- JUU
1976AkCHIEF
Biblioiheek van de
Iing
derScheen-NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
Bethesda, Md. 20084MANUAL
NSRDC SHIP-MOTION AND SEA-LOAD COMPUTER PROGRAM
by
W.G. Meyers D.J. Sheridan
N. Salvesen
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
NSRDC
SHIP PERFORMANCE DEPARTMENT
February 1975 Report 3376
b. v. Scheepsbouwkunde
Technische Hogeschool
The Naval Ship Research and Development Center is a U. S. Navy center for laboratory effort directed at achieving improved sea and air vehicles. It was formed in march 1967 by merging the David Taylor Model Basin at Carderock, Maryland with the Marine Engineering Laboratory at Annapolis, Maryland.
Naval Ship Research and Development Center Bethesda, Md. 20084
*REPORT ORIGINATOR
MAJOR NSRDC ORGANIZATIONAL COMPONENTS
OFFICER-IN-CHARGE CARDEROCK 05 SYSTEMS DEVELOPMENT DEPARTMENT 11 SHIP PERFORMANCE DEPARTMENT 15 STRUCTURES DEPARTMENT 17 SHIP ACOUSTICS DEPARTMENT 19 MATERIALS DEPARTMENT 28 NSRDC COMMANDER 00 TECHNICAL DIRECTOR 01 OFFICER-IN-CHARGE ANNAPOLIS 04 AVIATION AND SURFACE EFFECTS DEPARTMENT 16 COMPUTATION AND MATHEMATICS DEPARTMENT 18 PROPULSION AND AUXILIARY SYSTEMS DEPARTMENT 27 CENTRAL INSTRUMENTATION DEPARTMENT NDW-NSRDC 3960/43b (Rev.
UNCLASSI Fl ED
R TY CLASSIFICATION OF THIS PAGE en Data Entere
nrt FORM
1010 1 JAN 73
/An
Pi EDITION OF 1 NOV 65 IS OBSOLETE 5/N 0102-014-6601UNCLASSI Fl ED
REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORMREAD INSTRUCTIONS
I. REPORT NUMBER 3376
2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtitle)
MANUAL NSRDC SHIP-MOTION AND SEA-LOAD
COMPUTER PROGRAM
5. TYPE OF REPORT 6 PERIOD COVERED
6. PERFORMING ORG. REPORT NUMBER
7. AU THOR(e)
W.G. Meyers, D.J. Sheridan, N. Salvesen
B. CONTRACT OR GRANT NUMBER(e)
9. PERFORMING ORGANIZATION NAME AND ADDRESS Naval Ship Research and Development Center Bethesda, Maryland 20084
10. PROGRAM ELEMENT. PROJECT. TASK
AREA &WORK UNIT NUMBERS Work Units 1-1568-201 and
1-1568-101
11. DONTROLLING OFFICE NAME AND ADDRESS Naval Sea Systems Command Washington, D.C. 20362
12. REPORT DATE
February 1975
13. NUMBER OF PAGES
14. MONITORING AGENCY NAME a ADDRESS(Ifdifferentfrom Controlling Office) 15. SECURITY CLASS. (of this report)
UNCLASSI Fl ED
15e. DECL ASSI Fl CATION/ DOWNGRADING
SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report)
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
17. DISTRIBUTION STATEMENT (of the abatract entered in Block 20, if different from Report)
113. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse aide if electrum', and Identify by block number) Ship Motion
Strip Theory Computer Manual
20. ABSTRACT (Continue on reverse aide if neceeaary and identify by block number)
A description of the "NSRDC Ship-Motion and Sea-Load Computer Program" is presented. This program computes the six-degree-of-freedom ship motions, wave-induced loads and pressure distribution for a ship advancing at constant speed with arbitrary heading in regular waves. Program organization and structure, data card input and output
UNCLASSIFIED
UNCLASSI Fl ED
SECURITY CLASSIFICATION OF THIS I AGE(When Data Entered) :..L.C.URITY CLASSIFICATION OF THIS P AGE(When Data Entered)
(Block 20 continued)
format are described. A sample computational problem is included to aid in under-standing input and output format and to provide a test for proper implementation. A listing of the program, as used on the CDC-6700 computer system at NSRDC, is included.
TABLE OF CONTENTS
APPENDICES
A. PROGRAM ORGANIZATION AND STRUCTURE 57
B. SHIP DESCRIPTION 61
SELECTION OF STATIONS 61
ALLOWABLE SECTION SHAPES 68
SECTION-LENGTH COMPUTATION .
. ... .
..
. 69C. SELECTION OF FREQUENCY RANGE 71
D. PROGRAM LISTING 73
REFERENCES 129
LIST OF FIGURES
Pagc
Figure 1 Sign Convention for Translatory and Angular Displacement 4
Figure 2 Definition of Heading Angle, tt 5
Figure 3 Sign Convention for Dynamic Wave-Load Components 9
Figure 4 Sample Station Contour Illustrating the Specification of Offset Points for a Station
Penetrating the Free Surface 13
Page
ABSTRACT 1
ADMINISTRATIVE INFORMATION . . . . 1
I. INTRODUCTION 1
II. PROGRAM DESCRIPTION 4
A. OUTLINE OF THEORY .
...
4B. PROGRAM EXECUTION 10
III. DESCRIPTION OF INPUT SCHEME 11
A. PHYSICAL DESCRIPTION OF SHIP 11
1. SHIP GEOMETRY INPUT 11
2. MASS AND MASS-DISTRIBUTION INPUT
. ... .
143. VISCOUS ROLL-DAMPING INPUT 15
B. CONDITION INFORMATION 17
C. DATA CARD FORMAT DESCRIPTION
. ... .
17D. SAMPLE INPUT 30
IV. DESCRIPTION OF OUTPUT SCHEME 35
A. GENERAL OUTPUT FORMAT . .
. ... .
. 35B. SAMPLE OUTPUT 36
iv
Page
Figure 5 Sample Station Contour Illustrating the Specification of Offset Points for a
Completely Submerged Station 13
Figure 6 Weight Distribution Curve Used for the Mariner Sample Problem . . . 14
Figgie 7 Illustration of the Proper Association between XMAS (I) and the Stations along
the Ship 22
Figure 8 Typical Ship Cross-Section Illustrating the Geometric Parameters Required to
Describe the Location and Orientation of the Bilge Keels 28
Figure 9 Symbol Table for Computer Offset Plots .
...
. 54Figure 10 Computer Offset Plots of Forward Stations 55
Figure 11 Computer Offset Plots of Aft Stations . . 56
Figure Al Organization Chart of the NSRDC Ship-Motion and Sea-Load Computer
Program 58 Figure 131 Configuration 1 62 Figure B2 Configuration 2 63 Figure B3 Configuration 3 64 Figure B4 Configuration 4 65 Figure B5 Configuration 5 66 Figure B6-- Configuration 6 . . . 67
Figure B7 Cross-Section shapes that Violate the Requirement that y be a Single-Valued
Function of z 68
Figure B8 Modified Flat-Bottomed Section 69
LIST OF TABLES
Table 1 Ship Geometry Input
Table 2 Mass and Ma1,5-Distribution Data Table 3 Viscous Roll-Damping Input
Table 4 Condition In-put and List of Commonly Used Equations
Page
12 15 16 18
ABSTRACT
A description of the "NSRDC Ship-Motion and Sea-Load Computer Program" is presented. This program computes the six-degree-of-freedom ship motions, wave-induced loads and pressure distribution for a ship advancing at constant speed with arbitrary heading in regular waves. Program organization and structure, data card input and output format are described. A sample computational problem is included to aid in understanding input and output for-mat and to provide a test for proper implementation. A listing of the program, as used on
the CDC-6700 computer system at NSRDC, is included.
ADMINISTRATIVE INFORMATION
This study was authorized by the Naval Ship Systems Command under the NAVSHIF'S Program in Hydromechanics Budget Project 32, with funding under Element 62512N Subproject SF 35421, identified as Work Unit number 1-1568-201, and under the General Hydromechanics Research Program, with funding under Element 61151N Subproject SR 014 01 01, Task 0100, identified as Work Unit number 1-1568-101.
I. INTRODUCTION
The "NSRDC Ship-Motion and Sea-Load Computer Program" which is based on the theory by Salvesen, Tuck, and Faltinsen" predicts the motions and dynamic loads for a ship in six-degrees-of-freedom
advancing at constant speed with arbitrary heading in regular waves. More specifically, the program com-putes the amplitudes and phases for the surge, sway, heave, roll, pitch, and yaw motions and the vertical and horizontal shear forces, bending moments, and torsional moments. Furthermore, the program computes at any point on the submerged portion of the hull the hydrodynamic pressure due to the motions and the
in-coming wave. It is important to note that the computations are only for a ship in regular sinusoidal waves.
The use of the present program in connection with the irregular-sea program is demonstrated by Bales, Meyers, and Rossigno12 in an investigation of helicopter landing platform responses for destroyers.
It should be pointed out that the present program is not intended to replace "The Frank Close-Fit Ship-Motion Computer Program" by Frank and Salvesen.3 The Frank Program computes the pitch and heave motions for a ship in regular and irregular head waves, while it does not predict the wave-induced loads. HoWeyer, if the user is only interested in the head-seas motions and not the sea-loads or the oblique-wave responses, he may use the Frank Program which is easier to use and is considerably more efficient than this six-degree-of-freedom program.
The main objective of this manual is to provide the information necessary for the proper and effective use of the ship-motion and sea-load program. Details concerning the program structure and operation and the input and output schemes can be found in Sections II, III, and IV which also contain a sample run for a
Mariner type ship. The purpose of this sample run is twofold. Firstly, it is intended to be an aid for under-standing the data card format description presented in Section III. Secondly, it provides data on which a check of proper implementation of the computer program may be based. The theory used in developing this computer program will not be discussed in any detail since it is presented separately by Salvesen, Tuck,
and Faltinsen.1* It is strongly recommended that the user be familiar with the contents of this paper,
especially the assumptions and restrictions, before using the computer program. For convenience, some of the more important assumptions and restrictions in the theory are listed below:
the theory is linearized by assuming that the ship has "small" displacements from the equilibrium position and that both the incoming waves and those created by the ship are "small";
the water is assumed to be inviscid (all viscous effects other than roll damping are disregarded), and the ship length is assumed to be much larger than the beam and draft; so that each section can be treated as a two-dimensional "strip" with no interaction between sections.
The accuracy of the data obtained by this program will not be discussed extensively in this report. Comparisons between computed and experimental results have been conducted for some of the motion and load responses for some specific hull forms; however, there are still many unanswered questions with regard to the accuracy of the data. It is felt that additional correlation studies are needed in order to answer such questions. We have listed below some general conclusions with regard to the correlation between compu-tational and experimental data:
SHIP-MOTION RESPONSES Pitch and Heave Motions.
A large number of correlation studies for several hull forms have been conducted for the pitch and heave motions in head seas and it is generally recognized today that computer programs based on strip theory and with close-fit station representation can be used to predict with satisfactory accuracy the head-seas motions of regular hull forms (at moderate and at high speeds) and to a limited extent hulls with bulbous bow
configurations.4 Satisfactory agreement has also been found in general for the pitch and heave motions in
oblique waves; however, some discrepancies occur in following waves and particularly in the very low fre-quency range.
Surge Motions.
A detailed correlation study between the computed and experimentally obtained surge motions has not been conducted.
The program computes the six-degree-of-freedom motions, loads (except compressive loads) and pressures, while in the strip-theory derivation by Salvesen, Tuck and Faltinsen (1970) the surge motions, the compressive loads, and the pressures are not developed.
Roll Motions.
The computer program in its present form predicts the roll motions for conventional cruiser stern hull forms at moderate speeds in beam seas with reasonable accuracy;1 however, a recent investigation for high-speed ships5 indicates that accurate estimates are needed for the non-linear roll-damping coefficient in order to predict the roll motions with reasonable accuracy in the near-resonance frequency range.
Sway and Yaw Motions
No detailed comparison study has been performed for the sway and yaw motions so that no general conclusions can be given at the present time. "Neverthelesi, the good agreement shown for the horizontal shear forces,bending moments, and torsional moments (for Series 60, CB = 0.80, Fn = 0.15) in oblique waves suggests that the theory may also predict the horizontal motions quite well."1
WAVE-INDUCED LOADS
Vertical Shear Forces and Vertical Bending Moments.
Good agreement between theory and experiment has been established for the vertical shear and the vertical bending moments for conventional hull forms at moderate speeds. According to Reference 1: "The agreement is very satisfactory for the vertical loads in oblique and following waves as well as in head waves.".-Unfortunately there exists no detailed correlation study for the vertical loads for hulls with large sonar domes or for high-speed destroyer hulls in general.
Horizontal Shear Forces, Horizontal Bending Moments and Torsional Moments.
A detailed comparison between theory and experiment has only been conducted for one hull form, the Series 60 with block coefficient 0.80 and at Froude number 0.15. Reference 1 states that the com-parisons "show quite satisfactory agreement between the present theory and experiment;" however, "a more general experimental evaluation of the horizontal wave loads is required to confirm more precisely the accuracy."
WAVE-INDUCED HULL PRESSURE DISTRIBUTION
No detailed investigation has been performed on the accuracy of the pressure data computed by this program and extreme care is urged in using the pressure data for design work.
Finally, it should be pointed out that the motion amplitudes in quartering and following waves at very low encounter frequencies may be unrealistically large since the theory is not applicable at such fre-quencies. The motion data as computed by this program should not be used, therefore, for irregular quartering and following sea computations without first checking that the results are reasonable for low encounter frequencies.
The program was developed jointly by NSRDC and Det norske Veritas, Oslo, Norway. The basic six-degree-of-freedom ship-motion program was originally written by Werner Frank at NSRDC. The program was
later extended and improved at Det norske Veritas to include the wave-induced loads and the pressure distribution on the hull surface. Further modifications were made to the program at NSRDC principally in the areas of program operation and output format. It is anticipated that further modifications will be made to the roll-damping calculations to improve the roll predictions. The program is written in FORTRAN IV and is presently in use on the CDC-6700 computer at NSRDC. The computer time is approximately 1000 system seconds for a general run with 30 wavelengths, one speed, and seven headings. The sample problem presented in Section IV ran for about 600 system seconds.
II. PROGRAM DESCRIPTION A. OUTLINE OF THEORY
A brief outline of the most important aspects of the theory is presented in this section, while a more detailed presentation including the derivations can be found in Reference 1. The ship is Considered to be advancing at a constant forward speed with arbitrary heading in regular sinusoidal waves. It is assumed that
the six-degree-of-freedom motions are linear and harmonic and that for a given ship speed, heading angle, and frequency of encounter, wE., the motion displacements are
ni = di co.t. ( wEt ed = 1 6 , (1)
where ai is the amplitude of the Motion with i = 1 referring to surge, sway, heave, roll, pitch, and yaw, respectively. Here ei are the phase angles which express the lag with respect to the maximum wave elevation at the origin of the x, y, z coordinate system shown in Figure 1. This right-handed coordinate system, is defined so that z is vertically upward through the center of gravity of the ship, x is the opposite direction of forward motiOn, and the origin is in the plane of the undisturbed free surface.*
Figure 1 Sign Convention for Translatory and
Angular Displacements
It should be noted that this coordinate system is different from the one used in Reference 1 where the x-axis is positive in the direction of forward motion.
FOLLOWING, II=0°
Figure 2 Definition of the Heading Angle, g
Under the assumptions that the responses are linear and harmonic, the six linear coupled differential equations of motion can be written, using subscript notation, in the following abbreviated form:
6
HPlik Tik +
jk rik
Cjk nklk=1
=F1 .ei WE t j = (3)
where Mil( are the components of the generalized mass matrix for the ship' Ajk and Bjk are the added-mass and damping coefficients, Cik are the hydrostatic restoring coefficients,** and Fi are the complex ampli-tudes of the exciting force and moment given by the real part of F1 eiWE t. F1, F2, and F3 refer to the
amplitudes of the surge, sway, and heave exciting forces, while F4, F5. and F6 are the amplitudes of the roll, pitch, and yaw exciting moments. The dots stand for time derivatives so that Tik and ijk are velocity and acceleration terms.
- 180°, HEAD
Note thatAjk(forj #k)are the added-mass cross-coupling coefficients for the kth mode coupled into thejib mode
of motion, so that for example A35 is the added-mass coefficient for pitch coupled into heave.
**HereC./k are defmed as the hydrostatic restoring coefficients and hence independent of frequency, while the
added-mass coefficients Ajk are so defined that they include all the oscillatory hydrodynamic forces proportional to the
acceleration.
A ship advancing through regular sinusoidal waves will not respond at the frequency of the waves, but at the frequency of wave encounter,
co2v
CJE= CJ cos 12 , (2)
where V is the forward speed of the ship, 12 is the heading angle, and w =
27riT
is the wave frequency. Here g is the gravitational acceleration and X is the wavelength. The definition for the heading angle is illustrated in Figure 2.BEAM = 90°
If it is assumed that the ship has lateral symmetry (symmetric about the x,z plane) and that the center of gravity is located at (0,0,2 g), then the generalized mass matrix is given by
011
where M is the mass of the ship, I is the moment of inertia in the jth mode, and'jk is the product of inertia. Here the inertia terms are with respect to the Coordinate system shown in Figure 1. The only product of inertia which appears is 146, the roll-yaw product, which vanishes if the ship has fore-and-aft symmetry and is small otherwise.
For ships with lateral symmetry it also follows that the added-mass (or damping) coefficients are,
0 A13 0 A15 0
0
A22 0
A24 A26A. (or Bik
A31
. )=
jk 0 A33 0 A35 0
0
A420
A44 A46A51 0 A53 0 A55 0
0
A620
A64 A66.Furthermore, for a ship in the free surface the only nonzero linear hydrostatic restoring coefficients are
C33' C44' C -55' and C35 = C53
If the generalized Mass matrix (4), the added-mass and damping coefficients (5), and the restoring coefficients (6), are substituted in the equations of motion (3), it it seen that for a ship with lateral symmetry, the six coupled equations of motions (1) reduce to two sett of equations. One set of three coupled equations of motion for surge, heave, and pitch which can be written as
711 + 11 1 3 713 4. 3 7.13 + A 5 75 Bi 5 '17'5 ei (4)E t A31 B31 + (A33 + M) 773 + B33 713 . +C33 773 +H35 175 +D35 C35 rj5 = F3 (8) Mjk = M 0 0 0 Mz g 0 0
MO
0 -MZ g 0 0 0 M . 0 0 0 -Mzg 0 14 0 _1 46 Mz 0 0 0 15 0 0 00:
146
0 (4)(A 111Zg) 712 +B42 IQ ' 1 "1.144 '4)714 (" ÷B44) 774 (9) A51 +B51 3 ?713 # B53 173 C53 713 +(A55 +15)775 #B55 715 +C55 715 = F5 ei t and another set of three coupled equations for sway, roll, and yaw which can be written as
(A22+ M) 712 B 2 712 +(A24 - Mzg) 714 #B 4 714 # 4 # B26 71.6 = F2 ei (.°E t # C4.4 714 # (A46 - 146) 716 6 q6 = F4 ei and .. 7.12 # 862 712 # - 146) 714 # 864 714 +(A6
1 )n #13
6 6 66n =F
6 6 6-)E tThus for a ship with lateral symmetry, surge, heave, and pitch are not coupled with sway, roll, and yaw. it is important to recognize how the equations of motion are coupled since this implies that any error in the Sway, roll, and yaw Motion computations will not affect the accuracy of the surge, heave, and pitch responses. Hence, if the user is only interested in the surge, heave, and pitch results, he does not have to furnish accurate input data for the computation of the viscous roll-damping coefficient.
The most complicated and tithe-consuming part of the computer program eitecution is the compu-tation of the added-mass and damping doefficients, Ail( and Bik, and the exciting forces and moments Fi. As shown by Salvesen, Tuck, and Faltinsen in Reference 1 these three-dimensional hydrodynamic quantities can be expressed under certain assumptions hi terms of the solution to the sectional two-dimensional problem of a cylinder with the same shape as the individual cross-sections oscillating in the
free surface. Since an accurate solution to the sectional two-dimensional problem is absolutely necessary in order to obtain useful final results, this program utilizes a close-fit source-distribution technique developed by W. Frank.6
(10)
Nonlinear viscous roll damping is introduced in Equation (11) in the form of the quasi-linear term,
'9;4 = K ma. (13)
which is added to the linear damping coefficient B44. Here K depends on the frequency of encounter, the viscosity, the bilge keel dimensions, and the hull geometry. The method of Tanaka7 is used to
compute eddymaking resistance and the method of Kato8 is used to obtain the bilge keel damping. 174 max is the maximum roll angle, which must be determined for each waveslope, WS, definedas,
360
WS degrees (14)
where is the wave amplitude and X is the wavelength.
The program uses a "trial and error" procedure for solving the quasi-linear set of Equations (10), (11), and (12). First the roll responses are computed using an estimated value for 174 max keeping the waveslope constant, then the program compares the maximum-computed roll amplitude with the estimated value and if the difference is larger than one degree a new value for 174 max is estimated by the program
and the computations are repeated until the difference between estimated and computed max roll ampli-tude is less than one degree.
Presently the program computes the roll-damping coefficients; however, unpublished and published in-vestigations by Baitis5 show that more accurate estimates of these coefficients are needed in order to be able to predict the roll motions in the near resonance frequency range with reasonable accuracy. The program is now being modified so that in the future the user may supply the program with the roll damping coefficients obtained from experimental results for similar hull forms.
Provision is made in the program for adding end-effect terms to the added-mass and damping co-efficients, see Reference I. It is recommended that end-effects be included only if the ship has a transom stem, a very wide stem, or sharp discontinuities at the stern. For hulls with fine sterns, end-effects should not be included.
After the motions have been computed, the program computes the wave-induced loads at the cross-sections specified by the user. A right-handed sign convention as defined in Figure 3 is used for the shear forces as well as the bending and torsional moments.* Note that this sign convention applies to the forces and moments acting on the portion of the ship/forward of the cross-section in question.
As in the case of the motions the w/aVe-induced loads can be expressed in the form:
b cos (wEt i = 2,3 (15)
V1 = COMPRESSION FORCE V2 = HORIZONTAL SHEAR FORCE V3 = VERTICAL SHEAR FORCE V4 = TORSIONAL MOMENT V5 = VERTICAL BENDING MOMENT V6 = HORIZONTAL BENDING MOMENT
Figure 3 Sign Convention for Dynamic Wave-Load Components
The phase angles Si express the lag with respect to the maximum wave elevation at the origin of the x, y, z coordinate system. Note that the wave induced loads are functions of heading, speed, frequency of encounter, and location along the length of the ship. It should also be noted that the computation of the torsional moment, V4 requires specific knowledge of the roll-radius of gyration for each cross-section, which are quite difficult to obtain.
As noted earlier in this report, the surge, heave, and pitch motions are uncoupled with the sway, roll, and yaw motions, and hence the vertical shear forces, V3, and the vertical bending moments, V5, are independent of the sway-roll-yaw motions while the horizontal shear forces, V2, the torsional moments, 174, and the horizontal bending moments, V6, are independent of the surge-heave-pitch motions. This means that if, for example, only the vertical loads, V3 and V5, are of interest to the user, there is no need to provide accurate inputs for determining the viscous roll-damping coefficients or the sectional roll radius of gyration since errors in the roll predictions will have no effect on these loads.
In addition to the motions and loads the computer program predicts, at selected points on
the submerged portion of the hull, the amplitude and the phase angle of the hydrodynamic pressure due to the motions and the incoming wave. It should be recognized that the pressure distribution due to diffraction cannot be computed accurately by the theory of Salvesen, Tuck, and Faltinsen.1 In deriving the expression for the diffraction force they applied Green's second identity, so that the expression is only applicable to the total force and not to the pressure distribution. In the present program
the diffraction part of the pressure has been approximated by a uniform sectional pressure which when in-tegrated over the section is equal to the sectional diffraction force. This may result in quite accurate results since in most cases the contribution due to diffraction is a small part of the total pressure.
Unfortunately, no detailed investigation has been performed into the accuracy of the pressure data computed by this program and extreme care is urged in using the pressure data for design work.
B. PROGRAM EXECUTION
The "NSRDC Ship-Motion and Sea:Load Computer Program" is composed of a main program and a series of subprograms written in FORTRAN IV and arranged in an overlay pattern. Details concerning the organization of the program and a description of each subprogram are provided in Appendix A. The program is currently in use on the CDC-6700 Computer System at NSRDC.
The main program named HANSEL, controls calling in the various overlays to perform specific computations. In addition HANSEL reads the first two Data Card Sets and determines when the job is completed.*
The first overlay called by HANSEL reads in the remaining Data Card Sets 3-34, describing the ship and the operating conditions. Detailed information concerning this input is provided in Section III and Appendix B. Hydrostatic terms are then computed, such as volume, LCB, GM, and restoring coefficients. If both the motions and the loads are to be computed, the mass, LCG, and radii of gyration will also be computed within this overlay using the sectional mass values from the input data. For details concerning the various outputs see Section IV.
The second overlay called by HANSEL computes the speed-independent added-mass and damping coefficients for a range of encounter frequencies designed to cover all conditions. Appendix C provides information on the selection of the frequency range. Provision is made for interpolating over frequencies where the close-fit method fails to provide values for the added-mass and damping coefficients (irregular frequencies). In the case of irregular frequencies the interpolation routine requires calculations of added-mass and damping at several additional frequencies for proper operation, which appreciably increases the computer time.
The third and final overlay called by HANSEL is the largest overlay and computes the six-degrees-of-freedom motions, wave-induced loads, and pressure distribution for the specified conditions (heading, speed, and waveslope). For each condition, i.e., specific heading, speed and waveslope, the regular wave responses are computed as a function of encounter frequency. If the maximum computed roll amplitude is not within one degree of a prescribed value for a specific waveslope, then the process is repeated using a new computed estimate of maximum roll amplitude.
The added-mass and damping coefficients are obtained for each encounter frequency by linear interpolation of the speed-independent values computed in the second overlay. Viscous roll damping is
computed and added to the potential roll damping. The equations of motion are then solved, followed by the load and pressure calculations.
After completing these calculations for all specified conditions control is returned to HANSEL to determine if another ship is to be processed or the run ended. The final results are printed-out as well as stored on an output tape for later use with other compiiter programs as for example the "NSRDC Irregular Sea Response Prediction Computer Program."
III. DESCRIPTION OF INPUT SCHEME
The first two sections of this chapter give a general description of the required input, the third section provides data card format information, and the last section gives samples of input data cards. It is recommended that the user thoroughly read and understand these sections and Appendix B before
attempting to run the program. Simple errors can lead to extremely misleading and erroneous results.
A. PHYSICAL DESCRIPTION OF SHIP A.1 Ship Geometry Input
Station Numbers: The geometric description of the ship is based on a system of twenty-one stations
with the forward perpendicular (F.P.) as station 0.0 and the aft perpendicular (A.P.) as station 20.0. A length scale of 20 is thus established and all stations are located according to the base dimension of 20. More or less than 21 stations may be used in defining the ship, but the total number of stations cannot exceed 27. Stations forward and aft of the P.P. and A.P. are allowed with stations forward of the F.P. being negative.
In the hydrodynamic computations within the program the ship geometry is approximated by a number of discrete cylinders (or sections) with uniform cross-section and with midpoints at the given stations. Note that the extreme forward and aft stations are assumed to have zero cross-sectional area and hence, no cylinder is used for these two stations. The cylinder lengths are computed from the station numbers and in the case of 21 stations with even station spacing the hull will be approximated by 19 cy-linders all with lengths equal to the station spacing (see Configuration 1 in Appendix B). However, it be-comes rather complicated to determine the length and location of each of these cylinders when uneven station spacing is used and therefore, it is necessary to introduce several restrictions with regard to the station spacing. Appendix B gives a detailed discussion of these restrictions. It is recommended that this appendix be studied carefully before using the program with uneven station spacing. The program will fail if inconsistent station numbers are given in the input.
Section Shapes: Each station, except the extreme forward and aft stations, represents in the program a
section (or cylinder) of uniform cross-section. The shape of a section is approximated by a polygon with corners at the offset points for the station associated with the section. A maximum of eight offset points per station is allowed and the number of offset points must be the same for all stations. It has been found that this number provides an adequate representation of the station shape."
the points and the straight lines between them should provide a good geometric description of the station shape;
the offset points should be evenly distributed. The even distribution is necessary because the pressure is assumed to be constant over the straight line segments connecting the points. To allow for as accurate a sectional pressure distribution as possible, therefore, any one segment should not cover a disproportionate length along the station contour;
for partially submerged sections, the offset points must be given starting at the intersection of the waterline and the station contour, (y,0), then clockwise around the contour, with the last point being at the intersection of the centerline and the station contour, (0,z). Figure 4 illustrates this type of section. For fully submerged sections such as shown in Figure 5, the first point must be at the section of the part of the contour nearest the free surface with the z-axis and the last point at the inter-section of the z-axis with the part of the contour furthest from the free surface. Note that the z-coordinates
for both types of sections (partially and fully submerged) are negative since the origin of the coordinate system is at the undisturbed free surface and the z-axis is positive upward. Appendix B:2 provides
in-formation on section (station) shape restrictions. Sections that violate the shape restrictions could cause the program to fail or to compute incorrect hydrostatic quantities such as volume, LCB, etc. The
two-dimensional added-mass and damping coefficients may also be computed incorrectly if the shape restriction is violated (see Reference 10). Appendix B should be studied carefully by the user before selecting the offset points to be used in the input of the program.
Table 1 is designed to provide a reference list of the required ship geometric information. Included in the table is the number of the data card set to which reference may be made for detailed information on the preparation of input data cards. Individual data card set descriptions may be found in Section HIC.
TABLE 1 SHIP GEOMETRY INPUT
Physical Data Data Card Set
-Length unit description Number of offsets Number of stations Station numbers
Length between perpendiculars Beam at midships Offset points 4, part (1) 5, part (1) 5, part (2) 6 7, part (1) 7, part (2) 8
Controls for adding end-effect corrections to the added-mass and damping
LOAD WATERLINE
(Y8,z8) (Y71z7) (Y6,z6)
Figure 4 Sample Station Contour Illustrating the
Specification of Offset Points for a Station Penetrating the Free Surface
FREE SURFACE
(y5,z5)
Figure 5 Sample Station Contour Illustrating the
Specification of Offset Points for a Completely Submerged Station
(Y4,z4) 611,z1)
(Y2fz2)
A.2 Mass and Mass,Distribution Input
All mass and mass-distribution data are input through either Data Card Set 9 or Data Card Sets 10 through 14. If only the motions are desired, the total mass of the ship and the roll, pitch and yaw radii of gyration as well as the mass prodfict of inertia and the vertical location of the center of gravity of the ship are given by Data Card Set 9. On the other hand, if both the motions and the loads are desired, then the folloWing information should be provided for each station in Data Card Sets 10 through 14.
Sectional mass values are given for each station in Data Card Set 10. Figure 6 illustrates the weight distribution curve used for the Mariner sample problem. Note that mass values are to be given for the first and last stations whereas offsets are not.
Longitudinal locations of the sectional centers of gravity for each station referenced to the first station are given in Data Card Set 11. The mass of the section is assumed to be concentrated in the plane of the station.
Sectional yaw radii of gyration of the mass for each statiOn taken about an axis perpendicular to the waterplane and through the local mass center of the station are given in Data Card Set 12.
The z-coordinates of the centers of gravity of the mass at each station, refetencea to the
water-line, are giveninData Card Set 13.
Sectional roll radii of gyration of the Mass for each station taken about an axis perpendicular to the station and passing through the center of gravity of the mass at the station are given in Data Card Set 14. 2000 1500 500
_F11
I i i . 20 19 18 17 16 15 14 13 12 A.P. I I I 11 10 9 STATIONS 1 I I 1 I -I I - I'I
I 8 7 6 5 4 3Figure 6 Weight Distribution Curve Used for the Mariner Sample Problem _I I t 2 1 0 F.P. Ca 1000
Table 2 is designed to provide a reference list of the required mass and mass-distribution
infor-mation. It is very difficult to obtain good realistic estimates for the sectional mass values and it is often
necessary to use some approximate numbers for these values. It should be noted, therefore, that if the user only needs estimates for the vertical loads (the vertical shear forces, V3 and the vertical bending moments,
V5) and does not need the horizontal loads (the horizontal shear forces, V2, the torsional moment, F'4, and the horizontal bending moments, V6), it is only necessary to provide accurate values for the mass of each section (Data Card Set 10) and the location of the sectional CG (Data Card Sets 11 and 13).
TABLE 2 MASS AND MASS-DISTRIBUTION DATA
A.3 Viscous Roll-Damping input
In order to calculate roll motiOns which are reasonably accurate in the frequency range close to resonance it is necessary to obtain good estimates for the viscous roll-damping coefficients used in the equations of motion (see Section IA). In addition, if the toisional moments are to be computed the sectional roll-damping coefficients also have to be obtained for each section along the hull. The total and sectional viscous roll-damping coefficients are not generally available for most ship forms and they are extremely difficult to obtain. However, if the user only needs the surge, heave and pitch motions (which are uncoupled with the sway, roll, and yaw motions) or the vertical shear force and vertical bending moment (which are not affected by the roll motion), then accurate viscous roll-damping input is not required and dummy input values may be used. Example 2 of Section IIID illustrates this case.
For the usual case when roll motions are desired, the user has a choice of three options for com-puting the viscous roll-damping coefficients:
Option 1. The program computes the sectional and total viscous roll damping coefficients using the
hull shape and bilge-keel information given in the input data. This is the only option currently available in the program. Input data cards are provided for the other two options but they have not as yet been programmed. As experimental results become available these options will be implemented.
Physical Data Data Card Set Force and moment unit descriptions 4, parts (2) and (3)
Controls for reading-in mass
distribu-tion data 5, parts (3) and (4)
Total rhaii; roll, pitch, yaw radii of
gyration; centrifugal moment about x-z axis; ZG
included if only
motions are computed
Mass of each section
Distance from the first (reference) station to each sectional CG
Yaw radius of gyration for each section Z-coordinate of each section CG
Roll radius of gyration for each section 10
11 included if both motions and loads 12
are domputed 13
14
Control for motion and load
calculations
Option 2 (for future use). The user supplies the total viscous roll-damping coefficient. He has two choices for supplying the sectional coefficients:
Method 1. The user supplies the percentage of the total viscous damping which should be used
for each section. The program will compute the sectional damping using these percentages and the total damping_
Method 2. The user supplies the same information required by Option 1 as well as the total
viscous roll damping coefficients. The program will compute the sectional percentage of the total. damping using the calculations of Option 1 but the values of the sectional damping will be ad-justed so that the total damping is the same as the values supplied by the user. In other words: the damping computed in Option 1 is only used to compute the sectional percentages.
Option 3 (for future use). The program will supply the total and sectional viscous roll-damping
co-efficients from estimated values stored within the program for several different classes of ship hulls. Table 3 is designed to provide a reference list of the required input for each of the three options for computing viscous roll-damping coefficients.
TABLE 3 VISCOUS ROLL-DAMPING INPUT
Physical Data
Data Card Set Option 1
Option 2.
Option 3 Method 1 Method 2'
Controls reading in bilge-keel information, Data Card Sets 27-28 Controls the options used in predicting roll damping
Controls the method used within Option 2
Specifies viscosity, submerged length, and type of flow Specifies the section shape for eddymaking
Bilge-keel information Estimated maximum roil angle Total viscous roll-damping coefficients Percentage for each station
Specifies class of Ship and uses stored roll-damping values
23, part (3) 23, part (5) 24, parts (1,3,4) 25 26, 27, 28 31 23, part (3) 23, part (5) 23, part (6) 32
33
23, part (3) 23. part (5) 23, part (6) 24, parts (1,3,4) 25 26, 27, 28 31 32 23. part (3) 23, part (5)Method 2 of Option 2 should only be used when both motions and tomb are computed. ..
B. CONDITION INFORMATION
A condition is defined in the program as a particular heading, ship speed, and waveslope for which the ship's transfer functions will be computed as a function of encounter frequency. The input required (see Data Card Sets 16-20) consists of heading angle, pi, Froude number, F,,, ratios of wavelength to wave height, Ww, and ratios of wavelength to length between perpendiculars,
k4p.
Table 4 is designed to provide a reference list of the required condition input as well as the equations used for computing ship speed, waveslope, and encounter frequencies. Note that the encounter frequencies are not used as input values but are computed within the computer program from wavelength, heading, and speed (see Equation 2).It is recommended that a wide range of closely spaced Niro values be used (say a range from 0.2 to 3.0 with a spacing of 0.1). The two main reasons for the wide range and the close spacing are as follows:
For certain heading and speed conditions the hydrodynamic coefficients in the equations of motion as well as the motion and load responses may be a rapidly changing function with respect to encounter frequency.
When the program is used in connection with an irregular-sea program, a close spacing of the Xgo values is usually needed in order to obtain accurate statistical results.
Note that the same set of k/op values are used for each condition.
C. DATA CARD FORMAT DESCRIPTION
The input to this program for a particular ship is accomplished via punched cards. The exact number of sets of data cards (a set may require more than one card) will vary according to the requirements of a particular problem. The program is designed to handle more than one ship in a single computer run by in-cluding the data card sets for each extra ship after those of the first ship. Options and defaults* are described as they arise in the various data card sets. It should be emphasized that integers must be punched at the correct location within their specified fields while floating point numbers and alphanumeric information may be punched anywhere within their specified fields. There are a total of 34 different data card sets.
Data Card Set 1, one card, FORMAT (3A10).
This card contains three alphanumeric variables used to identify the output. NAME1, columns 1 - 10, identifies the user's name.
NAME2, columns 11 - 20, identifies the user's code,
NAME3, columns 21 - 30, identifies the user's telephone extension.
a
A default occurs when the program assumes a value for a variable when the field is left blank. This occurs on only a few variables in the program.
TABLE 4 CONDITION INPUT AND LIST OF COMMONLY USED EQUATIONS
Condition Input Data Card Set Controls for reading in X/LPP, Froude numbers,
headings and Xftw 16, parts (1,2,3,4) Ratios ofX8'w '17 Heading angles 18 Froude numbers 19 Ratios of X/L PP 20
Number of nondimensional frequencies and
maximum and minimum nondimensional frequencies 21, parts (1,2,3) Control for irregular frequency calculations 22
Commonly Used Equations
Encounter frequency Nondimensional WE Wave frequency Froude number Wave slope 2 co V cosp WE =w WEN = WE 27T g w =
1
X V Fn= N/1"--..pc, 360 WS= XV is the ship speed in feet/second g is the acceleration due to gravity
ii
is the heading angleX is the wavelength is the wave amplitude
L is the length between perpendiculars PP
-Data Card Set 2, one card, FORMAT (5X, A4, 7X, A3, 8X, A3).
This card contains three alphanumeric variables used as controls for a number of options. The spelling of the values of the variables is tested in the program against defined names. Hence care should be exercised in using the correct spelling.
IPASS, columns 6 - 9, is a control for reading in Data Card Sets 3 - 34. The options are, JPASS = GOGO, read-in sets 3 - 34.
IPASS = STOP, program stops.
IPASS undefined, GOGO assumed (default).
OTAPE, columns 17 - 19, is a control for positioning the output tape. Results are stored on an output tape as well as printed out. The options are:
OTAPE = NEW, no tape positioning, new tape.
OTAPE = OLD, output tape automatically positioned past previous results. OTAPE undefined, NEW assumed (default).
PRNTOP, columns 28 - 30, is a printout option. PRNTOP = MAX, maximum printing.
PRNTOP = MIN, printing of results suppressed, only data cards listed. PRNTOP undefined, MAX assumed (default).
NOTE - Data Card Set 2 provides a method for including data for more than one ship at a time. This set should be placed before and after the cards for each ship (Data Card Sets 3 - 34). After the data for the last ship use IPASS = STOP.
Data Card Set 3, one card, FORMAT (12A6).
This card contains alphanumeric inforrhation identifying the project, ship, calculations, etc. TITO (array), columns 1 - 72.
Data Card Set 4, one card, FORMAT (2A6, A8) This card contains three alphanumeric variables.
WORD, columns 1 - 6, identifies the input length unit used. A unit commonly used is FEET. All dimensional variables input to the program must be in units consistent with this length unit.
VVORD2, columns 7 - 12, identifies the force unit, if WORD = FEET then WORD2 = TONS. WORD3, columns 13 - 20, identifies the moment unit. If WORD = FEET then WORD3 = FT-TONS.
WORD; WORD2-, and WORD3 are printed out with the dimensional part of the output to identify the dimensional units.
Data Card Set 5, one card, FORMAT (416) This card contains four integer variables.
NUT <8, column 6, is the number of offset points used to describe each station. All stations must have the same number of offsets. It is recommended that 8 offset points be used.
NST <27, columns 11 - 12, is the number of stations used to longitudinally subdivide the ship.
NMAS = NST, columns 17 - 18, is the number of nia§s points. If IT 0 (see the next integer description) then punch a one in cOlurim 18.
IT, coltunn 24, is a control for reading in Data Card Set 9 or Data Card Sets 10 - 14. IT = 0, read in the inass and mass-distribution data for each station, contained in Data Card
Sets 10 - 14. This option must be used when load calculations are desired.
IT *0, read in the mass and mass-distribution data for the ship as a whole, contained on Data Card Set 9. This option is used when only motion calculations are desired.
Data Card Set 6, from one to four cards, FORMAT (8F10.4)
This card set contains the I1ST station numbers, ST 1(1), used to longitudinally subdivide the ship. The stations are input in the order they occur along the ship starting with the first station at the extreme forward point of the ship. For example, 0.0, 0.25, 1.0, 19.75, 20.0. See Appendix B.1 for recommended station numbering.
ST1 (array), columns 1 - 10, 11 - 20, 71 - 80/repeat for up to four cards, eight numbers per card.
Data Card Set 7, one card, FORMAT (2F10.4)
This card contains the following two floating point numbers:
ELL, columns 1 - 10, is the length between perpendiculars, lop, in WORD units. BEAM, columns 11 - 20, is the beam at midships in WORD units.
Data Card Set 8, two cards for each of NST-2 stations, a total of 2 (NST-2) cards, FORMAT (8F10.4) This card set contains the y and z coordinates of the offset points for each of NST-2 stations (see Figures 4 and 5). The foremost and aftermost stations have no offsets and are not specified in this data card set. Appendix B.2 provides information on allowable section shapes and contour specifications.
Y (array), first card, columns 1 - 10,11 - 20, 71 - 80, contains the NUT y coordinates of the offset points for Section I* in WORD units. The y coordinates (positive) are given proceeding clock-wise around the station contour, with the first y value at the intersection of the waterline and the station contour, and the last y value at the intersection of the centerline and the station contour. For fully sub-merged sections the first y value is zero.
Z (array), second card, columns 1 - 10, 11 - 20, 71 -80, contains the NUT z coordinates (negative) of the offset points for Section I in WORD units. The z coordinates are given in the same mariner as the y coordinates. For fully submerged sections the first z value is at the intersection of the station contour nearest the free surface and the centerline.
Data Card Set 9, one card, FORMAT (F10.4, 4F10.6, F10.4)
This card set is included when motions only are desired. In this case, IT 0 (see Data Card Set 5). This card set contains six floating point numbers.
TMASS, columns 1 - 10, is the total mass of the ship in units consistent with the WORD length
unit. For example, if FEET is the length unit, the mass unit would be TONS SECONDS2/FEET. E144, columns 11 - 20, is the square of the roll radius of gyration divided by the length between perpendiculars, (K4/40).2
E155, columns 21 - 30, is the square of the pitch radius of gyration divided by the length be-tween perpendiculars, (K0Np).2
E166, columns 31 - 40, is the square of the yaw radius of gyration divided by the length between perpendiculars, (K1JLpp).2 Usually E166 is set equal to E155.
E146, columns 41 - 50, is the mass product of inertia about the x and z axes divided by TMASS ELL.2 E146 is very close to zero for most ships and in fact equal to zero for ship with fore and aft symmetry.
ZG, columns 51 - 60, is the z coordinate of the center of gravity, CG, of the ship referenced to the waterline in WORD units (positive for CG above the waterline).
The next five Data Card Sets, 10 through 14, are included when load calculations are desired. In this case, IT = 0 (Data Card Set 5) and Data Card Set 9 is not required.
Data Card Set 16, from one to four cards, FORMAT (8F10.4)
This card set contains the NMAS mass values, PMAS(I), associated with each station along the hull, in units consistent with the WORD length unit. The mass values are input, eight numbers per card, columns 1 - 10, 11 - 20, 71 - 80. The reference system for mass point locations (see Figure 7) differs from the one used to locate stations. For mass data the first station (not necessatily the FP) is considered to be the reference station. The order is as follows:
PMAS(1) = mass associated with the first station after the reference (foremost) station. PMAS(2) = mass assOciated with the second station after the reference station.
PMAS(NMAS-1) = mass associated with the reference statiOn. PMAS(NMAS) = mass associated with the aftermost station.
Note that the mass data associated with the reference station is not the first mass data stated in the data cards. XMAS(20) XMAS(1) XMAS(21) XMAS(19) LINL
Figure 7 Illustration of the Proper Association between XMAS (I) and the Stations along the Ship
22
0 1 19 20
F.P.
Data Card Set 11, from one to four cards, FORMAT (8F10.4)
This card set contains the NMAS distances, XMAS(I), positive, from the reference station to the given station in WORD units, see Figure 7. The order of input is the same as for PMAS, i.e.,
XMAS(1) = distance between the reference station and the second station. XMAS(2) = distance between the reference station and the third station. XMAS(NMAS-1) = 0.0.
XMAS(NMAS) = distance between the reference station and the aftermost station.
Data Card Set 12, from one to four cards, FORMAT (8F10.4)
This card set contains the NMAS sectional yaw radii of gyration, YMAS(I), of the mass of each station taken about an axis perpendicular to the waterplane and through the local mass center of the station. These values, in WORD units, are generally small (except for very wide ships) and can be set equal to 0.0. The order of input is the same as for PMAS (see Data Card Set 10).
Data Card Set 13, from one to four cards, FORMAT (8F10.4)
This card set contains the NMAS values, ZMAS(I), of the z coordinate of the center of gravity of the mass at each station referenced to the waterline in WORD units (positive for CG above the waterline). The order of input is the same as for PMAS (see Data Card Set 10).
Data Card Set 14, from one to four cards, FORMAT (8F10.4)
This card set contains the NMAS sectional roll radii of gyration, RRG(I), of the mass of each station taken about an axis perpendicular to the station and passing through the center of gravity of the mass at that station. These values are given in WORD units. The order of input is the same as for PMAS (see Data Card Set 10).
Data Card Set 15, one card, FORMAT(I6) This card contains one integer variable.
IXAST, columns 5 - 6, is only used when end-effect corrections are made to the added-mass and damping coefficients for ships with transom type sterns (Data Card Set 23, IEND = 1). In this case, IXAST = NST - 2, which is the sequence number of the last section along the hull near the stern. Note that this card set must be included irrespective of the value of IEND.
Data Card Set 16, one card, FORMAT (416) This card contains four integer variables.
NOK <30, columns 5 - 6, is the number of wavelengths for which motion and load calculations are performed.
NOB <5, column 12, is the number of Froude numbers for which motion and load calculations are performed.
NOH <10, columns 17. 18, is the number of headings for which motion and load calculations are performed.
NWSTP <12, columns 23 - 24, is the number of waveslopes for which motion and load calculations are performed.
Data Card Set 17, one card, FORMAT (1216)
This card contains the NWSTP reciprocals of wave steepness, INWSTP(I), definedas the ratio of wavelength to wave height, Xftw, i.e., 50, 80, 110. Wave slope in degrees is determined in the program as 180/INWSTP(I). The program also computes a wave amplitude for each wavelength as
= XV
INWSTP(I)] where the wave slope is kept constant for each heading and Froude number. See Section IIA for a discussion of the use of wave amplitude in the nonlinear viscous roll-damping calculations and Section IV for a general discussion about the use of wave amplitude for scaling the output.
Data Card Set 18, from one to two cards, FORMAT (8F10.4)
This card set contains the NOH heading angles, HDG1(1), in degrees. The convention used in the program is head waves = 180 degrees.
Data Card Set 19, one card, FORMAT (5F10.4)
This card contains the NOB Froude numbers, FN(I). The Froude number is defined as,
/712
where V is the ship speed in feet/second, g is the acceleration due to gravity, and L is the length between perpendiculars.
Data Card Set 20, from one to four cards, FORMAT (8F10.4)
This card set contains the NOK numbers of nondimensional wavelengths, BAM(I), for which calcu-lations are to be performed. The wavelength is nondimensionalized by the length between perpendiculars,
X/Lpp.
Data Card Set 21, one card, FORMAT (IS, 2F10.4)
This card contains one integer variable and two floating point variables:
NFR < 40, columns 4-5, is the number of nondimensional frequencies of encounter, W EN'for which added-mass and damping values are calculated. The nondimensional frequency is defined by,
WEN = 1/73-p7i
where WE is the dimensional frequency of encounter, Lpp is the length between perpendiculars, and g is the acceleration due to gravity. Note that NFR is in an 15 field instead of the usual 16. If NFR is undefined, the program will compute a value for it.
OMIN, columns 6-15, defines the lower end of the range of wEN values. If OMIN is undefined, the program will compute a value.
(3) OMAX, columns 16-25, defines the higher end of the range of WEN. If OMAX is undefined, the program will compute a value.
See Appendix C for a discussion of the calculation of NFR, OMIN, and OMAX.
Data Card Set 22, one card, FORMAT (16) This card contains one integer variable.
IRR, column 6, is a control for interpolating the added-mass and damping values if irregular fre-quencies exist.
IRR = 1, no irregular frequencies. ERR = 2, irregular frequencies exist.
IRR undefined, program will supply the proper value.
See Appendix C for a discussion of the effect of irregular frequencies on the calculation of the range of nondhnensional frequencies and on the interpolation of the added-mass and damping coefficients.
Data Card Set 23, one card, FORMAT (616)
This card contains the following six integer variables:
ML, column 6, is a control for the motion and load calculations. ML 1, only motions are calculated.
ML = 2, both motions and loads are calculated. ML must be defined.
IEND, column 12, is a control for including endterms in the equations of motion. LEND = 1, end terms will be included. Set IXAST = NST-2 (Data Card Set 15). IEND = 2, no end terms.
IEND must be defined.
IBILGE, column 18, controls reading in Data Card Sets 27 -28 which contain bilge keel information required by the program for computing the viscous roll-damping coefficient when Option 1 or Method 2 of Option 2 is used. (For definitions of the options see Section IIIA.3.)
IBILGE = 1, the ship has bilge keels. Read in Data Card Sets 27-28. See 1DAMP and IPRCNT (integers 5 and 6 of this Data Card Set) for choice of option and method.
IBILGE = 2, no bilge keels. Skip Data Card Sets 27-28. IBILGE must be defined.
IPRES, column 24, is a control for the pressure calculations. It also controls reading in Data Card Set 29.
IPRES = 1, calculate pressures for the stations specified by Data Card Set 29. IPRES = 2, no pressure calculations. Skip Data Card Set 29.
IPRES must be defined.
IDAMP, column 30, is a control integer used to specify the option used to compute the viscous
IDAMP = 1, Option 1 will be used and the total and sectional viscous roll-damping coefficients will be computed by the program using information supplied in Data Card Sets 25-28.
IDAMP = 2 (Future option), Option 2 will be used and the total viscous roll-damping coefficients will be read in from Data Card Set 32. See IPRCNT (next integer description) for the choice of method for determining the sectional coefficients.
IDAMP = 3 (Future option), Option 3 will be used and the program will determine the total and sectional viscous roll-damping coefficients from defined classes of ships. The class of ship is specified in Data Card Set 34.
IDAMP undefined,, program will assume IDAMP = 1. If IDAMP = 1, Data Card Sets 32-34 will not be
read in.
(6) IPRCNT, column 36, is a control integer used to specify the method used in Option 2 to determine the sectional viscous roll-damping coefficients.
IPRCNT = 1, Method 1 is used and the percentage of the sectional roll-da.mping is supplied in Data Card Set 33.
WRCNT = 2, Method 2 is used. The program computes the percentages. Skip Data Card Set 33. See Section IIIA.3 Viscous Roll-Damping Input and Table 3 for a discussion of the various Options and Methods.
Data Card Set 24, one card, FORMAT (F10.8, 2F10.4, 16)
This card contains three floating point numbers and one integer.
VNY, columns 1 - 10, it is the kinematic viscosity of water, 1,, in units consistent with the WORD length unit. For fresh water at 70°F, = 1.059 x 10-5 FT2 SEC.
GRAV, columns 11 - 20, is the acceleration due to gravity in units consistent with the WORD length unit. For instance, if WORD = FEET, GRAV = 32.2 feet - seconds-2
AMODL, columns 21 - 30, is the total length of the submerged portion of the hull. It is used by the program for the calculation of the Reynolds number.
MOD, column 36, is a control integer for the type of flow around the hull. MOD = 1, laminar flow around the hull is assumed.
MOD = 2, turbulent flow around the hull is assumed. MOD must be defined.
Most cases require specification of turbulent flow. For small ships at slow speeds the flow may be laminar. NoteVNY, MODL, and MOD are required only when the program computes the roll damping (Option 1 or Method 2 of Option 2).
The next four Data Card Sets, 25 through 28, are not included when IDAMP = 2. They contain
in-,
formation the program uses to calculate roll damping.
Data Card Set 25, from one to two cards, FORMAT (1615)
This card set contains the NST-2 control integers, ITS(I), one for each station except the extreme for-ward and extreme aft stations. The values of ITS(I) are used in the calculation of roll induced eddymaking. They specify the local hull shapes at Section I and are determined according to the following procedure:
ITS(1) = 1, Section I has a V or U shape with a small radius at the keel (bow sections). ITS(I) = 2, Section I has a sectional area coefficient greater than 0.95 (parallel midbody with rectangular shapes).
ITS(I) = 3, Section I has a shallow V or U shape with a local beam/draft ratio greater than 1.0 (aft sections of destroyers or cruisers).
ITS(I) = 4, Section I has an extremely rounded shape (a destroyer hull section with extremely rounded bilges and no skeg).
Note that ITS is punched in 15 fields.
Data Card Set 26, from one to four cards, FORMAT (8F10.4)
This card set contains the NST-2 bilge radii, RD(I), in WORD units, one for each station except the extreme forward and extreme aft stations. RD(I) is defined as follows:
RD(I) = radius of bilge circle at Section I for, sections that have bilge keels,
sections with ITS(I) = 2. RD(I) = 1.0 otherwise.
The next two Data Card Sets, 27 and 28, are included only if the ship has bilge keels (IBILGE = 1
Data Card Set 27, one card, FORMAT (2F10.4)
This card contains the following two bilge keel parameters:
AKE-ELL, columns 1 - 10, is the total length of the bilge keel in WORD.units. BEAMKL, columns 11 - 20, is the maximum width of the bilge keel in WORD units.
Data Card Set 28, NST-2 number of cards, FORMAT (6F10.4)
This data card set provides a description of the bilge keel at each of the NST-2 stations. The extreme fore and aft stations are not considered. Each card contains the following six numbers (see Figure 8):
R.FD(I), columns 1 - 10, is the deadrise of Section I in WORD units. Set equal to 0.0 for stations
with no bilge keels.
DELTAD(I), columns 11 - 20, is the length of the bilge keel along Section I in WORD units. Set equal to 0.0 for stations with no bilge keel. The program tests for 0.0 in this case in order to by-pass a number of calculations.
RICD(I), columns 21 - 30, is the distance from the middle of the bilge keel at Section I to an axis through the center of gravity of the ship and parallel to the x-axis. It is in WORD units. Set equal to 1.0 for sections with no bilge keels.
SD(I), columns 31 - 40, is the distance from the root of the bilge keel to the waterline as measured along the countour of the hull at Section I. It is in WORD units. Set equal to 1.0 for stations With no bilge keels.
Figure 8 Typical Ship Cross-Section Illustrating the Geometric Parameters Required to Describe the Location and Orientation of the Bilge Keels
COSPHD(I), columns 41 50, is the cosine of the angle, a, between RICD(I) and the bilge keel at Section I. Set equal to 1.0 for sections with no bilge keels.
PHID(I), columns 51 - 60, is the angle, cf), in radians, formed by RIC.D(I) and a line connecting the center of gravity with the waterline at Section I. Set equal to 1.0 for sections with no bilge keels.
The next Data Card Set, 29, is included only if pressure calculations are desired (IPRES = 1).
Data Card Set 29, from one to four cards, FORMAT (8F10.4)
This card set contains the NST-2 control numbers, STPR(I), which determine at which sections the pressure distribution will be calculated. The program can compute the pressures for up to eight sections. There are two options:
STPR(I) = 0.0, the pressure on Section I will not be calculated; and STPR(I) = 1.0, the pressure distribution will be calculated on Section I. STPR(I) must be defined.
The next Data Card Set, 30, is included only if load calculations are desired (IT = 0).
Data Card Set 30, from one to four cards, FORMAT (8F10.4)
This card set contains the NST-3 control numbers, STLD(I), which determine at which sections the loads will be printed out.* This is a printing option only. Loads are calculated at each of the NST-3 sections independent of the value of STLD(I) and stored on magnetic tape. There are two options:
STLD(I) = 0.0, the loads are not printed out for Section I. STLD(I) = 1.0, the loads are printed out for Section I. STLD(I) must be defined.
The next Data Card Set, 31, is not included if roll damping coefficients are read in (IDAMP = 2).
Data Card Set 31, from one to seven cards, FORMAT (8F10.4)
This card set contains the NHF = NOH NOB NWSTP estimates of maximum roll angle (single amplitude), THMD(I), in radians. (See Data Card Set 16 for the definitions of NOH, NOB, and NWSTP.) The THMD(I) values are the initial values in the "trial and error" procedure used in solving the quasi-linear equations for roll. (See Equation 11 in Section IA.) These estimates are functions of wave slope, Froude number and heading angle. Eight THMD(I) values are given per card in a sequential order given by varying the wave slope first, then the Froude number and finally the heading angle. If THMD(I) is undefined the program will supply initial estimates. If accurate estimates can be provided by the user, the run time will be reduced substantially. Note that due to storage restrictions NHF 50.
Note that the loads are not computed at the stations [ST1(I+1)] but rather at the end of the sections. For example, if 21 equally spaced stations define the ship, the loads would be computed at the following station numbers 1.5, 2.5, IS,
The next Data Card Set, 32, is included when roll damping coefficients are to be read in (IDAMP= 2).
Data Card Set 32, frorn one to two cards, FORMAT (8F10.4)
This card set contains the following two roll-damping coefficients as a function of Froude number: B2(I), columns J - 10, is the linear viscous roll damping coefficient for the first Froude number. B3(I), columns 11 - 20, is the nonlinear viscous roll damping coefficient for the first Froude nurn-ber. If more than one Froude number is given, the remainder of the card should be filled with pairs of numbers, B2(l) and B3(I).
The next Data Card Set, 33, is included only when the roll-damping coefficients are to be determined for each station by the user (load calculations are desired and IDAMP = 2). In this case, IPRCNT = 1.
Data Card Set 33, from one to fifty cards, FORMAT (8F10.4)
This card set contains the percentages of B2(I) and B3(I) to be used for each of NST-2 stations. There are up to two cards for each station (excluding the extreme fore and extreme aft stations). The order of input per card is the same as in Data Card Set 32.
PB2(I,J), columns 1 - 10, is the percentage of the B2 coefficient as a function of Station I and Froude number J.
PB3(I,J), columns 11 - 20, is the percentage of the B3 coefficient. Note that, if IPRCNT = 2, the program will determine these percentages and Data Card Set 33 will not be required.
The next Data Card Set, 34, is included only if IDAMP = 3.
Data Card Set 34, one card, FORMAT (16)
This card contains one control integer, ICLASS.
ICLASS, column 6, specifies the class of ship for which roll damping will be computed. The program will use stored values for the roll-damping coefficients as a function of ship class. The options are:
ICLASS = 1, small boats.
ICLASS = 2, high-speed transom-stem hulls. ICLASS = 3, moderate-speed cruiser-stern hulls.
If data cards for another ship are to be included, first repeat Data Card Set 2 using IPASS = GOGO, followed by Data Card Sets 3 - 34 for the next ship. When no more ships are to be run, repeat Data Card
Set 2 with IPASS = STOP. This completes the data card input for the program.
D. SAMPLE INPUT
Two sample data decks are provided in this section for the Mariner hull form. The purpose is
three-fold. First, they are intended to be an aid for understanding the data card format arrangements presented in
the previous subsection. Secondly, they provide data upon which a check of proper implementation of the computer program can be based. And last, they illustrate the difference in the input required for the most complete case, Example Case I (six-degree-of-freedom motions and loads with bilge-keel information) and for a simplified case, Example Case II (surge-heave-pitch motions without bilge-keel infoitnation). The first
