Some effects of hull form on performance in head seas

SHIP MODEL EXPERIMENT TANK S ST ALBANS AND DLTI'tBARTON

SOME EFFECTS OF HULL FORM ON PERFORMANCE IN HEAD SEAS

by

D. C. P'iJJRDEY, B.Sc., Ainst.P, A.M.R.I.NA.

L,

DCM/ s ROTM 70/8

SOME EFFECTS OF H1JLL F0PJI ON PERFORMANCE IN BRAD SEAS

by

D. C. MURDEY, B.Sc., A.lnst.P., A.M.R.I.N.A.

SUI'4MARY

This paper describes and summarises estimating equations previously published by Moor and Murdey (References i and 2) and gives illustrations of their application to the design of a fast cargo liner and oil tanker form.

SYMBOLS

B : Breadth, feet

CB Block Coefficient

Waterplane area coefficient

D : Propeller diameter, feet

K : Longitudinal radius of gyration about an axis

yy

through the centre of gravity, feet

L, LBP: Length between perpendiculars, feet

LOB : Longitudinal position of centre of buoyancy from midships of LBP, percent of LBP

Increase in shaft revolutions per minute

P Propeller mean face pitch, feet

Power increase, horsepower

increase in propeller torque, ft-lbs

T Draught, feet

Increase in propeller thrust, tons

V Speed, knots

Z : Significant heave, feet

Bulbous 'bow factor, unity for forms with a

¡

bulbous bow and zero for forms without a

bulbous bow

1. INTRODUCTION

Considerable research has been directed towards the evaluation of the effects of changes of ship form on per-formance in still water, but very little information is available to the naval architect to guide him in the choice of ship form or proportions most suitable for operation in waves.

The complexity of the seakeeping problem is such that most of the research effort in the field has been directed

at the development of experimental and theoretical methods rather than the exploitation of available techniques, and although the results of specific detailed investigations into particular problems have been published (Reference 3 for

example), it has been very difficult for the naval architect to identify overall trends.

In order to produce results of immediate practical use, the seakeeping problem has been simplified. The sea has been considered as a series of irregular long-crested waves, and th.e effects of quartering, bow or stern seas subordinated in most investigations to those of head seas. Pitch and heave have been used to describe the motions of the ship rather than the very much more complex phenomena of wetness, slamming and accelerations. Only the overall trends of per-formance with the most fundamental ship parameters (length, breadth, draught and block coefficient for example) have been investigated; and it is not yet possible to give any quantitative estimate of tho effect of detailed changes in hull shape without carrying out model experiments. _Further simplifications are made if theoretical methods _{are employed,} but these will not be described in this _paper.

Three approaches to the problem of determining the effects of ship form on performance in waves are possible which are likely to yield useful results, subject to the

-3-A direct approach is to carry out model experiments to measure the effects of changing various form parameters. A well-known example of such exoeriments was carried out with Series 60 models at Wageningen (Reference 4). Un-furtunately no definite conclusions were drawn from the results of these experiments, and the results of' a further analysis (Reference 5) are very difficult to interpret in

general terms because changes in ship length were associated with simultaneous variations in other dimensions or

coefficients, together with a restriction of constant dis-placement.

An alternative to systematic model experiments is the use of theoretical methods to calculate the performance of a range of ship forms. This has been done by Vassilopoulos

(Reference 6) and Ewing (Reference 7), both using forms based on Series 60 parents. The validity of the theoretical approach depends upon the accuracy and reliability of the theory, and a satisfactory comparison of theory and results of model experi-ments for a range of ship forms is required before the use of' the theory can be justified. Theoretical methods are not yet available for calculating the power increase.

The third approach is the analysis of results of experi-ments with models of random ship forms. Stefun (Reference 8)

explored the trends of pitch and heave using data from model experiments on five ship forms, and more recently Moor and Murdey carried out analyses (References i and 2) with the

results of experiments with forty-three models of single screw

ships. The results of the latter analyses are equations which give significant pitch and heave, and mean increases in propeller thrust, torque, rate of rotation and delivered

horsepower required to maintain speed in a range of sea

con-ditions, as functions of principal dimensions, (length, beam, draught), form factors (block and waterplane area coefficients), weight distribution (longitudinal position of the centre of

buoyancy and longitudinal radius of' gyration), propeller (diameter and pitch), and speed.

in Section 2 below. The remainder of this paper gives

examples of the application of ths equations to the design of a fast cargo liner and an oil tanker.

2. TE MOOR-MURDEY ESTIMATING EQUATIONS

The equations are the result of an analysis of experi-ments carried out with forty-three models, all of practical ship forms and the majority of preliminary or final designs for actual ships. Seventeen of the models were of cargo liner forms with block coefficients between 0.55 and 0.71 and the remainder of tanker or bulk carrier fo±'ms with block co-efficients between 0.74 and 0.88. All the models were between 16 and 20 feet long. Experiments were carried out with twenty-nine models in a ballast as well as a load or

design condition. The speed or speeds at which the models were run corresponded to speed-length ratios in the range

0.55

to 1.00 for the cargo liner forms and

0.45

to 0.70 for the tanker forms.

The models were self-propelled, with no external tow force, in regular head waves. The waveheight was maintained at a constant value (usually one fiftieth of the length

between perpendiculars of the model) and the wavelength was varied from one half to three times the length between per-pendiculars.

The results of these experiments were curves in which the ordinate was proportional to the measured pitch and heave, and propeller thrust, torque, rate of rotation and delivered horsepower, and the abscissae proportional to wavelength. These curves were then used to compute, for irregular waves with significant wavoheights 9.0, 13.9, 18.8 and

_24.5

feet,

(assumed to correspond to Beaufort Numbers

_{5, 6,}

7 and 8), significant pitch and heave, and mean'increases in propeller thrust, torque and rate of rotation and in delivered horse-power above still water values for models of geometrically similar ships 400, 500, 600, 800 and 1000 feet long between the perpendiculars.

For these calculations the sea state as assumed to be represented by the British Towing Tank Panel 1964 One-Dimensional Sea Spectrum (Reference 9), reduced by the appropriate factor to model scale.

This generalisation of the results was possible because the original experiments were carried out in regular waves. The results of experiments in irregular waves only apply to the particular ship length the model is chosen to represent and to the particular wave conditions represented in the experiment tank.

While the results of these calculations applied strictly only to the models, it was convenient to express them in

dimensionless forms which enable easy calculation of full scale values on the assumption, as yet improved, of simple Freude scaling.

The results of this first stage of the analysis, in the form of predictions of performance in irregular waves, were examined with the object of defining quantitatively trends with the simplest parameters defining the hull, weight distri-bution and speed, which are known or easily estimated at the earliest stages of the design process.

The method of analysis was multiple regression supported by detailed inspection of the results at every stage in order to test the realism of the results obtained.

The final results are the equations which are reproduced in Tables III to VIII of this paper. Table V, the estimating equation for power increase, is taken from Table XI of

Reference 2 which superseded Table VIII of Reference 1. The values of the coefficients in each equation depend on ship length and sea severity.

It must be remembered that the equations may lead to unrealistic results if they are applied outside the range of data upon which they are based. These ranges for block and waterplane area coefficients are from 0.55 to 0.88 and from

to 32 and for length-beam ratio from 5.4 to 7.5 The equations should not be used to estimate the performance of cargo vessel forms at speed-length ratios less than

0.55

or tanker forms at speed-length ratios less than

0.45.

They are not applicable to twin screw ships. Since, as explained above, the data apply strictly only to models at model self-propulsion point, the same must be said of the derived equations.

The coefficients in the equations are tabulated only for the ship lengths 400,

_500,

600, 800 and 1000 feet. It is a valid procedure to interpolate (or even extrapolate to a small degree) to obtain estimates for other ship lengths. Vv'hen doing this it is recommended that the interpolation be carried out between final estimates, not between individual coefficients in the equations. Interpolation for intermediate sea states is best made in the same way, but interpolating on a base of significant waveheight, not Beaufort Number.

Although the equations themselves give the performance in terms of dimensionless parameters such as length-beam ratio or speed-length ratio, this in no way prevents their use to investigate the effects of changing beam or speed explicitly or maintaining constant beam or speed when investigating the effects of changing length. The form of the equations enables the effects of changing two parameters at _{any one ship length} to be added to give the effect of simultaneous variation in the two parameters.

3. APPLICATION OP THE ESTIÎ4ATING EQUATIONS TO A CARGO LINER FORM

The form chosen for this example is that of _{a fine} cargo liner with a nominal service speed of 21 knots. The basic design parameters for this form are given, together with the range over which they are varied, in Table I

TABLE I

Speed

(Knots)

The basic form has a bulbous bow.

The ranges of beam and draught correspond to the beam and draught of geosims of the basic form 440 feet and 600 feet

long between perpendiculars, and the ranges of the other para-meters have been chosen to include a wide variation of practical possibilities. The speed range extends from one knot above

the service 5peed down to the lowest speed at which the estimates may be expected to apply.

The equations were used to estimate significant pitch and heave and mean increase in delivered horsepower required to maintain speed for each of the four sea states corresponding to Beaufort Numbers

_5,

6,

₇ and 8. The results of variations in each design parameter in turn were calculated for the _range of ship length. _{Sorne of the combinations of beam and length,} and draught and length were outside the range of the data _upon which the equations were based, and the regions in which _this is the case are indicated by dotted lines in the figures des-cribed below. Except for the investigation into the effects of changing speed all the calculations were carried out for a speed of 21 knots. Basic Forni Range of Variation L 521 440 - 600 B 77.50

65.45 -

89.25 T 29.92 25.27 -

34.46

LCB 1.73A 2.73A - 0.73A

CB 0.592 0.552 - 0.632

0.730 0.705 - 0.755

The estimated performance of the basic form is shown plotted to a base of speed in Figures 1 and 2 for the motions and power increase respectively. As may be anticipated from the form of the estimating equations the heave and power in-crease inin-crease linearly with speed, while pitch shows a very small non-linear speed effect.

Also shown in Figure 2 is a line representing the power difference, in still water, between the power at 21 knots and the power at the lower speeds. The abscissae of the inter-sections between this line, and. the lines showing power

increase in waves, are the speeds obtained in waves with the power required to drive the ship at 21 knots in still water. The differences between these speeds and 21 knots are the speed losses which are shown plotted to a base of significant waveheight in Figure 3. The magnitudes of the speed losses are similar to those obtained from an unpublished analysis of data collected during a voyage of a ship built to the lines of the basic form used in this example.

Because speed losses depend not only on the power increase due to waves but also on the character of the curve of power plotted against speed in still water, the effects of variations in ship form on the speed loss will not be considered in this pape

The effects of increasing sea severity on ships of three different lengths are shown in Figures 4 and 5. It is em-phasised that the ships differ only in length and are NOT

geosims. The motions of the longer ships are less throughout. and the effects of increasing sea severity are similar for all three ship lengths.

The power increase depends much less on ship length than. do the motions. In sea states with significant waveheight

less than about 14 feet the longer ship shows a slightly smaller power increase, but the rate of change of power increase with significant waveheight is greater, so that power increase

increases with ship length for significant waveheights _{more than} about 18 feet.

-9-This complicated behaviour is partly due to the variation of the coefficients in the estimating equations with length and Beaufort Number; partly due to changes in

length-beam, length-draught and speed-length ratios, as length is changed and beam, draught and speed maintained

3'

constant; and partly due to the L 2 factor which converts the dimensionless power increase given by the equations into a power increase in horsepower.

Figure 6 shows the effect of changing beam for waves corresponding to Beaufort 7. Unfortunately lack of space prevents a demonstration o± the effects of changing the

design parameters at all Beaufort numbers, but the results for Beaufort 7 are typical. In the figure significant pitch and heave and mean power increase are plotted to a

base of length between perpendiculars for three values of beam.

Increasing beam is shown to increase power increase, decrease pitch and have very little effect _{on heave. The} combined effects of changing length and beam subject to a restriction of constant displacement are indicated by the dashed lines in the figure. _{Under these conditions the}

power increase becomes smaller as length increases, reversing the trend with length found when length alone was changed for ships larger than 500 ft. _{A similar decrease of the motions} as length increases with constant displacement maintained by reducing the beam was found by Vassilopoulos _{(Reference 6)} in a theoretical analysis.

The effects of draught are shown in _{Figure 7. The} deeper draught corresponds to greatest motions, _{but changing} draught has very little effect _{on power increase. Increasing} length and decreasing draught simultaneously _{in order to} main-tain constant displacement results in a rapid decrease of both motions as length is increased. _{This trend is again confirmed} by the theoretical analysis carried out _{by Vassilonoulos.}

Because of the interaction between the effects on the power increase of draught and the presence or absence of a bulbous bow, the effect of removing the bulb has been in-vestigated at each of three draughts and the results are

shown in Figure 7. The form without a bulbous bow has a smaller power increase than the form with a bulbous bow and changing draught has a greater effect in the former case.

Figures 8, 9, 10 and il show the effects of variations in block and waterplane area coefficients, longitudinal

position cl' the centre of buoyancy and longitudinal radius of gyration.

Because block coefficient enters the estimating equations for power increase as (CB - 0.5), the effect of block

co-efficient in the power increase is quite negligible for forms with block coefficients of about 0.6. Increasing block

coefficient increases pitch and heave, which are reduced by increasing the waterplane area coefficient. This effect implies that a V shaped section should give smaller motions than U shaped sections, and is confirmed by two independent series of model experiments (References 3 and lo) designed to investigate specifically the effects of U and V bows on

performance in waves. If the block coefficient is reduced as length is increased so that the displacement is maintained constant, the effect of changing length on the motions is

much less than when just length alone is changed. _{Vassilopoulos} (Reference 6) found very little effect on the motions in a

theoretical analysis in which longitudinal prismatic coefficient was reduced as length was increased. Moving the longitudinal position of centre of buoyancy forward increases heave and

decreases the pitch, trends also found by Ewing in _{a theoretical} analysis (Reference 7). The power increase also becomes

larger as the longitudinal position of the centre of buoyancy moves forward. Reducing the radius of gyration has a bene-ficial effect on both motions and power increase.

4. APPLICATION OF TF ESTIMATING EQUATIONS

TO A TANKER FORM

The basic design parameters of' a tanker with a service speed of' 16 knots are given in Table II below together with the ranges over which the design parameters are varied.

TABLE II

The basic form does not have a bulbous bow.

The ranges of' beam and draught correspond to the beam and draught of' geosims of the basic form 700 and 1050 feet long between perpendiculars and the variation in the remaining parameters have been chosen to cover a very wide range of

practical possibilities. The speed range extends from one knot above the service speed down to the lowest speed to which the estimating equations apply.

Figures 12 and 13 show the performance of' the basic form plotted to a base of' speed. Whilst the general picture is riot dissimilar to that obtained from the cargo vessel, the motions are much smaller, and the power increase greater.

For this reason some of the scales used in the figures illustrating the estimated performance of the tancer are different from those for the cargo vessel. _{Speed has only} a very small effect on the motions and on the power increase

Basic Form Range of' Variation L 875 700 - 1050 B 128.0 _{102.4 - 155.6} T 48.88 39.10 - 58.66 LCB 2.O5F 1.O5F - 3.05F CB 0.811 0.761 - 0.861 Cw 0.888 0.863 - 0.913 K /L yy 0.25 0.23 - 0.27 Speed (Knots) 16 14 - 17

except at the higher Beaufort Numbers. A curve of power differences in still water based on 16 knots has been used to derive speed losses which are shown plotted to a base of significant waveheight in Figure 14. The low range of wave-heights for which it is possible to estimate the speed loss emphasises the importance ci' carrying out model experiments in waves not only at the service speed but also at bhe lower speeds at which the ship would be forced to operate in the more severe sea states if a full interpretation is required.

Estimated curves of performance for three ship lengths are plotted to a base of significant waveheight in Figures 15 and 16 for a ship speed of 16 knots. The motions of the longest ships are in all cases smallest, a trend which is

also true of the power increase with significant height greater than 15 ft. The decrease of the power increase with length is also shown in Figure 17 for Beaufort Number 7 (significant waveheight 18.8 feet), and is opposite to the trend found for the fine form, and emphasises the necessity to carry out a

comprehensive set of calculations in any particular case rather than depending on generalisations from single published

examples.

Figure 17 shows the large effect of beam on power increase, and the simultaneous variation of length and beam at constant displacement, which results in a rapid reduction in power increase as length increases. The effect of changing beam on the motions is smaller than on the power increase, and in the opposite sense, the greatest beam being associated with smallest motions.

The effect of changing draught is shown in Figure 18, which also shows the effect on power increase of adding a

bulbous bow at each of three draughts. In the part of the figure showing power increase the lines showing simultaneous variations of draught and length and the dotting of the lines

indicating draught and length combinations outside the range of the data on which the equations were based have been

omitted for the purpose of clarity. The bulb has a smaller effect on the longer ships and at the shallower draughts.

13

-In no case is the effect of adding the bulb very great. Increasing draught increases both motions but the effect on pitch is much less than that on heave.

Block coefficient has an important effect on power increase as shown in Figure 19, which is to be contrasted with the absence of an effect on the cargo liner form. The

curves illustrating the effects of changing length and block coefficient simultaneously, reducing block coefficient as length increases in order to maintain constant displacement,

show a steep drop as length changes from

₈₅₀

ft. to ₉₂₅ ft.

These effects are due to the term (CB

5)5

in the estimating equations for power increase having an increasingly important effect as block coefficient is increased beyond a value of about

0.75.

Figures 20 and 21 show the effects of changing water-plane area coefficient and longitudinal position of the centre of buoyancy. These effects become generally smaller as length increases, a trend which is particularly apparent with the

effect of radius of gyration on pitch, Figure 22.

5. T}- MOOR-MURDEY EQUATIONS AS A STANDARD

Analyses such as those described in Sections 3 and 4 above give the naval architect basic design information which may he used in conjuiaction with all the other design considera-tions in order to make a choice of basic design parameters

for a particular ship. Having done this, there are infinite variations possible in the final hull form which will undoubtedly have effects on the seakeeping characteristics of the ship.

The most reliable way to establish the performance of the chosen ship form is to carry out model experiments. _{Having done this} a standard is required against which the performance of the model may be compared and a judgement made as to whether the form is good, bad or average.

The Moor-4urdey equations give the average performance of models with a particular set of design parameters, all of which are decided before the hull form is designed. Thus

estimates from the equations are suitable standards against which the performance of the particular form chosen may be

compared.

REFERENCES

Moor, D.I. and Murdey, JD.C.

Moor, D.I. and Murdey, D.C.

Motions and propulsion of single screw models in head seas.

Trans. R.I,N.A., Vol. 110,

1968, p.403.

Motions and propulsion of single screw models in head seas, Part II.

Trans. R.I.N.A., Vol. 112,

1970,

p.121.

Some effects of hull form on ship performance in a seaway. S.N.A.N.E., New York,

_1967.

Vossers, G., : Experiments with Series 60

Swaan, W.A. and models in waves.

Rijken, H. Trans. S.N.A.M.E., Vol.

68,

1960, p.364.

Swaan, W.A. : The influence of principal dimensions on ship behaviour in irregular waves.

International Shipbuilding Progress, Vol.

8,

1961, p.248.

Vassilopoulos, L. : Design data on motions in random

seas of Series 60 ships, Part 1. Department of Naval Architecture

and Marine Engineering, Massachusetts Institute ol' Technology Report

66-6, 1966.

Ewing, J.A. : The effect of speed, forebody shape and weight distribution on ship motions.

Trans. R.I.N.A., Vol.

_109,

1967, p.337.

Stefun, G.P. : The influence of ship form on

pitch and heave amplitudes. David Taylor Model Basin Report

1235, 1958.

Scott, J.R.

10. Swean, W.A. and Vossers, G.

15

-A sea spectrum for model tests a longterm ship prediction. JOurnal of Ship Research,

Vol. 9, 1965, p.l45.

The effect of forebody section shape on ship behaviour in waves.

Trans. R.I.N.A., Vol. 103,

TABLE III

ESTIMATING EQUATION FOR SIGNIFICANT PITCH

G

=

+ A1C

+ A2CB +

A3L/B + A4L/T + A5LCB + A6K/L + A7v//r

+ A0 Beaufort A A A A A Number LBP o 1 2 3 4 A5 A6 A7 5 400 3.65 -16.19 9.10 0.222 -0.0510 -0.069 14.8 7.60 500 3.96 -12.39 6.97 0.203 -0.0329 -0.068 5.0 5.76 600 3.38 - 8.21 4.43 0.165 -0.0167 -0.057 0.2 5.76 800 2.03 - 3.59 1.86 0.078 -0.0037 -0.052 -1.7 1.40 1000 1.17 - 1.61 0.85 0.038 -0.0001 -0.018 -1.7 0.40 6 400 5.33 -22.33 12.53 0.260 -0.0745 -0.095 25.2 9.09 500 5.07 -19.72 11.17 0.264 -0.0604 -0.093 15.7 8.86 600 5.12 -15.32 8.58 0.247 -0.0407 -0.085 6.1 6.94 800 3.66 - 7.87 4.15 0.160 -0.0139 -0.058 -0.9 3.38 1000 2.34 - 4.25 2.25 0.090 -0.0052 -0.037 -1.9 1.62 7 400 6.89 -26.65 15.00 0.317 -0.0923 -0.110 31.3 10.41 500 5.59 -24.45 13.78 0.315 -0.0803 -0.104 25.5 10.79 600 5.49 -21.45 12.11 0.309 -0.0652 -0.101 16.5 9.93 800 4.94 -13.28 7.25 0.243 -0.0310 -0.083 3.1 6.11 1000 5.57 - 7.83 4.13 0.155 -0.0138 -0.057 -0.4 3.28 8 400 8.74 -30.59 17.25 0.357 -0.1056 -0.124 36.5 11.54 500 7.17 -28.17 15.79 0.339 -0.0952 -0.113 32.1 11.33 600 6.16 -25.93 14.62 0.335 -0.0844 -0.113 26.2 11.36 800 5.95 -19.68 11.09 0.300 -0.0553 -0.104 10.9 9.00 1000 4.89 -12.83 6.98 0.236 -0.0291 -0.082 2.8 5.77

TABLE IV

ESTIMATING EQUATION FOR SIGNIFICANT HEAVE

Z

=

A

+ A1C

+ A2CB +

A3L/B + A4(L/TY1 + A5LCB + AK /L + AV/A/

o

oyy

I

Beaufort Number A A LBP o 1 A2 A3 A4 A5 A6 A7 5 400 -0.18 -13.30 4.62 0.100 78.6 0.205 23.5 3.83 500 0.96 -12.54 3.63 0.175 65.4 0.204 19.2 2.50 600 2.06 - 9.66 2.01 0.191 41.8 0.163 13.6 1.25 800 2.38 - 5.29 0.63 0.146 13.6 0.083 6.5 0.02 1000 2.18 - 2.67 0.04 0.097 0.3 0.035 2.4 -0.49 6 400 1.56 -18.19 6.52 0.066 108.0 0.262 31.5 5.79 500 0.49 -20.50 7.11 0.145 115.9 0.306 34.6 5.31 600 1.69 -18.71 5.38 0.234 97.0 0.299 29.3 3.70 800 3.17 -12.36 2.40 0.244 48.9 0.201 17.7 1.29 1000 3.12 - 7.90 1.11 0.197 22.9 0.122 10.5 0.15 7 400 5.31 -21.65 7.69 0.073 124.5 0.327 33.1 7.10 500 1.46 -24.91 8.91 0.140 146.5 0.371 42.8 7.75 600 0.85 -26.17 8.72 0.235 149.0 0.409 43.8 6.89 800 3.41 -20.94 5.07 0.344 100.7 0.349 31.0 3.62 1000 3.80 -15.18 3.08 0.307 60.3 0.244 21.6 1.72 8 400 10.92 -24.68 8.42 0.061 135.4 0.413 33.6 7.96 500 6.06 -28.14 9.72 0.109 162.8 0.440 45.0 9.21 600 2.53 -31.72 11.36 0.180 183.6 0.473 53.4 9.65 8GO 3.13 -31.20 9.33 0.321 169.7 0.512 48.7 7.26 1000 4.60 -25.12 6.10 0.403 118.3 0.413 36.9 4.33

TABLE V

ESTIMATING EQUATION FOR

AN INCREASE IN DELIWERED HORSEPOWER

=

1.74 x

io_6

x

+

Al(CB-0.5)5 + A2L/B + A3L/T + A4LCB + A5K/L +p(A6 + A7L/T) + A8VNT

L3rA0

Beaufort A A A A A A A A Number LBP o 1 2 3 4 5 6 7 5 400 -0.615 41.4 -0.115 0.0091 0.040 2.91 0.209 -0.0073 500 -0.408 28.5 -0.063 0.0086 0.026 1.68 0.109 -0.0037 0.891 600 -0.194 16.5 -0.034 0.0074 0.015 0.70 0.060 -0.0021 0.454 800 -0.044 6.6 -0.011 0.0034 0.005 0.11 0.023 -0.0009 0.128 1000 -0.016 2.8 -0.004 0.0014 0.002 0.03 0.009 -0.0004 0.041 6 400 -1.044 80.0 -0.247 0.0179 0.076 5.44 0.470 -0.0172 3.111 500 -0.919 63.2 -0.166 0.0149 0.059 4.22 0.297 -0.0104 600 -0.626 45.0 -0.101 0.0140 0.042 2.59 0.175 -0.0060 800 -0.185 19.0 -0.037 0.0092 0.017 0.61 0.069 -0.0026 1000 -0.066 9,4 -0.015 0.0047 0.007 0.17 0.032 -0.0013 7 400 -1.358 126.0 -0.394 0.0285 0.110 7.77 0.753 -0.0283 4.761 500 -1.308 97.1 -0.288 0.0223 0.092 6.59 0.539 -0.0195 600 -1.113 78.1 -0.201 0.0191 0.073 5.08 0.357 -0.0125 800 -0.496 39.9 -0.085 0.0159 0.037 1.89 0.153 -0.0054 1000 -0.179 20.4 -0.039 0.0098 0.017 0.58 0.075 -0.0029 8 400 -1.630 191.8 0.585 0.0413 0.150 10.58 1.061 -0.0405 500 -1.586 140.0 -0.431 0.0326 0.125 8.76 0.820 -0.0306 600 -1.481 112.2 -0.326 0.0264 0.105 7.41 0.605 -0.0219 800 -0.984 72.4 -0.171 0.0211 0.067 4.23 0.301 -0.0105 1000 -0.459 39.5 -0.084 0.0166 0.036 1.73 0.152 -0.0055

TABLE VI

ESTIMATING EQUATION FOR MEAN INCREASE IN PROPELLER TFUST

5T

= 0.253 x io_6 x + Al(CB_o.5)5

+ A2L/B + A3L/T + A4LCB + A5K/L +(A6 + A7L/T) + A8V/rj

L3[A0 Beaufort A A, A2 A3 A4 A5 A7 A8 Number LBP o 5 400 -0.089 13.8 -0.081 0.0031 0.013 2.69 0.148 -0.0053 0.540 500 -0.054 10.2 -0.044 0.0040 0.008 1.62 0.075 -0.0026 0.258 600 0.004 6.0 -0.025 0.0043 0.004 0.78 0.039 -0.0014 0.091 800 0.013 2.7 -0.008 0.0025 0.001 0.19 0.017 -0.0007 0.009 1000 0.001 1.3 -0.003 0.0011 0.000 0.06 0.008 -0.0004 0.001 6 400 -0.052 25.4 -0.178 0.0067 0.027 5.13 0.339 -0,0127 1.144 500 -0.134 21.4 -0.117 0.0058 0.020 3.92 0.215 -0.0078 0.767 600 -0.076 16.1 -0.071 0.0068 0.012 2.50 0.125 -0.0044 0.405 800 0.022 7.2 -0.028 0.0059 0.004 0.77 0.047 -0.0018 0.076 1000 0,012 3.9 -0.012 0.0033 0.002 0.28 0.024 -0.0010 0.014 7 400 0.074 40.3 --0.296 0.0118 0.039 7.72 0.535 -0.0205 1.763 500 -0.106 31.4 -0.207 0.0086 0.032 6.20 0.390 -0.0145 1.325 600 -0.155 26.7 -0.141 0.0079 0.024 4.76 0.258 -0.0093 0.909 800 -0.013 14.3 -0.062 0.0090 0.010 1.98 0.107 -0.0039 0.277 1000 0.039 7.7 -0.030 0.0065 0.004 0.74 0.053 -0.0021 0.072 8 400 0,275 62.9 -0.460 0.0186 0.055 11.34 0.746 -0.0292 2.478 500 0.035 45.1 -0.321 0.0137 0.044 8.61 0.585 -0.0223 1.918 600 -0.112 36.8 -0.235 0.0107 0.036 7.02 0.438 -0.0163 1.480 800 -0.112 25.5 -0.120 0.0101 0.020 4.08 0.215 -0.0078 0.708 1000 -0.002 14.4 -0.061 0.0098 0.009 1.91

O1O8

-0.0040 0.250

TABLE VII

ESTIMATING EQUATION FOR MEAN INCREASE IN PROPELLER TORQUE

=

0.567 x

io6 xL4[A0

+ A1L/B + A2L/T ± A3K/L + A4P/L +(A5 + A6L/T) + A7V/IT

Beaufort Number LBP A o A 1 A3 A4 A5 A6 5 400 -0.582 -0.414 -0.0041 12.07 35.4 0.754 -0.0230 500 -0.303 -0.232 0.0059 7.00 25.6 0.341 -0.0089 600 -0.047 -0.124 0.0114 3.24 16.8 0.151 -0.0037 800 0.084 -0.044 0.0067 0.85 5.4 0.036 -0.0008 1000 0.020 -0.015 0.0030 0.35 1.6 0.015 -0.0004 -0.015 6 400 -0.735 -0.906 -0.0098 23.49 68.2 1.712 -0.0552 500 -0.921 -0.606 -0.0023 17.85 53.3 1.021 -0.0299 600 -0.599 -0.368 0.0103 11.21 40.4 0.523 -0.0132 800 -0.035 -0.137 0.0160 3.39 18.5 0.142 -0.0031 1000 -0.072 -0.062 0.0094 1.30 6.7 0.055 -0.0012 7 400 0.367 -1.496 -0.0151 34.01 102.8 2.773 -0.0929 500 -0.779 -1.056 -0.0092 27.92 82.9 1.955 -0.0621 600 -0.872 -0.732 0.0001 21.15 66.5 1.234 -0.0364 800 -0.233 -0.310 0.0206 8.54 39.0 0.410 -0.0104 1000 0.078 -0.143 0.0175 3.29 18.4 0.161 -0.0040 8 400 2.559 -2.316 -0.0267 47.71 140.4 3.830 -0.1301 11.894 500 0.068 -1.621 -0.0172 38.18 115.8 2.992 -0.0990 600 -0.814 -1.195 -0.0074 31.46 95.0 2.178 -0.0688 800 -0.667 -0.623 0.0121 17.98 63.7 0.972 -0.0272 1000 -0.166 -0.308 0.0238 8.22 38.0 0.410 -0.0106

TABLE VIII

ESTIMATING EQUATION FOR MEAN INCREASE IN PROPELLER RATE OF ROTATION

=

Beaufort Number

1o1.3/,/rA LBP

+ A1L/T + A2K/L + A3P/L + A4L/D + A5P/D

A A o 1 A2 A3 A4 A5 + A7L/T) + A8v/ A6 A7 A8 5 400 - 7.217 0.0938 8.86 112.3 0.247 - 5.88 1.027 -0.0379 -0.632 500 - 5.024 0.0692 4.76 95.1 0.186 - 4.63 0.627 -0.0239 -0.787 600 - 3.081 0.0517 1.41 72.8 0.126 - 3.34 0.416 -0.0170 -0.752 800 - 1.298 0.0222 -0.02 37.3 0.056 - 1.60 0.186 -0.0082 -0.373 1000 - 0.583 0.0086 -0.03 17.3 0.024 - 0.72 0.078 -0.0036 -0.151 6 400 -14.357 0.2030 16.83 223.7 0.491 -11.87 2.410 -0.0914 -1.173 500 -10.976 0.1436 12.86 178.7 0.382 - 9.19 1.515 -0.0563 -1.121 600 - 7.944 0.1116 7.19 152.6 0.296 - 7.39 1.015 -0.0389 -1,283 800 - 3.612 0.0629 0.90 93.1 0.152 - 4.16 0.511 -0.0216 -0.971 1000 - 1.828 0.0303 0.09 51.5 0.077 - 2.21 0.260 -0.0115 -0.503 7 400 -21.464 0.3378 24.85 319.5 0.730 -17.41 4.156 -0.1624 -1.936 500 -17.252 0.2597 20.40 270.1 0.592 -14.23 2.755 -0.1040 -1.535 600 -13.434 0.1804 15.28 223.4 0.473 -11.42 1.869 -0.0702 -1.515 800 - '7.299 0.1167 4.37 161.3 0.289 - 7.51 0.989 -0.0397 -1.576 1000 - 3.898 0.0669 0.72 102.8 0.164 - 4.54 0.555 -0.0237 -1.037 8 400 -29.137 0.5085 37.96 363.6 0.957 -21.55 6.371 -0.2542 -2.881 500 -24.083 0.3708 27.64 364.3 0.823 -19.62 4.465 -0. 1736 -2.258 600 -.19.782 0.2775 22.92 314.5 0.683 -16.47 3.148 -0.1195 -1.883 800 -12.568 0.1770 11.97 232.2 0.462 -11.41 1.699 -0.0651 -1.871 1000 - 7.390 0.1202 3.93 168.8 0.295 - 7.79 1.027 -0.0417 -1.662

4

2

o

VARIATION OF ESTIMATED MOTIONS OF BASIC

CARGO LINER FORM VflTH SHIP SPEED

SEAU FORT N U M B E R 7 o 5 BEAUFORT N U M E E R 8 7 6 5 I I I

-12 14 16 18 20 22

SHIP SPEED (KNOTS)

s O e IO 8 6

z

20 ¶5

lo

15,000 OpOO

5,000

O 12 14 16 IB 20 22 SPEED LOSS (KNOTS) 6 4

VARIATION OF ESTiMATED POWER INCREASE

_OF

BASIC CARGO LINER FORM WITH

_{SHIP SPEED}

POWER DI FFERENCE IN STILL WATER BEAUFORT N U M BE R 8 5 N N

\

-k---

\

SHIP SPEED (I<NoTs)

ESTIMATED SPEED LOSS OF BASIC

CARGO LINER FORM

SIGNIFICANT WAVEHEIGHT (FEET)

FIGURE 2

VARIATION OF ESTIMATED MOTIONS OFA

CARGO LINER FORM WITH SIGNIFICANT WAVEHE1GHT

SHI P SPEED 21 ¡(NOTS

z

8 LBP 44 0 52 1

600

L BP

440

521

600

5 iO 15

20

₂₅ SIGNIFICANT WAVEHEIGHT(FEET)

e

lo

25 20 15

Io

20,000

15,000

10,000

VARIATION OF ESTIMATED POWER INCREASE OF A

CARGO LINER FORM WITH SIGN1FICANT WAVEHEIGHT

SHIP SPEED 21 KNOTS

5,000

o

-0

5 IO 5

LB?

440

521

600

J-SIGNIFICANT WAVEHEIGHT(FEET) 20 25

FIGURE 5

PERFORMANCE OF A CARGO LINER FORM

BEAUFORT NUMBER 7

SHIP SPEED 21 KNOTS

CONSTANT BEAM CONSTANT DISPLACEMENT

I4O0

2,000

10,000

e

B 7 5 B

8925 "

7750"

654 5

/

I,

B

6545

7750

G925 s B 65'45

/77.50

/ 8925

LBP

N

z

_18

16

400

450

500

5S0

600

14 12

FIGURE 7

EFFECT OF VARIATIONS IN DRAUGHT ON THE ESTIMATED

PERFORMANCE OFA CARGO LINER FORM

BEAUFORT NUMBER 7

SHIP SPEED 21 KNOTS

CONSTANT D.AUGHT WITh' BULBOUS BOW CONSTANT DRAUGHT WITHOUT BULBOUS BOW CONSTANT DISPLACEMENT 14,000 I 2,000 10,000

8,000

G e 6 5

400

T

252 7\

2992\

34'46

.

-.

.-2-

T

_/

2527 450

2992

3446

500

LBP

34'46 2)-92

2527

550 T 34' 46 2992 25' 27

z

Is 16 14 2

600

e

B

7

6

5

CONSTANT BLOCK oeEFFICIENT

--

CONSTANT DISPLACEMENT 14,000 I 12,000 t 0,000 Ca

O'632\

0592

O552 C3

0632

/0552

/

CB

,0632

0592

552 14 12

ESTIMATED PERFORMANCE 0F A

CARGO LINER FORM

BEAUFORT NUMER 7

SHIP SPEED 2! KNOTS

400

450

500

550

600

7 IB

EFFECT OF VARIATIONS IN WATERPLANE AREA COEFFICIENT

ON THE ESTIMATED MOTiONS OFA CARGO LINER

FORM

BEAUFORT NUMOER 7

SHIP SPEED 2 kNOTS

cw

Q705

0730

0755

cw

0'705

/

/ 0755

LBP

z

12 IB 16 14

FIGURE 9

5 I

400

450

530

550

600

CENTRE OF 6OUYACY ON THE ESTIMATED

PERFORMANCE OF A CARGO LINER FORM

BEAUFORT NUMBER 7

SHIP SPEED 21 KNOTS

7 o 5 LCB

073 A

I 734

2 73A

L BP LC B

073A

I 73A 2 73A LCB

273A

/ .734

/ 073A

'o 14 2

400

450

500

550

600

14,000

¡2,000

10,000

o

8

z

Is

14,000

12,000

10,000

EFFECT OF VARIATiONS IN LONGITUDINAL

RADIUS OF GYRATION ON THE ESTIMATED

PERFORMANCE OF A CARGO LINER

FORM

BEAUFORT

NUMaE

7

SHIP SPEED 2 KNOTS

o B

7-0270

02 50\

0230

-

_18

Kyy/L

0270

02 50

0230

K.yy/L

0270

0250

₀₂₀

z

16 I4 12

FIGURE 11

5f

I

400

450

500

550

600

Lß P

VARIATION OF ESTIMATED MOTIONS OF BASIC

TANKER FORM WITH SHIP SPEED

3 2 O 12 'O 6 4 2 O BEAUFORT N U M B E R 7 6 s

-

BEAUFORT NUM BER 8

7.

-6 5 H 14 15 16 '7

SHIP SPEED (KNOTS) G

SPEED LOSS

(KNOTS)

2

VARIATION OF ESTIMATED PO4IER INCREASE OF

BASiC TANKER FORM WITH SHIP SPEED

P

30,000

I 25,000

2OOO

IQ000

5,000

O POWER DIFFERENCE IN STILL WATER N N 14 15 16

SHIP SPEED (KNOTS)

BEAU FORT NUMBER 8

Ï

7 17

ESTIMATED SPEED LOSS OF BASIC

TANKER FORM

0

5 IO 5 20

SIGNIFICANT WAVEHEIGHT (FEET)

25 FIGURE 13

FIGURE 14

s N

N

LBP

875

loso

LßP

700

875

1050

4

12

Io

8 o 4 2

o

TANKER FORM WITH SGNIFICAT WAVEHEIGHT

SHIP SPEED 16 KNOTS

z

o

5

Io

_{15 20}

SIGNIFICANT WAVEHEIGHT (FEET)

e

5 4 3 2

o

6P

25,000

20,000

15,000 10,000

5,000

VARIATION OF ESTIMATED POWER INCREASE

OFA

TANKER FORM WITH S1GNIFICANT VJAVEHEIGHT

SHIP SPEED 16 KNOTS

T 5 lO 15 LB P

700

875

losO

20 SIGNiFICANT WAVEHEIGHT (FEET)

EFFECT OF VARIATIONS IN BEAM OF'S THE ESTIMATED

PERFORMANCE OF A TANKER FORM

BEAUFORT NUMBER 7

SHIP SPEED

f

KNOTS

2 CONSTANT BEAM

- CONSTANT DISPLACEMENT

B 153 6 I28

N

B

/i024

,123'O

i536

N

-.-

\

B 1024

I280

Z

/1536

'1024

700

800

900

1000 1100 LE3P 3P

20,000

I 5,000 10,000

z

10

FIGURE

EFFECTOF VARIATIONS IN DRAUGHT ON THE ESTIMATED

PERFORMANCE OA TANKER FORM

ßEAUFORT NUMOER 7 SH;P SPEED 16 KNOTS

CONSTANT DRAUGHT WITHOUT BULBOUS BOW

- CONSTANT DRAUGHT WITH BULBOUS BOW

CONSTANT DISPLACEMENT

20,000

5P

1 5,000

T 391 O iOpOO 48.88 5B66

T

58.66/"

4888

3910

LBP

T

5866

48 88

/ 910

T

39.10

4888

58.66 1100

800

900

1000

z

6 4

ESTIMATED PERFC:ANCE OF A TANKER

FORM

BEAUFORT NUM3ER 7

SHIP SPEED ló ZNOTS

CONSTANT BLOCK COEFFICIENT

CONSTANT DISPLACEMENT

700

CB

,08I I

o 76 I

c

0861 O8I1 O76I -O76I

800

₉₀₀

IO

₁₁₀₀

LBP

e

4 3 2

z

e 6 4

20,000

I 5,00C t O,OOc

-

_{FIGURE 20}

EFFECT OF VARIATIONS IN WATERPLANE AREA COEFFICIENT

ON THE ESTIMATED MOTIONS OF A TANKER FORM

BEAUFORT NUMBER 7

SHIP SPEED 16 KNOTS

o

4

700

800

900

LBP

Cw

O863

888 O91 3 Cw

0863

0888

0913

coo

z

-Io

i

1100 8 6

EFFECT OF VARIATIONS IN LONGITUDiNAL POSITION OF

CENTRE OF BOUVANCY ON THE ESTIMATED

PERFORMANCE CF A TANKER FORM

c

Arr

t' r t t t

SHIP SPEED 16 KNOTS

2OOO

I 5,OO( IO,0OC

e

4 3 2 LC

305 F

205 F

105F

LC B

305 F

205F

I OSF LCB

I O5F

2O5F

205F

4 8 o

700

800

900

1000

HO0

LBP

z

IO

I.,

20,000

15,000

10,000

3

E FF EC T OF VAR! AT ION S

IN LONG TUDI NAL

RADIUS OF GYRATION ON THE ESTIMATED

PERFORMANCE C.A TANKER FORM

BEAUFORT NUMBER 7

SHIP SPEED t6IZNOTS

N

027

023

NN

L KyyíL

0.27

025

o 2 3

z

Io

B 6 4

700

800

900

1000

1100

FIGURE 22