap

=

12.80 sq ft

_{Lp/B pX}

=

4.09 BpA

=

1.600 ft

_BpX/BpA

=

1.

22 BpX

=

1.956 ft

_BpT/BpX

=

0.64 BpT

=

1. 250 ft

_{Centroid of Ap}

=

3.91 ft fwd of transom

FORM CHARACTERISTICS

_I

-16

z:

L.Ll u

14 c::

L.Ll 0...

12 z:

10

~ u

8

0l I -:::>

6

co 0...

z:

...J

4

et: L.Ll :::E

2

I

-0

::x: V')

50 ~

c::

40 ~

_o

80

70

60 30 ::;

20

en

10 o

100

90

80

70

30

20

40

50

60 PERCENT OF Lp

Figure 2 - Body Plans and Form Characteristics of

Models 4667 and 4667-1

10 Bp/BpA

~ ~

.-

-

r--...

l--

~

I.-

....

_~

-

l--

_/

CENTROID OF Ap

~

K

AT 48.8% Lp

h

_V

"

S

1\

_[7

[\

\

MEAN BUTTOCK

_~

l.-

I '

\

o

z:

-12

(23)

lOO,OOO-Pound Boat, Derived from Fixed- and

Free-to-Trim Testing Techniques

'"

~

8

Cl z 2 4 6 5

'"

3

c<

f-6 5 4 3 F n'1 2

lI

1 ~

i

T

4_

..

I_

• ~

It

-4

_-

.

· 1

. 1

U

4

•

6

e.

_~

..

•

4

.,

_I

..

·4

_ •

4 .

.

'

2

• <-

RESISTANCE / LIFT

~

LI FT = 100,000LB, SEAWATER D B 6

I

4

o

MJDEL 4667 TYPE C TEST DATA

_}

CXJNVERTED TO

2 • MOOEL 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

.

-0.1

o

0.0 0.06 0.1 0.0 0.18 t 0.1 --' ; 0.1

:;;:

f-~ 0.0 v>

llJ

'"

w w

'"

'-" w Cl z ~

'"

f-4 7 9 6 8 6 5 4 F n'1 2

o

-•

-

T ~

I.

riiil

-•

_..

l b 8 I (;)

• lit

-

-W

4

~

-4

<~

1_. _

..

2 _v RES 1ST ANCE / LI FT 0 LIFT = 100,000 LB, SEAWATER 8 ( 6 4

2

o

MJDEL 4667 TYPE C TEST DATA } C~VERTED

TO • MODEL 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

_I

- -

-0.0 0.1 0.1 0.0 0.0 0.16

t:

0.1 --'

--..

wO•1 u

:;;:

f-~O.O

'"

llJ

...

tN

Figure 3b

A_p/ '12/3

=

5.50 LCG

=

12% 1__-p Aft of A_pCentroid

Figure 3a

.\ / '12/3

=

5.50 p LCG

=

8% Lp Aft of ~ Centrol d

(24)

U)

~

'"

~ z 2 :>: c;: >--1

o

4 6 4 3 F_nV 2

o

I

,

•

l ,.., I

••

!

•

T

• a ..

0 a

,

_••

_•

_..

••

•

I <I>

•

I I

It

t ;

• . 4

..

_•

. 4

Ia

~

,

.

to

•

0

~ ~o RESISTANCE / LIFT

•

LIFT = 100,000 LB, SEAWATER ) U I ; I I

o

MODEL 4667 TYPE C TEST DATA'} Ca;VERTED TO

! _• _MODEL _4667-1 TYPE A TEST OAT A • TYPE B TEST DATA

:

_.

I

1 I

I

-

- -0.06 0.2 0.1 0.1 0.02 0.04

~

0.08 0.1

Ii:

:::; 0.1 ... w U ~0.10 >-U) :>: 0:: >-4

o

5 6 6 4 3 F_nV 2

•

~l

'.

I

~~

l~

e

T

-.-.

•

• ·4

_•

••

~.

4t

0 ~ l~ 8

•

~l

_,

4t

a-•

4

-

-~

₀

• • 1

.4

t-2

_4

,

• 1

.0

RESISTANCE / LIFT 0 LIFT = 100,000 LB, SEAWATER '-' 8 6

•

4

o

MODEL 4667 TYPE C TEST DATA ' Ca;VERTED TO

l _• _MODEL _4667-1 TYPE A TEST DATA t TYPE B TEST DATA

I

-

-0.1 0.0, 0.16 0.2

o

0.0 0.0 0.1

t

--'0.1 ... w u ~0.1 >-U) U) ~0.08 f-' ~

Figure 3c

Figure 3d

A / v2/3= 5.50 P LCG = 6~ lp Aft of ApCentrold A /

v

2 /3= 5.50 P LCG = 4~ Lp · Aft of

Ap

Centrol d

(25)

6 7 2 Vl 5

~

to ~

4

~ :>: a: f-6 4 3 F_n\7

o

~

c

~

T

~

-Q

IW

_IS

e

--

e~

_~(J

·1

_.l

• _•

6

•

4 ~l

.

-

..

1J

-..,-~l

D

~ ~

e'

0

•

f) 2

<'

v RES 1ST ANCE / LI FT 0

e

LIFT = 100,000 LB, SEAWATER B 6

U~

4

o

KlDEL 4667 TYPE C TEST DATA } alNVERTED TO

1 • MODEL 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

"

.

-Vl w a: 0.0 O.lB 0.0 0.0 0.1 0.06

t:

0.1 --' '0.1 w (.) ~ t;;0.1 :>: a: f-4 6 5 B 6 5 4 Fn \7 2

o

I

'.

•

T

• _i

IW

t,

..

Q

-

-J

..

...

~

0 DO

B

l

'

.

•

• -,

_~

_..

4

••

O!

~

e

~

~O

b

0 ..

2

0

RES 1ST ANCE / LI FT LIFT = 100,000 LB, SEAWATER 0 B l~ 6 4

o

MODEL 4667 TYPE C TEST DATA ~ CONVERTED TO

2 • MODEL 4667-1 TYPE A TEST DATA ~ TYPE B TEST DATA

I

,

-0.06 0.0 0.0 ~O.O a: 0.1 0.16

...

U1 0.1

t:

::J0 . 1

,

w ~0,1 t;; A

p / \72/3 = 5.55 LCG= 12% lp Aft of Ap Centrol d Ap / \72/3 =5.55 LCG = 8% Lp Aft of "pCentrol d

(26)

::;:

'"

f-V)

~

fil

Cl 2 z -1 4 6 3

o

6 5 4 3 F_nV 2

- - -

f--I

• ( J .

_I OJ

•

T

04 -

,

,~

0 °1

_~

_{t .}

~

•

• ••

I 4

•

I .~ (~

•

i I

•

I

• . 4

_"

••

-

0

•

0 o(

O(

I>

0 (

,

to

RES I STANCE / LI FT

•

LIFT = 100,000 LB, SEAWATER I U

o

MJDEL 4667 TYPE C TEST DATA 1 CONVERTED TO

~ • MODEL 46f7-1 TYPE A TEST DATA

r

TYPE B TEST DATA

I

_I

.

-

-0.20 0.16

o

0.18 0.02 0.04 0.08 0.06 ~0.10 WJ ~0.1 f-V) t;: ::; 0.14 ::;:

'"

f-4 2 5

o

6 6 5 4 3 F_nV 2 I

r

-t

41 i

_t

8

T

• ••

8 ~~

I

• · 4

_{t .}

4

I l

4

• ~

It

-• 1

t

e

~

••

~

.

~~

v

-

DO 1>0

t o RESISTANCE / LIFT

•

LI FT = 100 ,000 LB, SEAWATER V I ; I

I

_I

o

M)DEL 4667 TYPE C TEST OAT A

-

CONVERTED TO

~ • MODEL 4667-1 TYPE A TEST DATA

,

: TYPE B TEST DATA

I

.

f t

-

-0.18 0.04 0.20 0.02 t;:0.14

o

0.06

::;

0.08 0.16

...

WJ0.12 u ~ f-~0.10 V) WJ

'"

...

Q\ A / v2/3= 5.55 p LCG = 6% Lp Aft of ApCentral d

"p /

v

2_{/ 3} ₌_5.55 _LeG₌ _4% _lp _{Aft of} _Ap _Centroid

(27)

en w

~

w o z ::;: 0- f-4 3

o

6 4 .FnV 2

~(

)~

•

4 )

.

_l

.~

t

• _n.

...

_•

••

4

•

2 II

4

•

0

4.

g

...

5 4

.-~

• ..

• • 4• • 4

••

2 ) U _{RES 1STANCE / LI FT}

. 0

0

. 0

LIFT =100,000 lB, SEAWATER

,0

r----~(

g 5

~

OMODEl 4667 TYPE C TEST DATA , CCl<VERTED TO

! • MODEL 4667-1 TYPE A TEST DATA

_-

.

TYPE B TEST DATA

I

_-

I

_-

I

-o

0.04 0.06 0.02 0.1

t

0.2 0.1 0.1 0.2 w U

~

0.1 en en ~ 0.08 -..J ... 0.1 ::;: 0- f-2 4 5 6 4 F_nV 2

o

-"

•

t ()

_I

()

..

-~

~

..

•

4

...

(t

• 4

• • 4

I

) I ₄ I

I

• I

_4.

i

•

4

•

I

4t

~

(

a·

l

~.4

t ·

••

(I) 2

~

RES IST ANCE / LI FT

4.

LI FT = 100,000 lB, SEAWATER )

~

1 5 ) ~

1

o

• llODEl 4667MODEL 4667-1 TYPE C TEST DATATYPE A TEST OAT A CONVERTED TOTYPE B TEST DATA

I

- - -

-0.16 0.0 0.06 en

~

0.08 0.18 0.2 0.0 0.14 t w U

~

0.10 co -..J ... 0.1 ~ -...J A_P/ v2/3= 7_•00 lCG= 12% _{lp Aft of Ap Centrol d} A I v2/3= 7.00 P lCG = 8% ~ Aft of ~ Centrol d

Figure 3i

Figure 3j

(28)

z ::E

rr

I-'"

UJ \il

'"

2 ~ -1 4

o

6 5 4 F nV 2

••

~e ~.

~

..

~ ~

I

'-'

-.

~

.

T ~

.

~

-•

•

~ I I

..

~

_•

I

l~

• 5

•

4

• d.

t .

4•

•

l

.1

--.

tl RESISTANCE I LIFT

0<

b O

LI FT =.100 ,000 LB, SEAWATER 0

°

B

•

6

~

i4

°

MODEL 4667 TYPE C TEST OAT A

}

CONVERTED TO

2 • 'U(U 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

- - -0.2

o

0.0 0.014 0.2 0.1 0.06 0.08 0.2

~

0.1 0.1

t

:::; 0.1

...

UJ ( ) ~0.1 l -V) ::E a: I-V)

~

'"

UJ Cl 2 z 4

o

6 5 4 F 3 nV 2

o

,

I

I __ • 4~

-~

~O

T

...

-.

...

.

,

..

_•

it

••

_

..

4 2

• ~

• ••

I

•

B

•

5

•

~

• ••

~

.

~

-2

- -

<

~ 0

<

~

RESISTANCE / LIFT

• .

(

0

LIFT = 100,000 LB, SEAWATER 0 ~O

.<

~ I '-' i

•

~

o

HODEL 4667 TYPE C TEST DATA

_}

CON VE RTED TO

~ • ~·lJD[L 4667- I TYPE A TEST DATA TYPE B TEST DATA

I

.

- -0.2 0.2 0.0 0.06 0.08 0.04 0.20 0.1 0.1

...

t

00 :::; 0.1

...

UJ ~ 0.1 l -V)

t:J

0.1 a: A p /

v

2/ 3= 7.00 LGG = 6% LpAft of

"r

r.entrol d

Figure 3k

A p/

v

2_/3_• _7.00 _LGG₌ _4%

_lp

_{Aft of}

_"p

_{Centrol d}

Figure 31

(29)

V> W W

'"'"

w o z :>:

'"

t-4 3 2 6 5 4 2 Fn~

o

~

! 8

T

-.

..

~

- 4

'.

· · 4

_•

,

•

)

•

I

4

;

•

4

~

.

•

-2

-l

,e

~RES I STANCE / LI FT n() LI FT= 100,000 LB, SEAWATER 0 I

n~

~

i

~

o

MODEL 4667 TYPE C TEST OAT A ) CONVERTED TO

2 • MOilEL 4667-1 TYPE A TEST OAT A

J

TYPE B TEST OATA

I

.

A

.

0.04 0.08 0.0 0.0 0.2 0.1 0.1 0.22

~

0.1 ...J ('j 0.1

:iE

t; ;;; 0.1

i:!!

:>:

'"

t--2 -1

o

2 6 4 3 Fn~ 2

o

o~

-

•

I T

• -~

• 4- •

4~

i

..

0

~

-

... II

•

I

• :

,

• ,

• -

.-o •

_.0

• ..

U RES I STANCE / LI FT LIFT= 100,000 LB, SEAWATER I

•

I ; ~

o

MODEL 4667 TYPE C TEST DATA ) CONVIiRTED TO

! • MO~L4667-1 TYPE A TEST OAT A

J

TYPE t!TEST DATA

I

-

.

0.2 0.0 0.06 0.1 0.08 0.0 0.1 0.22 0.24 0.26

t:

...J 0.14 w u

:iE

0.1 t-V> V> ~ 0.1

...

\0 A p/ ~2/3 =7.00

LCG= O~ Lp Aft of Ap Centrol d A_P/ ~2/3 _{- .}- 8 50 LCG= 12~ Lp Aft of

"'P

Centrol d .

(30)

:E

'"

>-Vl

~

'"

w o z 2

o

3 6 5 4 3 F nV 2

o

,

..

.C)

"

...

,

·4

-.4

~~

T

_{t .}

5

...

-•

() 11

• Wr

I

• 4_

..

4

..

4_

-•

4~

. 4

..

( RES I STANCE / LI FT ( ) DLIFT= 100,000 LB, SEAWATER 4

₀

I

~(

e(

i

•

I

,

o

MODEL 4667 TYPE C TEST DATA

}

alNVERTED TO • MODEL 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

-

-0.26 0.24 0.18 0.20 0.08 0.04 0.06 0.02 0.22 0.16

t

-' '- 0.14 ~

~

0.12 V)

i!i

0.10 ::E

'"

>-V)

~

'"

w o 2 z 6 5 4 FnV 2

I

f I

I

_I

I

,

.@

~ C)

-.

,

"'4

'·4

---:

~~

C) T

~.

.1

l ()

_w'lt

,

• 1

~

_4~

fa

•

( I I l

-•

;

•

I

~-•

.4'

4

~.

(

_I>

RESISTmCE / LIFT

LIFT = 100,000 LB, SEAWATER I

0 ---f---0

I

~(

e(

I

i 4

o

MJDEL 4667 TYPE C TEST DATA

_}

COOVERTED TO • MODEL 4667-1 TYPE A TEST DATA TYPE B TEST DATA

I

_I

-

-o

0.2 0.14 0.22 0.1 0.08 0.02 0.10 0.06 0.04 0.12 0.18 0.20' tv t 0 :::; ' -w U Z <C >-V) V) w

'"

Figure

30 Figure 3p

A /

v

2_/3₌_{S 50} P • LCG= B% Lp Aft of Ap Centrol d A / v2/3

=

8.50 P LCG = 6% lpAft of Ap Centrold

(31)

:E iY >--1

o

-2 5 4 3 Fn~ 2

o

I

...

-I.

e

~

-

..

-I

J .

_l T

J .

₄

I

.• e

...

I

•

;

• It

•

4.

•

I

4'

~

• I•

~

I. ..

•

• _•

RES I ST ANCE / LI FT

4.

LIFT = 100,000 LB, SEAWATER

•

0

I

"

<I>

:

•

6 ~,

2

o

MODEL 4667 TYPE C TEST DATA ; CCI'VERTED TO

• MODEL 4667-1 TYPE A TEST DATA '; TYPE B TEST DATA

I

0.2 0.2 0.0 0.0 0.2 O.lG 0.04 0.1 0.0 0.24 0.28 t;: 0.1 --' :: 0.14

~

>-~ 0.12 <J) UJ a:: :E a:: >-<J)

~

'"

UJ o z -1

o

6 4 2 F

_nv

o

e

l

·1

• • I

•

• ...

...

..

()

.

-

T - I

• •

4~

i () I

•

I.

0

I.

•

I

•

• .r

•

• .'

••

RES 1ST ANCE / LI FT ( ) LIFT = 100,000 LB, SEAWATER I

o

~

(

) U I

.0

0

5 I 4

2

o

_• KlDEL 4667_{KlDEL 4667-1} TYPE C TEST DATA_{TYPE A TEST DATA} CONVERTED TO_{TYPE B TEST OAT A}

I

-0.0 0.15 0.0 0.18 0.0 0.08 0.24 0.20 0.26 0.22 tj ~ 0.1 >-<J) <J)

1i

0.1

t::

--' --.. 0.14 N

...

A_P / v2/ 3= 8 50_• LCG= 4~ L_pAft of A_pCentrol d A / v2/3 = 8.50 P LCG~ 0% Lp Aft of Ap Centrol d