PROGRAM SCORES-SHIP STRUCTURAL
RESPONSE IN WAVES
This document has been approved
for public release and sale;
itsdistribution is unlimited.
SHIP STRUCTURE COMMITTEE
MEMBER AGENCIES:
UNI FED STATES COAST GUARD
NAVAl SHIP SYSTEMS COMMAND
MILITARY SEALIFT COMMAND MARITIME ADMINISTRATION AMERICAN BUREAU OF SHIPPING
Dear Sir:
AN INTERAGENCY ADVISORY COMMITTEE DEDICATED TO IMPROVING
THE STRUCTURE OF SHIPS
A major portion of the effort of the Ship Structure Committee
program has been devoted to improving capability of predicting
the loads which a ship's hull experiences.
This report contains details of a computer program, SCORES,
which predicts these loads. Details of the development and
verification of the program are contained in SSC-229, Evaluation and Verification of Computer Calculations of Wave-Induced Ship
Structural Loads. Additional information on this program may
be found in SSC-23l, Further Studies of Computer Simulation of
Slamming and Other Wave-Induced Vibratory Structural Loadings. Comments on this report would be welcomed.
Sincerely,
ADDRESS CORRESPONDEN SECRETARY
SHIP STRUCTURE COMMIUEE
U.S. COAST GUARD HEADOUA WASHINGTON. D.C. 20591
SR-174 1972
W. F. REA, III
Rear Admiral, U. S. Coast Guard
Chairman, Ship Structure Committee
E TO:
SSC-230
Final Report on
Project SR-174, "Ship Computer Response" to the
Ship Structure Committee
PROGRAM SCORES - SHIP STRUCTURAL RESPONSE IN WAVES
by
Alfred I. Raff Oceanics, Inc.
under
Department of the Navy Naval Ship Engineering Center Contract No. N00024-70-C-5076
This document has been approved for public release and
sale; its distribution is unlimited.
U. S. Coast Guard Headquarters Washington, D. C.
Information necessary for the use of the SCORES digital
compu-ter program is given. This program calculates both the vertical and
lateral plane motions and applied loads of a ship in waves. Strip
theory is used and each ship hull cross-section is assumed to be of
Lewis form for the purpose of calculating hydrodynamic forces. The
ship can be at any heading, relative to the wave direction. Both
regular and irregular wave results can be obtained, including short
crested seas (directional wave spectrum). All three primary ship
j hull loadings are computed, i.e. vertical bending, lateral bending
and torsional moments.
L
All the basic equations used in the analysis are given, as
well as a description of the overall program structure. The input
data requirements and format are specified. Sample input and
out-put are shown. The Appendices include a description of the FORTRAN
program organization, together with flowcharts and a complete cross-referenced listing of the source language.
Page
INTRODUCTION 1
METHOD OF ANALYSIS 1
VERTICAL PLANE EQUATIONS 3
LATERAL PLANE EQUATIONS 8
WAVE SPECTRA EQUATIONS 16
NON-DIMENSIONAL FORMS 19 PROGRAM ORGANIZATION 20 GENERAL 20 RESTRICTIONS 21 RUNNING TIME 22 DATA INPUT 22 UNITS 22
DATA CARD PREPARATION 23
SAMPLE INPUT 30 PROGRAM OUTPUT 29 DESCRIPTION 29 SAMPLE OUTPUT 32 ERROR MESSAGES 37 ACKNOWLEDGEMENTS 37
APPENDIX A - PROGRAM DESCRIPTION 38
APPENDIX B - FLOWCHARTS 40
Capt. J. E. Rasmussen, USN Head, Ship Systems Engineering
and Design Department Naval Ship Engineering Center Naval Ship Systems Command
Mr. K. Morland, Vice President
American Bureau of Shipping
The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research
program to improve the hull structures of ships by an extension of knowledge
pertaining to design, materials and methods of fabrication. RADM W. F. Rea, III, USCG, Chairman Chief, Office of Merchant Marine Safety
U. S. Coast Guard Headquarters
Mr. P. M. Pafermo - Chairman
Mr. J. B. O'Brien - Contract Administrator Mr. G. Sorkin - Member
Mr. H. S. Sayre - Alternate
Mr. I. Fioriti - Alternate
U. S. COAST GUARD
LCDR C. S. Loosmore, USCG - Secretary
CAPT C. R. Thompson, USCG - Member
CDR J. W. Kime, USCG - Alternate
CDR J. L. Coburn, USCG Alternate
MARITIME ADMINISTRATION Mr. F. Dashnaw - Member Mr. A. Maillar - Member Mr. R. Falls - Alternate
Mr. R. F. Coombs - Alternate
MILITARY SEALIFT COMMAND Mr. R. R. Askren - Member
LTJG E. T. Power, USNR - Member
AMERICAN BUREAU OF SHIPPING
Mr. S. G. Stiansen Member
Mr. F. J. Crum - Member
iv
SHIP STRUCTURE SUBCOMMITTEE
The SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committee on technical matters by providing technical coordination for the determination of
goals and objectives of the program, and by evaluating and interpreting the
re-sults in terms of ship structural design, construction and operation.
NAVAL SHIP ENGINEERING CENTER OFFICE OF NAVAL RESEARCH
Mr. E. S. Dillon Chief
Office of Ship Construction Maritime Administration Capt. L. L. Jackson, USN
Maintenance and Repair Officer Military Sealift Command
Mr. J. M. Crowley - Member Dr. W. G. Rauch - Alternate
NAVAL SHIP RESEARCH & DEVELOPMENT CENTER
Mr. A. B. Stavovy - Alternate
NATIONAL ACADEMY OF SCIENCES
-Ship Research Committee Mr. R. W. Rumke, Liaison Prof. R. A. Yagle, Liaison
SOCIETY OF NAVAL ARCHITECTS & MARINE ENGINEERS
Mr. T. M. Buermann, Liaison BRITISH NAVY STAFF
Dr. V. Flint, Liaison
CDR P. H. H. Ablett, RCNC, Liaison
WELDING RESEARCH COUNCIL Mr. K. H. Koopman, Liaison Mr. C. Larson, Liaison
This manual describes in detail the use of SCORES, which is a digital computer program for the calculation of the
wave-induced motions and loads of a ship. Both the vertical and
lateral plane motions are treated, so that results for vertical
bending, lateral bending and torsional hull moments can be
ob-tained. The principal assumptions of the method are that the
motions are linear, can be solved by "strip theory" and that
the ship sections can be approximated by-"Lewis forms" for the
purpose of calculating the 1-iydrodynamic forces, that is, the
required two-dimensional added mass and wave damping properties
Both regular or irregular waves can be specified, and for the
latter multi-directional (short crested) seas are allowed.
SCORES was written in the FORTRAN IV language and
checked out and run on the Control Data 6600 Computer using the
SCOPE operating system (version 3.1.6). The program is
un-classified.
The method of analysis used in SCORES is outlined below
in Section II. All the equations of motion and loadings are
given. In Section III, the organization of the SCORES program
is discussed briefly. An explanation of input data card
prepara-tion is given in Secprepara-tion IV, and of program output in Section V.
An example problem is shown. Error messages which can appear
during program execution are described in Section VI.
The Appendices include a description of the FORTRAN
program organization, flowcharts for each subprogram and a
com-plete cross-referenced (to the flowcharts) listing of the source
language.
METHOD OF ANALYSIS
The analysis used in SCORES was developed and investigated
to some extent in work supported by the Ship Structure Comrnittee.*
The exposition to be given here will serve as a convenient listing
of the equations, but for the full derivation and explanation of
the analysis method, the references listed should be consulted. *Kaplan, Paul, "Development of Mathematical Models for Describing
Ship Structural Response in Waves," Ship Structure
Committee Report SSC-l93, January 1969 (AD 682591)
Kaplan, P., Sargent, T.P. and Raff,A.I., "An Investigation of the
Utility of Computer Simulation to Predict Ship
Structural Response in Waves," Ship Structure
Committee Report SSC-l97, June 1969 (AD 690229)
Kaplan, P., and Raff, A.I., "Evaluation and Verification of Computer
Calculations of Wave-Induced Ship Structural Response."
The relationship between the water wave system and the
ship coordinate axes system is shown in Figure 1. The wave
propa-gation, at speed c, is considered fixed ìn space. The ship then
travels, at speed V, at some angle, with respect to the wave
direction. The wave velocity potential, for simple deep-water
waves, is then defined by:
_aceZ'cos
k (x' + Ct)w (1)
where a = wave amplitude
c = wave speed
2iî
k = wave number =
-A
X = wave length
z' = vertical coordinate, from undisturbed water surface
positive downwards
= axis fixed in space
t = time
The x-y axes, with origin at G, the center of gravity of the ship,
translate with the ship. The x' coordinate of a point in the x-y
plane can be defined by:
x' = -(x+Vt) cos +y sin (2)
Then, the surface wave elevation n (positive upwards) can be
ex-pressed as follows:
li WI
n = = a sin k (x' + ct)
IZ '=0
since
C2 =
where g = acceleration of gravity
In x-y coordinates we have:
n = a sin k [-x cos + y sin +(c-V cas )t] (4)
Dn B
=
= -v -) n (x,t)
= akc cas k [-x cos +y sin 3 + (c-V cos )tJ (5)
n
direction of ship travel at speed, V
wave direction of
propagation at speed, C
Fig. 1.
Wave and Ship Axes Conventionand..
D
rl = = -akg sin k [-x cos +y sin -f(c-V cas )t]
The results of the equations of motion, etc., will be referenced to the wave elevation n at the origin of the x-y axes,
that is: n = a sin k'(c-Vcos ) t or r = a sin w t e where 2iï w e (c-V cas )
and we is known as the circular frequency of encounter.
A. Vertical Plane Equations
The coupled equations of motion for heave, z (positive
downwards), and pitch, O (positive bow-up), are given as:
a w u w a dZ - dx + Z dx w (6) (9) Xb mz = s
and
I,= mass moment of inertia of ship about y axis
local sectional vertical hydromechanic force on
ship
X , xb= coordinates of stern and bow ends of shIp,
S respectively
Z, M
= wave excitation force and moment on shipThe general hydromechanic force is taken to be:
dZ
(-x+V8)
T_NI (_x+V8)_pgB*(z_x8)dxDt _33
j zwhere
p = density of water
A3- local sectional vertical added mass
N' = local sectional vertical damping force Z
coefficient
B* = local waterline beam
dx
N'
pg2Aw3
(12)z
with
A = ratio of generated wave to heave amplitude for
vertical motion-induced wave
Expanding the derivative, we obtain:
I y where 8 -xb dZ - x dx + M dx w s m = mass of ship (10)
The coefficients on the left hand sides are defined by: a' = m+
b=
e=
g'= pgA= I +
y N' dx -V B * dx x dx N'xdx -2V z B*xdx -VbA3 x2dx
d (A3)A3dx-V
dZ - A3 (z-xO+2V0) - pgB*(z_xO) N'-V z dA' (-xÔ+VO) (13) dxThe equations of motion, (9)
the familiar form as follows:
and (10) are then transformed into
a'z + b + c'z - de - e - g'e = zw (14) AO + Bé +Ce - Dz - E - G'z
=M
w (15) xd (A3) (16) c'= pgd= D =
z w M w
3=
C = pg3=
Nx2dx -2v s r Xb dZ xsThe local sectional vertical wave force acting on the
ship section is represented as:
w_
dZ [pgE*n + (N'_VdA3
dx B*x2dx_VENxdx-V
A3xdx v
xd (A3) x2d (A')where all the indicated integrations are over the length of the ship.
The wave excitation, the right hand sides of Eqs. (14)
and (15), is given by:
dx (17) x dx -kh e (18) (19) G'= pg B*xdx
sin sin 8 rB*
sin 8
The value of is approximated by:
= HC
s
where H = local section draft
C = local section area coefficient
s
The steady state solution of the equations of motion are
obtained by conventional methods for second order ordinary
differential equations, using complex notation. The solutions are
expressed as:
z = z sin (w t+)
o e
e = e sin (w
t+)
o e
where the zero subscripted quantities are the amplitudes and are the phase angle differences, i.e. leads with respect to the
wave elevation in Eq. (7).
The local vertical loading is given by:
df
dx - m (z-xe) +
Z
...dz +dZw
(23) (22)
where I = mean section draft. Substituting the expressions for n,
and from Eq. (4), (5) and (6), with y=O and applying the
approximate factor for short wave lengths we obtain:
dz
w -kh
= - ae
f dA'
(pgB*=A3 kg)sin(-kx cos 8) +
dx kc (N'-v cos(-kx cos dA' 8) cos w t + e (pgB*_A3kg)
J
z dxcos(-kx cos 8)-kc N'-V sin(-kx cos 8) sin w
e
z dx
(20)
where 5m = local mass, per unit length.
Eq. (23) is simply the summation of inertial, hydrodynamic,
hydro-static and wave excitation forces. The latter terms are given in
Eqs. (l3)and (20). The vertical bending moment at location x0 is
then given by:
BN (x ) =
z o
s
where I = mass moment of inertia of ship about z axis
= mass moment of inertia of ship about x axis = mass product of inertia of ship in x-z plane
'X o
or
s o
and is expressed in a form similar to the motions, i.e.
BM = BM sin (w t+a) (25)
z zo e
B. Lateral Plane Equations
Xb
df z
(x-x ) dx (24)
o cix
The coupled equations
starboard), yaw, i (positive
starboard-down) , are given
of motion for sway, y (positive to
bow-starboard), and roll, (positive
as: Xb my = dx+Y dx w (26) X s I ; -i z xz = 'X b s dY - x dx+N dx w (27) Xb
'ï-'
q; X XZ = dx-mg ? 4+K (28)ay
= local sectional lateral hydrodynamic force on ship
= local sectional hydrodynamic rolling moment on ship
Y , N , K = wave excitation
force and moments on ship
w w w
= initial metacentric height of ship (hydrostatic).
The hydrodynamic force and moment are taken to be:
dY
= -
D E L M5 -N5(+x-V) + N
rs dK D dx Dt_r
I
-Msc(+x-V) j -N
r NS4(+x-V)
- (M )-
N -t S4 s dxwhere 0G = distance of ship C.G. from waterline, positive up
M = sectional lateral added mass
s
N = sectional lateral damping force coefficient
= sectional added mass moment of inertia due to lateral motiön
sectional damping moment coefficient due to lateral motion
sectional added mass moment of inertia sectional damping moment coefficient
sectional lateral added mass due to roll motion sectional lateral damping force coefficient due to
roll motion
(29)
(30)
and the sectional added mass moments and damping moment coefficients
are taken with respect to an axis at the waterline.
N =
'r =
Nr =
Frs = Nrs =
The additional roll damping moment to account for viscous
and bilge keel effects is taken as a particular fraction of the
critical roll damping, as follows:
=
C/L-N(w)
(31)
where = sectional damping moment coefficient due to viscous
and bilge keel effects
= fraction of critical roll damping (empirical data)
critical roll damping
L = ship length (LXb_Xs)
= natural roll (resonant) frequency
N (w ) = value of Nr at frequency
w.
r
The critical roll damping is expressed in terms of the natural
roll frequency by:
C
=2mgoi1
C
with mg GM
+ 1r »dX)
2
where the integral is over the ship length. The calculation of
the natural roll frequency, w , as indicated above is carried
out by means of successive aproximation.
Expanding the derivatives, we obtain
/dN
-M (y+x-2V) +
'V-- -N
(î+x-V)
dx s dx sj (33) dF +(F+
M + [Nrs+ N -( dx + ) ] dK dx (32) I + 0G rM +F
s rs+0GM
- 'dl dM+ v+ö
s dx dxa16 = -Va12
= I + 1M x2dx
a24
j s
The equations of motion, (26), (27) and (28) are then transformed
into this familiar form:
= Yw
=
The coefficients on the left-hand sides are defined by:
+ IM dx a1 = N dx-V jd(M ) a11 = m j a14 = IM xdx , a15 =
fNxdx
-2V fM5dx -Vf
xd(M5) s = - dx - ö 1M dx , a17jrs
js
a18= -
1N dx + V Jd(M5)_5 fN5dx + V 1d(F J rs rs a = 1M xdx = TN xdx -V Ixd(M 21Js
,a22
Js
j s a25 = JN5x2dx_2V fMxdx_V fx2d(M5a26 = -Va22 , a27 = - JFrs xdx -
JMxdx
a = - IN
xdx+V
Ixd(M ) - IN xdx+V Ixd(F 28 j rs j s j s j rsJ
(36) 37) - 0G-N
r + N + N \rs _N* r 0G N5-V S4+N
dM ) + sj M + sqs+
5v
\ M s dF dM rs -(34) s (/+xV-2V)+oG-ux
dx(r+x-Vip)
dx dx = N (35)a31 =
-f
Mdx -
fMdx
a32 =_fNdx
-ö
JNdx
+vJd(M)
+V íd(Ms) a34 =_fMsxdx
-OJMXdX
a35 =-JNSXdX
-ö
f
xdx +V fxd(M )+V Jxd(M)_2Va3i a36 =-Va32
a =1 +II
dx + IN dx +5 IF dx+ö2
IM dx x j r j s j rs j s a38 = J(N+N*) dx+ ö
f
Ndx
JNdX
JNdx
- L'
f d(M)+
Jd(Frs)+2
f
d(M)
a39 = mgwhere all the indicated integrations are over the ship length.
The wave excitation, the right-hand sides of Eqs. (35) is
given by:
Xbay
w y = -wdx
X s xl- -j-.ay
w s xl-L) dK w s dx dx (38) dx (39) x dx (40) dx (41) N = w K = wThe local sectional lateral force and rotational morflent
due to the waves acting on the ship are represented as:
w s dY Dv dN - ( Dv dM =
(pS+M ) - Vv - +N
V +k -M dx V s Dtwdx
sw
s ITB* sin sin 8 dK w dx = - (M y )+p IB*3 _\ Sz N V s w Dt s w /and then we have:
Dt TB* sln8 y =
-w ay -kFi y = - akc esinsink
w 71B* sin -y---ITB* sin 8 (42)-x cose + y sin+ (c-V cos)t1 (44)
Dv
-w -kh
- akg e sin cos k [_x cos + y sin + (c-V cos )tj (45)
dY
dx (43)
where y = lateral orbital wave velocity
w
S = local section area
= local sectional center of buoyancy, from
waterline
The lateral wave orbital velocity is obtained as follows:
w
-J
After substituting these expressions and expanding terms, we obtain dY T.?
sinwt
(46) e 2 e---T1coswt+T
with T1 = T3 gT4 cos T6 + c T5 sin T61
T2 = T3 _gT4 sin T6 + c T5 cos TJ sin
-
7rB* sin T3= -
ake sine 71B* sine T4 = pS+M5-kM5 dM dM T5 = N5-V!
k V T6 = -kx cos dK and e (47)with T7 = T3 g T9 cos T + C T1 sin T61
T8 = T3 [-g T9 sin T6 + c T10 cos T6 B*3 -T9 = p Sz -M5 -0G T4 dM
T1 =N
+V O s dxThe steady-state solution of the equations of motion are expressed as:
y=y sin
(wt+
K)o e
1) = 1) sin (w t + )
x
and again they are expressed in this form:
BM =BM
sin (wt+T)
y yo e TM TM sin (w t + ) X XO e q, = q, sin (w t + y) o ewhere the zero-subscripted quantities are the amplitudes and K1 c
and are phase angle leads with respect to the wave elevation.
The local lateral and rotational loadings are given by:
df dY dY -
m (+x-) +
+ dx drn ¡3*3_\
+ ôm(+xß)+ pg
Sz _SOG) -g6mq, dK + + dx dxwhere = local center of gravity (relative to ship C.G.)
positive down
= local mass gyradius in roll
and the hydrodynamic and wave excitation terms are given in Eqs.
(33), (34), (46), and (47).
The lateral bending and torsional moments at location
(50) xo df
BM(x)=
yo
or s o (x-x ) dx (53) o dx o b L. dm TM (x ) = X O or L o_ X dx (54) dxThe requirement on the local vertical mass center is: Xb
6m. çdx = 0 (56)
xs
Similarly, the requirement on the local roll gyradius is:
Xb
6nîy2dx = IX (57)
s
The product of inertia in the x-z plane is defined by: -Xb
I =
Xz
s
C. Wave Spectra Equations
The wave spectrum for calculations in irregular seas is
considered to be a separable function of wave frequency and
direction as follows:
ämxdx
(58) S (w,p) = S1(j) S2(p) forO<w<
71 71 and - - p (59)where S (w,p) = directional spectrum of the seaway (short
crested sea spectrum)
w = circular wave frequency
p = wave direction relative to predominent direction
S1(w) = frequency spectrum (long crested sea spectrum)
S2 (p) = spreading function
The SCORES program includes various spectra that can be
chosen as desired. However, in all cases, the following
relationship between the spectrum, or spectral density, and the wave elevations, or amplitudes, is used:
where a = root-mean-squared wave amplitude rms
a = average (statistical)wave amplitude
avg - oe Tr 2 S (w, dwdi (60) o 2
where a2 = mean squared wave amplitude.
Since we impose: rT 2 S2(ij) di = 1.0 (61) 'T 2 we then have: a2 = S1 (w)dw (62) O
Additional statistical properties are formulated from the mean
squared amplitude: a rms (63) a =1.25 a avg rms a1,,,3 = 2.0 a rms a1/10 = 2.55 a rms
a1,,3 = significant (average of 1/3 highest)
/ wave amplitude
a1/10= average of 1/10 highest wave amplitude.
Neumann Spectrum (1953)
This frequency spectrum (as used) is given by:
S1(w) = 0.000827 (67)
where U = wind speed
The constant is one half that originally specified by
Neumann so that this spectrum satisfies Eq. (62). Thus, originally
the Neumann spectrum required only a factor of /2 in Eq. (65),
instead of 2.0.
Pierson-Moskowitz (1964) This is given by:
S1(w) = 0.0081 (68)
and was derived on the basis of fully arisen seas.
Two Parameter (1967)
S1(w) = ABwe-
(69) where = 0.25 H1,,,32 2 B = (0.817 --r-) TH1/3 = significant wave height (=2.0a1/3)
T = mean wave period
This spectrum is usually used in conjunction with "observed"
wave height and period, which are then taken to be the significant
height and mean period. This spectrum is similar to that adopted
by the I.S.S.C. (1967) as T1nominal", except that it is expressed
in circular wave frequency instead of frequency in cycles per
Uni-Directional Spreading (Long Crested Seas) This is obviously: S2(p) = 6(p) (delta function) Cosine-Squared Spreading 2 S2(p) = - coszp Responses
All of the motions and moments calculated are considered to be linear and the principle of wave superposition is assumed.
Thus for each response a spectrum is calculated by:
S(,p)
= LTi(w,P)12
S (,p) (72)where
T.(w,p)
= response amplitude operator (amplitude of responseper unit wave amplitude) We then have, similar to the wave amplitude:
O 7I
2
lT
dui dp
Eqs. (63) - (66) then apply to each response.
D. Non-dimensional Forms
w2
Frequency parameter: --f-- H
S2 (p) T1(w,p) S1(t) dw dp (73) 71 O 2where a2 = mean squared response amplitude. a. 2
Non-dimensional moment:
Non-dimensional shear:
III. PROGRAN ORGANIZATION
A. General
Non-dimensional linear motion (heave, sway)
BM (orBM or TM z y X
pg BL2a
Shear Forcepg BLa
motion amplitude aIn general, the SCORES computer program has been arranged and organized to both keep a) the coding simple and flexible (for possible future modification) and b) the running times low (for
obvious reasons). Thus, precision of computation has not been of
major priority in program development. This approach is considered
reasonable at the present time because precise correlation (to less than about 5%) with independent data (model or full-scale ex-periments) is not envisioned, and the theoretical analysis itself
is an approximation.
Aside from the actual coding and data structure in the program, which will not be discussed here (see Appendices A, B
and c of this report), this approach manifests itself primarily
in two aspects. The first is the precision with which the local, or
two-dimensional, sectional added mass and damping characteristics
or properties, are calculated. For vertical oscillation, the method
of Grim* is used. For the two-dimensional properties in lateral
and roll oscillations, the method of Tasai** has been programmed. In general, these methods can be carried out to increasing degrees
of numerical accuracy. For practical purposes of keeping running
time reasonable, these calculations have been limited. For example
in the lateral and roll computations, the infinite series of terms representing the velocity potential is truncated to nine terms and only 15 points along the Lewis form contour are used for least
square approximation purposes. While the full range of section
properties and frequencies has not been explored in detail, results on the order of 1% accuracy or better are obtained for average sections over a wide frequency range.
* Grim, O., "Die Schwingungen von schwimmeden, zweidimensionalen Korpern," HSVA Report No. 1171, September 1959.
Grim, O.., and Kirsch, M., private communication, September 1967.
**Tasai, F., "Hydrodynamic Force and Moment Produced by Swaying and Rollinç Oscillation of Cylinders on the Free Surface," Reports of Research Institute for Applied Mechanics, Kyushu University Japan, Vol. IX, No. 35, 1961
Non-dimensional angular motion motion amplitude
(pitch, yaw, roll):
The second aspect of program organization is related to the
above. While the computations of the two-dimensional properties
are limited as described, they still are relatively lengthy. That
is at a particular condition of ship speed, wave angle and wave
length, the bulk of the computation time would be devoted to these
calculations rather than the formation of the coefficients,
wave excitation, solution of ship motions and the resulting
calculation of applied moments. Therefore, it was decided that
rather than calculate for each frequency at each cross-section the above mentioned dimensional properties, instead the two-dimensional properties are calculated first at 25 values of frequency over a wide range and then interpolated (or
extra-polated) for each subsequent frequency. The results of the initial
calculation over the frequency range are saved in the computer
memory for the calculations at hand, and can also be saved on a
permanent disc file (or magnetic tape storage), for later usage. In this way, a large range of ship speeds and headings can be run, each over the appropriate frequency range, without excessively
high running times. The interpolation procedure used is a
six-point continued fraction method which gives results that are generally well within 1%.
In other respects, the SCORES program is organized in a
fairly straightforward manner. The input consists of:
basic data which specify the hull form and weight
distribution and
conditional data which specify the speeds and wave
parameters.
Repeated sets of conditional data can be run with the same basic
data, that is, for the same defined ship. A fair amount of input
data verification is incorporated into the program.
The core storage requirement is about 25,000 cells as
compiled on the CDC 6600. This includes the program instructions,
data storage and system routines to handle input-output system
control and provide mathematical functions. It would be possible
to decrease this core requirement via program overlay and
linkage techniques, should the need arise. However, it probably
would be relatively difficult to fit the program within a 12K
core restraint.
B. Restrictions
the following
The main restrictions in the program concern items:
Maximum no. of ship cross-sections
(stations 0 to 20)
21
Maximum no. of wave angles (in one run) 25
Maximum no. of wave lengths (in one run) . .51
*Two.dimensional properties
The word length on the CDC 6600 is 60 bits. No loss in
overall computational accuracy would be expected if this were
reduced, as in other digital computers, to 36 bits.
A special system subroutine called DATE is used which
provides the current date. This is used only in the heading on
the output.
C. Running Time
The following approximate times are for running under the
SCOPE operating system on the CDC 6600 computer.
Program compilation (RUN compiler) 10.0 secs.
Program loading into core 1.0 secs.
Calculation of TDP* Array (21 sections,
both vertical and lateral modes) 25 secs.
Calculate motions, moments at one condition,
(21 sections, both vertical and lateral
modes) 0.14 secs.
Calculate spectral response, for each
spectrum, for each condition 0.006 secs.
Thus, for a run with two ship speeds, 7 headings (at 30° increments from head to following seas), 21 wave frequencies (to adequately cover the spectral energy bands) and 5 sea states, the incremental time once the program was compiled, loaded and the TDP Array was
calculated, would be estimated as follows:
(2) (7) (21) [0.l4+(5) (0.006)] = 50 secs.
IV. DATA INPUT
This section of the manual describes the details of data
card input to the SCORES program.
A. Units
For calculations in regular waves, there are no inherent
units assigned to any of the variables in the program. Thus, the
user is free to choose any desired set as long as they are
consistent for all input parameters. The units are established
by the input values of water density and gravity acceleration.
Wave direction angles are always specified in degrees,
rather than radians.
However, for spectral calculations in irregular waves, using either the Neumann or Pierson-Moskowitz spectra, the SCORES
pro-gram assumes ft.-sec. units, full scale. The input wind speeds
used to specify spectral intensities, or sea states, are then
assumed to be in knots.
The following input data description indicates typical
consistent units for all parameters. Other systems of units
could be used, as noted above.
B. Data Card Preparation
Every data card defines several parameters which are
required by the program; each of. these parameters must be input
according to a specific format. "I" format (integer) means that
the value is to be input without a decimal point and packed to
the right of the specified field. "F'T format (floating point)
requires that the data be input with a decimal point; the number
can appear anywhere in the field indicated. "A" format
(alphanumeric) indicates that certain alphabetic characters or
title information must be entered in the appropriate card columns.
If the field is left blank for either "I" or "F" format,
a value of zero (0) is assigned to the parameter. Thus, parameters
not required by the program for a particular problem need not be
specified.
The card order of the data deck must follow the order in
which they are described below. Cards which must be present in
every run, regardless of options, are marked with an asterisk (*) The first eight types of cards are considered the basic data set, while subsequent cards are the conditional data set(s).
1) Title Card (*)
Columns Format Entry
l-80 A Any alphanumeric title
information, used to label job output
Water Density lbs./cu. ft. tons/cu. ft. metric ton/cu.
meter
Gravity Accel. ft./sec.2 ft./sec.2 meter/sec.2
Resultant Unit System
ft.-lbs.-sec. ft.-tons-sec. meter-metric
The first 30 columns are used as a label for the TDP array file. Thus, subsequent runs using the file must duplicate these first
30 columns which are then checked against the file label before
using the data. This avoids inadvertent use of an incorrect
TDP file.
Each option control tag is given a value of 0, 1, 2 or 3
where the meaning of each is given in the table below. The last
entry of the card, the number of ship segments, corresponds to the even number of equal length segments, or strips, into which the ship hull is divided lengthwise for purposes of calculation.
OPTION CONTROL TAG INTERPRETATION
Letter Tag
Code Descriptor Options Available
0: Simple summation 1: Trapezoidal rule
0: Caic. motions only, use summary mass properties
Caic. motions only, use
mass dist.
Calc. moments, use mass
dist. 0: Input masses 1: Input weights 0: Regular waves Neumann spectra Pierson-Moskowitz spectra Two parameter spectra
(continued on next page)
2) Option Control Card (*)
Columns Format Entry
i-2 I Integration option control tag
3-4 I Moment option control tag
5-6 I Mass dist. option control tag
7-8 I Wave spectra option control tag
9-10 I Degrees of freedom option control tag
il-12 I Directionality option control tag
13-14 I TDP file option control tag
15-16 I Moment closure option control tag
17-18 I Output form option control tag
19-20 I Torsion axis option control tag
21-22 I Number of ship segments
A Integration
B Moment
C Mass dist.
OPTION CONTROL TAG INTERPRETATION, Continued Tag Des criptor Letter Code H I J F Direction-ality G TDP file Moment closure Output form Torsion axis Options Available
0: Vertical plane only
Vertical and lateral plane
Lateral plane only 0: Uni-directional waves 1: Cos-sq. wave spreading 0: Generate TDP file, write
on file (Tape 10)
Read TDP file, (Tape lu), print out TDP data
Read TDP file,(Tape 10), no
print-out
0: Suppress closure calcs.
1: Calc. and print out
closure results 0: Dimensional 1: Non-dimensional 0: Center of gravity 1: Waterline Length Card (*)
Columns Format Entry
11-20 F Ship length (ft.)
21-30 F Water density (tons/cu.ft.)
31-40 F Acceleration of gravity (ft./sec.2)
41-50 F Ship displacement (tons)
The entries on this card are self descriptive and determine the units to be used for all other parameters, except as noted
earlier.
Hull Form Cards (*)
Columns Format Entry
l-10 F Section waterline breadth (ft.)
11-20 F Section area coefficient (-)
21-30 F Section draft (ft.)
31-40 F Section centroid (ft.)
E Degrees of
One card is used for each section to be specified, in order
along the ship length starting at the bow. For example, if the
number of segments is 10, and the integration option tag is 0, then 10 hull form cards are required which correspond to the hull
at stations 1/2, 1 1/2, 2 1/2, ..., 8 1/2, 9 1/2. If the
integration tag is 1, then 11 hull form cards are required at
stations 0, 1, 2, 3 9, 10.
The entries for sectional waterline breadth, area
coef-ficient and draft are straightforward. The fourth entry, the
section centroid, is measured downwards from the waterline If
no entries are given and the centroids are needed for lateral plane motions calculations, approximate controids are then
calculated based on the area coefficient and draft (using a two-dimensional version of the Moorish Approximation).
Lateral Plane Card
Columns Format Entry
1-10 F Ship vertical center of gravity (ft.)
11-20 F Radius of gyration in roll (ft.)
This card is used only if the degrees of freedom option
tag is i or 2, indicating lateral plane calculations. The ship
vertical c.g. is measured from the waterline, positive upwards. Summary Mass Properties Card
Columns Format Entry
l-10 F Radius of gyration, longitudinal
(ft.)
11-20 F Longitudinal center of gravity
(ft.)
This card is used only if the moment option tag is 0. The longitudinal center of gravity is measured from amidships,
positive forwards.
Sectional Mass Properties Cards
Column Format Entry
l-10 F Segment weight, or mass (tons,
or tons-sec2/ft.)
il-20 F Segment vert. c.g. (ft.)
21-30 F Segment roll gyradius (ft.)
These cards are used only if the moment option tag is
i or 2, in lieu of the summary mass properties card above. One
card is used for each section to be specified, in a similar
manner as the hull form cards described earlier.
The first entry on each card is the segment weight, or mass, depending on whether the mass dist. option tag is 1, or 0,
respectively. The second entry, the segment vertical center of gravity, necessary only for lateral bending moment calculations,
is measured, positive downwards, with respect to the ship's over-all vertical center, as specified on the lateral plane data card
above. Since it is required that the vertical mass moment
integral satisfy the specified overall v.c.g., the input segment
v.c.g. 's are shifted by an equal amount, up or down as necessary
to exactly balance the vertical moment for the hull. This
minimizes the effort required to obtain precise balance in input
data preparation. The third card entry, the segment roll gyradius,
is needed only for torsional moment calculations. If no entries
are given the overall ship value is used at each segment. Moment Station Card (*)
Column Format Entry
l-10 I First station for moment calculations
11-20 I Last station for moment calculations
21-30 I Increment between stations
The parameters on this card determine where along the ship
hull the moment calculations are to be performed. Station numbers
are defined as zero at the forward end of the first segment. increasing to N, the number of segments, at the after end of the
last segment. If the calculations are required only at one station,
then the first two entries on the card should be equal to that
station number.
The moment results at only one station are stored for
subsequent irregular seas spectral calculations. In the calculations
over a range of stations at which moments are calculated (and printed), then only the results at midships are stored for the
subsequent spectral calculations.
The first entry, the run control tag, determines program
continuity:
9) Run Control Card (*)
Columns Format Entry
l-10 F Run control tag and. wave
amplitude (ft.)
11-20 F Initial wave length, or
frequency (ft. or rad./sec.)
21-30 F Final wave length, or frequency
(ft. or rad./sec.)
31-40 F Increment in wave length, or
frequency (ft. or rad./sec.)
4-50
F Initial ship speed (ft./sec.)51-60 F Final ship speed (ft./sec.)
Thus, if the run control tag is not greater than 0.0, then
the remaining parameters on the card are irrelevant. A blank
card, for example, is used to stop calculations and proceed to read a complete new set of data starting with the title card
1) above. This parameter is also used as the wave amplitude, and
is usually set to 1.0.
The next three entries determine the wave lengths to be
used in the calculations. If the wave spectra option control tag
is 0, indicating regular waves, then these entries are the initial,
final and increment in wave length. If the wave spectra option
control tag is greater than 0, indicating irregular wave calculations, then these entries are the initial, final and increment in wave
frequency. The increments should always be positive, so that wave
length, or frequency, increases from initial to final value.
The last three entries are similar parameters for ship speed. If calculations are required at only one value, then the initial and final values should both be set equal to it.
Roll Damping Card
Column Format Entry
1-10 F Fraction of critical roll damping
(empirical data)
This card is used only if the degrees of freedom option control tag is 1 or 2 indicating lateral plane motions calculations
are included. The calculated wave damping in roll, at the natural
roll frequency, is increased so that the total damping is the
specified fraction of critical damping. The additional roll
damping thus determined initially is then used for all subsequent
calculations.
Wave Angle Card (*)
Column Format Entry
1-10 F Initial wave angle, degrees
11-20 F Final wave angle, degrees
21-30 F Increment in wave angle, degrees
These entries specify the wave direction angles to be used
in the calculations and are always given in degrees. For
calculations with uni-directional waves, the meaning of the
parameters is as indicated. If the directionality option control
Run Control Tag Action
Greater than 0.0 Continue calculations, using this as
wave amplitude
0.0 (or blank) Stop calculations; read new basic
data set
tag is greater than 0, indicating calculations for a directional
wave spectrum, then only two choices exist. If the initial wave
angle is 180.0 the calculations proceed for head seas only,
including the wave directionality. If the initial wave angle is
not 180.0 the calculations proceed for all angles from following
seas to head seas, in steps according to the wave angle increment
specified.
In both cases the integrations with respect to wave angle
use the same increment, as specified.
12) Wave Spectra Card(s)
Columns Format Entry
1-10 I No. of sea states (wave spectra)
11-15 F First spectra parameter
16-20 F Second spectra parameter
21-25 F Third spectra parameter
(5 col.
fields) F
56-60 F Tenth spectra parameter
This card is used only for calculations in irregular seas
(wave spectra option control tag is greater than 0). The first
entry specifies the number of sea states (spectra) to be used
(maximum 10). For both the Neumann and Pierson-Moskowitz spectra
(wave spectra option control tag equals 1 or 2), the parameters
to be specified are the wind speed, in knots, for each sea
state. For the two parameter spectrum (option tag equals 3),
the parameters on this card are the significant wave heights
for each sea state. A second card is then used which contains
the mean periods for each corresponding sea state, as the
spectral parameter entries specified above.
C. Sample Input Deck
A sample input card deck listing is given on the next
page. The units are meters, metric tons and seconds.
V. PROGRAM OUTPUT
A. Description
The printed output from the SCORES program depends on the
option control tags set as input. Each output section will be
described, though in any given run not all sections will be
printed. Each section starts a new page and is labeled with the
title information and date.
The first part of the output is a listing of the basic
input data as processed. This defines the hull form and weight
distribution. Then the conditional data cards are printed out.
For irregular seas cases, the wave spectra will then be printed,
together with internally generated wave statistics. If the TDP
array is calculated diagnostic messages concerning these
The next output will be the listing of the two-dimensional
properties (TDP array) for each station and each frequency. If
the data is being read from file, this output can be suppressed.
For lateral plane calculations, the natural roll frequency and
roll damping information will then be printed.
Then, the vertical and/or lateral plane responses will be
printed out with all frequencies, or wave lengths, for a given
ship speed and wave angle, on the same page. For irregular seas
calculations, this will be followed by a print-out of the
response spectra and statistics (long crested seas) . These pages
will be repeated for each wave angle at the initial ship speed.
Then directional seas calculations results will be output, if
specified. The output is, of course, then repeated for
additionally specified ship speeds.
B. Sample Output
A sample output listing, in abbreviated form, is given
following the sample input listing.
Sample Input Card Deck Listing
0.-" rLL)C0 Tir))) OPT. '3. OO S) OCEAF.JICS PRr.gECT oo. 1053
240.5 481.3 1203.2 2406 3 3850.1 4090.1 4331.4 4331.4 3388 R 1584.4 1684 4 1443.5 2195.5 3b335 3466 I 3146.3 1955.1 721.9 120.3
---Ó_...-w---Y -
1.0 0.3151 1.3079 0.0451 ---8.5257 6.5251 1.0 --.----10.0- 115.0 20.0 10.0 SL8IES 6 kULL 35M, 1 2 1 3 1 () 1 1 1 1U 153.0 )fl?0 9.80655 4M1?5. 00.00 .0 00.00 14.3Q .R2 11.0.3 22.85 .R4 11.03 28.55 .29 11.03 21.54 .90 I 1.(3 27.57 .Q1 11.03 27.57 .Q4 11.03 27.57 054 )1.03 27.57 .9s4 11.13 21.57 994 11.33 27.57 .994 T1.3 27.57 .994 jl.03 27.57 .993 11.03 27.57 959 11.03 27.57 .OoR 11.03 21.24 .921 11.03 25.94 .551 11.03 23.46 76R 11.03 19.63 .527 11.03 13.57 415 11.03 4.41 .53 1.1) -3.0955 5.95025OPTION CONIMOL
Sample Input Listing
SEMIES 60 MULL FORM. 0.80 44LUCK CINQ RPI. MO. loo 5) OCEANICS PROJECT NO. 1093 SEP 24' 1910
TAGS - A B C I) E F G N I J
1 7 1 - 1 i i
OISPL. 44126.40 ORAVITY 9.806650
STATION BEAM AREA COE. ORAFI Z-BAR .EIGNT ZETA
OEQIvtD RESULTS
(.UNS. C.B. 4.(16 CFtTOFPWMIPST
LONC.. =
4.875 CFMO. OB MIDSHIPS)SEHIES '0 HULL FORM. 0.80 MLUCM (TAlO HBf. NO. loo S) OCEAF'ICS PoIJECT NO. 1093 SEP 74. 1970
CONDITIONAL INVIIT1ThTACABD PRINT OUT
1.0000 .3157 1.3079 .0451 ¿.257 6.5257 1.0100 .1000
10.0000 170.0000 20.0000
1 8.4 -0.0 -0.0 0.0 -0.0 -0.0 -0.0 _0.0 -0.0 -0.0
Ío.øÇ-0.05.o-.5 -0.0 -0.0 .0.0 -0.0 -0.0
SERIES 60 NULL FORM. 0.80 HLOCB (TAlO RPT NO. 100 Sl OCEAAIICS PROJECT NO. 1093 SEP 74. 1970 WAVE SPECTRAL UENSITV, IWO PARAMETER. ZSSC 1967 SPECTRA
I5PL.(WTS.L 48126.50
tVOt 1 4Bfl77 53
-LrAlG. GYPADIUS = 46.159 GM 1.378 CALCULATE MOMENTS AT STATION 10
ST8TTONS 00 --GYP. P OLL .00 0.0000 0.0000 0.0000 0.O00 240.6005 0.0000 8.9402 1.00 14.3900 .8720 11.0300 5.0444 481.3000 0.0000 8.9602 ?.o0 22.88011 - .8940 11.0300 S.125i 1203.2000 0.0000 8.9602 3.00 26.5800 .0290 11.0300 5.204r, 2406.3000 0.0000 8.9602 4.00 27.0400 5.00 27.5700 .0T0Q1Í.ojU.0910 11.0300 3.a04,5.481m 3BSQTIVUu 4090.7000 0.00000.0000 8.960Z8.9602 6.0U 27.5100 .9940 11.0300 5.492o 4331.4000 0.0000 8.9602 7.00 27.5700 .0940 11.0301 5.492, 4331.4000 0.0000 8.9602 8.00 27.5700 .0940 [1.0300 5.49?, 3368.8000 0.0000 8.0602 9.00 27.5700 .9940 11.0300 5.492o 1684.4000 0.0000 8.9602 T0W0
2100
11.00 27.5700 .09409941T.o30011.0300 5.492,92., I6B4.0001443.8000 0.00000.0000 0.96028.9402 U.0027.07on .930 11.0300 5.489. 2195.8000 0.0000 8.9602 13.00 27.5700 .9890 11.0300 5.474 3290.7000 0.0000 8. 96 02 14OO27.57on 10.00 27.2400 .0210.068011.030011.0300 5.397,5.224 3633.IO03465.1000 --0.00000.0000 8.96028.9602 14.00 25.9400 .ABi 11.0300 4.9672 3146.3000 - -- 0.0000 - 0.06 02 17.00 23.4,00 .1580 11.0300 4.625o 1965.1000 0.0010 8.0602 r8.00 19.,30fl .6270 11.0300 4.j43, 721.9000 0.0000 8.9602 19.00 13.8100 .4190 11.0300 3.378, 481.3000 0.0000 8. 9602 20.00 - 4.4100 .5305 1.1000 .3777 120.3000 0.0000 8.9602 RTuSRaLr-. 8.960 SIG.HT. 8.400 SPECTRA Alo. WAVE FREO. .314 .360 .361-
3.328 .406 5.610 .451 12.254 -496 12.954 541 11. 743 .586 9.B24 .631 7 886 67f, 72? 6.2064 846 1 1 73 .533 .767 3 782 t218-
443 -.812 7.941 1.263 371.1:3 .857 2.331 .902 .047 1.847i .475ooso-
A 99? 3.186 R.M.S. 2073 1.037 .961 AvO. .S34 1.082 .784 500.8V1/t0 4.146 1.127 p644 0.277 BASIE!i'íøijI raTS - LENGTf4 - 193.00 - I)EoSIrY 1.025000Sample Output Listing, Continued
SIRIFS I0 HULL FOP. 0.$0 HLUCIt
tONO tIPI. NO. 100 5)
OCFANICS
PROJECT
NO.
1093
5P '4' 1970
TIlO-t)TMFSIONAL SLCTI()N PNOP1HtIFS
F HL f) PNA1. 4-pH1MF(i) ACIIAKISO. Il-SUN(S) NSUfttS) M(S.PHI) N(S.PH1) I-SURIR) MSUS(R) F-SUIO(R.S) STA 00 0,0000 INFTNTTV 0 0. 0. 0. 0. 0 0. 0. .0100 u. (1. 0. 0. 0. 0. 0, 0, 0. .0300 0.
0
0. 0. 0. 0. 0. 0. 0. u. , --. - o-.- ---o. 0, .1000 u. (t. 0. 0. 0. 0. 0, 0. 1500 0. 0. 0, 0. 0. 0. 0. 0. .100 U. 0. 0. 0. 0. 0. O 0. 2R00 0. 0. 0. 0. 0. 0. 0, 0. .3M0 0. 0. 0. 0. 0. 0. 0. 0. 0. .450Ó U. 0. 0. 0. 0, 0. .r,0o u. 0. 0. 0. ü. 0. o, 0. t;700 U, 0. 0. 0. 0, 0. O 0, .871(0 U. 0. 0. 0. 0. 0. 0, 0. 1.0100 u. 0. 0. 0. 0. 0. 0. 0. 150fl (J. 9. 0. 0. 0. 0. 0. 0, )550Q u. 0. 0. -0, 0, O. 0 0. 1,9500 U. 0. 0, 0. n. n. o. 0. 2.4500 0. 0, 0. 0. 0. 0. 0. 0. 3.0500 0. o. 0. 0. 0, 0. ø. o. 3.8000 0. 0. 0,.--0. 0. o. o o. --o, 4.7000 U, 0, O 0. 0. 0. 0, o, S.8oQo U. . 0. 0. 0. O. 0. o. 7.1900 0. 0. 0. 0. 0. o. 0. 0. 0. 11.7000 U, -0 0, 0. - o.-o. o. 10.7000 ii, 0. 0. ø. o. o. o, o. SIA 1.0 0.0000 INFINITY 0. 2.19861.01 0. 6.84851.01 0. 2.25631.02 0. - T6134rrU2,2216E,01 9U(J9104b.9340tE.Or3.1 1381-03Z.281 1E,0Z97815k.O3 .0300 2,141140+01 1.3423E-03 2.29141.00 .1.5649E-02 7.12281.01 4.90801-02 2.33780.02 1.53991-01 .0600 1.t,541E.n1 4.8738E-03 2.39620*01 9.06251-02 7.'317E.OI 2.8326E-01 2.42ç50.02 8,86351.01 .1000 1.31361.01 1.21191-02 2,54451.01 3.36011-01 7.86741.01 1.04551.00 2.55040.02 3.25950.00 .1SOO oA9oE.o1 2.4115E-02 2.72821,01 9.62261-01 8.40071.01 2.97731.00 2.71450,02 9.23801*00 .2100 9374E.flO 4.1333E-02 2.91371.01 2.30210.00 8.92541.01 7.07471*00 2,86391.02 2.1824E.01 2AOW76792E.8O63506E-D2 3.02510,01 4.72781.009.20821.F 1.441510I 2,93491.02t4l58E'Ol .3600 b.8104E.00 8.96T1-02 2.96)51.01 8.31971.00 8.91831.01 2.51410*01 2.82060.02 7.63791.01 4500 6.25011.00 1.18011-01 2.62341.01 1.24240.01 7.86351.01 3.71640*01 2,4923E.02 - 3.11831+02 5500 5.9141E.00 1.40'501-01 2.10021*01 1.b8451+Ø1 6,26761.01 4.68691.01 1.99990*02 ¡.3949E.02 .6700 5.81150.flO1.T5091.01 1.51881*01 1.19030.01 4.48901,01 5.22471+01 1.46300.02 1.53391+02 .8200 5.81681.00 2.01101-01 9.9189E.00 1.b3321.00 2.92971.01 5.26061'Ol 1.00300.02 1.51730.02O100b. 1z1yr.wz1v83ru1 b.0943E00
v.74J8E.ox1-.8289F.Or4.8978E'o1 6,8 4080 1j18011402 1.2500 b.53861.nO 2,25061-01 3.78681.00 1.57760*01 1.15E.01 4.31191.01 5.18760,01 1.17831.02 1.5500 7.o401E.b02.13011-01 2.65391,00 1.37971,01 9.12541,00 3.64391+01 4.55090.01 9.5675.01 1.9500 (.59931.00 1.82781-01 2.3021E.00 1.16191.01 8.60711,00 2.92960*01 4.59o8(.O1 7.27961+01 2.4500 8.10791.00 1.41421-Il 2.49371,00 9.52251+009.5750E.00 2.26311.01 5.OsiSE,01 5.24101+01 3,0500 h5jS3E.flQ 1.00181_01 2,97650,00 7.65740,00 3.12231.01 1.69180,01 5,65n80.01 3,60081.01 3.B000 8.03iU,o0 6.45010? J.6135E4O0952E'00 1.31311.01 1.2046E.0T6270.012l159E*01 4.7000 9,07221,00 3.893o1-02 4.2775E,0O 4.62760.00 1.4921!.01 8.25281*00 6.81,5E,O1 1.41921*01 5.8000 9.24501.00 2.2481E02 4.91491,00 -3.52621*00-1.64851.01 5.3919E'0O 7.25670*01 8.25391.00 7,1000 9.37851.00 1.3106E-02 5,47161,00 2,69390,00 1.71131.01 3.41761*00 7.58521.01 4,68381.00 0.7000 9.4760E.0 7.9342E-03 5.95721.00 -2.05661,00r.86881,01 2.10031.00 7.83480.01 2.56741*00 10.7000 9.55490.00 5.2372E-03 6.3716E.00 1.57791.00 1.9467E.01 1.29700400 8.02560.01 1.36940400 --0.0000 INFINITY 0. 2.34761.01 0. 2.35831.01 0. 8,8941E401 0. .0100 1.05601.01 4.00331-04 2385O0.O1 1e4770-03-2.39661'OI 1.37820.03 8.93341.01 1.15181-03 .0300 b.o561E.ol 3.26121-03 2.48171.01 2.59291-02 2.48011,01 2.20011-02 9.0179E.0I 1.86670.02 .OAOO 3.8666E.51----F.16121-02 2.60231.01 1.49101-01 2.61771.01 1.2924E-01 9.151160,01 1.11991-01 .1000 3,07621.01 2.83141-02 2.78551.0) 5.4371-01 2.81081.01 4.85491.01 9.36111*01 4.3214E-01 0. 0. 0. 0. 0, -o. 0. 0, 0. 0. 0, 0. o. 0. 0. 0. 0. 6,84830.01 b.93490.U1 7,12591+01 7.4392E.O12i1342E'01 7,88081.01 5.42171,01 0.95541.01
- 9.2479E+01-X1444E401 8.96681.01 7 .9 19 11.0 1-317273E. 6.32771.01 4,55441.01 --5,2400(.0t--- 3.0041E.01 _1 91851+0*i90SIf0T 1.30730.01 I .05701.O1-3.63200ò0r 1.04801*01 I .19591.0l-2.23l6E50r 1.41640.01 T6614E*1 1,90691.01 2.121?1.Ol----5134181400- 2.29700.01
3,49451.00
2.44200e012i23771.00 2.5594E.03 2,35031.01 2 1959t.0t-1j3flbEä03 2.47960.01
2.2000E-02
2.6173t.O11-it922070I - 2.81120.01
514 3.0 0.0000 INFINITy 0. 2.54000,01 0. -.0100 9.36350.0T5.3571!-04 2.5840E.O1 2.1594E-03 0300 6.68130.01 4.32090-03 2.68440,01 3.39910-02 005 51o7rr1152i4o-o2 2.54410.01 1.95!40.01
CONTINUED FOR M.L SECTIONS....
Sample Output Listing, Continued
9.61?91,01 1.CBi1t+00 3.04050.01 9.85000.01 3.13590,00 3.24160.01 9,97950.01 6.42050.00 3.29040.01 9.84710,01 1.10120.01 3.09950.01 9.43420.01 1.59700.01 2.64940.01 8.85500.01 2.01800.01 2.0811E.01 .20,R0.612.3326E0I1 .4930E.0F 7.57450.01 2.52450.01 9.64830.00 7.01.50,01 2.59440.01 5.44160.00 6.56750*01 2.55060.01 2.42570.00 6.22930.01 2.40210*01 4.96040-01 5.99060.01 2.13960*01 -5.7060E-01 5.87os.WI1.79250.0F.8.26890-01 5.85230.01 1.4135E'01 -5.03140-01 5.90690+01 1.03360.01 2.00200-01 6.00170*01 1.08700.00 1.07180.00 6.10.00.01 4.54660.00 1.9786E.00 6.20480.01 .7963E.00 2.7982E.00 6.35740,01 9.24540-01 4,12500.00 1.03170*01 0. 2,48541,02 0. 1.03170.01
104730.01 -1.5145E-024866E.02 1.0849E.o5r0457E.01r.53obE-04- 1.0804E.01 -j.37S1E-03
2,48.50,02 b.8115Eo5 1.07840.01 -1,4055E-03 I .14950.01 S9735E0 2.49820r-l.99330-o5 1.15910.01 .1000 4.07020.01 3.67380-02 3.06200+01 7.1333E-01 1.23680*01 4.2262E-02 2.49,10.02 2.5176E-03 1.23780.01 .1500 3.37920.01 Y11110-02 3.28940+01 9746E0U1.3813E,0j P.50100-01 2.5Q79E,020.1748E-02T,824E.0T2.5038043 .2100 ¿.90190.11 1.181.90-01 3.43010,01 4.42290,00 1.55890.01 9.00570-01 2.51520,02 1.83870-01 1.56050.01 .2500 ,58390.1 1.77220-01 3.36400.01 8.1507E100T7091E.0j23495E.0O 2.S2930,026.79520-01 1TI16E.01 1.78830.00 1,74540.01 59450.00 1.8E77E'07.50S3E+00 5.90640.00 1,36740.01 8.64980.00 1.03940.0I1.28130,01 3600 ¿.311580.01 2.42900-01 2.96070,01 1,24240+01 1.74230.01 4.70450.00 2,54240,02 .4500 1.600(0.01 1.6143001f.5687E41)0 2.54,00.02 3, .5500 ¿.24510.01 3.723-30-01 1.77050.01 1.81630.01 1.36390,01 1.03320+01 25458E,02 .6708 .26690.01 4.27830-01 1.22850,01 1.8984Ei01 1.03630.01 1.27800,01 2,53330,02 2.51110,02 1.16820.01 6.76410.00 2,40030.02 1.47290401 3.1813E4001i6067r40T-2,44301,02 1.73710.01 .3,44330.02 2,40480.02 .91006.01 -2.85720.00 2.36,80,02 1.94530.01 -4.66540.00 33i5E.02 1.8067E*015.82240.001.3169E40t 2.32120*02 1.53270.01 .6,20540.00 231590.02 1.1792E'0156.0183Es00 2,31910.02 8.33660.00 .5.47900.00 ¿.32,70.04346E.0u ...,78020400 2,3301E,02 3.36430.00 4,08680.00 2.3432E.02I,'769E.0O3j45090.00-tj9686E.00- 2.34980.02 1.11720.00 .2.90380.00 8200 ¿.34200.01 4.68570-01 8.00070,00 1.86760,01 b,7375E.00 1.47260.01 T0108 2.46490+01 4.83710-01 5.00980.00 1.75350401 3.16110.00 1.60170.01 1.2500 2,61980.01 4,6323E-01 3.20360.00 1.58680,01 -4.7056E-02 1.65400.01 1.5500 2.7002.OTTiI678E-01 3)3E.o5T)929L.01 -2.66140.00 1.62410+01 1.9500 2,95040.01 3.1852E-01 2.14100*00 1.17590.01 -4.65980,00 1.50470.01 2.4501F 3.0593E.fl12.2l49E-01 2.4472E.009.b3b1E.00 -5.80680.00 1.311 10.01 3,0500 3.19460.01 1.38130-01 3.02490,00 7,73730+00 6.18070,00 1,08000.01 3.8000 3 .27c1E.017.4'00E-02 3.74210.006.04910+00 -5,98,50.00 8.3448E400 4.7000 .3.33340.01 3.43400-02 4.41030.00 4,67260.00 -5.4443E.00 6.12390.00 5.8000 .3.37108rTT23o9L-o2 sr56gE40o 3.01380.00 -',74830900 8.26(06+00 7.1000 3.40550.01 2.8468003 5.74890.00 ¿.75240.00 -4.06300,00 2,88230.00 8.7000 34338E976226E-05 b.2604E.O021307E.0034379E.001,8754E+00 10.1000 4.45370.01 6,25810-04 6.69310.00 1.67045+00 -2.90280.00 1.17420.00 S7A 40 - --0.0000 INFINITy 0. 2.7810E.01 0. 2.93490.01 0. .0100 [Ö094140Z 0,731,0-os 8333E90iT.5S97E032.9r080.ul 6.39520.04 .0300 7.21360.01 4,60050-03 2,94990,01 4.04130.02 3.06440.01 1,17420-02
O6055.531 30+51 16098E-02 3.13950,012,3344E+0T- 3.21790,01
8i678E-02 .1000 4.43850+81 3.8573E-02 3.3'027E'Ol 8.5687E-01 3.45190.01 3.6515E-01 Th007050Eo8T7,39510-02- 3.65560.01 2,3837E,00--3.76o50.0r 1.23260.00 2100 .3.21380.01 1.2185E-01 3.80050.01 5,34210.00 4.07230.01 3.31290.00 .2800 ¿.89770.01 t.1940E1rr3.6S500,01 9.7o.00t.00 4.22270.01 .15210'00 3600 2.71600.01 2.41400-01 3.15240.01 1,46150.01 4.04750.01 1.24430+01 .5500 2,63200.3T 30041E-01 2.4422E,Q1T8.oYt+01 3.5525E.01ri7910E'o1 5500 2,62670.01 3.52570-01 1.75060.01 2 4.82,4E.02 0. 2,93490.01 4,63760+ 2159510.042i91530'01 4,84040.02 3.40810.03 3.06510.01 4,05390e02 2.8594r-023.2200E.01t4699E-02 4.87540.02 1.55940-01 3,45090.01 4,90720.02 6.39630-01 3,76720,0V 1.23470.00 4,94750.02 2.06440.00 4.08210,01 48470.02 5,27040.00*.235?0r01 .998A0.02 1.06670.01 4.06270.01 497p 0E. 021i Ysiez. O 13i568500ttiT479EoO2 0402E.Oi 2,90170.01 2.23830.02 4.92740.02 2.47690.01 2.91740.01 .1600 ¿.52990+01 5.54110-02 2.98+90*01 1.1.2151.00 i.0394F.01 1.39111.00 .2100 ¿.14 E.nj 9.3511E-02 3.14,OE.o1 3.47120.00 3.23970.01 3.29820*00 .21000 1.881010,01 1.41630-nI 3.13750.01 6.60b71.00 3.?9S4.Ú1 10.50940'OO .3600 1.71390*11 1.9711001 2.87730.01 1.05130.01 3.09570*01 1.07510*01 .4500 1.61130.01 2.559+0-01 2.39810.01 1.41450.01 2.64510,01 1.50151.01 .5500 1.66?9E'nl 3.13500.01 l.84590,0I 1.66131.01 2.07640,01 1.82070.01 .61001.55740*n1 3.6 -51 h3t62E*o1 1.T980.01T48020.Ó1 2.0345E,0[ .8200 1.59330+11 4.110170-01 8.78190.00 1.77881+01 9.60010.00 2.1154E+0l 1.0100 1.610790.11 4.46760-015.6428E,00 1.68600.01 b.3'016E.00 2.08710.02 1.2600 1.77300.01 4.410640-01 3.69860,00 1.531.00+01 2.37150.00 1.97400.01 1.5500 1.89290.01 4.1723E-01 2.71010.00 1.35400.01 4.34270-01 1.79850.01 1. '0 So o ¿.01970.01 3.52tE-o1 2.40360.00 1.14900+01 -6.44990-01 1.56300.01 ¿t3IT4ì.i11
.6dE-0T2.6052E.00 9484E.00 -.r93ot-or1.29RoE.o1
3.0500 ¿.21910.01 1.894.0-01 3.09070.00 1.64030+00 -6.17580..01 1.03470.01 -3.8000 ¿.28770*01 1.211+0-01 3.72950.006.00850.00 b.8613002 7.82630+00 4.7000 ¿.33810*01 7.1904E-02 4.39490.00 4.65921.'OO 0.99830-01 5.6793E'OO -0.8000 ¿.37670.81 3.9093E-02 5.0335E.00.5693E+00 1.7729E.00 3.94110.00 7. 1000 ¿.40350.01 ¿.0667E-02 5.59140,00 2,74460.00 2.55800*00 2.66140.00 -5.7000 ¿.42600,OF J.24ST00 1.73570.00 10.7000 ¿.44210.01 4.60310-03 6.49380.00 1.63936.00 3.8210.0o 1.0958E.00
Sample Output Listing, Continued
SPEED
6.5251
WAVE ANGLE
10.00 DE..
VERTICAL PLANE RESPONSES (NON-DIMENSTONAL)
VERTICAL REND.MT. AMPLITUDE
PHASE wivE LENGTH Il PHASE WAVEENCoUNTtH F R E Q u E N r I r S fl/SflIP u t A Vt LENGTH MPL. PHASE P 1 T C AMPL, .31570 .25039 618.232 3.2033 8611 179.3 .8729 -85.8 4.075E-03 11.2 2.4525 TT6 178.8 .8089 -84.2 6.543E-03 14.5 36080 .215' 473.334 .40590 29793 373.992 1.9378 6657 178.0 .7262 -82.4 9.6030.03 17.9 .45100 .3117 302.934 [.5696 5308 176.16252 -On.1 1.300E-02 21.7 .49610 33481 250.358 1.2977 .3791 174.0 5091 -77.4 1.631E-02 25.7 .54120 6 210.371 [.0900 2263 16T4 .3A41 74.2 1.895E-02 30.0 .58630 .36103 179.251 .9288 0961 142,6 .2591 -70.2 2.026E-02 34.6 39,8 63140 .37014 154.558 .8008 0749 59.5 .1449 -64.! 1.9680.02 .61650 31659 134.637 .6916 1254 31.0 .0523 -53.4 1.696E-02 45.8 .T2160 3037 T10.33i .W[)[1381 238 .01 83.3 1.237E-02 53.5 .76670 38148 104.821 .5431 1077 20,0 .0456 115.1 6.793E03 66.4 .81180 .37993 93.6OL .4K4. 0513 124 .0487 124.9 2.164E-03 116.8 .85690 .37571 #3.915 .4348 0140 98.7 0331 135.3 3.321E-03 -150,1 .36882 70.. 133 .3924044y -139 .0117 160.4 4.363E03 -131.4 .90200 .94710 .35927 68.692 .30.59 .0451 -143.2 .0086 -76.8 3.069E-03 -120.7 34706 62.590 .3243 --0211 -143,3.... 0133 -40.5 5,262E04 -90,3
-.020
1.03730 .33211 57.2*.5 .2967 0084 31.1 .0086 -32.4 1.670E.03 60.2 .3140.3 52.593 .2725 0210 30.3 0026 57.7 1.938E-03 73.5 1.0G40 1.12750 .29441 48.469 .2511 0103 14.5 .0059 119.2 7.459E04 132.6 .003q 122.5 3 .930E-03 -144.6 1.17260 .27153 44.813 .2322 r241329-1.21710 24599 41.555 .2153 0221 -157.8 .0019 -28.8 2.316E03 -163.6 2T7i738.639 -.2002 0165 149.0 .0052 -49.4 1.008E_03 170,7 l.24280 1.30790 .18690 36.021 .1866 0250 12.7 .0035 -85.3 1.8210.03 69.7 518 20,0 0.0000 .0100 0300 0600 .1000 .1500 .2100 2800INFINITY .373RE*00 1.6719F+oo 1.?HlIE*0U l.0357E.00 ,2)ÁE-0I 1.5915E-01 b7964E-01
1.5164E-01 1.4460E-03 1.0.327E-01 1.145E-O2 1.0.687E-01 4.00510-02 1.62180-01 9.72810-02 1.6 191E-Dl i .91-01171b9E-01 3.3080E-01 1.7062E-01 5.11FE-01 1.639RE0l
0. 4.100.3E-05 6.190L-04 3.3197E-03 1.0910E-02 2.6235E-02 4.9848E-02 7.8405E-02
-.8796V-01 -2.9162E-01 -?.0958F-01 -3.1172E-01 -3.24940-01 -3.339lE-Ol -3.3268E-01 3.1871E-01
-9.0894E-05 -1. 370.7E-03 -7.4049E-03 -?.4482E02 -5.9314E-02 -I 1373E-01 -1 .80R2E-01 66338E-01 6.7142E-01 6.8935E-01 7.1637E-01 7.4630E-01 7.6718E-01 7. 652.E- 01 7,34noE01
2,0124E-04 3.05610-03 0.6530002 5. 4985E-02 1.3415E-81 2. 59 170-0 1 4,1519E-01 -2.8796E-01 -?.91690-01 -2.9997E-01 -3. 123 10-01 -3.2585E-01 -3.3510E-01 -3.34010-01 -3 1999E-01
.3600 .4500 .5500
6.7300E-01 b.$249E-01 5,5394E-01 b32S6E. .01 b.17°E-oL .0R97f-01 5.06810-01 5.9Q4E-f1 5. 3H
ifE-ñ1
5,39910-01 5.s7530-o1 5.HjRhEOl 5.94E-fll h.06750..01 6.1266V-01 b.1986E01
I .50.10630-01
7.590.10-01 1.05200.00 1 .3986E,00
1.5311E-01 1.40600-01 1.2865E-01
1.060E-01 -2.9490E-01 -2.4827E-01 1.2912E-01 -2.67030-01 -3. 060 lE-0 1 1.4526E-01 -2.4008E-01 -3.5008E-01 [.5580E-0TT492E-0TB345E -01 1.6104E-01 -1.9276E-01 -4.0735E-01 1.6126E-01 -1.1497E-01 -4.2294E-01 1.5716E-01 -1.6252E-01 -4.3199E-01 1.4977E-01 -1.50.77E-01 -4.3672E-01 1.3945E-01 -1.5'50E-01 -4.3575E-01 lainE-or -T.5ff210-01 -4.2764E-01 1.1584E-01 -I.64620-01 -4.0865E-01 1.0385E-01 -1.71660-01 -3.7829E-01 9.253E-02 -1.7803F-01 -3.40.14E-01 8.1933E-02 -1.8444E-01 -3.1302E-01 1.2513E-02 -1.90390-01 -2.79250-01 6,40760-02 -1.95740-01 .2.4862E-01 5.6098E-02 -2.0115E-01 -2.19'6E-01
793 4e-0 1
6.1403E-01
lE-01
* Bio 3E-01 4.3143E-01 3.8396E-01 3.481 3E-01 3,2550E-01 3 1599E-01 3. 10v, 7E-0 1 3.3147E-01 345qAE-0 1 3.5978E-01 3. 7471E-01 3,8930E-01 4,0287E-01 4.1714E-01 5.7410E-01 7.11910-01 8.1809E-01 8,9828E-01 9.5333E-01 9.8324E-01 9.8938E-01 9. 7473E-01 9.40230-0 1 8.90490-01 8.3156E-01 7.6443E-01 6. 94 580-0 1 6.2335E-01 5.5596E-01 4.9244E-01 4.2975E-01
-2.95900-01 -2.6752E-01 -2.3987E-01 2. I 369E-ß1 -1.90010-01 -1.69940-01 -1. 54 120-01 -1.4255E-Il -1.3430E-01 -1.2945E-01 -1.27210-01 -1.26710-01 -1.2739E-01 -I .2881E-01 -1.3055E-01 -1,3258E-01 -1.3506E-01
6700 .8200 1;01ö 1.2500 1.9500 2. 4-5 3.0500 38000 4.7000 5.8000 7.1000 8.7000 10.7000 18T6E,O0 1,1 ?50T ?.380lE.00 1.0776E-01 3.1119E,00 9.9705E-02 4.03220*00 9.3615E-02 5.18440,00 8.9413E-02 6.(5660.00 8.6679E-02 -8.176aE008.53270-n2 1 1318E.01 8.4952E-02 I .41070.01 8,5198E-02 1,5681F_.01 8,5816E-02 1 .564.0o 1 8,6632E02 1 556 lE 01 8.7497E-02 1 .545E.0l 8.8413E-02 1.5360E *01 8.9443E-02
NATIPAI HOLL FREOUFNCY *
.3745
ÄLCuLATEWÀV
I7AMPINW1Ñ
flLL
3 .469E * 02
AOOITIO6AL vISCOIIS 1880110G 110 POLL *
3.50,20*04
SERIES 60 HULL FORM, 0.80 RLOCK ITNO RPT. 100.
100 5)
OCEANICS PROJECT 100.
1093
SEP ?4
Sample Output Listing, Continued SERIES 'fl Hul t FORM, .R0 HLUCE (160 RPT. 80. lOO S)
OCEANICS PROJECT NO. 1093
SEP 74' 1970
SPEED
6.557
WAVE ANGLE
10.00 DE,.
LATERAL PLANE PFSPONSES
(NON-DIMENSTONAL) y Y A'PL. A w R O L I. LATERAL REND.MT. PHASE AMPL, PHASE AMPLITUDE PHASE
TORSIONAL MOMENT AMPLITUDE
WAVE F RL QUE ENCO(JNTER WAVE WAVE/SHIP S W A NC I E S LFNIOTH LENGTH MPL. PHASE 31570 .25o19 518.23? 3.2033 .1696 90.6 .1807 -.4 .2474 -9c,3 2.182E-04 97.0 2.362E-OS .36080 .40590 270,49 473334 2.4520, 15229O8 .29793 373.99? 1.9378 1285 91.1 .1110
.L9O .2609
-97.2 3.938E-04 .5 .2675 .100.2 6.777E-04 96.1 95.1 3.730E-95 5,440E-05 .45100 .31771 302.934 1.5696 0990 91.1 1567 1.1 .2593 _104.8 1.087E.03 94.4 7.2960-05 .49610 .33881 260.368 1.297? 0651 91.0 .1367 1.8 .2235 -11i. 1.623E-03 94.0 8,766E-05 54120 ,3492t. 210.371 1.0900 0299 88.4 .1108 2.7 .1483 -119.1 2.235E-03 94.0 8,903E-05 .58630 .36103 179.251 .9288 0045 -36.4 .0822 3.6 .0398 ..117. 2.823E-03 94.2 6.846E-05 63140 .51014 1S4 .8b00u28R -76.4 .0539 4.4 .0058 2n.8 3.219E-03 94.9 3.369E-05 .67680 37689 134.637 .6976 0431 -71.8 .0761 3.9 .1773 19.0 3.311E-03 96.0 5.905E-05 7216o .38037 118.333 .6131 0439 -77.5 .0046 -11.6 .2224 16.2 2.994E-03 97.6 1.158E-04 76610 38148 104,821 643) 0320 -77.7 .O10 -168.4 .2166 17. 2.298E-03 100.0 1.611E-04 8l1Ho .37993 93.4911 .4844 0121 -85.2 0161 -160.6 .1651 20.3 1.381E-03 103.4 1.795E-04 85690 .37571 3.15 4348 0100 130.1 .0147 -158.9 .0814 20.9 4.924E-04 108.6 1.602E-04 .9O200 6827s.733 .3924 0241 121.6 .0086 -156.4 0094 -17o.1 1.287E-04 -71.3 1.047E-04 .94110 35071 f8.69? .3559 0260 122.0 .0010 -163.3 .0685 -131.7 3.433E-04 -58.5 3.800E-05 .99?20 .34706 62.590 .3243 0152 120.3 .0051 35.8 .0779 -119.9 1.995E-04 -34.8 2.6880-05 1.03730 .33211 N(765 .2967 0047 -9.8 .00/5 41.8 .0501 -11n.0 2.077E-04 99.5 4.028E-05 1.08240 .11463 i2.S93 .2(25 0209 -35.2 .0056 46.9 .0161 -loq.7 5.314E-04 126.5 3.338E-05 1.12750 .29441 48.469 .2511 0248 -36.3 .0007 28.8 .0064 118.3 6.654E-04 j38.4 1.879E-OS LT726 77j3 44.811 .2322 0103 -53.6 .0047 -111.9 .0116 104.0 5.206E-04 145.5 1.815E-05 1.I770 .24599 41.555 .2163 0213 173.5 .0069 -111.7 .0080 108.2 1.163E-04 138.3 2.649E-05 1.2628ñ ?1777 38.639 .2002 0423 166.4 .0037 -113.8 .0029 108.3 1.880E-04 3.7 2.678E-05 1.30790 .18690 36.021 .1865 0235 167.0 .0044 87.2 .0009 _.9 2.812E-04 -.7 1.997E-05 5ERIES Ffl HUIJ FORM, (1.80 HL,JCO (760 (IPI. O. 100 S) OCEANICS PROJECT NO. 1093 SEP 24' 1970 SPEED 6.5257 WAVE ANGLE -10.00 flE,.SHEAR AND MOMENT CLOSURE RESULTS
WAVE -ENcAOUNEER 46VE P E Quo NC! F S LFN1,TH WAVE/SHIP LENOTH VERTICALBENDING SHEAR MOMENT LATERAL BENDINO SHEAR MOMENT TORSIONAI_ MOMENT .31570 .251139 618.232 3.2033 1.031E-16 8.752E-14 2.301E-17 .916E-13 6.415E-14 . 3OWö Th89 473.334 2.555 I .4030-I5T.B25E-I48.1035Ej7 5.938E13 9.406E14 .40590 29793 373.992 1.9378 .118E-lb 8.797E-14 5.652E-17 2. 119E.. 13 6.568E-14 .45100 .11771 352.936 1.5696 .317E-15 1.745E-14 4.2930-17 7 .944E-i 4 5.475E14 .49610 .33481 250.358 1.2972 c.9900-16 9.131E-14 7.023E-17 2.688E_13 6,542E-14 .54120 .38975 210.371 1.0900 ç.204E-16 7.048E-14 5.040E-17 7.668E-14 4.618E-14 .58530 .&3Í40 .361n3 .37W04 119.251 .9288 80118 .144E-11 i.227E-1T 3.022E-14 2.594E-14 3.719E-17 3.814E-17 2. 00 1.639E-06 4.568E-14 3.98 1E-14 r5458 .61650 .37859 134.631 .6916 .1790-16 1.490E-14 5.627E-17 1.9520-14 7.864E-14 .12160 .381137 118.333 .6131 ,.2650-1b 1.991E-14 2.169E-17 1.392E-14 8.095E-14 .16670 .38148 104.82) -.5431 .551E-16 4.6900-04 1.3620-17 2. 178E14 3.905E-14 .81180 .37993 93,498 .444 i.435E-17 6.3550-F4 3.189E-18 4 4a6E- 1 3.2960-14 .85590 .37571 83.915 .4348 ,.9090-17 2.704E-18 7.272E-18 1.365E-13 2.190E-14 .90200 .36s2 7573Y .3924 o65?ETT 4.749E-1 2.879E-11 3.2380..I 3 3.786E-15 .94110 .35927 68.692 -3558 .974E-17 1.739E-14 0.626E-11 6.087E-14 .99220 .34706 62.590 .3243 4.510E-17 2.122E-13 9.272E-18 1.748E_13 1.939E-13 1.03710 .33217 57.265 .2967 .338E-(7 1.660E-11 1.114E-17 2. 047E_13 1,104E-13 1.08240 .31463 S.593 .2726 4.646E-17 1.302E-13 2.656E-17 1.9320-13 3.218E-18 1.12(50 .29441 48,469 .2511 a.43(E-11 9.369E-14 2.042E-07 4.012F-14 1.227E-13 I.I765 44.813 .2322 ,,6300.17 1.461E-13 6.4180-18 1.3330-13 3. 06 1.21170 .24599 41.555 .2153 1.256E-17 1.538E-13 8.624F-18 3.6090.13 2.199E-14 1.26286 21777 38.639 .2u02 8.653E-17 2.410E-13 2.495E-11 0. 9.469E-18: 1.30(90 .18690 36.021 .1866 ,.503E-17 1.491E-13 1.176F-17 6. 33 3E - 1 7.501E_18:
Sample Output Listing, Continued
SENTES 60 HULL F0880 O ,80 SLUCK flNO HP).
NO. WAVE ANGLE s 10.00 DEr,,. LOO Si OCEANICS PROJEÇrNO. 1093 HT. 8.40. MEAN PERIOD SEP . 1970 SPEEL) 6.5257 SIS, WAVE 10.00
RESPONSE CAMPLITUDE) SPECTRA
WAVE ENCOUNTER WAVE TWU0U L NUE S LEÑGTi4 HEAVE PITCH S W A Y Y 6 W UD L i VERT.W.MLATiWMT TORSNtiMi .31570 25839 618.23 2.660E-01 9.290E-02 1.035E-0 2 3,980EO3
