R-\k2B

DAVIDSON LABORATORY

Report SIT-0L-70-I428

June 1970

A MODEL STUDY OF THE HYDROOYNAMIC CHARACTERISTICS OF A SERIES OF PADDLE-WHEEL PROPULSIVE DEVICES FOR

HIGH-SPEED CRAFT

by

Wray Gilbert A

and

James A. Starre

D D C i !

minn

J Jul 1

till UJL^J

prepared for

SDUTLl 3. ^

Dep tment of Defense under £'

Contract DAAE-07-69-0356

(Project Themis)

This document has been approved for public release and sale; its distribution is unlimited. Application for copies may be made to the Defense Documentation Center, Cameron Station, 5010 Duke Street, Alexandria, Virginia 22314. Reproduction of the document in whole or In part is permitted for any purpose of the United States Government.

70 1

00

II Q

DAVIDSON LASORATORY

Stevens Institute of Technology Castle Point Station

Hoboken, New Jersey 07030

Report SIT-DL-70-1^'8

June 1970

A MODEL STUDY OF THE HYDRODYNAMIC CHARACTERISTICS OF A SERIES OF PADDLE-WHEEL PROPULSIVE DEVICES FOR HIGH-SPEED CRAFT

by

Gilbert A. Wray

and

James A. Starrett

prepared for

Department of Defense under

Contract DAAE-07-69-0356

(DL Project 351^A06)

This documpnt has been approved for public release and sple: its distribution Is unlimited. Application for copies may be made to the Defense Documentation Center, Cameron Station, 5010 Duke Street, Alexandria, Virginia 2231^. Re- production of the document in whole or In part Is permitted for any purpose of the United States Government,

!

I I

I. Robert Ehrlich, Manager

Transportation Research Group

f I I r i

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f

ABSTRACT

This report covers an investigation of the hydrodynamic characteristics

of a series of scale models of paddle wheels with fixed radial blades,

designed for speeds in excess of 20 knots.

The results indicate thai a six-bladed wheel has higher propulsive

efficiency and thrust than a twelve-bladed wheel. Peak efficiency is in

the neighborhood of kl percent and occurs at slip values of 30 to ko

percent. Thrust increases with immersion depth, within the range tested

(16 percent of the wheel diameter immersed). There is a slight break in

the thrust curve over a span of 10-percent slip, after which the thrust

again increases with increasing slip.

There is evidence of scale distortion, and It is felt that the present

model, with a scale factor of 8.5 to I, may have been too small.

Keywords

Hydrodynamics

Amphibians

Paddle Wheels

Propulsion

ii

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CONTENTS

Abstract ii»

Mst of Figures vll

Nomenclature ix

BACKGROUND AND INTRODUCTION I

OBJECTIVES OF THIS PROGRAM 5

ANALYSE 7

Wheel Dynamics ...... 7 Scale-Model Relationships 10

MODEL AND APPARATUS 13

Paddle-Wheel Kodel , 13 Water Channel \k Instrumentation 1** Paddle-Wheel and Water Speed Control 15 Water-Channel Speed Measurement 16

TEST PROGRAM AND TEST PROCEDURE 17

FORMULAS FOR DATA ANALYSIS 19

Method 1 19 Method 2 20

RESULTS 21

PREDICTION OF PROTOTYPE PERFORMANCE 25

CONCLUSIONS 29

RECOMMENDATIONS 31

REFERENCES 33

APPENDIX A 35

APPENDIX B 39

FIGURES 1-52 , .... 63-11^

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LIST OF FIGURES

1. Model Paddle Wheel with Fixed Radial Blades and End Plates ... 63

2. Paddle Wheel Test Assembly Installed in Water Channel 64

3. Davidson Laboratory Free-Surface Variable-Pressure Water Channel 65

k. Recording Equipment for Wheel Thrust and Torque, and Wheel Speed Controller 66

5-10. Wheel Thrust Versus Wheel Speed for Various Advance Velocities (VQ), for a 6-blade and 12-blade Wheel with a Blade Immersion Depth of 0.80 inch, 0.50 Inch and 0.30 inch . . . 67-68

11-13. Composite of Data Presented In Figures 5 through 10: Effect of Number of Blades and Blade immersion Depth on Wheel Thrust, for an Advance Velocity (VQ) of 7.7 fps, 5.4 fps, and 4.6 fps (the first number by each curve indicates the number of blades; the second, the immersion depth in inches) 73-75

14-19. Wheel Torque Versus Wheel Speed and Froude Number for Various Advance Velocities (Vo), for a 6-blade and 12-blade Wheel with a Blade Immersion Depth of 0.80 inch, 0.50 inch and 0.30 Inch 76-81

20-25. Thrust Versus Effective Slip for Various Advance Velocities (VQ)» for a 6-blade and 12-blade Wheel and a Blade Immersion Depth of 0.80 Inch, 0.50 inch, and 0.30 inch . . . 82-87

26-31. Propulsive Efficiency Versus Wheel Speed and Froude Number for Various Advance Velocities (V0), for a 6-blade and 12-blade Wheel with an Immersion Depth of 0.80 inch, 0.50 inch, and 0.30 inch 88-93

32-37. Propulsive Efficiency Versus Effective Slip for Various Advance Velocities (VQ), for a 6-blade and 12-biade Wheel with a Blade Immersion Depth of 0.80 inch, 0.50 Inch, and 0.30 inch 94-99

38-43. Wheel Thrust and Torque Coefficients (KT.KQ) Versus Effective Slip for Various Advance Velocities (V0), for a 6-blade and 12-blade Wheel with an Immersion Depth of 0.80 inch, 0.50 inch, and 0.30 inch 100-105

v! i

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List of Figures (cont'd)

W»-l»9. Wheel Thrust and Torque Coefficients (KT>Kq) Versus Wheel Speed and Froude Number for Various Advance Velocities (VQ). for a 6-biade and 12-blade Wheel With a Blade Immersion Depth of 0.B0 Inch, 0.50 inch, and 0.30 Inch 106-111

50. Drag Versus Advance Velocity for a Prototype Vehicle woth a Planing Hull 112

51. Reduced Drag Curve of Prototype Vehicle with Some Model Test Data Shown for Performance Hatching 113

52. Simplified Concept Drawing of a High Speed Amphibious Vehicle Utilizing a Paddle Wheel Propulsion System 114

viii

i

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NOMENCLATURE

D outside diameter of paddle wheel

V Fr Froude number , /gD

KQ torque coefficient

K- thrust coefficient

N rotation speed of wheel (rpm)

Q torque

T thrust of paddle wheel

V relative velocity between water and blade tip speed (i.e., blade tip speed minus advance velocity of vehicle)

V inlet or advance velocity (knots)

V inlet or advance velocity (ft/sec)

V1 water velocity at wheel blade

V3 exhaust velocity

b span (width) of blade

d blade Immersion , -r - h

g gravitational constant

h height of wheel axis above free water surface

m mass flow rate of water

n rotation speed of wheel (rps)

r effective radius to midpoint of blade, (y + h) 1/2

s slip , l-^i

ix

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Subscripts

m model properties

p prototype properties

Greek Letters

U, propulsive efficiency

^i advance ratio

p mass density of water

9 angle Included by t/2 Immersed arc at radius r , cos 6 « —

I I

il

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I 1 I I

BACKGROUND AND INTRODUCTION

Historically, the use of paddle wheels of one form or another, to

propel a vessel, can be traced back to the days of the Egyptian and Ronan

Empires. The use of paddle-wheel boats was first recorded In 1^72, in the

thesis "Oe Re Militari," by R. Valturius.

With the Invention of the steam engine and later the diesel engines —

both of which were low-speed devices and hence well suited to then current

designs — the state of the art progressed. By the I880's the wheel designs

had reached a high state of development. A Ikd-ft long vessel of the

BELLE type, built for use on the Thames River, achieved a measured peak

propulsive efficiency of almost 60 percent, at a speed of 12 knots over a

measured mile.1'8'3 The cross-channel packets of 1880-1890 were paddle

propelled, and two of these ships, the PRINCESS HENRIETTA and the

PRINCESS JOSEPHINE, which were 300-ft long, attained measured-mile speeds

of 21 knots.

Studies of paddle wheel-propel led vessels4"9 have revealed that they

were successfully used in shallow draft, weed-infested areas. They fell

into disuse over the years, for a variety of reasons. The principal

reasons are listed below.

(1) The variable immersion of the paddle wheel under different ship-loading conditions inhibited use on cargo vessels.

(2) The alternating rise and fall of the wheels at the water level, while the ship was rolling, created a differential thrust or yaw moment, causing the ship to follow an irregular course.

(3) The low speed of paddle wheels required large gear reductions if high-speed prime movers were to be used,

(k) By the time experimenters began systematic model tests and general research in the area of propulsion, the paddle wheel had in most instances been replaced by the screw propeller (as a result, the paddle

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wheel has been treated as a specialized Item, and published data on design parameters and model experiments are not only very difficult to find but are generally Incomplete).

Only a limited amount of significant research has been conducted on

paddle wheels, since the early ISOO's. A summary and analysis of

conventional paddle wheels was published recently by Gerbers, Volpich, and

Krappinger,1,3'3,5,6 They based their study on a series of open-water

model tests (there was no ship hull in front of the wheel). Below are two

general conclusions that may be drawn from their work:

(1) The propulsive efficiency of a wheel with feathering paddles can be as high as 80 percent, in practice, however, this efficiency falls closer to 50-60 percent, which is what can be expected from well- designed propellers and is much higher than can be expected from water jets. Wheels with fixed radial blades may be approximately 10 percent lower in efficiency than the feathering type.

(2) Efficiency, thrust, and torque generally increase in proportion to rotational speed, up to a slip of approximately 33 percent. At this point, a breakdown in efficiency occurs due, probably, to the losses which accompany entrance and exit of the paddles and to their mutual interference. However, thrust continues to climb with slip.

In recent years, there has been an accelerated development of small

high-speed craft for operation in inland waterways. These craft will be

able to negotiate the swamps, marshes, and tall grasses that often border

these areas, and also operate in open coastal waters. Operational

experience in such environments has demonstrated the need for a simple,

shallow-draft, weed-free propulsion system for use on such craft. A

renewed interest in paddle wheels has developed, as evidenced by the

testing currently under way in Europe and the United States.

A few conceptual studies of slow-speed oaddie wheels have been

conducted.4'7 Although these paddle wheels have proven quite successful

in grass and marsh, they have not been able to generate high speeds in

open water, mounted (as they usually were) on craft with displacement-type

1

I

I I i

R>1428

huffs. Screw propellers are efficient and provide good maneuverability,

but are easily fouled by weeds and require a moderate draft. Axial-flow

Jet pumps provide good maneuverability and require only a shallow draft,

but they are vulnerable to need Ingestion and their low efficiency requires

large ins tailed-power levels with the attendant weight, space, and noise

penalties.

it seems apparent that a paddle wheel of small diameter, with high

rotational speed, can be effectively applied to a planing-hull patrol boat

of shallow draft. It is not difficult to imagine a high-speed stern wheel

operating entirely within the boundary layer, close behind a planing craft

where Inflow conditions are constant (perhaps even controllable by

transom-mounted flaps). The stern-wheel propulsion device would be of the

fixed radial-blade type and would be ventilated at high speeds, instead of

having spokes or support arms, the blades would extend from a large central

hub and would be supported by concentric discs or end plates. This

configuration Is simple and rugged and will resist fouling by weeds. The

end discs and the blade ends could be used for support during operation in

the land environment.

The disadvantages of the paddle wheel will not apply in this case,

sine? ~

(1) A patrol boat will generally be operating near a single loading condition, and variable imersion of the paddle wheel would not present a problem.

(2) The paddle wheel of a patrol boat will be operating In the wake aft of the transom of a planing hull, and the paddle wheel therefore will not experience differential submersion due to roll motion.

(3) Any speed-reduction problem that is likely to arise can be overcome by the application of modern lightweight power-transmission designs.

I I 1

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OBJECTIVES OF THIS PROGRAM

The basic objectives of this program were as follows:

(1) To determine, by means of systematic model experiments, the hydrodynamic characteristics of a series of paddle-wheel propulsive devices with fixed radial blades.

(2) To determine the feasibility of applying the high- speed paddle wheel to a high-speed planing hull of shallow draft.

(3) To develop and extend paddle-wheel design parameters for high-speed use.

1 f Preceding page blank

5

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ANALYSIS

t\> obtain some paddle-wheel performance data in the high-speed range

(I.e., hirh advance velocity and wheel revolutions), a simplified analysis

of the wheel dynamics was performed. Scale-model relationships were derived

for the paddle wheel so that the results of the model tests could be

related to prototype sizes. The analysis is based on an "ideal" situation

and does not take into account such factors as turbulence, cavitation,

ventilation, splash, etc. It does, however, yield an upper limit for the

expected performance characteristics of the paddle wheel and a means of

comparing actual model-wheel operating conditions with the "ideal."

WHEEL DYNAMICS

From momentum theory, thrust can be defined in terms of water inlet

and exhaust velocities and wheel geometry (see Nomenclature for definition

of symbols).

Wheel Blade

v-

Utilizing the momentum equation, we write

T = m/W = m(Va- V0)

= pbdvl(v3- vo)

(1)

(2)

Preceding page blank 7

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But shaft work is represented by

TVi ' Vim(Va- V0)

which is equal to the change Jn the kinetic energy of the fluid, or

^(V83- V0

a) (3)

vas- v0

a va + v0 Therefore V. = J^T^) = —T"- ^

Substituting Eq. (k) into Eq. (2), we get

Va + V0 T - pbd ^ (V8 - Vo) = ipbd(V8

s - V0a)

Rearranging, we have

if we assume that the downstream velocity vector of the water leaving

the blade is tangent to the blade arc, as shown in the sketch on the next

page, we may write the relationship of the wheel rotational speed, the

water exhaust velocity, and the angle 6 as shown below (Eq. [6]),

V3 = 2nrn cos 9

(6) = 2TThn

Transposing, we obtain

I I

V

2TTh

I I I I I I I I

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A conservative approximation of torque, in terms of thrust, is

Q = Tr

cos e

III h

(7)

Solving for efficiency, we write

TV

ZnnQ

■ m (8)

1 I

It will be noted that efficiency is proportional to the ratio of the inlet

and exhaust velocities and is very sensitive to the ratio of the height of

the paddle axis to the effective radius.

I

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Although this analysis is, admittedly, rather simplified, it

nevertheless serves to indicate that efficient paddle-wheel propulsion

systems can be designed within practical limitations, using existing

power-transmission equipment (see Appendix A).

SCALE-MODEL RELATIONSHIPS

Scale-model relationships were derived in order to have some rational

method of selecting a wheel size and to make possible the correlation of

the results with results for prototype wheels and earlier studies.

Sine? frictional effects are considered small as compared with

inertial forces, we choose to scale by Froude Number , Fr , where

Fr - ■*- /go

Let V be the relative velocity between water and blade-tip speed (i.e.,

blade-tip speed minus advance velocity of vehicle). Then

TTnD - V Fr = 2

Let \ = Dp/D , the scale factor. Then for equal Froude number,

I I !

fTTnO - V \ /TTnD - V o\ I o

/gÖ I model \ ZgD / prototype

TTn D Vn Tin D Vn m m 2D1 P P ^£

/r yr /ö: /or mm P P

(9)

10

I I I n fn /0~ - n /D" 1 - V / /iT - V / /D~

[ m m p p J om mo p

I

1 I

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and therefore

(10)

Or, on substituting the relationship for the scale factor into Eq. (10),

we can write

n/O" (n - A n ) = I //D~ (V -V /A) (II) mm p moo r m p

To fix the model, we choose to make both sides of Eq. (II) equal to

zero. Then the linear water speed or advance velocity is

vn - AV (12) o o p m

and the rotational speed is

n. - Ann (13) m p

From dimensional analysis, the tnrust forces may be expressed as

T T » -ß

m X3 (14)

Since d = F L = \3F \L = X*Q p p p mm m

-• torque may be represented by

Q

m \4

and since

F L \3F \L 7/s p = _p = —SLJS = k

/ p

P TP ^\

II

power can be written

X

Efficiency is expressed as

I p

Pm " XT/3 (16)

\ ' \ W

A calculation of the forces expected from a scale model are given in

Appendix A.

12

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MODEL AND APPARATUS

PADDLE-WHEEL MODEL

I I I I I

On the basis of the scale-model analysis and sn consideration of the

I test facility's limitations, it was decided that the paddle-wheel model

should have an outside diameter of 5 inches and be 5-in. wide. The scale

I model was a radial wheel with fixed paddles and end plates (Fig. I). Two

paddle wheels were constructed. Their dimensions were identical, but one

Ihad six blades and the other had twelve blades. To reduce cavitation and

entrapped air, holes one-half inch in diameter were drilled in the end

plates between the blades. The wheel was driven by a ?-hp d-c motor in a

closed-loop servo. The speed of the motor was measured by a d-c tachometer

and fed back to the control amplifier. Speeds were set on a ten-turn dial

and checked with an electronic strobe light.

The entire wheel, drive, motor, and tachometer assembly was mounted on

a three-component balance system. The balance system was set up to measure

the torque, thrust, and lift produced by the paddle wheel. Preliminary

data showed the lift component to be negligible, and the lift element was

therefore removed to reduce vibration and noise In the over-all recording

r system.

The entire assembly, including paddle wheel, drive, tachometer, torque

balance, thrust balances, and the necessary counter-balance weights, was

mounted on a base plate. The base plate had screws for leveling, raising,

or lowering, and served as a means of clamping the entire assembly into

1 the test section of the water channel (Fig. 2). A height-adjustable,

flat-bottomed plate, simulating a boat planing hull, was mounted just

forward of the paddle wheel. This plate provided a flow to the wheel

similar to that which would appear on a moving boat, and served as the

j reference line from which paddle immersions were measured.

13

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WATER CHANNEL

Tests were conducted in the Davidson Laboratory's variable-pressure

free-surface water channel (Fig. 3). This facility has a 6-ft-long test

section 13-in. wide and 13-in. deep, with a 7-ln. water depth. The

maximum water speed is 18 fps. The water channel can be completely closed

and operated at reduced pressures (in which case it would be referred to

as a water tunnel), but this was not required for the present study. The

photograph shows that the return section and pump are located on the right.

The water flows in a clockwise direction up to the contraction nozzle

located just forward of the test section. The test section has windows on

both sides for almost the entire length. The two hand wheels can be used

to tilt the floor of the test section, to reduce the standing waves which

develop at certain water velocities.

The paddle wheel, planing hull, and balances were inserted through the

top of the channel and positioned midway in the test section. The water,

after passing to the rear of the paddle wheel, was collected in the upper

right-hand separating chamber. The main stream of water was deflected down

into the return section. The upper portion of the separating section

skimmed off the turbulent and aerated water and allowed it to settle before

it flowed back to the return section.

The various pressure taps and the manometer bank are not shown in the

photo. A k-ft high platform provides a work area and serves as an

observation post.

INSTRUMENTATION

Force Balances and Electronic Recording Equipment (Fig. ^t)

The force balances are designed around specially machined spring

flexures which introduce almost no cross-coupling or hysteresis when

properly used. For each force input, the spring flexures allow a given

displacement which is sensed and measured by linear variable differential

transformers (LVDT).

!'♦

I I I I I I

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The output from the torque and thrust balance LVOT's was fed to a

Sanborn carrier amplifier (350-1100) and recorder. To reduce distortion

and overloading, due to vibration and the impact noise superimposed on the

steady-state readings, the carrier amplifiers were set at very low gain.

This was done so that the composite signal would be passed without

asymmetrical clipping. After the signal was demodulated and fed to the d-c

output, it was filtered to remove the unwanted vibration and noise, leaving

the steady-state d-c level. This signal was then fed to a Sanborn d-c

amplifier (350-1000), where It was amplified to drive an 8-in. Minneapolis-

Honeywell Vislcorder. Each signal channel was adjusted to give 7-in. chart

| deflection for full-scale torque and thrust.

The thrust and torque calibrations were fixed by using weights in a

fline and pulley arrangement to apply a known force to the paddle wheel and

blade.

* Paddle-Wheel and Water Speed Control

Constant paddle-wheel speed was maintained by means of a tachometer

attached to the drive motor shaft. The output of the tachometer was fed to

the control amplifier as one of two summing inputs. The other input was

from a 10-turn speed-control potentiometer. When this speed-control

potentiometer was adjusted, it supplied a fixed voltage reference, unique

to that particular speed setting. To balance the amplifier input the

tachometer had to be driven to a voltage level very near the speed reference

voltage but of opposite sign. When the two voltages were balanced, the

wheel speed remained constant even over fairly large increases or decreases

in load.

A similar summing input ana amplifier arrangement was used for the

speed control on the water channel. The drive-motor armature voltage was

sampled and summed with the reference from the speed-control potentiometer.

For the final control, a General Electric Thymotrol was used to supply

armature current. The inertia of the large mass of water, and the fact

that only a relatively small amount of energy from the model was available

1 to accelerate the water, combined to keep the channel velocity constant

over large changes of model speed.

15

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Water-Channel Speed Measurement

The water velocity was evaluated by measuring the difference in static

pressure at the entrance and outlet of the nozzle. The taps in the side of

the channel were connected to manometer tubes, calibrated in millimeters

of water. Thus,

V(ft/sec) - J75gf/MW

based on a contraction ratio of \:k in the nozzle. Results obtained with

the manometer tubes and static-pressure taps were checked with a Prandtl

tube mounted in the test section of the channel, and were found to be

valid.

16

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TEST PROGRAM AND TEST PROCEDURE

Four experimental variables were involved In the test program:

immersion depth (d), wheel speed (n), water velocity or advance velocity

(V0}, and the number of blades on the paddle wheel.

The test points for each variable were —

'o

d

3.6, 4.6, 51», and 7.7 fps

0.3, 0.5, and 0.8 in.

up to I600 rpm in increments of 100 rpm

Number of blades: 12 and 6

The wheel was tested for all combinations of the above variables; and

fhe thrust, torque, wheel speed, wheel immersion, and water velocity were

recorded.

The test sequence was as follows:

(1) Select a water velocity (V0).

(2) Select an immersion depth (d).

(3) Vary wheel speed (il), throughout the range and record the thrust, torque , N , and V0 .

CO Repeat step (3) with a different V0 untii the range of V0 is covered,

(5) Repeat steps I to k with a different d until the range of d is covered.

(6) Repeat steps i to 5 with the next model paddle wheel having a different number of blades.

17

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I I I I 1

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FORMULAS FOR DATA ANALYSIS

From the data obtained in the model tests, various dimensional and

non-dimensional parameters were calculated. For convenience, these were

programmed to be run on an IBM 36OAO computer. Program and data are given

I in Appendix B.

The Input data consisted of —

I Number of blades Wheel diameter , D (in.) Blade immersion depth , d (in.) Ratio of d/D Advance velocity , V0 (fps) Wheel speed , N (rpm) Wheel thrust , T (lbs) Torque input , Q (ft-lb)

Two similar sets of parameters were calculated for purposes of analysis

and comparison with results reported in the literature. These sets are

labeled Method I and Method 2.

METHOD 1

n(rps) N(rpm) 60

2 d

k 1 =

12 V ^ D = advance ratio (not the scale factor)

T(12)4 IC = —J—*— = thrust coefficient

pn D

Preceding page blank 19

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KQ - a^- " torque coefficient pn D&

Fr » n /o « Froude number based on wheel speed

s » (l-^i) = slip

IL, X TL ■ -j^—2" " propulsive efficiency

METHOD 2

— (I2)J » a frequently used thrust parameter pB3

-*- (I2)4 • a frequently used thrust parameter PD4

V = 0.5921 V (knots)

V a frequently used velocity parameter

/DTTI

^ N -rr = a frequently used velocity parameter

"V^- a frequently used velocity parameter

!

T V

\ = "QN2 55Ö "s propulsive efficiency

nn{| + h) - 12 V 12 V s = ■— = 1 — = effective slip

reff nn(| + h) nn(| + h)

20

I I I !

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RESULTS

The preliminary tests showed a high torque input to the wheel, with a

corresponding low thrust, which resulted in a low propulsive efficiency.

It was believed that there was insufficient venting of the cavity formed

between adjacent blades and that an "air pocket" was being formed that

prevented the water from filling the cavity. Vent holes 0.5 inch in

diameter were therefore drilled into the side plates between adjacent

blades. These vent holes insured sufficient ventilation and improved the

performance slightly over some ranges of operation.

The test results for the final configuration are presented in graphical

form (Figs. 5 to ty). The computer program used to calculate the various

dimensional and non-dimensional parameters, and the test data and

performance parameters, are given in Appendix B.

The primary results are shown in Figs. 5 to 16 as thrust and torque

versus wheel speed, with advance velocity, blade Immersion depth, and

number of blades as changing parameters. Comparison of rig. 5 with 6, 7

with 8, and 9 with 10 (these are plots of thrust versus wheel speed for

three different immersion depths) indicates that the slx-bladed wheel

usually generates more thrust than the twelve-bladed wheel. This can also

be seen quite clearly in Figs. II to 13, which are composites of Figs. 5 to

10. A similar comparison of Fig, 14 with 15, 16 with 17. and 18 with 19

shows that the torque is also larger for the six-bladed wheel.

An interesting feature that should be noted on almost all the figures

is the apparent break in the thrust and torque curves which occurs at high

advance velocities.

Figures 20 to 25 are plots of thrust versus effective slip for various

advance velocities, blade immersion depths, and number of wheel blades.

Here, also, thrust can be seen to increase smoothly with increasing slip.

At the higher advance velocity, however, there is a thrust "breakdown"

which occurs at about 40-percent slip. This breakdown appears to occur

21

R- |1»28

over a span of about 10 percent In slip, after which the thrust again

continues to increase with increasing slip.

Similar breakdown phenomena have been reported in the literature, *

but no satisfactory explanation of why chis phenomena occurs Is available.

By comparing Fig. 20 with 21, 22 with 23, and Ik with 25, It can readily

be seen that this phenomenon is more pronounced in the case of the

six-bladed wheel.

It can also be noted, in Figs. 20 to 25, that rhe thrust curves do not

go to zero for zero effective slip. This is because or the "form" drag of

the wheel itself, and other losses. Comparison of the curves for different

blade immersions shows that for smaller immersions (i.e. , d ■ 0.5 , 0.3)

the thrust at zero slip more closely approaches zero, which is to be

expected since there is less wheel in the water and hence less loss.

Figures 26 to 31 are plots of propulsive efficiency versus wheel

speed at various advance velocities, blade immersion depths, and number of

wheel blades. Figures 32 to 37 are plots of the same data versus effective

slip. Comparison of the figures shows that the six-bladed wheel also has

a higher efficiency than the twelve-bladed wheel, with the maximum

efficiency occurring in the vicinity of 30~ to 4C-percent slip. The

maximum value of propulsive efficiency achieved is k] percent, which is in

agreement with some of the more recent 1iterature,10 but considerably lower 1 2

than that presented in some earlier reports. » The efficiency curve is

very "peaky"; that is, the high values of efficiency occur over a rather

narrow range, then fall off sharply. The twelve-bladed wheel usually

develops its maximum efficiency at a slip value that is somewhat higher

than that for the six-bladed wheel.

Figures 26 to 37 show that the peak efficiencies increase with

increasing immersion. This result is not what would normally be expected,

and a completely satisfactory explanation is not available. A partial

explanation may be that the "form" drag of the wheel does not vary

linearly with immersion depth and may affect the ratio of net thrust to

input torque in such a manner as to produce a maximum efficiency for some

value of immersion depth above which the efficiency may again decrease.

It is also of interest to note that all the efficiency curves, regardless

22

I I

R-l<«28

of blade immersion depth or number of wheel blades, join to form a single

line at slip values above 70 percent.

Figures 38 to <t9 present the test data as functions of torque

I i

coefficient and thrust coefficient, common parameters utilized by naval

architects.

23

R-1^28

PREDICTION OF PROTOTYPE PERFORMANCE

If we choose as our prototype a small "Jeep size" vehicle having a

planing type hull, we can estimate quite accurately the power required to

propel it at any given speed. The model paddle wheel test results can then

be scaled up to match the vehicle.

Assume that the prototype characteristics are:

Overall length = 18 ft

Width (beam) = 5 ft

Gross weight = 4000 lb

Center of gravity location = 7.5 ft from bow

Deadrise = 15 degrees

Hull type = planing

The Davidson Laboratory "SPDBOT Program"11 will then predict the

drag versus speed curve shown In Figure 50. As a compromise between wheei

size and efficiency, we have selected a 4 ft diameter wheel, k ft wide,

with six paddles.

From dimensional analysis

x - S2 - ITÖTTI = s-6 m

N = -i N = 0.323 N (18) p /r m m

T = \3 T = 88k T (19) p m m v >/

Vo = ^ Vo = 3-095 Vo (20)

p m m

,7/2 p = IT^T ^ N = 0.0436 d (in-lb)N (rpm)) (21) p 5252 mm m ' mv r ' x '

25

Preceding page blank

R-1428

For ease of discussion, we shall scale down the full-scale drag versus

speed curve of the prototype from Figure 50 to mutch that of the model test

results. To do this, we divide the drag values by X3 and the speed values

by A . We now have a curve of drag (or thrust) versus speed which we can

match with experimental test data from the 5 inch model paddle wheel,

Figure 51. In Figure 51, lines o' thrust ver? » advance velocity for

constant wheel speed have been added to illustrate the reserve capability

of the wheel.

By determining the required thrust at 3.6, 4.6, 5.4, and 7.7 fps from

Figure 51, we can determine from figures 5, 14, and 26, the required wheel

operating conditions (Tm, «„,, Q,^ \ and horsepower) to match the prototype

requirements. Substituting these values of model wheel operating conditions

into equations 18, 19, 20 and 21 gives us the operating conditions of the

prototype vehicle and wheel.

From Figure 51 we see that the model operating conditions which match

the model advance velocity of 7.7 fps are

T = 0.660 lb m

N = 620 rpti m

Vo - 7.7 fps m

Q = 3.40 in-!b m

T] = 26 percent

Substituting these values into equations 18, 19, 2C and 21 yields the

following prototype conditions:

N = 200 rpm P K

T = 58811b P

V = 14.i knots = 16,3 mi 1 es/hour P

Required horsepower shaft = 92 hp

26

I I I I

i i

R-l*»28

These values are well within the realm of practicality for a usable

reconnaissance vehicle.

From the dynamic analysis on page 7, the following equation was

generated for the thrust of a paddle wheel.

T • i pbd(Va3-Vo3) » i pbd [(2Tihn)a-Vo

8]

If we take the same data from page 26 (d = 0.8 In., V0 ■ 7.7 fps, b = 5.0 In.,

and n ■ 10.3 and 16.7 rps), we get

and

T - 0.0269 [81».2-59.31 = 0.67 lb for n = 10.3

T - 0.0269 [221-59.31 " 05 lb for n - 16.7

Under these operating conditions, however, our model generated a thrust

of 0.665 lb and 1.0 lb which indicates that the simplified analysis gives

good agreement (0.665 lb vs. O.67 lb) provided the wheel speed is

sufficiently slow so that cavitation and/or ventilation does not occur.

When the wheel speed is sufficiently high to cavitate and/or ventilate,

the simplified analysis predicts results which are quite optimistic

(4.35 lb vs. 1.00 lb).

The measured test data does not extend above a prototype speed of

l6.3 mph for the vehicle size chosen. However, It can be seen in Figure

50 that the drag curve is fairly flat at the speeds near to 42 fps (29

mph). It is therefore reasonable to assume that the paddle wheel will be

able to provide the required thrust for speeds near 30 mph with somewhat

greater horsepower. Figure 52 is a simplified concept drawing of a

possible configuration of a high speed amphibious reconnaissance vehicle

utilizinc, a paddle wheel propulsion system.

27

R-1^28

CONCLUSIONS

(1) There is a considerable amount of mechanica! vibration to the

system, because of the impact loading of the paddle wheel.

This must be filtered out. Special procedures must be

employed, when using filters, to eliminate the noise in the

thrust and torque signals and ensure that asymmetrical

"clipping" of the signals In the amplifiers does not occur.

(2) The six-bladed wheel generates more thrust than the twelve-

bladed wheel.

(3) The six-bladed wheel is significantly more efficient than the

twelve-bladed wheel.

(k) Maximum efficiency occurs at about 30- to M)-percent sl'p for

the six-bladed wheel and at about 50-percent slip for the

twelve-bladed wheel.

(5) Thrust and efficiency increase with increasing immersion depth,

within the range of immersions tested (d/D = 0.06 to 0.16).

(6) A maximum propulsive efficiency of k] percent was obtained

with the six-bladed wheel.

(7) There is a break in the thrust curves, in the region of 30-

to 50-percent slip, which spans about 10-percent slip (Figs. 19

to 2k). It is most noticeable on the six-bladed wheel and

occurs at high advance velocities. A satisfactory explanation

has not been found. However, it is felt that the break may be

due to some type of flow instability or wave interference.

(8) There appears to be some type of flow phenomenon which more

seriously affects a wheel of small diameter than a wheel of

large diameter. This is especially noticeable in comparing

the efficiency curves with those obtained by other

experimenters who used a wheel of larger diameter. '' ' The

29

Preceding page blank

IM*»28

curve for the small wheel may have the same peak value of

efficiency, but it occur« over a narrow range and falls off

sharply.

(9) Because of the relatively high peak efficiency found in this

seriet of experiments, the application of a high-speed paddle

wheel to a planing hull of shallow draft Is deemed feasible.

30

R-\k2S

RECOMMENDATIONS

A design study of a smell, high-speed vessel propelled by a paddle

wheel should be undertaken. On the basis of the results of this study, a

smal! prototype could be built, instrumented, and tested.

To avoid possible deficiencies in any full-scale design based on the

test model, it is recommended that any future experiments and tests be

performed on a wheel of larger diameter, since scale distortions were

evident with a scale factor of about 8.5:1. A scale factor of 3:1 or 2:1

would be most desirable.

31

R-ikze

REFERENCES

1. VOLPICH. H. and BRIDGE. I. C. "Paddle Wheels, Part I: Preliminary Model Experiments-" Institute of Engineering and Shipbuilding in Scotland, 1S55.

2. VOLPICH. H. and BRIDGE, I. C, "Paddle Wheels, Part 11: Systematic Model Experiments," Institute of Engineering and Shipbuilding in Scot lend; paper presented 13 March 1956.

3. VOLPICH, H. and BRIDGE. I. C, "Paddle Wheels, Part HI: Ship/Model Correlation," Institute of Engineering and Shipbuilding In Scotland; paper presenteu 36 February 1957.

1». EHRLICH, i. R.t KAMM, I. ö., and WORDEN, G., "Studies of Off-Road Vehicles in the Riverine Environment. Part I. Performance Afloat," Davidson Laboratory Report 1382, October 1968.

5- KRAPPINGER. 0.. "Schaufebradberechnunq." Schifftechnic. 1951».

6. GERBERS, F., "Das Schaufeibrad in Modelsversuch," Springer Verlag, Wien. 1952.

7. BARNES, S., "The Army's Wacky Watercraft." Mach ine Design. 15 February 1968.

8. VAN MANEN, J. D., "Fundamentals of Ship Resistance and Propulsion, Part B. Propulsion," Netherlands Society of Engineers and Shipbuilders, Publication No. 132A of the N.S.M.B.

9. BRAGG, E. M.. "Feathering Paddle Wheels." Paper presented at the Twenty-fourth Genera) Meeting of the Society of Naval Architects and Marine Engineers, New York, 16 November 1916.

10. VON KURT, HELM, "Untersuchung eines Schnei laufenden Schaufelrades als Antrleboorgan für Flachgehende Binnenschiffe," Schiff und Hafen, Heft, 10/1967, 19 Jahrgang.

11. SAVITSKY, D., "Hydrodynamlc Design of Planing Hulls." Marine Technology. Vol. I, No. I, October 196^.

Preceding page blank

33

R-1^28 Appendix A

Appendix A

A CALCULATION OF THE FORCES EXPECTED FROM A SCALE MODEL

For a 30-knot craft with a gross weight of 12.000 to 15.000 lb, w. can

determine the characteristics for one unit of a twin-stern wheel-propulsion

system by using the equations derived In the dynamic analysis of a paddle

wheel. The required thrust is known because the h.H shape, drag

coefficient, and required vehicle speed are known, or can be estimated

accurately.

T ■ 1200 lb/unit

V « 30 knots » 50.7 ft/sec o

Choosing the dimensions

D » 3.5 ft , d - 0.5 ft , h - 1.25 ft , r - 1.5 ft , b - 3.5 ft

for the wheel, then

" = 2^ = 2"\u2S) * 7.20rps ; N = (7.2C)(60) = 432 rpm

Q = ^ = Lnm^f = 2160 ft.lb

^N_ = (2160) (432) = snp 5252 5252 i///jnit

ehD!S üo = (1200)(?0.7) = ehp 550 550 lu'u

Preceding page blank 35

Appendix A R-IU28 |

I I

„ . *E "0 0.62 p shp 177

The size of the paddle wheel and the size of the power units are well

within practlca! üml tat ions.

TO SCALE THE EXAMPLE. USING A MODEL PADDLE WHEEL

Prototype characteristics are as follows:

T - 1200 lb

V - 30 knots - 50.7 fps o

D « 3.5 ft , b - 3.5 ft , h - 1.25 ft

Vb - 56.6 fps

N - kU rpm

Q « 2160 ft/lb

shp - 177

ehp ■ JlO

^p' 62

Using a 5.0 by 5.0 in. model, we obtain

X . £ . B.U

Hm = v/^ ^32^ = ,250 rp^,

T = -im = 203 Ib m {Q.kf

Q = 2l60 = o.43^ ft-lb = 5.22 In.-lb (8.M4

36

I

R-)<f28 Appendix A

P « 2L_ « 0 J028 shp

\ - 0.62

V - 5^1 « 17.5 fps 0:n /BA

V - ^^ - 19.5 fps

SPECIAL CASE (MAXIMUM ACCELERATION OR THRUST) WHEN VQ - 0 and N « MAXIMUM FOR d/0 » 0.143

li Va » |~- + V_ r - 2"hn Ibdp ¥o J

Therefore T - 2TTVnabdp

when V0 « 0 ; and for X » B.k,

j . 2(3.lM6)2(l.786)3(5.0)(0.7lM(62)(20.7)a

32,2 x 12 x 1728

= 8.95 lb

n 8.95(2.I43)a „ . t ,. Q = V.M " 23•, fn"lb

ek 2TT(20.7)(23.1) rt Kr,- shP r 550^12 = 0-kSS

These calculated values of thrust and torque will, however, be

unattainable, because of the ventilation and/or cavitation of the paddle

what;'. They do, however, give an upper limit to the forces that can be

expected,

37

R-11*28 Appendix B

Appendix B

DATA REDUCTION PROGRAM AMD LISTING OF DATA OUTPUT

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39

Appendix B R-IU28

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Appendix B R-1428

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9-

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ke

I I I

R-1^28 Appendix B

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-J • III

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«-4 <H <H r-< H

^7

Appendix B R-\k2S

'"■' t B

s »- u

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tal «tf*M»-SMM« »

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^8

i R-1^428 Appendix B

I I

U o

V a

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mmmmmmma^mmmm mmmmmmmmm&mmm

mmmmmmmmmmmmn

u c *«

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I W wi ■» •« P- (\; n (• U- «i r r-. — IT rvrMnrvrv^ntnrvv.n^iArM

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fj r^ (V i\< tj lA r. m ^- us ^ u\ ir\ *>- <- <j c- a, »i- IM *f j ir 'i r~ w

I h3

Appendix B R-1^28

rtimf nm*n> -ir^m U •> ^ r>. r~ »-«c« « N • «

• » mmmimmmmmmm u. »

8 • a B w o «i ca «i e* a a •- • • * #** • IM * • w •«

it o «««(*« tt ««»n » iv»

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X «k Y « « « rwrt««»»««

j O nm«r>v^ivnnKiw ws o » «t • K « »%« new *« v« M

^ O MfO niO« « «r^ «4WM M ««««««V«V«« O B S» «t «ft ^ (B ^ «* ^ *4 •» X

?tt iUMei^«9f»fs»«h*ahi

n«wnFif»*4«v«« t>>io*onr>inmp>r>rm

cu •* v ^ '* *« %i r,* M n» o*

faRia»i«'v*ni'vnm«ica

•r o »o t> <* « •'. rf» .-»in r. a r: "> -« <« H -c 4- fv ^i r> «f

ft» r« e. r* o % (ij rj 4* c. r* w pv ^ < <! m « n r^ tt r« f«

frf tJ f ffc .». fj ^t *# r. ^J fj «M %i n* r J fj INJ »M rj ru f J A* f. r. % ". •., ■■ r. '* r» < tj

■O n* r x (j> i . »^ s/. . * r^ *.

K p» ' f* I* •> «. r» p.« rot is .- ^. ...•*...••.>

•o KJ P ^ p. r. pi m »o - r< _• • it ■o m in ^. -- ui rj i J K> tH « o •

T bt n» ri f.* P. r« f« m rj (w m c r« is« >. ft ru rj '^ m r« fj m *-I r* r-, iTi ■* u> r~ r* *\ <ii t. r* » i r. »ttn^icr^rvmtf'fr. UJ a « * n rv iv a. »- m n »o CM ui a ^i^niMOajr^mMrjcj J a «-««-« *lr4r* 1U vt rt rt r* **

50

I

I I I

R-{U28 Appendix B

t « « « MOt ««f« h*

s 8

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r» m «K *M « <« »-. »4«\

o Ot u

m ** « ra r^ t ea r» rj PJ o _j i» n si ra ^ ni n fa A

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> tfi «\ tn m «MA ntft «\

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ift fi ft* »■- '• fi ',■ '. r. •_ •< » ^ r* r» «i p«. i

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i I I

1 if* -* if v« i»» irv ,4 r- •') -* rr »o o 4" o i» > '* -^ r^ I •■■ (» in ^ ■• (i < «> f" *r

IJ V -o IM r^ u> -o (M ,i OJ K)

-j <l "i 4» 4i *a ^J n« tti •'y r»" ^m* «or^w-i'jrv

m *> 'i? . < <' m "* ■ J »^ • . - ..-^-....f^

r\l ^4 r* T» •#> '. 'O c* rf» .-( rv ni '* n .♦ .« •" •

Ui C »O K) »-4 »J fj o :n ^ 10 ft f"» "> »4 U ^ O »r* ^ fO

51

Appendix B R-1428 I !

i j* • • Ä ••**■ »te** *•* "• w • •*■

o »- 8

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a o a o

• ■ana «<•••« B>vi»a

« nt iMiwotMNniniMivnrxfMC

nMMNNNnmNCUfWNMN

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r 3

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52 I I

i R-\k28 Appendix B

I I

8

o o

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« .............. »- t mmmmmmntammmmm M

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53

Appendix B R-I'rtS

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at. •«««nM«N«^A^ a toaaa a an aa w« a a «.

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•* 4 C» Ui in tt: o o ir i*i i •-* Ui o c* >.-►-.- X a X blAlMMAaUe^fAMIrfAlAlinin l AiAiAiaMff4r4nit.baiAiHntni- OUUII- U X »- * lOfO-W-W^^IOWlO-tjMKJIMlA ►- i ioro««««m»io<O^Kilvi^>- itl S .1 s X 3 ui a avrani<Ha&»^r^<o>iia«c>i uia a«ioi>i^Aior^r«<o<oa«(Mxo IACJUI'I I- X X Sk rl ri ri ■,-*** -t J O ** * * i w* r* ri Ui* * U f'l IV

54

R-IU28 Appendix 6

M «I M MM M ««««»«««»«»* «ID

•

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•

B *«vlv«««»«*«*««4Mv4MnMn

u

j *•.••..•...'•••

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w «9mat«M«^ siMwint^Mn «* o » n ■n»Mr> n« ^r « «/r>» ncfc

ut •••-•-••••-•••- fe. mmmmmmm&mmmmmmm h. » • M

u » • «-af» « « tft « « «i^ v « M r^

M

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•4

o «no « «» «M « «»«\»in « X « MM« «n*t-«»rftP'-v« « fs, •«

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MMMMMCJWfV IM o< rv fv f>j rj rv

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o •-•

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55

J

Appendix B R- l*i 28

at

o

■ o

o u

»- «i « • «« « B • « n r» nw w •• M

ETi w OniA V n A K « |K v N««4

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56

R-1^28 Appendix B

S

« « • « n ^ «« « • *«»> 9 K • •

r •

o

O »»«%*«»«'nitft fc v n « s «M «

b. • r M

M N,

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CM CMMCMCMIMCVCMfMCMCMCMfMCMni

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ft»iMCucHcw(^ikrh(.c>(^cuA.r4w

o>(reir^fMr^M <c^ 'ß »■- r. o^ f- « r-

xt 0rM'OO>«v4«-«M «^ r> ur\ n fo ra

ft* rj ^ *v f- r-- f J e; *. t- r^ P^ i*^ r,* *v

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o •-•

I «u BJ t« ai M CJ &t f^ rj ^ tn "- r* ft* tf\

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fa tv Cu Ti. >■« r« rj "u [-.j ft. m ^ u\ r* ir* ^ IM r- rj (i tn « «• «t UN r- (Nt w m r^ fo»0(Mrj,-i»M «>«)•-. o in ir» M »oiM

i 57

Appendix B R-tt28

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5ö

R>|1(28 Appendix B

t 9

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td r. fs< C« i- fi* c. r. r. t. : > F. t. r* r« in m m <• ^ K/ • ^ I*J Oi •-* •* T» r* i

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r> tn m *} r* t* ft n r r r- ft. »o t*» r>

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59

Appendix B R-1^28

t t

M

w T«NM« rnnnw « KI ««««in« »«•

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60

I

R-l^28 Appendix B

X

a

z

o X

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ii»

v4»4f»«4«4vinN*4e«iMr^

»- « «•»«*«!« oi «• b a WM M i I «^

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til

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61

R-11*28

I .i C ll ■ , li ZU

5.0"

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FIGURE 1. MODEL PADDLE WHEEL WITH FIXED RADIAL BLADES AND END PLATES

63

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R-1428 f

FIGURE *. RECORDING EQUIPMENT FOR WHEEL THRUST AND TORQUE, AND WHEEL SPEED CONTROLLER

66

I

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1.2

1.0

0.8

^ 0.6

V) 3 I.

0.4

0.2

100,

-0.2

R-I428

V0 - 5.4 fps

V0 » 4.6 fps

\0 = 3.6 f|)s

700 900 1 100

Wheel Speed (rpm)

I I 1300

I I 5.36 6.55 7.74 1.79 2.93 4.17

Froude Number (Based on Wheel Speed)

8.93

FIGURE 5. WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.80 INCH

67

R-1428

J.79 2.98"^" CJ7 573^ 6.55 7.7'+

Froude Number (Based on Wheel Speed)

Vo - 7.7 fps

V - ^».6 fps o

V0 - 5.*» fps

V - 3.6 fps

\ 1 1 1 1 1 1 1 f—1 700 900 1100 1300 1500

Wheel Speed (rpm)

i. w

FIGURE 6. WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A I2-BLADE WHEEL WITH A BUDE IMMERSION DEPTH OF 0.80 INCH

68

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R-1428

Vo = 7.7 fps

700 900 1100

Wheel Speed (rpm)

1.79 2.98 4.17 5.36 6.55 7.7^

Froude Number (Based on Wheel Speed)

V = 5.4 fps o

V = k.6 fps o r

1500

8.93

FIGURE 7. WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (Vo), FOR A 6-BLADE W'KEL WITH A BLADE IMMERSION DEPTH OF 0.5 0 INCH

69

R-1428

1

V0 - 7.7 fps

yo» SA fps

OV - 4.6 fps o

I I I—h-H—I Ü 500 700 900 1100 1300 15Ö0

Wheel Speed (rpm)

I 79 2,98 4.17 5.36 6,55 7.7^

Froude Number (Based on Wheel Speed)

8,93

FIGURE 8. WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BUDE IMMERSION DEPTH OF 0.50 INCH

70

I

R-\k2B

i.Ur

1.2

1.0

0.8

« 0.6 M 3

O.li

0.2

■0.2

^^ H—h—I—I—f 700 900 1100

Wheel Speed (rpm)

VQ = 7.7 fps

V0 = S.1» fps

VQ = ^.6 fps

1300 1500

1.79 2.98 M7 5.36 6.55 7.7^

Froude dumber (Based on Wheel Speed)

8.93

FIGURE 9- WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

71

R-\kZ8

500 700 900 1100

Wheel Speed (rpm)

1

1 r I

Vo = 7.7 fps

1

V0 - SA fps

Vn » ^.6 fps

\—I—I—I—I—HH—I .11 .1 I 1300 1500

1 1.79 2.98 k.\7 5.36 6.55 7.7^ 8.93

Froude Number (Based on Wheel Speed)

FIGURE 10. WHEEL THRUST VERSUS WHEEL SPEED FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

72

R-I42Ö

\.k

1.2

1.0

0.8

^ 0.6 -

n I-

£ O.if

0.2

■0.2 -

6; 0.30 6; 0.50

100

12; 0.30

700 900 iioo 1300 1500

Wheel Speed (rpm)

.73 2.98 4.17 5.36 6.55 7.7^

Froude Number (Based on Wheel Speed) 8.93

FIGURE 11. COMPOSITE OF DATA PRESENTED IN FIGURES 5 THROUGH 10: EFFECT OF NUMBER OF BLADES AND BLADE IMMERSION DEPTH ON WHEEL THRUST, FOR AN ADVANCE VELOCITY (V0) OF 7.7 FPS (THE FIRST NUMBER BY EACH CURVE INDICATES THE NUMBER OF BLADES; THE SECOND, THE IMMERSION DEPTH IN INCHES)

73

\.k

1.2 -

1.0 -

0.8

^ 0.6 -

o.k -

0.2 -

-0.2

R-11*28 I I I

i

! 4

Froude Number (Based on Wheel Speed)

FIGURE 12. COMPOSITE OF DATA PRESENTED IN FIGURES 5 THROUGH 10: EFFECT OF NUMBER OF BLADES AND BLADE IMMERSION DEPTH ON WHEEL THRUST, FOR AN ADVANCE VELOCITY (V0) OF 5.^ FPS (THE FIRST NUMBER BY EACH CURVE INDICATES THE NUMBER OF BLADES; THE SECOND, THE IMMERSION DEPTH IN INCHES)

7^

I I I I I I

R-1428

12; 0.3

700 900 1100

Wheel Speed (rpm)

1.79 2.98 4.17 5.36 6.55 7.74 8.93

Froude Number (Based on Wheel Speed)

FIGURE 13. COMPOSITE OF DATA PRESENTED IN FIGURES 5 THROUGH 10: EFFECT OF NUMBER OF BLADES AND BLADE IMMERSION DEPTH ON WHEEL THRUST, FOR AN ADVANCE VELOCITY (VQ) OF 4.6 FPS (THE FIRST NUMBER BY EACH CURVE INDICATES TNE NUMBER OF BLADES; THE SECOND, THE IMMERSION DEPTH IN INCHES)

75

R-1U28

7.0

6.0

5.0

k.O

J3

7 3.0

JT 2.0 o

1.0

100 300

Vo= 7.7 fps

Vo = 5.^ fps

700 900 1100

Wheel Speed (rpm)

1 1.79 2.98 ^.17 5.36 6.55 7.7^

Froude Number (Based on Wheel Speed)

V = ^.6 fps

V0 = 3-6 fps

\ ! 1 1 1 1 ! 1—I 1300 1500

8.93

FIGURE ]k. WHEEL TORQUE VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.80 INCH

76

R-1^28

Vo = 7-7 fps

V » 5.^ fps o

V = 3,6 fps

700 900 1100 1300 I5üc

Wheel Speed (rpm)

1.79 2.98 h.]7 5.36 6.55 7.7^ 8.93

Froude Number (Based on Wheel Speed)

FIGURE 15. WHEEL TORQUE VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.80 INCH

77

R- ^28

7.0 ,-

6.0 -

5.0

4.0 -

ja

V 30 c

o cr S 2°

1.0

7.7 fps

VQ - S.1» fps

V0 « 4.6 fps

I h—H 1 1 1 700 900 MOO 1300 1500

Whee' Speed (rpm)

I 1 I 1 .79 2.98 4.17 5.36 6.55 7.74 8,93

Froude Number (Based on Wheel Speed)

FIGURE 16. WHEEL TORQUE VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

78

I I

I !

y.Or-

6.0

5.0

i».0

■a 7 30

o cr fe 2.0

1.0

ft-1428

7.7 fps

V. - 5.4 fps

V0 - 4.6 fps

700 900 1100

Wheel Speed (rpm)

I I I 1.79 2.98 4.17 5.36 6.55 7.74

Froude Number (Based on Wheel Speed)

8.93

I

FIGURE 17. WHEEL TORQUE VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A I2-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

79

R-\k26 I

7.0

6.0

5.0

k.O

7 3.0

Z 2-0 i2

1.0

V0 - 7.7 fps

V- - 5«» fps

V0 - ^.6 fps

700 900

Wheel Speed (rpm)

1 1.79 2.98 U.I7 5.36 6.55 7.7^ 8,93

Froude Number (Based on Wheel Speed)

FIGURE 18. WHEEL TORQUE VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

80

I I I I I

I

7.0

6.0

5.0

k.O

• 3.0 c

6 3

2" 2.0 o

1.0

R-1428

700 900 1100

Wheel Speed (rpm)

1 1.79 2.98 4.17 5.36 6.55 7.74

Freude Number (Based on Wheel Speed)

V0 - 7-7 fps

V - 5-4 fps

V =4.6 fps o

8.93

FIGURE 19. WHEEL TOPQUE VERSUS WHEEL RPM AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

81

R-|i»28

20 30 ^0 50 60

Effective Slip (%)

70 80 90

I I I

:

i

FIGURE 20. THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.8C INCH

82

I

i I I

R-1428

].k ' ' ■

1.3 —

1.2 —

I.I —

1.0 ~

0.9 —

£ 0.8 —

5 0.7

0.5 —

O.k —

0.3 —

0.2 —

0.1 —

i 1 1 ! 50 -30 -10 T 30 ko 50 60 70 80 90

Effective Slip (%)

FIGURE 2).

!

THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), FOR A 12-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.80 INCH

83

R-1428

FIGURE 22. THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.50 INCH

\

I

I

I

I.

I I

8k

I

ft-|Jf28

I I I

1.3

1.2

1.1

1A a.

in a. a.

* •

n « - H

FIGURE 23. THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.50 INCH

85

R-11*28

30 k0 50 60 Effective Slip (%)

80 90

I I

FIGURE 2k. THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), FOR A 6-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.30 INCH

86

R-1t»28

FIGURE 25. THRUST VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL AND A BLADE IMMERSION DEPTH OF 0.30 INCH

87

R-1428

a*

o c <u

>

a o u

A . Vo - 3.6 fps

O . Vo - k.6 fps

, Vo - 5.*» fps

D . Vo - 7.7 fps

,79 2.98 4.17 5.36 6.55 7.7^

Froude Number (Based on Wheel Speed) 8.93

FIGURE 26. PROPULSIVE EFFICIENCY VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.80 INCH

88

I

R-1U28

»s

>• o c V

ui

V >

3 a o u a.

30

L-

Ä , Vo - 3.6 fps

0 . Vo = i*.6 fps

26

[

22 K- 0 . Vo = 7.7 fps

18 i— i \

]k —

i V "^X ̂ i^ ^v^ -^N, 10 —

/ /

\ v ^S

^^^

6 —

/

,

/

2 7 h\ L i, 1 1 | | 1 1 1 1 1

L'- In \ 500 700 900 1100 1300 1500

Wheel Speed (rpm)

1.79 2.98 4.17 5.36 6.55 7.7^ 8.93

Froude Number (Based on Wheel Speed)

FIGURE 27. PROPULSIVE EFFICIENCY VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.80 INCH

i

89

R- I<f28

a«

^

v c 0)

V >

3 a o k. a.

38

3^»

30

26

22

18

]k

IC

A . V - 3.6 fps o

O , V ' h.6 fps o

. Vo « S.k fps

D , Vo - 7.7 fps

700 900 1)00 Wheel Speed (rpm)

J I L.

I I I I

I I i I I I I 1500

1.79 2.98 M7 5.36 6.55 7.7^ Froude Number (Based on Wheel Speed)

8.93

FIGURE 28. PROPULSIVE EFFICIENCY VERSUS WHEEL SPIED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.50 INCH

90

K-IW8

30 | •■■— A , Vo - 3.6 fps

26 — 0 . Vn - ^.6 fps

• . Vo - 5.4 fps

* 22 j u-

0 . Vo = 7.7 fps f^^

r i

Ü

g o 4- «♦-

18

II»

t— f ̂̂ ^Ötr^Jl V >

's a o u a.

10

6

2

; (7 l ^^^

i II ' i ii 1 1 i 1 1 1 1 ! 1 1 1 i

J 300 500 700 900 1100 1300 5500

L 6 Wheel Speed (rpm)

1 1 1 1.79 2.98 h.M 5.36 6.55 7.74

Froude Number (Based on Wheel Speed)

8.93

FIGURE 29. PROPULSIVE EFFICIENCY VERSUS WHEEL SPEED AND FROUDE NUMBI * FOR VARIOUS ADVANCE VELOCITIES (Vo), FOR A 12-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.50 INCH

91

R-I^S

•r«

a

> u c

at

>

3 a o L. a.

30

26

22

18

!<»

10

tt

0

300

A . V0 - 3.6 fps

O . V0 - ^.6 fps

Vo - S.k fps

O . V0 - 7.7 fps

I I ! I I I I i I I i I

0 500 700 900 1100

Wheel Speed (rpm)

1300 1500

1 1 1 1 JL. 7.7^ 8.93 .79 6.55 2.98 4.17 5.36

Froude Number (Based on Wheei Speed)

FIGURE 30. PROPULSIVE EFFICIENCY VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.30 INCH

92

I

ft-1428

c

V >

a o

30 r A , Vo - 3.6 fps

— O . Vo « 4.6 fps

26 — • . Vo - 3.4 fps

22 —

'■fl

D . Vo - 7.7 fps

18 — \ \

Sä^

14 —

►-^j

^

^ S* 10

:/

^^-2^

6 —

2 MM

| 1 /I 1 1 | J. | 1 1 i i i i t / 500 700 900 1100 1300 1500

1— Wheel Speed (rpm)

1 1 1 1 1 1.79 2.98 4.17 5.36 6.55 7.74

Froude Number (Based on Wheel Speed)

8.93

FIGURE 31. PROPULSIVE EFFICIENCY VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.30 INCH

93

R- I'»28

A , V =3.6 fps

O , V ~ k.S fps

, V -5.'» fps

D . Vo = 7.7 fps

l

20 kO 60

Effective Slip (0/

00

FIGURE 32. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BUDE IMMERSION DEPTH OF 0.80 INCH

9^

R~1*»28

30 A , V - 3.6 fps

O , Vo - ^».6 fps

25 . Vo - 5.^ fps

5«

U c V

ü . Vo - 7.7 fps

20 —

^ 15

> (A

3 a o u a.

10 —

I I I 1 J L J__L 20 kO 60

Effective Slip (%)

80 100

FIGURE 33. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), KOR A I2-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.80 INCH

95

ko

R-\k2B

A .V - 3.6 fps o

I I

35

30

s<

^

c V

0! >

25

o u a.

20

I 15

10

o . vo « ^.e fps

. vo - 5.^ fps

i? , V - 7.7 fps o

J I I i I I I I L_J 20 '♦O 60

Effective Slip {"/< 80 100

FIGURE }k. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

96 I

R-11*28

30 ß , Vo = 3.6 fps

O , V * k.e fps

25 , Vo 'S.** fps

a«

u c V

41 > in

3 a o i.

20

15

10

a , vo » 7.7 fps

I I I I I ' I I I 20 kO 60

Effective Slip (%)

80 100

FIGURE 35. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0)f FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

97

ft-11*28 I

30 A .V «3.6 fps o

a. o

25 -

20 &s

Q.

>■ o c V

UJ

v >

10

O . V = 4.6 fps o

. Vo = 5.4 fps

J I I L I I I 20 ho 60

Effective Slip (%]

80 100

FIGURE 36. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

98

I

i

R-1428

30r-

25

»« 20

>. u

J 15 u

>

3 a o u a.

10

A , V «3.6 fps

O , Vo - 4.6 fps

, Vo » 5.4 fps

a , vo = 7.7 fps

I I I I I i I I I 20 ^0 60

Effective Slip {°/,

30 100

FIGURE 37. PROPULSIVE EFFICIENCY VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (Vo), FORA 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

9?

R-1428

20 k0 60

Effective Slip

100

FIGURE 38. WHEEL THRUST AND TORQUE COEFFICIENTS (KT.KQ) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.80 INCH

i I I

100

I

R-1^28

I I

O.IOr-

0.08

a» 0.06

3 o.otf in 3 L. X

0.02

I I I I I I I L-J.

40 60 80

Effective Slip (%)

FIGURE 39. WHEEL THRUST AND TORQUE COEFFICIENTS (KT.K,) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A I2-BLADE

WHEEL WITH AN IMMERSION DEPTH OF 0.80 INCH

101

R- |i*28

I I 1 I i I L_L

0.12

0.10 —

*•* Or

* 0.08 : /

)eff

icie

nt

g 7 O 7/ 0^Rt V

o- 0.0^

° 7 i f

\

i 1 1 I i i i i i i i i -20 20 k0 60

Effective SUp (%)

80 100

FIGURE 40. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (Vo), FOR A 6-3LADE WHEEL WITH AN IMMERSION DEPTH OF 0.50 INCH

I i

102

I

R-1428

0.10

^ 0.08 _

c - 0.06 u

^" i ^

% u 0,(A > / v ̂ Ljk

«1 J

*" 0.02

^

;

? o t \i ̂

^ ̂

1 1 'l/ _L 1 1 JL 1 J« J. -1

0.12

0.10

or

* 0.08 c

t 0.06

Li I I i I I I I i I I ■20 20 ^0 60

Effective Slip (%)

80 100

FIGURE 41. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (Vo), FOR A I2-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.50 INCH

103

R- I<l28

O.lOi-

0,08

S 0.06 u

3 o.ok

I.

0.02

I I i I I I I I

0.12

0.10 —

5 0.08

Coeffic

ient

o

; rf

\ a 0.0k L. o

- / \ 0.02 -4

\

ri 1 1 1 1 1 1 1 l 1 1 20 hO 60

Effective Slip

80 100

FIGURE hi. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,Kg) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (VQ), FOR A 6-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.30 INCH

104

1 I

R- )<*28

0.10 r-

0.08

I 0.06 u

»*- 14- V

o 0.04

I.

0.02

1,1 I I I I I I { 1

0.12 i-

0.10

£ 0 ^0.08 *J c V

Ü

^ 0.06 V O o V

§•0.04

0.02

I I I I 20 kO 60 80 100

Effective Slip (%)

FIGURE 43. WHEEL THRUST AND TORQUE COEFFICIENTS (KT.KQ) VERSUS EFFECTIVE SLIP FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH AN IMMERSION DEPTH OF 0.30 INCH

105

R-1428

1.79 2.98 4.17 5.36 6.55 7.7^ Froude Number (Based on Wheel Speed)

FIGURE kk. WHEEL THRUST AND TORQUE COEFFICIENTS (KT.KQ) VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF O.BO INCH

106

I

R-]k2B

0.10

^ 0.08

• 0.06 u «*-

8 " 0.04

«A 3

C «

<+-

s O

4) 3

? O

0.02

0.12 i-

0.10 -

0.08 -

0.06 -

0.04

0.02 -

I I I i i I I I i I I I I I { I i

I I I I I I I I I I I I I I i I 100 rpm 500 700 900 1100 1300 1500 1700

J I I I I I I 0.60 1.79 2.98 4.17 5.36 6.55 7-74

Froude Number (Based on Wheel Speed) 8.93

FIGURE 45. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ) VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.80 INCH

107

R-Ii*28

0.10 i-

-- 0.08 -

4J c « u

§

0.06

O.O'f

M 3 1. X 1- 0.02

0

0.12

c

V o o 0) 3 o- k. o

—

0.10 —

0.08 ~

0.06 - i 0.04 -1 0.02

V

n 1 Lr 100 rpm 1100 1300 1500 1700

0.60 1,79 2,98 4.17 5-36 6,55 7.74 8.93 Froude Number (Based on Wheel Speed)

FIGURE 46, WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ) VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

108

R- ll»28

I r i i u

s o

o.io r-

^ 0.08 -

• 0.06 -

or

C «

4» O

«

cr u o

0.04 -

0.02

0

0.12

0.10

0.08

t 0.06

0.04

0.02

100 rpm 1700

1 0.60 1.79 2.98 4.17 5-36 6.55 7.74

Froude Number (Based on Wheel Speed)

8.93

i FIGURE 47. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ) VERSUS WHEEL

SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.50 INCH

109

R-1428

0.10

0.08

c •mm

U 0.06

U 0.04 M 3 U

0.02

0

0.12

i I I I I I i I I I I I I

rl I I i I I I I I ! I I I I I 100 rpm 500 700 900 1100 1300 1500 1700

J J I I -J L I I I 0.60 1.79 2.98 4.17 5.36 6.55 7.74 8.93

Froude Number (Based on Wheel Speed)

FIGURE 48. WHEEL THRUST AND TORQUE COEFFICIENTS (Ky.K,,) VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 6-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

110

I I I

I R-1428

o u

M

OdO

0.08

£ 0.06

0.04

0.02

I I I i I I I i ! i I I I I I I i

i i

ll

I I I I

c 4)

u

« o u 0) 3 IT t. o

U. iZ

0.10 —

0.08 —

/V\ s^K 0.06

/XN 0.04 ■"■

/^ ^^^

0.02 — i ^ t,^-~^^i^ n 1 i i i i i i i i i i i i i i i i

100 rpm

J 500 700

I

900 1100 1300 1500 1700

0.60 1.79 2.98 4.17 5.36 6.55 7.74

Froude Number (Based on Wheel Speed)

8.93

FIGURE 49. WHEEL THRUST AND TORQUE COEFFICIENTS (KT,KQ} VERSUS WHEEL SPEED AND FROUDE NUMBER FOR VARIOUS ADVANCE VELOCITIES (V0), FOR A 12-BLADE WHEEL WITH A BLADE IMMERSION DEPTH OF 0.30 INCH

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USCUSSIFiED S.-1 lint» C'ijVMifu «Ilnft

OOCUMEHT CONTROL DATA R&D

• CHIC:N* "VC >c tiwi T^ rCsrpiKal« «ufftar/ |l«.«e«"OHT tefUHllv C L *SS>r ir * < IOM

Oavidson Laboratory, Stevens Institute of Technology Hobcken. New Jersey 07030

UNCLASSIFIED Ik. OOUP

t *fO»1 tltk.1

A MODEL STUDY OF THE HYOROOYNANIC CHARACTERISTICS OF A SERIES OF PADDLE-WHEEL PROPULSIVE DEVICES FOR HIGH-SPEED CRAFT

* DC»cm»fivt NotesfTVy* Wra^MI •n<lKrliml*« *3*«>

Final Report 5 au TMoniti (Flfl iMM», mid*» hsUlei, Mai mSSS)

Gilbert A. Wray and James A. Starrett

• «CVtrllT o»tt

June 1970 tm. TO»»L NO. O* »ACS*

lUt Tft. MO OF nr.r»

M •a. CONTKJICT OK OAANT NO. •a. OniOiNATOM'* MC^OKT NUMacnlSI

DAAE-07-69-0356 *. »"ojeef NO.

SIT-DL-70-1428

•6. OTHCH HCWORT NOI«I (Anr elhmt namb»n Mai mar <>• »»'Ignrd IM 1 npott)

t oitTKiaurioN STATCMCNT j^js ju^-jju^pj. ^35 ^gp approved for public release and sale; its

distribution is unlimited. Application for copies may be made to the Defense Documentation Center, Cameron Station, 5010 Duke St., Alexandria, Va., 22314. Reproducti m of the draument I» whole or In part Is perm II. SltPOLCMeNTAUT NOTCt n

»tpd fnr any nnrnn«» nf thf II It- dPONtOfllNO MIUTA^V ACTIVITY

S Rnvprnmpnt

Department of Defense Washington, 0. C. 20301

13. «etTRACT

this report covers an investigation of the hydrodynamic characteristics of a series of scale models of paddle wheels with fixed radial blades, designed for speeds in excess of 20 knots.

The results indicate that a six-bladed wheel has higher propulsive efficiency and thrust than a twelve-bladcd iheel. Peak efficiency is in the neighborhood of k] percent and occurs at slip values of 30 to 40 percent. Thrust increases with Immersion depth, within the range tested (16 percent of the wheel diameter immersed). There is a slight break In the thrust curve over e span of 10-percent slip, after which the thrust again increases with increasing slip.

There is evidence of scale distortion, and it is felt that the present model, with a scale factor of 8.5 to I, may have been too small.

DD .'T J473 S/N 010!-P07-€8I I

(PAGE 5) UNCLASSIFIED Security Ctassidration

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UNCLASSIFIED "Serurtiy Cla««lflr*Uan

I T -

■ It »ONOt LINK A

MOLC «T

t,IM« •

•ecc I «T ■out

Hydrodynamics Amphibians Paddle Wheels Propulsion

DD .'r..1473 (BACK) S/N 0101-807-«S?l

UNCLASSIFIED Security Classification »•31»Oi