Manoeuvring experiments using two geosims of the Esso Osaka

U

National Maritime Institute

Manoeuvring Experiments using

Two Geosims of the <Esso Osaka

by

I W Dand and D B Hood

NMI R163

May 1983

National Maritime institute

Feitham

Middlesex TW14 OLQ

Te1:0-977 0933 Telex:263118

MsIIwsg 2, 2628 CD Dellt

LO$5àiwi.F O15.7816

This report is NNI Ltd Copyright but may be freely reproduced for all purposes other than advertising providing the source is acknowledged.

MANOEUVRING EXPERIMENTS USING TWO GEOSIMS OF THE 'ESSO OSAKA'

BY

I W DAND and D B HOOD

Summary

Two geometrically-similar models (geosims) of the VLCC 'Esso Osaka' have been used in a series of constrained and free-running manoeuvring experiments in various water depths. Forces, moments and trajectories have been measured in order to derive the coefficients needed for the NMI Cruising Speed

Manoeuvring Simulation model. Detailed results are presented and discussed and some limited simulations are compared with both free-model performance and that of the ship. Some conclusions are drawn regarding scale effect on manoeuvring predictions derived from model measurements.

CONTENTS Page Introduction 1 Experimental Details 1 2.1 Ship Models 1 2.2 The Experiments 3 2.3 Analysis 5

Results Obtained and Discussion

3.1 Constrained Model Experiments 6

3.1.1 Resistance Experiments 6

3.1.2 Bollard Pull Experiments 8

3.1.3 Oblique Tow Experiments 8

3.1.4 Rudder Angle Experiments 9

3.1.5 Combined Drift and Rudder Angle Experiments 9

3.1.6 Rotating Arm Experiments 10

3.2 Free Running Experiments 11

Manoeuvring Coefficients and Simulation 13

4.1 General 13

4.2 Simulation Model and Manoeuvring Coefficients 14

4.2.1 Linear Motion Coefficients 16

4.2.2 Rotary Motion Coefficients 19

4.2.3 Remaining Coefficients 19 4.3 Simulation Results 20 General Discussion 22 Conclusions 24 References 25 Acknowledgements 26 Nomenclature 27

Introduction

In July and August 1977 a comprehensive series of manoeuvring trials was carried out on the 278,000dwt tanker 'Esso Osaka' in the Gulf of Mexico (ref. 1). A

variety of manoeuvres was carried out in three water depths - deep, (water depth (h)/at-rest draught (T) = 4.2), medium (h/T = 1.5) and shallow (h/T = 1.2). For all trials the ship was loaded to a draught very close to the Summer Freeboard waterline and measurements were made of ship track, engine r.p.m., forward speed,

rudder angle, lateral speed, rate of turn and change of heading.

The compendium of results thus produced, while of interest in their own right, also provided a valuable source of data with which to compare predictions based on measurements made with geometrically-similar models (geosims). Accordingly the Maritime Administration of the United States Department of Transport initiated the Joint International Manoeuvring Programme (JIMP) to encourage ship model

basins throughout the world to test models of the 'Esso Osaka' on a co-operative basis using the full-scale data for comparative purposes. The National Maritime

Institute, with funding from the Maritime Technology Committee of the UK

Department of Industry took part in JIMP; this report describes the work done and presents some of the results.

Prior to NMI's involvement, model experiments had been carried out at Hydronautics

Inc. (ref. 2) and the Davidson Laboratory of the Stevens Institute in Hoboken, New Jersey. The models used at both these establishments were made available and it was decided that NMI would provide a third geosim. This allowed the Stevens and NMI models to be tested in a complete programme of experiments normally carried out by NMI to obtain manoeuvring coefficients. It therefore provided a unique opportunity to study the effect of model scale on measured manoeuvring data.

Experimental Details

2.1 Ship Models

-2

to be too large for all except the largest of NMI's towing tanks. As this would have restricted experiments to oblique tow and planar motion mechanism tests in deep water only, it was decided in the first instance to concentrate attention on the other two models. However a comparison of all three models and the ship is made in Table 1:

TABLE 1

Item Ship Models

Hydronautics Stevens NMI

Length between perps. L(m) 325.0 7.257 1.625 3.536

Breadth mid, B(m) 53.0 1.183 0.265 0.577

Trial draught, T(m) 21.8 0.487 0.109 0.237

Trim,

t

level level level level

Displacement, volume V (in3) 311,669 3.470 0.0389 0.401

Block Coefficient, CB 0.830 0.830 0.830 0.830

Midship Section Coeff., C, 0.998 0.998 0.998 0.998

Prismatic Coefficient C 0.830 0.830 0.830 0.830

Scale 1:1 1:44.783 1:200 1:91.91

Rudder area! (L.T) 0.0169 0.0169 0.0169 0.0169

Number of rudders 1 1 1 1

Rudder Type balanced balanced balanced balanced

simplex simplex simplex simplex

Number of Propellers 1 RH 1 RH 1 RH 1 RH

Diameter, D (m) 9.10 0.204 0.044 0.099

Blade Area Ratio, B.A.R. 0.682 0.682 - 0.683

Mean Face Pitch, Pm(m) 6.507 0.146 - 0.077

Number of Blades 5 5 4 6

and along the line of the bilge.

A six-bladed stock NMI model screw propeller was fitted whose parameters were similar to those of the full-scale propeller. This was driven by a 75 watt DC printed-armature motor.

The Stevens model was fitted with similar printed-armature motor and both models had rudders which could be set to any required rudder angle, S, in the range

.35° tS 350

For the free-running experiments the NMI model was fitted with proportional radio control of rudder and shaft revolutions. It was also equipped with a heading gyro and a transmitter for the NMI ultra-sonic position-plotting equipment.

Heading signals, drift angle, rudder angle and shaft rpm were telemetered ashore where they were combined with the position-plotting signals to give information on

position, speed, heading, drift angle, rate of turn etc. during the experiments.

2.2 The Experiments

A set of constrained model experiments was carried out on the Stevens and NMI models. Although the results were obtained over a range of drift angles from 00 to 1800, _{we concentrate in this report on experiments and analysis relevant} to the NMI 'cruising speed' simulation model. This is valid for drift angles up to about ± 200 and relates to the case where the ahead or astern velocity

of the ship dominates the motion. This is comprehensively documented in reference 3 and has formed the basic mathematical model used in several UK ship simulators. As it is therefore widely known it seemed appropriate to compare its predictions with ship behaviour and also to use it as a comparison with other, similar, models world-wide. Results from the large drift angle experiments will be reported at a later date.

Accordingly the experiments and parameter ranges considered in this report are given in Table 2. No planar motion experiments were conducted.

4

Experiments 1 to 5 áove were carried oüt.in the

no.2 towing, tank with a deep

water section ll9m long, 6 lm wide and 2 74m deep and a shallow water section

BOrn long whose depth can be varied from zero to

0.. 5Gm., The rotating arm,

experiments were carried. out in. the 30m square

4A tank with a maximum epth

of 2.44m.

. Figure 3 shows the Steven

model under test. on the rotating arm.

ForOes and, moments on the NMI model were

measured using a four-component

strain-gauged dynamometér mounted in.

tie mol and measuring in body axes.

This

instrument

was too large for the Stevens. rode1 so

fot this, surge and sway

forces, together with yaw moment, were initially, measured using threemodu ar

force gauges of 50N capacity.

They wer.e mounted on an earthing beam aboye the

model, the forces being transmitted to them via pins fixed to the force gauges

and lightweight rollers motinted

n the mo1el.

This arrngement was satisfactory

EXPERIMENT

h/1

r*

pRIFr ANGLES

RUDDER ANGLES

S.

1. Resistance and

1.2

0.02-0.12

0.0

0

0.

Propulsion

1.5

0.02-0.13

0.0

0 0

0.02-0.16

0.0

0 0

2. Oblique tow

1.2

0.034

0.0

-25° to +25°

0

1.5

0.051

0.0

-16° tO +16°

0

0.102

0.0

-25° to +25°

.0

3. Rudder angle

1.2

0.34

0.0

0

-30° to +300

1.5

0.068*,0.085**

0.0

0.0

0.102

.

0.0

0.0

4. Bollard Pull

1.2*

0.0

0.0

0.0

.

.15*.

0.0

0.0

0.0

'I

0.0

0,.0

0.0-5. Comb'ned Drift Angle

1.2

0.34

0.0

0° to -20°

-30° to +30°

and Rudder Angle

1.5

.0.068*,0.085**

0.0

0° to -20°

-

0.102

.

0.0

00 to -20°

6: Rotating Arm

1.2*

0.051

0.29-0,79.

-25° to 20°

0

1.5*

0.051

0.29-0.7.9

!' ₀ - -

0.068*,,0.l02**

0.14**_9.79*

U ₀

7. Free Running

. .

1.2*

-

-

-30° to +30°

1.5*

. . .

0.102

. .-

-

.

--.---

. --. .

-N.B. *

= NMI model only

TABLE 2

for sway for.ce and, yaw mome±t, theasurement,:but unsatisfactory. for, the measurement

of surge force.

The surge force gauge was therefore :relaced by a sensitive

arallel-liiik straIn-gauged fiexure.

Freerunning eperiments were run in- the 60m square butdóor thàhoeUvring

ta±-k.

using the NMI model dnlr:.

_{As mentioned in section 2.-i above,' the model was fully}

instrumented, the comp]ete model- and shore-based System being shown

in

Figure 4.

In the constrained mQdel experiments, results were integrated Over a period of 30

seconds to give mean values.. Preliminaiy anal'sis. were. óaried out using a, Commodore

?ET:micro.computerduting the experiments and all non-dimensiona1sèd raw data

storedon floppy di. On-line analysis. of the free-model résults

was

ôàrried out on a Tektronix 4051: systeIn, results being stored

on punched. paper

tape for later more detailed analysis.

2.3

Analysis

The resuith obtained in. the experiments have generally been non-dimensionaliSed

ccording to the following, well-known, scheme using the axis system

á.nd

efin-itions of Figure 5.

x' =X/½pLU,.

Yl = Y/½LU0.

,

N". = N/½PLU

here X, Y, N are surge and sway forces together with yaw moment

Do

is a reference velocity and

p

is water density

As stated above, initial data processing was carried out using a micrO.cOmputer

during the exper-iments.

_{miS' entailed: conversion of: the amplifier outputs. to}

forces and moments using 'appropriate' calibration factos (obtained before -the

experiments) ,

OorréctIng for zero values, nohdimensi'onal.isation: and plotting.

The purpose of 'this report, and indeed one of

th

thain aims of the project, is

to present this raw data in its entirety and, incidentally, to compare results

cbta-ined with two gebsiins.

However, only kinematic results are available from

the full-scale. tra1s of ref. 1 so tat in order to use these for comparative

purposes,, it was necessary to relate the constrained model measurements o the 'free running' trial measurementS.

This was done, naturally, by means of a simulation thode-1 and as mentioned

above, the NMI tcruislng speed' model was used This entailed further off-line analysis of the. data to obtain the coefficients using methods described in

reference 3.

-Results from the rotatinq arm were analysed to remove inertial and translatory effects leaving 'rotary' surge and- sway force and yaw moment coefficients

XR', 'ER' and NR'. ThiS was done both by the method of referenc 3 in hich.

part of the simulation model is used as an interpolator,' and also by a, straight

subtraction of the measured xanslãtory effects at the appropriate. condition.

These calcuIat-Ons were also carried out on the micro-coputer.

3. Results Obtained and DiscussiOn

Results Obtained from the experiments are presented here in graphical form; the numerical data from which the various figures were obtained is held at NMI

Ltd.

The results are segregated for ease of preSentation; each main series of experiment data is discussed in turn and, where appropriate,, cOmpariSons between results obtained with the .NMI and Stevens geosiths are made.

3.1 constrained Model Experimens

3.1.1 Resistance Experiments

Resistance measuréehts obtained at each depth/draught ratio are shown for

both models in Figure 6. As might be- èxpected.some differences between results from. the twO geosims are apparent. The Reynolds Numbers of the experiipes

point.

TABLE 3

It is seen from Table 3 that resistance values for the Stevens model were obtained at a limited number of speeds only. It may be noted from Figure 6 that, not unexpectedly, resistance is not proportional to the square of the speed over most of the

range. As will be: seen later, coefficients in the simulatron model for hull resistance were obtained locally at the reference speed, at which a

was assumed to apply.

Resistance values for all conditions were estimated using references 4 and 5 and results are shown on Figure 6 from which it is seen that in deep water reasonable agreenènt was obtained wjth the i4I model measurements. The limited measutements made with the SteVens model and their scatter makes comparison of estimation and measurement difficult, but -itappeãrs that the estimated values do not disagree significantly with the measurements. Shallow water estimates fOr theI model

using reference 5 consistently under-estimate the measured values.

Propulsion experiments were also rn to find the model self-propulsion point fOr

each model at each depth. It should be noted that the coefficients or the NMI cruising speed equations are obtained at model- rather than ship self-propulsion point Both constrained and free running experiments are run at this condition so that all experiment results are consistent The propeller model incorporated in the NMI equations (ref. 6) uses data at model self-propulsion point so that at full-scale the correct propeller r p m /speed relationship is obtained The

above should be borne in mifld if the data presented here is to be used with

another propeller simulation model, should this operate at the ship self-propulsion

h/T NMI Model Stevens Model

3.65.lO to 2.92.106 4.84.lO, 5.8l.lO 1 5 3 65 lO to 2 47 106 2 90 i05, 4 84 lOs, 5 81 l0

3.1.2 BollardPull Experiments

Bollard pull experiments ze±é cärriéd out at all depths tO Obtain:

- screw bias data fOr the sway and yaw equatjon

- bollard pull data as part: of the propeller thrust Odel.

Results are shown in Figure 7 from which 'it is seen that an expected variation of X' with (n')2 was obtained. It 'is also notable that the effect of' shallow water is to increase X" 'at a given n'.

The variation of Y' with n' shows some scatter fOr n' < 0 and there appears to be a tendency for Y' to change sign as h/T decreases for astern revolutions.

Generally good agreemnt is found with N' at all depths for n' < 0 but for n' > 0 some scatter is apparent with disagreement between the NMI and Stevens

model results in deep water. It may be noted however that the turning moment due to screw bias for n' > 0 generally increases with decreasing underkeel clearance.

Bollard pull results for the Stevens model were obtained in deep water only; they ar shown in figure 7.

It should be noted that the reference shaft revolutions n0 used in the bollard p11 analysis' were those appropriate to the reference velocity U used to compute

the non-dimensional force and moment coefficients.

3.1.3 Oblique Tow Experiments

The oblique tow experiments were carried out with rudder, amidships 'at a' speed

representative of' a manoeuvring speed in the depth of water under coñsideràtion. The results are shown in Figures 8th' 16 in which results from both models 'are compared. I is apparent that fOr the sway force and yaw moment there is good

agreement between the results obtained from, both models over a drift angle

range of about _8o to +80. At angles, larger than thrs where non-linear viscous-dominated effects become important the results of the two models diverge slightly although there is still a large measure of agreement.

3.1..4 Rudder Angle Experiments

Results obtained from runs at zero drift angle, model self-propulsion and .

-contant speed, in which rudder. angle was varied, are shown in Figures 17 to

25, These indicate once again quite good agreement bet een results obtained with each geosim for. sway force and yaw moment with increased catter and less satisfactoy agreernent with surge force..

:3.1.5 COmgined Drift and Rudder Angle Eeriments

easurements obtained with combined drift and rudder angles are shown in.

'igures 26 to 38. Differences in absolute measured X1, Y' and N' alUes are apparent in the results obtained with the NMI and Stevens' models Whereas good agreement in t _{and N' against}

for zero drift angle occurred, progressively poorer agreement was found as increased. This was especially notable in the :.Y' méasiirëmënts as shown in Figures 35 and 37 where crossplots = 15° are

shown for deep: arid shallo water.

In spite of the poor agreement between absolute measurements, it is apparent

frOth the Y'. and N' plots in Figures 27 to: 34 that the lppe of the curves obtained from the two models show reasonable agreement.

Agreement between X' values measured with the two models is generally poor.

-This is not altogether unexpected as: jt is these values whidh may be expected to be thot affected by viscous, and hence scale., effects.

3.1.6 Rotating Arm Experiments

Results obtained from the rotating arm experiments are, shown in Figures 39 to 56. The plóttings are axraiiged in two groups; One (Figures 39 to 47) show X'R, _R

and N'R for both models plotted against r* (= rL/U) for various drift angles while the second group (Figures 48 to 56) show cross-plots of X'R, Y' and N'R

against for va±ious r*.

It may be.noted'that in the axis system of Figure 5 a negative drift angle is bow-into a clockwise turn; this is normal for most displcement ships in

a steady turn. It will be seen however that rotating arm experiments were also carried out at positive (bow out) drift angles whiOh were almost as large as the maximum negative drift anclês tested. The purpose of this was

two-fold.

to allow for' any major transient behaviour in future simulation models in which large positive drift angles may. be associated with positive rates

of rotation. .

- to proVide sufficient data. to explore the validity of the cubic terms involving combination5 such as v2r and yr2 which are often used in manoeuVring simulation models.

For the NMI model in deep water, it s apparent from the cross-plots at various r* against drift angle that for positive there is little 'variation o Y' or N' whereas major variations are obtained for negative .

However results from the Stevens model in deep water show a different sway force behaviour with at a given. r*. In Figure 49 it i clear that a minimu value of 'R is reached at 50 after which an increase in sway force accompai4es

an increase in at constant The yaw moment variation with at constant r* also differs from that of the 4I mbdel for positive (seeP Fig 50).

It may also be noted that whereas the magnitude of XtR and N'R of the NMI and Stevens models agree reasonably well, at a given and .r*, this is not the case with _R The Values obtained from the Stevens model are about half the.

In shallow water the 'R results obtained with the NMI ode1 are interesting. It is seen bycomparison with the deep water values (Fig. 49), that at both medium

(:.5) and shallow (1.2) depth/draught ratios!

th

'R values increase with increasing positive drift angle and decrease after reaching a maximum for decreasing negative drift angle. _{Indeed at large enough negative drift angles} rptary. sway :crce becomes negative. This .mày in part be due .to bloökage effects present in the linear motion results obtained in the towing tank No blockage cprrection has, yet been applied to the shallow ater-esults.

Changes of N'R with depth (rigs 50, 53 and 56) are not so dramatic although it is clear that for positive drift angles N'R becomes less negative with decreasing

hIT. Indeed at = 200 and h/T = 1.2, N'R does.in fact become positive.

The increased magnitudes.of X'R, _{and N:'R with reduction in water depth may} also be noted as may the rather- less linear variation of _{'R with r* at some} positive drift angle as water. dpt s reduced. .

3.2 Free ,RunMng Experiments

Results from the free-running experiments were obtained by analysis of the track 1Ots, an example of which is given in Figure 57. _{Analysis yielded rates.of turn,} turning radii, v1ocity. in the turn and drift:angles. As mentioned in section

2. 2,. only the NMI mode-i could be run free and the experiments were -confined to

-teady state turning circles and pull-outs.

Rate of- turn against rudder ngie for the three water. depths is shown in Figure 58 while Fiur-e 59 shpws.tack speed on thë- turn. -.

It is seen in Figure 58 that good agreement between model and full-scale. measurements of rates of turn are obtained in shallow water (h/T = 1.2) while

12

-particular interest is the fact that the marginal instability noted in reference 1 at h/T = 1.5 is correctly reproduced by the model measurements although in

general the rate of turn of the mode-i was somewhat less than that of the ship for this water depth.

This also appears to be the case in deep water although.. in this case it was not possible. to obtain reliable model resUlts- at rudder angles less than 5° starboard or 10° port. It was therefore impossible to determine whether the margiial dynamic

stability measured on the ship in. deep water was correctly reproduced by the

model. . .

The observed differences between rates Of turn measured on the free model and at full scale may be due entirely to scale effectS, but model aid full-scale thasurement accuracy should also be borne in mind. Some discussion of the measurement problems at full scale is given in reference 1. where it is pQinted out that it was necessary to correct all measurements for the effects of current. No current was present in thea model experiments.

Another difference between the model and full-scale trials was that whereas the full-scale rates of turn were obtained from a spiral manoeuvre the ode1 results were obtained from steady state turning circles, measurements being initiated after the model heading had changed by 3600 and continued until the heading had changed by 7200 after the. initial setting of the rudder to the required angle. It is possible that, Should the rate of turn take some time to settle to a truly steady value, the. spiral tests of ref. I could have yielded rates of. turn which

were higher than those in the model tests.

Speed lOss measured in the turn is shOin to be reasonably well pedicted by the model at least for hard-OVe turns. The expected greater speed loss in deep

compared to shallow water is apparent from the model results in Figure .59

Measured drift angles in a steady turn are shoi itt Figure .60 for the }4I

free,-running model. Although sject to sOme. scatter, the reduction of 'dr4ft angle with reduction ofunderkeel. clearance is notable.

4. Manoeuvring Coefficients and Simulation

4.1 General

It is straight-forward to compare free-running model measurements with results obtained from the full-scale trials. But in order to assess the validity of the constrained model measurements it is necessary to use them in a simulation model the

resu±tB of whfch may thn be compared with both free-model and full-scale measurements.

Clearly such a procedure is as much a test of the simulation model as of the model measurements themselves and as such it allows an opportunity of assessing the suitability of various features of the chosen simulation model. In this section therefore manoeuvring coefficients for a chosen mathematical model are presented and discussed after which they are used to simulate steady turns for comparison with free-model and full-scale measurements.

4.2 Simulation Model and Manoeuvring Coefficients

The NMI cruising speed model has the form (ref. 3):

m*(uI_vIrv) ₌

_XU'2

+ X2v'r' + X3A1c52 + X4v'2 + X5r'2 + X6n'2 + X7U'n' + X8u' + _XE

m*(v'

+ u'r')

= Y1v'U' + Y2U'r' _{Y4vhIv'I+ Y5r'Ir'I} + Y6n'2 +

(Y7 +

m*/2) v'2r'/U' _{+ Y8v'r'2/U'} + Y9u1 + Y10r +

I r' = N v'U' + N2tPr' + N3X S + N _v'Iv'I + _{N r'}

Ir'I

+ N6n'2 + N7v'2r'/U'

zz 1 2

_4.

5

+ N8v'r'2/U' +

N9t

+ N10r' + _NE

where XE, _E and _NE represent external forces and moments and

= a1r.j'2 + c2n'2 + (l-cL1-c12) U'n' + cz3Iv'-kr'IU'

A2

. 14

-The regressIon model given by equations i) to (3) has been found to represent adequately the behaviour of a range of ship types and has been used extensively in. UK-manufactured ship simulators designed both for training and research roles.

Coefficients, in the simulation pde1.we obtained ii groups using results from 'linear motion' and rotating arm experiments. In all cases standard errors of each coefficient were calculated and these are listed below.. The 'linear, motion' results

showed characteristics which were simil.r. over the-whole drift angle range, to those obtained with other models at NMI. This was not the case with the rotating

arm results however and these. are therefore

discused separtely.

4.2.1 Linear Motion Coefficients.

The 'linearmotion' experiments (resistance, bollard pull, oblique tow, rudder

angle and combined drift and ruder angle epariments) yielded the coefficients

in Table 4. Some coefficients for the Stevens model have had to be estimated and

these are marked.

..

... . . .. .

Comparison of these coefficients wIth others .given

n reerpe

show that they

are generally of .imilar magnitude and sign.

The errors given with the coefficients are as much a measure of the accuracy of. the experiments as they are of the adequacy of 'the regression model (equations (1) to (3)) to fit the experimental data. In general it is seen that the fit for

both the NM and Steyens model data is good with one or- two exceptions, primri1y

associated with non-linear terms such as X4v'2 and, y4v'

Iv'

_.

-The rudder effectivene'ss ( and ) coefficients (obtained from the combined

driftand rudder angle experiments.) show .goo agreement between, the two sets of measurements from each model with the. exception of However the error size in the coefficients from the Stevens model data should be npted;

their lage

size suggests that the 3lv'-kr'I term is not a good fit to the experiment data.

In general however the agreement between results obtained from both models is reasonably good for linear motion and. differences which do occur, notably in

the resistance (X1) some non-linear and rudder terms are not altogether unexpected, and probably not significant when the error bounds a considered.

MODEL COEFF. DEEP

1.5

.

1.2

X1

-1.75(0.034)

-2.14(0.076)

-4.22(0.010)

-2.16(0.061)

-2.30(0.18)

-.3.22(0.15)

X4

2.65(1.80)

7.07(2.32)

- .

68.4(6.92)

x6

2.21(0.07)

2.36(0.035)

3.05(0.05)

-0.46(0.08)

-0.22(0.084)

1.17(0.086)

-15.7(0.86)

.

-17.0(3.7)

-119.0(16.7)

5.14(0.31)

5.74(0.17)

8.10(0.32)

-49.3(4.9)

-0.045(0.042)

-412.0(22.5),

-0.38(0.08)

-408.0(83.1)

-0..25(0.022)

N1

-6.96(0.28)

. .

-24.9(0.84)

.

-34.7(1.89)

N3

-2.22(0.09)

-2.22(0.046)

_-2.44(0.07)

N4

-9.67(1.61)

_3.13(5.14)

_-43.9(8.51)

N6

-0 042(0 003)

_{-0 014(0 008)}

_{-0 025(0 010)}

sTEVEi1s

_{_2.05*}

_2.i*

.

4.91

x3

-.2.40(0.4.5)

_-3.43(0.37)

_-2.91(0.59)

0.55(2.81)

.

83.7(2.53)

2.6,4(0.04i)

2.82*

364*

X7

.0..59(0;04i)

. '

_0.3l*'

1.27*

Y1

'20.3(1.,32).

-24.4(2.71)

.

.196.:0(13.9)

8.20(0.67)

Y4

-57.1(5.43)

. .

-374.0(16.0)

-161.0(82.5)

-0.165(0.005).

_0.2.5*

7.88(O.67).

-23.2(0.4i)

.

-17.9(2.15)

N3

-2l7('0I.4)

'

-2.49 (0.20)

-.2l (0.18)

0.756(2.4l)..

,.

93.7(i2.3)

N6

-0 042(O 002)

-0 014*

_{-0 025*}

NMI -

0.l650.035)

0.190(0.23)

0.2090.38)

0.481(0055)

0294(0.077)

0.484(0.04)

0.Q'.

.

.

0 152(0 037)

0 086(0 040)

0 052(0 009)

0.3'30(0.033)::.

0.340(0.064)

-

0.173(0.014)

k

.0.5,60(0.44) ,

05*

.

2.330(0.&)

.

05*

3.150(1.04)

Q5*

svis

0 310(0 13)

0 136(0 13)

0 092(o 16)

0.452(0.07l)

.

0.84W.0i8'

.

l.87(0.35)

0.0*

O.O

..,

QQ*

0.189(0.028)

. 0.022(0.047)

'

. 0.035(0.060)

82

0.365(0.073)

0.405(0.053)

0.450(0.048)

83

-11.91(5.98)

-14.08(12.02)

-19.08(28.7)

k

0.5*

05*

0.5*

Notes ] *Estjmated value TABLE 4

Figures in parentheses are standard errors All coefficients app].y to ahead motion only

16

-4.2.2 Rotary Motion Coefficients

As mentioned above, the rotating arm experiments were carried out with a drift angle range of -25° to 200. This was done to enable the range of validity of the rotary term model: (ref. 3)

XR = X2v'r' + X5r'2 (4)

= Y2Utrt + Y5r' Ir' I + Y7V'2r'/tJ' + Y8v'r'2/U' (5)

NR = N2U'r' + N5r' Ir' _I + N7v'2r'/U' + N8v'r'2/U' (6)

to be assessed. In equations (4) to (6) XR, _R and are the rotary surge and sway force and yaw moment obtained from the measured data after removal of centripetal and linear motion effects.

Multiple regression fits using equations (4) to (6) were made for various drift angle ranges and for the whole r' range tested (including r' = 0). Multiple correlation coefficients and F values for these fits are shown in Table 5.

It is clear from the multiple correlation coefficients than for -25° 20° ,the

regression model is a poor fit to the _R data in deep water for the Stevens model and does not fit the _R data in shallow water. Clearly the changes in form of the -curves of

R against in shallow- water are not well-fitted by the

regression model.

The situation is considerably improved by reducing the drift angle range to _150 S 50 and a further marginal improvement is obtained if the range is

further reduced to -10° 5°. However the improvement is so small that it

seems unnecessarily restrictive to limit negative drift angles to -10°. It is therefore apparent that the model given by equations (4) to (6) is valid over

a drift angle range of _150 E 50; _{the computed regression coefficients,}

TABLE 5

Model Item Range Multiple Correlation Coeff. F Value h/T

NMI _XR

-25°

to

200

0.97996

_1404.03

deep 'I

0.98146

747.46

0.98730

1100.638

Stevens _{XR 'I}

_0.89850

_261.85

It

0 86635

92 52

0.98746

1202.74

NMI _XR

-25°

to

200

0.95261

_568.84

_1.5

0.62968

18.72

1

0.93791

208.36

XR

-15° to 5°

0.97871

636.5

II

_0.96660

192.04

II NR

0.96547

185.43

XR

-10° to 5°

0.98593

765.54

0.97314

187.62

NR II

0.97449

197.95

II NMI _XR

-25° to 20°

_0.91122

_286.28

_1.2

0 64364

20 34

NR

0.88806

107.27

XR

-15° to 5°

0.95272

280.22

It II

_{0 97073}

224 58

NR It

0.95272

_280.22

XR

-10° to 5°

0.96310

288.12

U

_0.97473

204 69

NR It

0.94394

87.91

18 -TABLE 6 MODEL

h/T

COEFF 10 VALUE

SThNDAD

ERROR SIGNIFICANCE NMI

deep

X2 12.93 0.244 H X5 . 0.66 0.139 H -25° 20 ₂ 11.81 1.136 H y -4.36 . 1.329 H 40.04 3.459 H -41.39

1207

. N2 -5.49 0.393 H 0.13 0.461 N N7 =20.98 1.198 H N8... .8.9.4... 0.418. .., H STEVENS 7 25 0 320 H 0.07 0.143 . N 2.33 0.551 . H Y5 -0.38 0.533 N 20° 11.60 899 H YB. -.3.03 0.611 H N2 -2.16 . 0.149 H 0.34 0.144 S C N7 -10.49 0.51.5 H 0.. 52

0166

H. NMI

15

X2 62.95 . . 1.97 H H X =1.88

0.S3

H

1108

3214

10.97 :3.832 . -15°

5°

. . -232.38 37.183,. -129.53 ' 1L34.4 H N2 -8.76 1.4$ H N5 2.04 . 1.767 N N7 -66.59. .17.147 H N8 25.23 5.23 H, 1.2 68.15 3;074 H X5 -0.64.. 0.928 N -15° 5° Y.2 14.73 4.641 . H Y5 28.13 5.522 H -473.50 53.707 H -172.34 . . .16.422 H N2 -13.46 . :- 2.i45 H N5 6.15 2.553 . S N7 -82.63 24.825 H N8 20.78 7.591 'S

In Table 6 the significance of each term has been obtained from its 't' value, values of significance being assigned on the following scale for the appropriate degrees of freedom.

H: Highly significant 0.5% significance

S: Significant 2% to 0.5% I'

N: Not significant

Comparisons of coefficients obtained for the Stevens and NMI models show good agreement on the whole except for the highly significant Y2, Y7 and Y8 values for which the values from the Stevens model are much smaller than those from the NNI model. This is simply a reflection of observations made above regarding the model measurements.

It is apparent from the Table that most terms in equations (4) to (6) are highly significant for the 'Esso Osaka' hull form. The exception is N5r' r' which is consistently shown to be of low or negligible significance. This does not mean of course that it would hot be significant for some other hull form.

The terms

Y7v'2r'/U', Y8v'r'2/U', N7v'2r'/U' and N8v'r'2/U'

are all significant or highly significant with the two sway equation terms being consistently highly significant.

4.2.3 Remaining Coefficients

All of the coefficients in equations (1) to (3) have now been determined from the constrained model experiment results except for the acceleration terms

X8u', Y9v', Y10r', N9v', N10r'

These are usually determined by inspection or identification from comparison of simulation results with free model transient manoeuvres such as pull-out or zig-zag manoeuvres. Assumed values, based on model results obtained previously at NMI, were used in the following section.

TABLE 7

It is also apparent from the magnitude of the C values in Table 7 that the increased directional stability in h/T = 1.2 is correctly predicted by the constrained model results.

Drift angles in the turn are apparently well-predicted (where it is possible to make a comparison) except that those measured on the free model at hIT = 1.2 are significantly smaller than predicted.

Loss of speed in the turn for both free-model and ship are generally quite well-predicted although once again the greatest discrepancy occurs at the

smallest h/T value.

Predictions of the transient effects associated with entry into a hard-over turn are compared with full-size measurements (ref. 1) in Table 8:

TABLE 8 h/T (Y 2_m*).l03 Y i.l0

N 2l0

N _.lO3 C.103 -6.43 - 15.7 - 5.49 - 6.96 41.44 1.5 -7.16 - 17.0 - 8.76 -24.90 -29.36 1.2 -3.51 -119.0 -13.46 -34.70 1479.94 RUDDER h/T AT 900 HEADING CHANGE

ADVANCE (m) TRANSFER (m) SPEED LOSS%

meas. sim. meas. sim. meas. sim.

350 350 1.5 1.2 1.5 1.2 1005 915 1190 1015 990 1180 d 946 999 1010 971 967 971 310 385 555 360 405 705 458 612 631 463 573 582 -35 32 26 33 33 35 36 38 38 36 41 41

- 22

-In general it is seen that while the advance t 90° heading change is predicted. to within 2-10% in deep and medii depths (15-17% in h/T = 1. 2), the transfer

is generally predicted no better than to about 14% of full scale with discrepancies of nearly 60% in one case. This direct comparison between a full-scale and

simulated mafloeuvre apparently reflects the fact, noted above, that model and simulated rates of turn were lower than observed at full scale. This may be a genuine scale effect and, in conjunction. with discrepancies between.full-scale

and model prediction in speed loss and drift angle, combine to produce the differences apparent in Table 8.

5. Genéral DiscussiOn

It has not been the purpose of this report to provide any comprehehsive comparison of model simulation and full-scale results, but rather to 'present the model data, discuss it and compare sorne limited simulation resu1t with full-scale measurements

from reference 1. Further comparisôn between simulation and f'Jil-scale must clearly be made before the magnitude of any scale effects can be decerinined and, naturally, this rémàins to be done for the zig-zag manoeüvres, coasting and accelerated turns described in reference 1.

However, it is significant 'that the simulation model, using Coefficients 'Obtained directly from constrained model experiments, predicts free model behaviour ('at

least in steady turns) rather better than full-scale. This suggests that the form of the mathematical model given by equations (1) to (3) adequately represents the free-running behaviOur of the physical model from which it was derived, On the evidence given above it does not represent certain aspects of full-scale behaviour quite as well. This discrepancy may be'descrbed as scale effect and may be due tq:

- viscous scaling 'effects -existing between model and full-scale behaviour.

- a form of mathematcalmodel which is inappropriate for full-scale. This may be special1y true of terms describing rudder beha'iour in which viscous effects are combined wjth the effect of using model - rather than

- errors in model and full-scale meàsurément. These have been given above for the model-derived manoeuvring coefficients and it is clear that some

have large errors and .theréfo±e -:Ooüld be 'adjusted to 'iniproie the ageeinent

with full-scale.

- other effects. Mong these may be numbered blockage effects on the linear

motion cäefficietit -ho biockaqe cOtréction was applied tO the data. It may also be mentiOned that asirnulation model is only as goodas the

understanding àf.rthè physics of ship behàviour in deep and shallow water will allow. It is Ossib1e that' a better uderstanding of shallow-water

effects (in particular the problems of scale) will allow improved simulation

models to be developed. ' '

-It is clear frOm the donstrainêd model results that In bOth the linear and rotary motion experiments significant differences between some of the NMI and Stevens model results existed. '- These were hOwever balanced, to -a certain extent, :b

areas of substantial agreement. These areas of agreement and difference are reflected' ih the' manOeuvihg OOëfficieht in Tàblès 4 and 6 with perhaps the most 'notable disagreement being Obtained

wi.th

ome'of the rotary terms. It. would appear

therefOre that model size has sotheèffect on the results, but again the reasons for this axe not altogether'cleàr-cut. For example, viscous scale effects on a small model may well be wholly Or partially offset by a reduction in blockage

effects. This in turn may be óffet by' problen ih'maintai'ning measurement accuracy tqith' the smaller forces obtained ith small models together with a greater possibility with such models of a greater tendency for laminar flow (see Table 3).

It is clear therefore 'that further iok remàihs tO be done in the analysis of 'the data presented here and this will fall ubder the following main headings:

- investigation of' 'blOckage effecti

- presentation. and analysis of linear motion data' obtained for drift angles

in' excess of 250. Results (not presented here) have been obtained, with

both the NMI and Stevens models, with linearmotion having drift angles

0 in the range 0 180

-.24 -.

- further comparison of simulation and full-scale results for zig-zag, accelerated turns and low speed manoeuvres.

The results of these further investigatibxs will be presented in due course.

6. Conclusions

Two geosims.of the 'Esso Osaka' have been. the. subjecs'of' a series 'of constrained and free-running experiments to .co,llect data on their manoeuvring behaviour in different water depths for comparison with full-scale measurements. As a. result

of thi study the follOwing tháin conclusions have emerge4:

i) Results obtained in constrained model experiments using 3. 536m (4I) and

1. 625m (Stevens) long models showed areas of agreement together with significant areas of disagreement. The most notable disageemen'was in the measurement of the' rotary sway force coefficients Y'R whose magnitude in deep wate was much less from the small Stevens model compared to the. ti model.

ii). Free sailing, results obtaitèd wi,th the NMI model gave the same qualitative

steady turning' behaviour as the ship. While the. steady ra of turn was only moderately well-predicted in.deep water, 'aqreement between the free-sailing

model and ship progressively improved as watr depth.was reduced...

Changes in' controls-fixed directional stability wh 'water depth, observed on the ship, were correctly represented by both the free and constrained NMI

model results. . . '. ' ,.

Simulation of the steady turn'tesults, made using the NI cruising speed model, agreed reasonably well with results from the NMI free-sailing model.

The transient 'behaviou± of the simulation model at the entry to 'a hard-over turn showed reasonable agreement. with full scale advance (at 90° heading change), poor agreement transfer, and reasonable agreement with speed loss.

There may be blockage effects present in constrained model results obtained

ith large ditanqiès and linear -mOtion in a towing tank.

yiii) Further analysis of blockage effects, large drift angle. results arid transient Motion is required.

7. References

1. cRANE. c L 'Marioeuvring Trials of 278,000 dwt Tanker in Shallbs4 and Peep Waters' Trans. SNAME vol. 1979, p.

MILLER, E R: 'Status Report on a Model-Full Scale Correlation study Based on the 'Essö Osaka' Manoeuvring Dàtà' 19th ATTC, Michigan, 1980.

GILL, A D: 'The Analysis and Synthesis of Ship Manoeuvring' NMt Report R90, October, 1980.

GERTLER, M: 'A Re-analysis of the Original Test Data for the Taylor Standard Series'. DTMB report 806, March. 1954.

SCHLICHTING, 0: 'Ship Resistance i±i

Water of Limited Depth - Resistance of

Sea-going Vessels in Shallow Water' Jh±buch der STG,

vol. 35, 1934 pp.127-148.

GILL, A D: 'The Identfcation of Manoeuvring Equations from Ship

Trials Results' NMI report R3, August 1976.

7. COMSTOCK, J P (ed) 'Principles of Naval Architecture' SNAME, New York, 1964, Chapter 8 by P Mandel.

26

-8. Acknowledgements

The authors gratefully acknow1edge theassistance of Messrs. G L Taylor,. G Meek, and Mrs J Salter Of the Hydrodynamics Division., NMI Ltd. Special mention is made of the late W H Sims who carried out much of the experimental work on this - his last - project It is hoped that this work will serve as a memorial to him in special recognition of the contribütion he made to the study. of manoeuvring in NMI. . .. . .

moulded beam

linear stability criterion

block coeffiàient

midship section coefficient prismatic coefficient

propeller diameter

Froude Number = Ui i4L Froüde Depth Number = UI gravitational acceleration

water depth Izz/½pL5.

rotary inertia in yaw

lever arm between origin of axes and ruddêr length between perpendiculars

rn/½pL3

ship/model mass shaft rpm

reference rpm

n/n0

mean face pitch

yaw rate

rL/U

rLp/U0

at-rest draught

track velocity = V'U2 + V2 reference velocity

surge velocity sway velocity U/U0

v/U0

external surge and sway forces and yaw moment XR,YR,NR rotary surge and sway forces and yaw moment

drift angle rudder angle

A A _{.rudder coefficient modification parameters}

P water density

trim angle

denotes non-dimensional quantities mainly: forces w.r.t.

½L2

₀ and moments w.r.t.

½PL3UO2

Cm Cp D F Frth g

IzzI

Izz m* U 'U0 U! VI XE,YE,NE

--V

F2

-T&i

11

t

I,

IL_________

IL_ I IL

91/.2

UI

11_ 11

1

12 m 4 34 rn

28m

20 m

_7-5

21 97-mLWL

I-AP

1/4

BOW PROFILE AND WATERLINE ENDINGS

0 SCREW w2 as STERN ARRANGEMENt SCALE(m) E 10 -I-1/2

I

S

DRIFT ANGLE VANE

HEADING GYRO BATTERIES ETC ULTRA-SONIC TRANSMITTER

'ESSO OSAKA' MODEL

EXPERIMENT TANK

DIAGRAM OF FREE RUNNING EXPERIMENT SET UP

ULTRA SONIC R ULTRA-SONIC

PLOTTING

SYSTEM TELEMETRY Rx _ETC RADIO CONTROL Tx TEKTRONIX I 4051 1

PAPER TAPE PUNCH

CHART

AXIS SYSTEM AND DEF1NITIQNS

(POSITIVE DIRECTIONS. ANGLES AND ROTATIONS

DICATED)

-2 -.4

-!ES.ISTPNCE

.ö4

A

ESTIMATE

-i

N-a

1 DEE P

] h

/ T -1 5

______

hIT-li

4 . 16

BIJLLq!D PULLS

24

a

DEEr. NEF VoD ar. VMI

V LV. -STO V .2. 550 X 0 lEEr. 'aec STEVENS BOLLPIO PULLS Y' (1 DEEP. EF ND42 5PM. MIS! to a IS. co -0 1.2. 580 0 0EEr 080 STEVENS BOLLRD PULLS N' '0 '0 0 DEEP. Er-sso=4?o-prM. MM! DI (I LV. SIO (1 .2. SaD 0 DEEP. '000 STEVENS

DEE? WRTEL, y'

O RUIDDE! RNCLE. NM! FWOEL

U STEVENS

DEEr WPTEt,

ai

10 15 20 25

h/T = 1.S,

>(

-25

-20

-15

0 UODE

RNLE. NMI t1OEL

El 0 STEVENS

15 20 25

DRIFT RNGLE

H/T =

0 STEVENS

jo

:0

-25

-20

-15

-10

S 5 10 15 20 DRIFT GLE

0 UODE RNGLE. NMI M0EL

0 STEVENS

I-l/T

= 1.S,

N

F1/T= 1.2w

X

18

x' *O**3

a

a

0

10

iS

20 25

0IFT flMCLE

h/i = 12,

I

p

C UDER RNGLE. NMI MODEL

0 STEVENS 10 15 20 25 DRIFT RNCLE

0

0

FIG. 15.

h/T. = 1:2,

o

10 15 20 25

DRIFT RNCLE

-40. -30. -20. -10. . 10. 20. 3O 40

RUDDER ANGLE

0

DEEP,

x

0

0 DRIFT .qNGLE. . NMI MODEL

0 STEVENS MODEL

0

0

-40

G

DEE?,

5-'f'

_*(o**3)

G 4 -

--I

-20 30 40 R1JDDE ANGLE

FIG. 19.

-40 -.30

.20

10

ii 1.0 30 - 40

RUDDER RNGLE

0 DRIFT RNGLE. NM! MODEL

W 0 STEVENS MODEL

UEEP,.

N

H/T =

H/T = L5,

I

T' *(I0**3) 4 3 2 I -40

-(1

2C) -!0 ]0 20 30 40 U00ER NCLE III lii Lii 5

-0 DRIFT RNGLE, WHI W0EL

E!J 0 STEVENS !WOEL

a'

a'

FIG. 21.

-2

H/T

1., S,.

I-

- I - ___

--40

--30 -20

-10

1.5

-1. 5

I i__: I 20 30 40 RUDDER ANGLE

III

-40 -.30 --20

10

- 10 20 30 40

UDDE N.GLE

--1

D

0 DRIFT PNGLE. NM! MODEL

0 STEVENS MODEL

H/T

L2.,.

I

I

6 'r' *(IO**3) .;

-40

0

H/T =.L2,

'.4-30 .4,. X'

'*(1Oc*3)

20

10

1 10 20 30 40 LJDOER RNGLE

-.2

1.4'

t1EL

-40

-30

--20

-10

10 20 30 40 RUDDER ANGLE..

0 DRIFT RNCLE, NM! MODEL

0. STEVENS MODEL

H/T =

D

Vø.

DEE? WPTE,

-io

a .iS a

-zo

o STEVENS -5 a -30 a

-is

-zo

a 10 ZD 30 RUDDER qNGLE

x

DEEP WRTE, 1'

18 'r

ti0''3)

16 14 12 i C o

DRIFT PNL. NNI 111DfL

-s

-0

-Is

-20

0

x

x

STEVENS

FIG. 2.

0

x

-20

10

10 20 30 RUDDL RNGLE

z

x

2:

A

DEEP ,jpTE

''

2:

A

-15

-20 sTEVENS

0'

-S

-10

2:

-20

10

0

2:

A

0

2:

A

.z0 33 UD0E NCLE

1.5::

X'

0 20 30

-40

-10

IUDOE RNGLE 0

DfT PNGLE.

ii

-s

-10

x

-is

a

o

a 5 a a t:

-io

a a

-20

Nt-Il 1OEL

ST,Vr4S

0

0

FIG. 29.

-3D cD 20 30 RUDDER RNGLE STEVENS

-10

-Is

-20

0

-5

-10

-15

-20

0

x

z

x

14

N 'iO31

-30

-20

-10

0 DRIFT GLE.

4r1I tlDEL

-5

0

0

m 20

RUDDER NLE

FIG.. 31.

h/T = i.E.

N I

-10

-15

-20

0 STEVENS

-5

-10

-Is

-20

qc 10 20 10 U0DE ANGLE STEVENS

0

x

I

h/i = 1.2,

X

h/T = 1.2

0

DRIFT P.NGL. JWJ

IWDEL

-5

-10

-Is

-z0

0

-5

-I0

-]:5

-20

STEVr'S

FIG. 33.

hIT = L

-10

-Is

-z0

o

-s

-10

-15

-20

STEVEt'IS

z

ib

,...2O

3D RUflDE qNCLE

DEEP WPTE,

-

UCDE PNGLE.. NMI !1OEL

Is.

-15

STEVENS

x

is

.

4

-15

stvs

FIG. 37.

.

-5

UDOER qcLE. NtII NaDEL

is

STEVENS

-IS

STEVENS

OLICC QtfCCU CCfl--NLfl--NN,J I I I I EJ

MS''

M N,X N N U, 41

9M

'dO 0 0 N

9O

E N 8 8 -fltflO

_.-.NLflNN

ClLflClU) 9 9

--N

N N N

9

C-N FIG. 39

-'

fl 'J b4

8

1

d'M

0 oi

-

-'E'

JN N

'

N N IJ U, -U, N

88

ee

N N E

EB

ThJ '

DEEr W'PTE'I,

1 .2

-s

0

IflI!FT

GLE., STEVENS MODEL

S 13 Is 20 -ID Is -20 -ZS m 0 '0

x

x. V 'b. ci

x

x

' 0 En 0 ci A En A .5

flEEr Wfl TElL

0

DRIFT pILE. Mlii MODEL

S 10 15 20, _{-10 -15 -20 -25} 0 -.2 4 -..6 S 4.5 a 3.,5 3 2.5 (

(13

x

0

22 20 1 6 16 14 12 *(Jfl*3)

z

8

z

z

4.

2

I

0.

--3.

DELF W-T1E,

"H :K D!FT NLE. TiEVE.'1S MflEL w a NR *(l0**3! ₁ --5 - 9

-DEEr WRTEI,

N 2

z x

x

.0

DRIFT PNGLE. NM! MODEL

S _.10 X 15 ID 20 -5 -m -ia & -IS Z -20 c -25-S

x

18 --6 -32

1.1/-I

=

1

,

X!

.4

10 15 20

-5

-30

-is.

-20

-25

.6

0

0

XR

15

-12 9 S

.(10$31

0

0

x

0

0

0

x

20

is

-S

-Ic

IS

20

H/T = 1...S.

1i

0

0

0

OIFT PNLE. rIMI MODEL

5 10 :15 zD

.5

-.

10

-.

L5

-z

FIG.. 43.

30

-'r

103)

25

-0

0

h/T.= LS,

NR:

0

10

x

is

zo

-s

-ID

-IS

X

-20

-0

0

3

15

-12

-6

--9 12

h/T

2'

2.,

0

4

-

.4

x

I

0

0JfT PrIGLE.

jj 1WDEl.

5 4 4 .1 10

Is

20

.-5

-10

-45

-2 D -2.5

.6

A

A

A

FIG. 45.

2 N!

M0*3)

tt/T

=-

1.2,

N .-10

',

1s

. _z0 c

25

. 0 OR!T-R!'lGLE.: NM! MODEL s 10 -

is

20

-x

x

FIG. 47.

--20 -IS -U) -2.5 1,5 0 1' lB x DI 2 lB

x

lB 2 . l3 9 STEVENS I00EL DI .!E .21? X .255 CD ID lB 0 !.S 20 25 fINGLL DI -2S -20 '-15 -10 O'EEI

wfrrE

X 0 ID 0 .ZG R. MM) MODEL ED .36 £ .44?

x 0

788

.0

0

x

-x 0 DRIFT RNGLE

lEE' WqiE

J35 STEVENS MODEL w .iss -.2-I? X .25 .555 < .4S DEEI WP1EF.

iI

--25 --20 .28G . NM! MODEL W -. -' .q4?

37

cn 78 10 IS 20 25 091Ff PNGLC

IJEE!

N -2 -!5 .lO --S

x

J 'zi R. STEVENS !11DEL fl

fl?

X .23S D. .353 DEELD WPT-EI, NM :zaG M*. NM! MODEL In .3 .447 X .637 Q

7a

3D IS DRIFT

0

0

0

t-1/T

= 1.S;

XR

-25

-2D -1.5

-iD

-xg

ro'-3)

.15 9 6 3

.287

*.

NtlI MODEL

.355

.44?

X

0

0

0

K

K

I - I 1O 15 20 25 DRIFT RNCLE

FIG. 51.

K

-12

-s

D

z

0

h/T = 1.5,

'r

.36

A

.44?

X

0

.788

0

0

A

A

x

0

A

A

0

0

X

x

A

0

₀

A

_x

0

0

25

-0

-15

-10

10 15 20 25 DJFT PNGLE

-S

-iD

A

-1.5

A

-20

it

30

IiD3)

x

25

0

0

0

x

20

x

is

-25

-20

-15

-10

-S

5 10 15 .20 25

K

K

C

C

K

C

0

. NM! MODEL

D!FT ANGLE

x

x

C

C

FIG. 53.

0

C

C

x

C

C C 10 IS 20 2S DRIFT NCLE

Is

)(R

(iO3)

C

.12

x

x

9

x

4

x

x

4

_C

6

4

.44?

.i32

h/T = L2,

XR

x

H/T

.o.

cD S 0 'rR

(1O3)

40 .1 -] 0

-20

-30

-40

.282

Fk

_{NM! NDEL}

.3S

.447

XG3?

cD

:7. ..-..

I--- -5 10.

r15

20 25

D!f1

NCLE

FIG. 55.

H/I

12J C

K

2 T.

Ng *(IO*3)

-2

1Q

-14

- I

-.447

..

x.

. 1FT RNCLE III

0

C

TYPICAL RUN PLOT

RUDDER - 200 P

DEEP WATER

RUN NO 14

DEEP WATER

+ NMI MODEL MEASUREMENTS

- FULL SCALE

SIMULATION (NMI MODEL)

+

1' -i.o

h/T-i5

-O5

1-

-05

-4--K

h/T= 12

-1--10

-05

I I I

-30

-20

-10 10 20 30

-30

-20

-10,

\

10 2O 30

-30

-20

-10 10 6DEGREES X1 6 DEGREES

-05

-10

-10

-10

RATES OF TURN IN DEEP AND SHALLOW WATER

FIG. 59.

KEY 1- DEEP

o

h/T=15

NMI MODEL

hjNF2

x

DEEP 1 E'f

_hlT=15}'SHIP

Lr

hJT.12J

40

30

20

10 10

20

30

40

(DEGREES)

p

KEY

-30

-20

-10

1O

₂₀

₃₀

40

A

£

_S(DEGREES)

+

MEASURED DRIFT ANGLES IN STEADY

TURNS IN DEEP AND SHALLOW WATER

(.NMI MODEL MEASUREMENTS)

.DEEP)

h/TF5

FREE MODEL

h/T12J