' I
lab. V . ScbeeosbouwItunJ.
Deift
J O U R N A L
O F
S H I P R E S E A R C H
volume h number
7
A P R I L 1 9 5 7
-^ r e w o r d . -^A Commenf on Ship Research ^o"» 3
The Force and Moment on
a
Body in
a
Time-Varying Potential
Flow
Dr. William E. Cvmmins 7The Forces and Moments on a Heaving Surface Ship . . . .
Poo/Go/ovate 19
Application of Ship-Wave Theory to the Hydrofoil of Finite Span
Dr. John P. Breslin 27
Water Tunnel Techniques for Force Measurements on
Cavltat-ing Hydrofoils . Dr. B.
R. Parkin and Robert W. Kermeen36
A Study of Midship Bending Moments in Irregular Head Seas
Prof.
Edward V. Lewis
43
Published by
THE SOCIETY OF N A V A L ARCHITECTS A N D M A R I N E ENGINEERS 7 4 TRINITY P L A C E , N E W Y O R K , N. Y.
skin Friction Resistance of Ships
. . . . and the Problem of .
By m. T e d d ^
Extrapolation from Model to Ship
The International Towing Tank Conference (ITTC) is to hold its 8th meeting in Madrid in September of this year. One of the subjects to be discussed w i l l be the perennial one of how to estimate the resistance of a ship from that meas-ured on a small-scale model in a towing tank. The Skin Friction Committee of the Conference was charged at the last meeting in Scandinavia in 1954, with reviewing the available data and making recommendations to the Conference in Madrid which w i l l , it is hoped, be universally acceptable. Such a decision would remove one of the principal difficulties experienced in the use of model data in comparative studies. It is believed that a review of the present status of our knowledge in this field may be of interest to the members of the Society at this time.
The proper correlation of the resistance of ship models of different sizes and the reliable prediction of actual ship resistance f r o m model I'esults lie at the very founda-tion of towing-tank work. The first step towards the solution of these problems was taken by William Froude when he proposed to divide the t o t a l model resistance into two parts, one due to wave-making, which he called residuary resistance, and the other due to frictional re-sistance, or, i n coefficient f o r m
= + CV [1] He showed that the wavemaking resistance would
scale directly as the displacement at "corresponding speeds"; i.e., at the same value of F / a / L , Cr would be the same f o r any size of geometrically similar hull. To determine the frictional drag he made the assumption that the frictional resistance of the curved surface of the model or ship would be the same as that of a smooth plank having the same length and wetted surface, and
1 Technical Director, Hydromechanics Laboratory, David
Tay-lor Model Basin, Navy Department, Washington, D . C. Member SN.A.MÈ.
gave frictional coefficients for different lengths of plank. This entire technique, as exemplified b}^ Equation [1], may be called the "Froude assumption." I t has stood the test of time so well that i t is still used b y all ex-periment taiilvs and, however imperfect, still remains the basis of all methods of ship power predictions f r o m the results of model tests. The two methods at present agreed upon hy the International T o m n g Tanlc Confer-ence for use in all published work are based on this as-sumption, one using the Froude friction coefficients, the other the American Towing Tank Conference 1947 line, originally derived by Schoenherr.
A Common Fofmulation?
What of our present knowledge of the subject, and the chances of agreement on a common formulation?
I n 1954 the Skin Friction Committee of the I T T C i n its report stated that i t believed a proper correlation of model and ship resistance must take account of the ef-fects of three-dimensional flow, and that a suitable basis f r o m which to develop a method for such correlation would be the smooth turbulent friction line f o r two-di-mensional flow. The experiments considered b y Froude, Schoenherr and others were made on planks of a variety of sizes and shapes, geometrical similarity being ignored. The results suffered i n varying degree f r o m lack of t u r b u -lence stimulation, aspect ratio and edge effects, and sur-face Avavemaking.
I n the past few years Hughes has published results of careful experiments on planks and pontoons covering a great range of size, and by extrapolation has derived a two-dimensional line for turbulent-flow f r i c t i o n over a smooth surface (1).^ This is compared w i t h the Ameri-can T o m n g Tank Conference ( A T T C ) 1947 line i n Fig. 1. The Hughes line is higher and steeper for values of log E, below 5.65 and lower for all values of R above this point, although i n the ship region i t is somewhat less steep than the A T T C line. I t should be remembered t h a t the Hughes two-dimensional flow line is derived f r o m three-dimensional data and so depends upon the method of extrapolation used. That i t is not necessarily a unique Hne may be concluded f r o m the fact that Weighardt, using Hughes' data but a different method of
2 Numbers in parentheses refer to the Bibliography at the eiid
of the paper.
Fig. 1 Nozzle arrangement of a shallow-draft vessel
R e
Research
The paper deals with the vortex system of the
"screw + nozzle" propeller. The results
ob-tained from systematic experiments with
propel-lers in nozzles in which the length-diameter
ratio of the nozzle, the number of blades, and the
blade-area ratio of the propeller have been varied
are discussed. In addition the results of
experi-ments carried out for determining the optimum
diameter of the nozzle system behind the ship
are described. Explanatory comments on
noz-zle design are given, including diagrams for
determining the radial inequality of the axial
velocities in the nozzle and for making
computa-tions with regard to cavitation and strength.
The influence of the clearance between blade tip
and nozzle wall is discussed.
By ïiv. k. J. 0 . vc«i Me.ihen''
N o m e n c l a t u r e
The following nomenclature is used i n the paper: clA
=
Cu = Cs = D = ƒ =l i f t force per unit length of blade element of screw
propeller loading coefficient
induced velocity i n screw race of screw w i t h nozzle
S
• = thrust constant, where thrust includes friction effects
diameter of screw
camber of profile (general)
1 Head of the Research Department of the Netherlands Ship Model Basin, Wageningen, The Netherlands.
©f ¥ ( i r u l € o f l M @ d i © i (ct)f H I
p
I ¥ibF(Qiïfo[[ii
While the inertia effect of the surrounding water is known to be very large, and is always taken into account in calculating the natural freciuencies of hulls, the buoy-ancy or elastic effect invariably is neglected. Thus the hull is actually treated as free i n space -with a distributed mass added to account for the effect of the water.
I n the repljr to the discussions of reference (1)^ the authors pointed out the artificiality of this concept of the vibrating hull and, as showi i n reference (2), i n dealing w i t h the heaving motions of ships, not only the inertia effect of the water, but also the buoyancy or elastic effect, and the damping effect are taken into account.
Since the buoyancy effect yields an elastic term which appears i n the formula for the heaving period, strictly speaking, i t adds a term to the diff'erential equation for the vibratory motion and i n fact such a term is gi-^'en in the h i i t i a l equations of reference (3).
I f the frequency of the classical or Euler-Bernoulli uniform beam w i t h free ends and having a uniformly dis-tributed elastic support is derived f r o m the differential equation, the formula obtained for the natural frequen-cies is
+
wherecon = circular frequency of n t h mode (pn = root of equation Cos <j> Cosh 0 = 1 H = mass of beam per unit length
L = length of beam
A; = restoring force (due to elastic support) pei' unit length per unit transverse displacement I t is seen that the effect of the elastic support is to i n -crease the flexural frequency by the factor
1 + fc/M 4>/ EI/pL^J This factor also is equal to
1 + oir' 2 \ V 2
where a)„„ is the n t h natural frequenc}^ of the free-free beam without elastic support and cor is the frequency of the beam as a rigid body on the elastic support.
This formula conforms w i t h the general theorem due to Southwell (4) stating t h a t i f coi is the frequency of a system calculated on the basis of one elastic effect, and
C02 is the frequencj'- calculated on the basis of a second
By R. T. McGoldrieki
elastic effect the actual frequencj^ is given approximately by
provided the potential energy due to a given displace-ment is the sum of the potential energies due to the elastic effects considered separately. I n this case the inde-pendent mode shapes are quite different.
While the effect of buoyancy on the frequencies of ver-tical flexural modes of hulls is negligible i n most cases, and its inclusion as a nonuniform elastic restoring force in the calculations would add further complications to a calculation which many consider alreadj^ too compli-cated, i t may be of interest that a simple estimate shows the effect on ships having extremelj^ low fundamental vertical frequencies is not negligible.
Erom the simple rule of Southwell i t follows that the effect can be estimated bj^ considering the ratio of the heaving frequency to the fundamental vertical flexural frequencjf computed without the buoyancy effect. I n reference (5) the calculated value of the fundamental vertical frequency of the ore carrier SS E. J. Kulas is given as. ,31 cpm. This calculation was made for a dis-placement' of 19,500 short tons. The estimated heaving frequency for this displacement is 7.8 cmp. From the equation
there is obtained
P ^
3 P - I - 7.8^ƒ t« 32 cpm
This indicates an increase of about 3 per cent i n the f u n -damental vertical frequency due to buoyancy. Because of the nonuniform load distribution this effect may be-come greater at lighter displacements.
This ship has the following characteristics L = 580 f t
B = 60 f t D = 32 f t L/D = 18.1
For most ocean-going ships this effect would be less than 1 per cent.
{Continued on page 63)
1 Phj^sicist, David Ta3dor Model Basin, Navy Department,
Washington, D . C. Member S N A M E .
2 Numbers i n parentheses refer to the Bibliography at the end of
the paper.
What fJ'je Siuiety Is
'Doing to Advance Its
S G l D p ^ S S ( i € ! l
i y K l e m m e M . Jeines
Technical C o o r d i n a t o r of tiie Society
Historically, the Society's research program goes back to World War IT and essentially was a supporting effort to the work that was undertaken to understand brittle fracture i n ship steels. A f t e r the War, the practicality of the Societ3'' functioning as industry's central agency for research i n the marine field was recognized. I n 1947, dur-ing the term of Vice Admiral E. L . Cochrane as President, subcommittees on Hydromechanics, H u l l Structure and Ships' Machinery were formed, thus establishing the foundation for the present structure. The early re-search programs were modest and supported entirely by the Society's Endowment Fund Income account. Staff functions i n connection w i t h the program were carried out hy the Secretary.
As the program expanded to include operational studies, the committee structure likewise grew and the budget requirements outgrew the Society's ability to sup-port. I n 1953, the Society enlisted the help of the marine industry and established the Research Fund. The Technical and Research Committees were reorganized, a staff position. Technical Assistant, was provided and the entire structure as i t now exists evolved. For both his-torical and organizational details, reference is made to Vice Admiral E. L . Cochrane's paper, "The Technical and Research Committees of The Society of Naval Architects and Marine Engineers.
I t should be emphasized, however, that every effort has been made to assure that the Research Fund is avail-able for research expenditures to the greatest extent possible. OfEce overhead and expenses, including re-search staff salaries, are assumed b y the Society out of its Endowment Fund Income. The majority of Committee travel expenses are covered by the individual member's own expense account, although where such privilege is not available the necessary travel costs are defrayed. M u c h effort has been expended on projects by individuals and companies which were absorbed by them. I t is esti-mated conservatively that for each Research Fund dollar
1 SNAME Transactions, vol. 62, 1964, pp. 62-96.
ït(ëh
[ F i
. r ( o ) | ! ] 0 ' O [ f i f i j
Wide acfivify in solving the problems of
ship and machinery design reported by
Re-search Committees and Panels
o f
The Society
of Naval Architects and Marine Engineers
spent, five times that amount of services have been re-ceived.
The Current Program
The current research program covers four broad areas; hull structures, hydrodynamics, ship machinery, and technical problems of ship operation.
Structural Research
The major emphasis in structural research is divided between investigations of the longitudinal bending moments experienced by a ship moving i n waves, experi-mental evaluation of thermal responses i n a ship's struc-ture, and the measurement of full-scale stresses i n a ship's hull. The bending moment work is being pursued by Prof. E. V . Lewis under the direction of the S-3 Panel and the H u l l Structure Committee. T o date, a program of model tests i n waves has been developed, using a T-2 tanker model. The first phase of tests i n head seas has been completed and has appeared i n the A p r i l issue of the Journal. A series of tests i n oblique waves is soon to start which utilizes the new square-tank testing facili-ties at Stevens' Experimental Towing Tank. Evaluation employs the strip theory which has proved to be useful i n many applications i n the past. I t was found t h a t the necessary three-dimensional correction applied as an over-all factor to motion calculations was not adequate since such correction is very sensitive to the longitudinal distribution of the virtual mass and damping forces. As a result, the Panel is now setting irp a laboratory study of the v i r t u a l mass and damping of a model i n pitch and heave, both at rest and at forward speeds. While arising out of a specific need, this study should be of very broad and general interest,
S - 1 0 Panel—Full Scale Measurements
The thermal-stress program had as its first objective the measurement of diurnal variations i n a ship's hull.
Fig. 1 Typical 6 0 0- f t . tanker i n United States coastwise service: SS P. C. Spencer of ttie Sinclair Re-fining Company fleet.
.Q r'CQ o
On the premise that optimum ship hull
character-istics can only be determined by economic studies
of operating costs, a survey is first made of
dif-ferent types of design problems and of the factors
involved in the choice of proportions and fullness.
A distinction is made between designs in which
size (displacement) or dimensions (particularly
length) are fixed. I t is shown that different
solu-tions are to be expected in each case and that
op-timum characteristics depend also on relative
length of time i n port and on the severity of wind
and sea conditions in the intended service. As an
example of an economic study to determine
opti-mum fullness for a particular case in which
di-mensions are fixed, a detailed study is presented of
oil tankers i n Gulf-East Coast service. I t is
con-cluded that when designing for a
moderate-weather service such as this the choice of optimum
block coefficient can be made on the basis of
calm-water considerations. Hence, in this case the
optimum fullness for a given speed appears to be
at or just above current practice. I f designing for
a particular size of power plant, however, fullness
can be increased economically, as far as practicable,
with corresponding reduction in speed.
This paper attempts to explore some aspects of the broad problem of optimum hull form and proportions for ships of difi'erent types operating i n sei'vices of various degrees of weather severity. The basic principle foUow^ed is that optimum ship characteristics cannot be deter-mined f r o m technical considerations alone. Optimum here means most economical, and therefore the problem is considered to be fundamentally an economic one. However, to obtain satisfactory solutions a knowledge of the performance of difi'erent hull forms i n calm water and i n waves is required. The present project involved both experimental studies of models i n waves and operat-ing cost comparisons. The detailed work of Part 2 was limited in scope, as will be discussed later, to the specific problem of optimum fullness f o r deadweight cargo car-riers i n moderate weather services.
I n order to present this rather limited piece of research i n proper perspective, a general survey of the problem of optimum hull lines for difi'erent types of ships under various service conditions will first be given i n Part 1. The characteristics which are of particular importance
1 This paper is based on a thesis submitted to the faculty of Webb Institute of Naval Architecture, June 1954, in partial fulfillment of the requirements for the degree of Master of Science, under a joint curriculum with Stevens Institute of Technology. I t was presented as a paper before the Philadelphia Section, S N A M E , October 19, 1966.
' Naval Architect, Experimental Towing Tank, and Research Associate Professor, Stevens Institute of Technologj', Hoboken, N . J .
Forms Oieillo'u'ing in o ¥mm Syrfoe
By Dr. I. L a n d w e f a e f ^ a n d M . C. de Moieeign©^The purpose of the present note is to give a unified
treatment of the added mass for either horizontal
or vertical oscillations at high frequency in a free
surface. Although the results for the case of
verti-cal oscillations are more or less known, some of
them, such as the remarkably simple connection
between the added mass and the area of section,
are so obscure that they are worthy of emphasis.
The review (1)^ of the little work that has been
published for the case of horizontal vibrations
in-dicates that the general results presented here for
this case are new.
I n a recent paper (1) some new results on the added mass of a particular f a m i l y of ship-lilte two-duuensional forms, oscillating horizontally i n a free surface, were pre-sented. The aforementioned family is the one employed by F. M . Lewis (2) in his classical work on the added mass of ships vibrating vertically.
. The previous paper (1) was essentially a partial sum-mary, without mathematical derivations, of the results of present work. General expressions are derived for the added mass of arbitrary two-dimensional forms and ap-plied to obtain curves of added-mass coefficients f o r the Lewis forms. The coefficients for these forms are pre-sented as functions of two parameters, the section-area coefficient and the draft-beam ratio, f r o m which the added-mass coefficients for a particular section re-sembling a Lewis form can be read easily. A f u r t h e r study of the geometry of the Lewis forms, beyond that reported i n the previous work (1), has incUcated addi-tional limitations on the values of the two f o r m parame-ters which give real or ship-like forms. I n order to ob-tain the added-mass coefficients for forms whose shape parameters lie outside this permissible range, i t appears necessary to employ a more general class of forms which requires at least one additional geometric parameter for
1 This work was sponsored partly by the Office of Naval
Re-search, under Contract Nonr-1611(01), and partly by the Society of Naval Architects and Marine Engineers.
" Research Engineer, Iowa Institute of Hydrauhc Research, and Professor, Department of Mechanics and Hydraulics, State Uni-versity of Iowa, Iowa City, Iowa.
' Research Associate, Iowa Institute of Hydraulic Research. - Numbers in parentheses refer to the Bibliography at the end of the paper.
its description. This has not yet been accomplished, al-though work on a generalized f a m i l y of forms is already under way.
Nomenclature
The following nomenclature is used i n the paper: ttn = coefficients of series for transforming a profile
into a circle
a, i = complex conjugate of a,i ai = «1 —
a„i' = identical to a,„, m = 2, 3, 4, . . . h = half beam (width) of profile b, i = coefficients of complex potential b, i = complex conjugate of bn
Cn = —ib,i
Crs = coefficients i n expression for An
C = designation of circle i n f-plane A, B
C, D = points i n 2-plane (plane of profile) A', B'
C', D' = points i n f-plane (plane of circle)
AH = added mass for horizontal vibrations i n a free surface
Aji' = added mass for horizontal vibrations i n un-bounded fluid
Ay = added mass for vertical vibrations i n a free surface
Cii = added mass coefficient corresponding to Aj, CH' = added mass coefficient corresponding to A^'
c, = added mass coefficient corresponding to Ay G,G' = designation of profile and its image
H = draft (depth) of profile m, 11
r, s = indices
n = distance measured along normal to profile ?• = distance f r o m origin i n f-plane
?'o = radius of circle corresponcling to profile s = arc length measured along profile S = area of profile
T = kinetic energy of fiuid
Tc = kinetic-energy integral evaluated over circle C U = horizontal component of velocity of profile V = vertical component of velocity of profile w = complex potential, ID = 4> -\- i\p
X, y = horizontal and vertical co-ordinates i n plane of profile
z = complex variable z = x + iy a = a parameter, a = 2/b
cavitation number
NornenelatUi-e
Tire following nomenclature is used i n the paper: = velocity at upstream infinitjr p„ = pressure at upstream infinity
Pc = pressure inside of cavity p = density of fluid
^ ^ P . - Pc
cr„ = "blockage" cavitation number (in-finite cavitjr)
l i f t coefficient
local angle of attack of f o i l
upper and lower wall height, respec-tively
hi/hu
I = cavity length C = chord length of foil
7 = C/li, chord-wall height ratio
=
a =
=
X =A linearized version of the transition-flow cavity
model is used to obtain the effects of solid channel
walls on cavitating hydrofoils. The formulation is
in terms of two dimensional flow but includes
any shape hydrofoil within the scope of the linear
theory and any location of the foil between the
walls. The case of the flat plate foil is considered
in numerical detail. Three special cases of
posi-tion, the foil midway between walls, near to only
one wall, and the foil in an infinite stream (walls
infinitely far apart), are taken up. The effect of
the walls on lift and cavity length are discussed for
each case.
/ / / / / / A / / / / / / / / / / / / / / / / / / / / /
/77r777^7777p77777777777777
Fig. 1 Transition flow model f o r cavitating flow i n channel
Z-PLANE y=h„ v=o
u=TCru„ V' 0
y = h.j. v = 0 x=0
Fig. 2 Linearized transition flow i n a channel
Z = Vc. B, E, Dl, A b, e, dl, di c = bl, ei, 7i &2, 62, 72 bi, 63
X -\- iy, co-ordinates i n physical plane, Fig. 1 and linearized plane, Fig. 2
ordinate of free streamline
5 -|- iv, co-ordinates in mapped plane, Fig. 3
points on cavity i n 2-plane, Fig. 2 images of B, E, Di, Dz, i n f-plane.
Fig. 3
image of C i n f-plane. Fig. 3 defined i n text, case 1 defined i n text, case 2 defined i n text, case 3
1 The results reported in this paper were obtained in the course
of research sponsored by the Mechanics Branch of the Office of Naval Research.
^ Department of Mathematics, Rensselaer Polytechnic Institute, Troy, N . Y . -d, S-PLANE v=0 v = 0 Fig. 3 f-plane N O V E M B E R , 1957 31i
A p p l l k c i t i o n of
(S2fWfU
O O O OTo
F o r c e s
Acting on 5u ö m e r g e d
B o dfes
a n d
S u r f a c e S h i p s in RegularW a v e s '
Nomenclature The Aix) a h c 7 ) ntfollowing nomenclature is used i n the paper: = cross-sectional area of submerged body = wave amplitude
= f i n semi-span
= wave-propagation speed = total time derivative
vertical force due to ship motions
vertical force due to waves acting on a surface ship
g = acceleration due to gravity
h = depth of centerline of submerged body below calm free surface
i = \ / — 1 = imaginary unit
/ci = longitudinal virtual mass coefficient for a spheroid
= virtual mass coefiicient i n two-dimensional vertical flow about a ship section
ki = correction coefficient for effect of free surface M = pitching moment, positive'bow up
Mu = pitching moment due to ship motions
M „ = pitching moment due to waves acting on a surface ship
m = Adrtual mass or mass of displaced water = yawing moment
p = pressure
R = radius of circular or semi-circular cross section r = radial polar co-ordinate
S{^) = cross-sectional area of submerged portion of surface ship
t = time
V = forward speed
V = lateral velocity IV = vertical velocity
-iüö = vertical velocity due to ship motions
lOo = vertical orbital velocity
, y, z = rectangular co-ordinates V = lateral force
Z = vertical force
1 This work was supported by the Bureau of Ships fundamental hydromechanics research program, administered by the David Tajdor Model Basin, Contract Nonr 263 (15). Reproduction i n whole or i n part is permitted for any purpose of the United States Government.
' Head, Mathematical Studies Division, Experimental Towing Tank, and Research Assistant Professor, Stevens Institute of Technology, Hoboken, N . J.
The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow con-cepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Ras-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also in-cluded.
z'
=
heave displacement, positive upward a angular polar co-ordinate13
=
angle between longitudinal tangent to ship surface and .^-axisf = y iz = complex co-ordinate
0 angular polar co-ordinate
X = wave length
?
=
longitudinal co-ordinate of ship, measured f r o m GG of shipP = water density
$ velocity potential
velocity potential due to ship motions <f>m = velocity potential of waves
<t>wb
=
velocity potential due to wave-bodyinterac-tion
= pitch angle, positive bow up
Introduction
The problem of determining the forces and moments on a body moving under waves has attracted the attention of many hydrodynamicists, and in the past few years has been treated successfully by Havelock (1),^ Cummins (2),
' Numbers in jjarentheses refer to the Bibliography at the end of the paper.
