The princilples of naval architecture series : Propulsion

The Principles of

Naval Architecture Series

Propulsion

Justin E. Kerwin and Jacques B. Hadler

J. Randolph Paulling, Editor

2010

Published by

The Society of Naval Architects

and Marine Engineers

601 Pavonia Avenue

Jersey City, New Jersey 07306

Copyright © 2010 by The Society of Naval Architects and Marine Engineers.

The opinions or assertions of the authors herein are not to be construed as offi cial or

refl ecting the views of SNAME or any government agency.

It is understood and agreed that nothing expressed herein is intended or shall be construed

to give any person, fi rm, or corporation any right, remedy, or claim against SNAME or

any of its offi cers or member.

Library of Congress Cataloging-in-Publication Data

Kerwin, Justin E. (Justin Elliot)

Propulsion / Justin E. Kerwin and Jacques B. Hadler.

p. cm. — (The principles of naval architecture series)

Includes bibliographical references and index.

ISBN 978-0-939773-83-1

1. Ship propulsion. I. Hadler, Jacques B. II. Paulling, J. Randolph. III. Title.

VM751.K47 2010

623.87—dc22

2010040103

ISBN 978-0-939773-83-1

Printed in the United States of America

First Printing, 2010

An Introduction to the Series

The Society of Naval Architects and Marine Engineers is experiencing remarkable changes in the Maritime Indus￾try as we enter our 115th year of service. Our mission, however, has not changed over the years . . . “an internation￾ally recognized . . . technical society . . . serving the maritime industry, dedicated to advancing the art, science

and practice of naval architecture, shipbuilding, ocean engineering, and marine engineering . . . encouraging the

exchange and recording of information, sponsoring applied research . . . supporting education and enhancing the

professional status and integrity of its membership.”

In the spirit of being faithful to our mission, we have written and published signifi cant treatises on the subject

of naval architecture, marine engineering, and shipbuilding. Our most well known publication is the “Principles of

Naval Architecture.” First published in 1939, it has been revised and updated three times—in 1967, 1988, and now

in 2008. During this time, remarkable changes in the industry have taken place, especially in technology, and these

changes have accelerated. The result has had a dramatic impact on size, speed, capacity, safety, quality, and envi￾ronmental protection.

The professions of naval architecture and marine engineering have realized great technical advances. They in￾clude structural design, hydrodynamics, resistance and propulsion, vibrations, materials, strength analysis using

fi nite element analysis, dynamic loading and fatigue analysis, computer-aided ship design, controllability, stability,

and the use of simulation, risk analysis and virtual reality.

However, with this in view, nothing remains more important than a comprehensive knowledge of “fi rst princi￾ples.” Using this knowledge, the Naval Architect is able to intelligently utilize the exceptional technology available

to its fullest extent in today’s global maritime industry. It is with this in mind that this entirely new 2008 treatise

was developed—“The Principles of Naval Architecture: The Series.” Recognizing the challenge of remaining rel￾evant and current as technology changes, each major topical area will be published as a separate volume. This

will facilitate timely revisions as technology continues to change and provide for more practical use by those who

teach, learn or utilize the tools of our profession.

It is noteworthy that it took a decade to prepare this monumental work of nine volumes by sixteen authors and

by a distinguished steering committee that was brought together from several countries, universities, companies

and laboratories. We are all especially indebted to the editor, Professor J. Randolph (Randy) Paulling for providing

the leadership, knowledge, and organizational ability to manage this seminal work. His dedication to this arduous

task embodies the very essence of our mission . . . “to serve the maritime industry.”

It is with this introduction that we recognize and honor all of our colleagues who contributed to this work.

Authors:

Dr. John S. Letcher Hull Geometry

Dr. Colin S. Moore Intact Stability

Robert D. Tagg Subdivision and Damaged Stability

Professor Alaa Mansour and Dr. Donald Liu Strength of Ships and Ocean Structures

Professor Lars Larsson and Dr. Hoyte C. Raven Ship Resistance and Flow

Professors Justin E. Kerwin and Jacques B. Hadler Propulsion

Professor William S. Vorus Vibration and Noise

Prof. Robert S. Beck, Dr. John Dalzell (Deceased), Prof. Odd Faltinsen Motions in Waves

and Dr. Arthur M. Reed

Professor W. C. Webster and Dr. Rod Barr Controllability

Control Committee Members are:

Professor Bruce Johnson, Robert G. Keane, Jr., Justin H. McCarthy, David M. Maurer, Dr. William B. Morgan,

Professor J. Nicholas Newman and Dr. Owen H. Oakley, Jr.

I would also like to recognize the support staff and members who helped bring this project to fruition, espe￾cially Susan Evans Grove, Publications Director, Phil Kimball, Executive Director, and Dr. Roger Compton, Past

President.

In the new world’s global maritime industry, we must maintain leadership in our profession if we are to continue

to be true to our mission. The “Principles of Naval Architecture: The Series,” is another example of the many ways

our Society is meeting that challenge.

A DMIRAL R OBERT E. K RAMEK

Past President (2007–2008)

Symbol Units Description

( r ,  ) (m, rad) 2D right-handed polar co￾ordinates

( u , v , w ) m/s velocity components in the

(x , y , z ) directions

ua, ur, ut *** m/s (axial, radial, tangential) in￾duced velocity on a propel￾ler lifting line

( x , r ) (m, m) coordinates of the meridi￾onal plane

( x , r , o ) (m, m, rad) propeller coordinate system

(axial, radial, azimuthal)

( x , y ) m 2D cartesian coordinates

(stream wise, vertical)

( x , y , z ) m 3D cartesian coordi nates

(streamwise, spanwise,

vertical)

(  ,  ) m ( x , y ) coordinates mapped

into the  plane

a – parameter in the NACA a￾Series of mean lines

an – series coeffi cients

c m chord length

ct / cr – ratio of tip chord to root

chord

ds m shaft diameter

f ( x ) m camber distribution (mean

line)

f0 m maximum camber

f0 / c – camber ratio

f ( k ) ig ( k ) – H2

k iH2

k 1 0

 2i / k

, Sears

function

g m/s 2

 9.81, acceleration due to

gravity

h ( x ) m cavity thickness

ia(rv , rc) – Lerbs axial induction factor

it ( rv , rc ) – Lerbs tangential induction

factor

k – 2U  c , reduced frequency

n rev/s rotation rate

n – index of chordwise positions

n – harmonic number

n – unit surface normal vector

p ( x , y ) Pa pressure fi eld

p Pa pressure far upstream

pmin Pa minimum pressure in the

fl ow

pv Pa vapor pressure of the fl uid

q m/s total velocity vector

Nomenclature

Symbol Units Description

q ( x , y ) m/s U u

2 v  2

, magni￾tude of the total fl uid

velocity

q ( x) m/s magnitude of the total ve￾locity on the foil surface

qp ( x ) m/s velocity distribution on

the surface of a parabola

r m distance vector

rc m circle radius in confor￾mal mapping

rc m control point radius

rh m hub radius

ri m image vortex radius

ro m core radius of the hub

vortex

rH m hub radius

rL m leading edge radius of

curvature

s m span

s – nondimensional chord￾wise coordinate

t ( x ) m thickness distribution

t0 m maximum thickness

t0 / c – thickness ratio

uarc * m/s induced axial velocity at

radius rc

uarc, rv * 1/m axial horseshoe infl uence

function

uarc, rv 1/m axial velocity induced

at radius rc by Z unit￾strength helices

utrc * m/s induced tangential ve￾locity at radius rc

utrc, rv * 1/m tangential horseshoe in￾fl uence function

utrc, rv 1/m tangential velocity in￾duced at radius rc by Z

unit-strength helices

uc ( x ) m/s perturbation velocity due

to camber at ideal angle

of attack

usrc, rv 1/m induced velocity along a

wake helix

u t ( x ) m/s perturbation velocity due

to thickness obtained

from linear theory

ut m/s tangential component of

the velocity

utmr * m/s circumferential mean

tan gential velocity

xx NOMENCLATURE

Symbol Units Description

uw m axial induced velocity far

downstream

w – VS

 VS  VA, wake fraction

w ( x , t ) m/s velocity induced by the

bound and shed vorticity at

a point on the x axis

w *( y ) m/s downwash velocity distri￾bution

wij m/s downwash velocity at con￾trol point ( i , j )

wnm,ij 1/m horseshoe infl uence func￾tion for ( i , j )th control

point vortex

wn,m 1/m downwash velocity in￾duced by a unit horseshoe

vortex

x˜ m angular coordinate defi ned

by cosx 2

c

x

xc m control point positions

xm ( r ) m rake of the midchord line

xv m vortex positions

xL ( y) m leading edge versus span￾wise coordinate

xT ( y) m trailing edge versus span￾wise coordinate

y˜ rad angular cosine spanwise

coordinate, defi ned by

cosy 2

S Y

yu ( x ) m y ordinate of 2D foil upper

surface

yl ( x ) m y ordinate of 2D foil lower

surface

yp ( x ) m y coordinate for a parabola

z  x iy m complex coordinate

z0 ( y ) m vertical displacement of the

nose-tail line

( Fx , Fy , Fz ) N force components in the ( x ,

y , z ) directions

( Va , Vr , Vt ) m/s time-averaged velocity in

the ship-fi xed propeller co￾ordinate system

( VA , VR , VT ) m/s (axial, radial, azimuthal)

effective infl ow velocity

A m 2

/s vector potential

A –  s2

/S, aspect ratio

An , Bn – Fourier series harmonic

coeffi cients

C m/s strength of the leading edge

singularity

C ( x ) m/s suction parameter

CA – correlation allowance co￾effi cient

CD – drag coeffi cient

Symbol Units Description

CDf – frictional drag coeffi cient

CDp – pressure drag coeffi cient

CDv – viscous drag coeffi cient

CL – lift coeffi cient

CL

ideal – ideal lift coeffi cient

CM – moment coeffi cient with

respect to midchord

CN – normal force coeffi cient

CP – pressure coeffi cient

[ CP ] min – minimum pressure coeffi -

cient (also denoted CP , min )

CQa – Q

VA R3

2

1 2

, torque

coeffi cient based on volu￾metric mean infl ow speed

CQs – Q

VS R3

2

1 2

, torque

coeffi cient based on ship

speed

CS – leading edge suction force

coeffi cient

CTs – T

VS R2

2

1 2

, thrust

coeffi cient based on ship

speed

CTa –

A

T

V2 R2

2

1 , thrust

coeffi cient based on

volumetric mean infl ow

speed

D m propeller diameter

D N drag per unit span

DS m full-scale propeller di￾ameter

DM m model propeller diameter

E J fl uid kinetic energy

Fh N hub drag

Fn – n gD

nD

g

D ,

Froude number

FN N force normal to a fl at plate

FS N leading edge suction force

G N/m 2

shear modulus of elas￾ticity

G – 2RV2

 , nondimen￾sional circulation

H –   */  boundary layer

shape factor

Hr – root unloading factor

NOMENCLATURE xxi

Symbol Units Description

Ht – tip unloading factor

H1 0

2

k, H2

k – Jn ( k ) iYn ( k ) ( n 0,

1), Hankel functions of the

second kind

Jn ( k ), Yn ( k ) – Bessel functions of the fi rst

and second kind

JA – nD

VA , advance coeffi cient

JS – nD

VS , advance coeffi cient

K N/m 2

QLS / , calibration con￾stant

KQ –

n2

D5

Q , torque coeffi cient

based on rotation rate

KT –

n2

D4

T , thrust coeffi cient

based on rotation rate

L N lift (per unit span in 2D fl ow)

LS m length of shaft over which

 is measured

M – number of vortex panels

along the span

N – number of panels along the

chord

P m blade pitch

PB W 2 nQ , brake power

PD W delivered power

PE W RTV , effective power

PS W shaft power

PT W TVA , thrust power

Q Nm propeller torque

Q Nm brake torque

R m propeller radius

Rn – V

c0.7VR , Reynolds number

RT N resistance of the hull when

towed

Rw m slipstream radius far down￾stream

Re – Reynolds number

S m2

/s point source strength (fl ow

rate)

S m2

projected area

T N propeller thrust (or total

thrust of propeller and duct)

U m/s free-stream speed

U m/s fl ow speed at infi nity

Ue m/s boundary layer edge velocity

Ui m/s U  ut(0), “free stream”

speed at the local leading

edge of a parabola

V m/s ship speed

V m3

cavity volume

Symbol Units Description

Vx, y, z m/s velocity vector

V * m/s total infl ow speed

VA m/s speed of advance

V A m/s volumetric mean ad￾vance (infl ow) speed

VR m/s A

1/2

V2  0.7nD2 , re￾sultant infl ow velocity

VS m/s ship speed

Vc m/s velocity on the upper foil

surface

Vl m/s velocity on the lower foil

surface

Vm m/s mean foil velocity

Vd m/s difference foil velocity

W Nm work

W ( x , t ) m/s gust velocity

Wo m/s sinusoidal gust amplitude

Z – number of blades

 rad angle of attack

 rad free-stream inclination

with respect to the x

axis

0L ( y ) rad angle of zero lift

0 – normalized sinusoidal

gust amplitude

deg arcsin

rc

yc , negative an￾gular coordinate of rear

stagnation point

rad undisturbed infl ow pitch

angle

c rad wake pitch angle at ra￾dius r rc

i rad total infl ow pitch angle

v rad wake pitch angle at ra￾dius r rv

w rad wake pitch angle

( x) m/s vortex sheet strength (cir￾culation) per unit length

f m/s free vortex sheet strength

b m/s bound vortex sheet

strength

s m/s shed vorticity (per unit

length of wake)

 rad inclination of a spanwise

vortex with respect to

the y direction

 m boundary layer thickness

 * m boundary layer displace￾ment thickness

k rad blade indexing angle

 – open-water propeller ef￾fi ciency (also denoted o )

xxii NOMENCLATURE

Symbol Units Description

D – PD

PE; quasipropulsive co￾effi cient

H – PT

PE, hull effi ciency

u ( x ), l ( x ) n/a (upper, lower) foil surface

 ( x ) m mean camber distribution

( r ) – circulation reduction factor

(Prandtl tip factor)

 – 2  / n , sinusoidal gust

wave length ( n is the har￾monic number

 – DM

DS , scale model geometry

ratio

 kg/(m-s) dynamic viscosity

 ( x ) m 3

/s dipole sheet strength

 1/m gradient operator

 2

1/m 2

Laplacian

 m 2

/s kinematic viscosity

rad/s propeller angular velocity

(counter-clockwise direc￾tion when looking down￾stream)

1/s vorticity vector

 rad angular coordinate of a

general point on a helix

 ( x , y ) m 2

/s velocity potential

i m2

/s velocity potential in the in￾terior of a foil

p ( r ) rad blade pitch angle

 – 3.14159265. . .

 ( x , y ) m 2

/s stream function

kg/m 3

density

 ( x) m/s source sheet strength (fl ow

rate) per unit length

 – cavitation number

Symbol Units Description

 Pa steady state tensile

stress in the blade

a Pa magnitude of the alter￾nating stress in the blade

R Pa the estimated level of

residual stress from the

manufacturing process

 deg tail angle

 – duct loading factor

w Pa wall shear stress

 ( x ) m thickness distribution

 m momentum thickness

 ( x ) rad arctan( df / dx ), slope of

the mean line at point x

c rad projected chord

m ( r ) rad skew angle of the mid￾chord line

s deg angular coordinate of a

stagnation point

w m momentum thickness in

the far downstream wake

 ( Z ) m mapping function

 m2

/s vortex circulation (posi￾tive counter-clockwise)

 ( r ) m 2

/s circulation distribution

over the span

 ( y ) m 2

/s circulation distribution

over the span

nm m2

/s circulation of bound vor￾tex element at panel ( n , m )

o m2

/s circulation at the blade

root

 – J /  , absolute advance

coeffi cient

 m sinusoidal gust wave

length

 ( z ) m 2

/s complex potential

dz

d m/s u iv, complex velocity