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A

UNIVERSITY

CALIFORNIA

INSTITUTE OF EN

ERING RESEARCH

BERKELE

ILIFORNIA

SHIP RESISTANCE IN UNIFORM WAVES

AS A FUNCTION OF WAVE STEEPNESS

AND BEAM OF THE SHIP

BY

OJ. S!BUL

FOR PRESENTATION AT TWELFTH MEETING OF AMERICAN

TOWING TANK CONFERENCE SESSION ON SEAGOING QUALITIES

AT UNIVERSITY OF CALIFORNIA, AUGUST 959

Lab. y.

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SHIP RESISTANCE IN UNIFORM WAVES AS A FUNCTION OF WAVE STEEPNESS AND BEAM OF THE SHIP

by

O. J. Sibul

For presentation at

Twelfth Meeting of Anierican Towing Tank Conference Session on Seagoing Qualities

at University of California, Berkeley, California August 1959

Institute of Engineering Research University of California

Berkeley, California July 1959

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I. ABSTRACT

I

-A series of experiments were performed to study the effect of width (beam) of the ship and the wave steepness on the added resistance of a ship in uniform waves. A 5-foot model of Series 60, block coefficient 0.60, was used as the parent form. Two additional models were similar to the parent except for the beam, which was 0.75 of parent for one model and 1.25 of parent for the

other. All of the models were towed in waves 5 feet long at seven different wave steepnesses between 0.0146 and 0,0684. The

resistance of the models in still water was measured in separate experiments so that the added resistance due to the oncoming waves could be computed.

The results indicate that the added resistance coefficient depends upon the beam of the ship, the Froude number, and the steepness of the waves. On the average, the added resistance seems to increase as the 1.2 power of the wave height for the narrow model; as approximately the 1.75 power of wave height for the intermediate model: and as the 1.80 power of wave height for the wide model. For lower speeds the increasing wave steepness has a considerable effect on the added resistance coefficient Ca. The effect seems to be at a minimum for Froude number equal to 0.15 and then increases somewhat with increasing speed.

It has been pointed out that for steeper waves the model has definite speed ranges in which change in thrust would affect very little or not at all the forward speed of the model. The

speeds between these particular ranges cannot be achieved in

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to the discontinuity in damping moment curves as discussed by

Have lock.

II. INTRODUCTION

-

2-The requirements for faster and better ships-have brought out the necessity of changing the present testing procedures and

criteria. Very much has already been done in studying the mo-tions, such as heaving and pitching, of a ship, but there is still a long way to go before we shall understand the complete

problem concerning ship motions, as well as loss of speed in stormy seas.

The testing procedure for ship resistance in still water is well established, and the resistance coefficients for different designs or alterations can usually be compared within one per

cent. However, the design which proves to be the most effective

for still-water conditions does not necessarily prove to be the best for seaways. As far as the resistance is concerned, there is only some scattered data available for the relationship be-tween the waves and the added resistance of the ship in these

waves. The speed loss at a given thrust has a very definite re-lationship to the ¡notions of the ship, so that the phenomena should be observed together.

Most of the available theories for ship motion assume that the pitching and heaving motions are proportional to the wave

height. This has been proved to be approximately true for waves of small steepness. For very steep waves the linear theory may not be satisfactory.

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3-To study the effect of ship geometry as well as the wave characteristics upon the loss of speed in waves, the following testing procedure was decided upon:

Establish the effect of beam on the added resistance in

seaways.

For this series of experiments, a 5-foot model of Series 60, block coefficient 0.60, was chosen as the parent

form. Two additional models are to be built. The lines

of these two models are to be similar to the parent form, except for the transverse scale; they are to be 0.75 of

the parent for one model and 1.25 of the parent for the other model. The block coefficient is not affected by this conversion.

Establish the effect of block coefficient on the added resistance in seaways.

Here again 5-foot models of Series 60 with block coe-fficients 0.60, 0.70, and 0.80 were chosen. In addition to these models, a model of a destroyer with a block coefficient of 0.50 was selected.

The experiments described under A and B are to be completed in uniform waves with length equal to the model length. The wave steepness is to be varied from experiment to experiment.

Establish the effect of wave length on the added

re-sistance in sea'ways.

Here Series 60, block coefficient 0.60, parent form was chosen. The wave lengths are to be between 0.75 and

1.5 of the model length, with sufficient variation in wave steepnesses.

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-4-.

The experiments under A have already been completed. The results for the parent form of Series 60 were reported in

Refer-ence 1. The present paper discusses the added resistance in waves for the beam ratios of 075 and 1.25 of the parent beam and compares the results for all of the three models, including the parent form.

III. EQUIPMENT

The Tank

The experiments were completed in a tank which is 200 feet long, six feet deep, and eight feet wide and has a rectangular cross-section.

The Carriage is self-propelled. The speed of the carriage can be varied between O and 15 f t./second. Constant-speed

opera-tion is obtained by using a General Electric Speed Variator. The

carriage speed is measured by utilizing light impulses (generated by a trailer wheel) and a photo tube. The light impulses are counted and recorded by a Berkeley Scientific Company Universal

Counter. The speed of the carriage is given directly in knots. The accuracy of the speed measurement is tO.001 knots (an average reading for a period of one second).

The model is towed under constant thrust, utilizing a small subcarriage suspended on ball bearings underneath the main car-riage. (See Figure 1) The speed of the main carriage is adjusted to fit the constant thrust applied to the subcarriage.

The Wave Generator is of bulkhead type, driven by a 20 H.P.

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-5.-feet by means of a variable-position crank pin on the flywheel, which effects the change of the bulkhead oscillation amplitude.

The wave energy is dissipated by a sloping beach (1:5) at the opposite end of the tank. The beach is composed of stainless steel shavings and hence is permeable. The reflection coeffi-cient of the beach is below 5 per cent for the waves shorter than about 5.5 feet and below 10 per cent for waves of 9 feet length.

The Models

The 5-foot model of the DTMB Series 60 with block coefficient 0.60 was used as the parent form in the experiments. The two additional models are similar to the parent, except for the transverse scale, which is 0.75 of the parent for one model and 1.25 of the parent for the other model. The block coeffi-cient remains the same, 0.60, for all the models. The models were adjusted as follows:

Parent

B/B= 1.00 B/B= 0.75 B/B= 1.25

Displacement of the model in fresh water - in lbs.

33.27 24.9 41.6

Longitudinal radius of gyration

0.25L=l.25ft. 0.25L=1.25ft. 0.25L=1.25ft. Wetted surface area S

in ft2

4.26 3.94 4.76

Longitudinal center of gravity

1.5% aft 1.5% aft 1.5% aft

Center of gravity above baseplane 1KG] in ft.

0.185 0.169 0.235

Draft in ft. 0.267 0.267 0.267

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IV. PROCEDURE

-6-The model was attached to the carriage as shown in Figure 1. It could pitch around the pivot point inside the ship; could heave together with two vertical rods, guided by linear ball bearings; and could surge or travel back and forth together with the subcarriage along the track on the main carriage. The model was restrained against yawing and rolling. Constant thrust was applied to the subcarriage by weights over a differential pulley. The whole carriage system was towed at a constant speed.

To start a run, the subcarriage was fixed to the main car-riage and was released after constant speed was well established. It was important to release the model at the moment the wave nodal point was passing the centerline of the model, because at this moment the surging force should reverse its direction and therefore the surging velocity would be zero and the arresting mechanism would have the least effect on the motion. When the applied thrust and the constant speed of the main carriage were not in equilibrium, the model had a net drift relative to the main carriage aft or fore9 depending on whether the thrust was too small or too large for the speed of the model. After each adjustment of the speed, time had to be allowed to establish the equilibrium and compare the speeds. It takes about three runs to obtain the proper relationship between the thrust and the

speed. At each successive run the model was accelerated to the proper speed, which was determined upon at the previous run. Then after releasing the model, any necessary adjustments were made. Some very accurately conducted experiments have indicated

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-.7...

that it is advisable to slightly overaccelerate the model rather than to underaccelerate and to depend upon the applied thrust to establish the equilibrium. In the case of a slightly overaccel-erated model, the equilibrium speed is reached much sooner than with a model underaccelerated to the same degree. For reliable results, however, the model must be brought as close as possible to the equilibrium speed. This statement is especially important for tanks of short length.

In addition to the resistance and speed measurements, the following other measurements were made and recorded by a six-channel Brush recorder:

Waves were measured one wave length ahead of the model by the use of a streamlined resistance-type wave gage. The reason for keeping the wave gage ahead of the model was to minimize the distortion of the original oncoming train of waves by the model. However, for lower speeds of the model, waves reflected and generated by the model reached the wave gage and made the wave height measure-ments uncertain. In this case the wave generator was calibrated without the model present, and the 'wave heights so obtained were used for the computations. A

great number of tests indicated good repeatability for wave heights at the same wave-generator setting. The

wave record during the actual experiment was used to establish the phase relationship between the waves and the motions of the model.

Surging and drifting of the model were recorded by a potentiometer at the center of the differential pulley

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8-(Figure 1). The drifting record was also used to make smaller corrections to the measured speed of the main

carriage. The drifting velocity is the relative velo-city between the main carriage and the subcarriage.

The distance of one wave length between the CG of the ship and the wave gage was fixed for the case where the subcarriage was at the center of the main carriage. The drift-record measures any deviation from this posi-tion, and so the correct values for phase-relationship can be obtained regardless of the relative positions of the two carriages.

Heaving of the CG of the model was measured and recorded by a poteniometer fixed to the subcarriage. The refer-ence elevation for heaving was the track on the main

carriage.

Pitching of the model was measured by a potentiometer fixed at the pivot point which in turn was arranged to go through the CG of the model.

Bow emergence was determined by observation.

For

this

purpose a scale was marked along the bottom and on one side of the model.

Bow submergence was determined by observation. It is

hard to establish any definite scale for this purpose, so it was decided to mark a degree of severity for each run where bow submergence occurred. O in this scale means that the bow is almost submerging, but no green water is taken on the deck. 5 means that the

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The results are tabulated in Tables I and II for the two models 'with beam ratios of 0.75 and 1.25. The results for the

parent form of Series 60, block coefficient 0.60, was given in Reference 1. Tables I and II give the complete data, including

the motions of the model. This paper discusses, however, only the resistance and speed reduction in waves as a function of wave steepness and the beam of the ship. The complete data will be analyzed and discussed at a later date.

The relationships between the total resistance Rt and the Froude number are given in Figures 2 to 4. The experiments were completed for 7 different wave heights. Each curve in these figures represents the results for a particular wave height, as

indicated. To obtain the reference resistance values, the model was towed in still water, first without and then with turbulence stimulation. A 1-inch sand strip 2 inches aft from the forward perpendicular was used for turbulence stimulation. The sand was fixed to the hull with rubber cement. The size of the sand was 14 and 20 meshes to the inch.

The results for the still-water towing are also given in Figures 2 to 4. These results were used to compute the added resistance due to the oncoming wave as follows:

Ra = Rt - R0

-9.-submergence may cause the sinkage of the model. This

particular observation is more qualitative than

quanti-tative.

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Here Ra is the added resistance in pounds due to the oncoming

waves;

Rt

is the total resistance in waves; and R0 is the still-water resistance at the same speed at which the total resistance Rt was measured in waves. The values for Ra are given in Table I and Table II.

The still-water resistance coefficients were computed for the three models and are given as the function of Reynolds number

in Figure 5.

The Added-Resistance Coefficient Ca is plotted in Figures 6, 7, and 8 as a function Froude number. Each curve represents the results for a particular wave height as indicated. The compu-tation of the added resistance coefficient was based on the following formula:

CG

-

Ra

+ Pv2S

where P is the density of water, V is the velocity of the

model in ft/see, and S is the wetted surface of the model in

ft2.

It has to be pointed out that for steeper waves the model has definite speed ranges in which change in thrust would affect very little or not at all the forward speed of the model. This

is very weil demonstrated in Figures 2, 3, and 4 as definite steps in resistance curves. The curve is almost horizontal

be-tween the steps (given in dotted lines), indicating that the particular speed range cannot be achieved in actual tests. The

steps in Figures 2, 3, and 4 are represented by definite humps in Figures 6, 7, and 8, where the added resistance coefficient is plotted as a function of the Froude number.

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Io-- ilIo--

il-Observations indicate that adding thrust starts to increase the speed of the model. Increased speed reduces the wave period of encounter and causes the model to pitch more violently, which in turn increases the average resistance and slows the model

down. Slowing down reduces the motions and hence the resistance. The model speeds up and the cycle starts over again. The pheno-menon is indicated in surge record as a long period surge upon which the regular wave-to-wave surge is superimposed. A sample of this kind of record is given in Reference 1, Figure 13.

Havelock discussed in Reference 2 the effect of speed of advance upon the damping of heave and pitch. He indicated that for a two-dimensional case of a submerged circular cylinder mak-ing heavmak-ing oscillations of frequency w and advancmak-ing with

velocity y , that at zero speed there are two wave trains, one

on each side of the cylinder. At speed y , if w

----

<* it can

be shown that there are four wave trains, one in advance and three to the rear, the wave train in advance being that for which the group velocity is greater than the speed of advance. If the

speed is increased, the amplitudes of two of these trains be-come infinite at the critical point when u

= and for

higher values of the speed these two trains disappear, leaving only two wave trains, both to the rear of the cylinder. Turning to the three-dimensional case of a point source, he shows that the infinity would not disappear through integration. The solu-tion contains integrals which are finite in general, but become infinite at the critical value.

Havelock made the calculations for an especially simple case, which may be taken to correspond approximately to a long

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-

¡2-narrow plank moving forward with velocity y and making forced pitching oscillations of frequency u . His curves indicate

infinity at the critical value w --_ = with a steep fall after this point, followed by a small gradual rise.

Golovato has made similar observations in his experimental work (Reference 3). He gives also additional data in his writ-ten discussion to Reference 2 which show startling similarity between his experimentally obtained plots and the calculations Havelock has made for the long narrow plank.

To apply the foregoing discussion to the present observa-tions, one should remember that the model is heaving and pitching with frequency equal to the frequency of encounter. Hence the critical value is we -Y--

=

; it has the physical meaning

of the ratio of model speed to the speed of waves generated by the pitching and heaving model. The critical value was computed

for wave length equal to the model length (i.e. 5.0 ft.) to occur at Froude number equal to 0.083. This critical value is indi-cated also in Figures 2, 4, 6, and 8.

it is interesting to observe that the

most

pronounced steps in resistance curves occur just around the critical value. What causes the additional steps is not quite clear. They may be due to additional humps in the damping moment curves or they may

have other causes. The effect of wall reflection in narrow tanks should not be excluded from consideration. Additional experi-ments with different wave lengths may cast more light upon the phenomenon.

As already mentioned, the added resistance in waves depends very much upon the motion of the ship in waves. Especially

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ness is given in Figures 9, 10, and 11. Froude numbers are used as parameters for the various curves. In some cases it take imagination to represent the experimental data by straight lines on log-log scale. However, for Froude numbers above 0.15 the approximation is not too bad.

If we assume that the added resistance could be calculated by the formula

R0 = K(vJs)

g H,

where Ki

s) is a function depending upon the wave

character-istics and the geometry of the ship, and n is the exponent to the wave height H , then the exponent n can be evaluated as the slope of lines in Figures 9, 10, and 11. This has been doné

- I

3-pitching motion has a very close relationship to the resistance. Hence, it seems to be very important to record all of the motions as 'well as the phase relationships, in addition to the resistance and velocity measurements. This has been done for the present experiments. The complete data will be published at a later

date. Figure 21 gives a sample of the measurements. Again, it is interesting to note that at the critical value of

uiei-=+

a sudden change in heaving and pitching will occur. The

pitch-ing angle undergoes a sudden increase, while the heavpitch-ing is some-what reduced. The data in this range have a considerable scat-ter, which could be related to the steep slope of the damping curve in this range. A small change in frequency of encounter may have a very pronounced effect on damping and hence the

motion.

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steep-- i 4steep--

4-and the proper values written for each curve.

Figure 12 tries to establish a relationship between the beam of the model and the exponent n . We have again a

consi-derable scatter for low Froude numbers. For higher Froude numbers the data is somewhat better. On the average the added resistance seems to increase as the 1.2 power of the wave height for the narrow model with B/Br = 0.75; as about the 1.75 power for the parent form and as approximately the 1.8 power for the wide model.

In general, the data gives the impression that the beam of the ship does not have a considerable effect on the added-resistance coefficient as the wave heights increase, provided that it is wider than a certain value. What is the critical 'certain value for the beam of the ship is hard to estimate on the basis of

available data.

There seems to be also a definite relationship between the speed of the model and the exponent n . For lower speeds

infl-creasing wave steepnesses have a considerable effect on the added resistance coefficient C0 . The effect seems to be at

a minimum for Froude number approximately equal to 0.15 and then increases somewhat wïth increasing speeds.

The bow emergence and submergence of the model was observed and recorded for each run. The range where the bow was emerged is indicated by a shaded area in Figures 9 and 11. The condition of maximum bow emergence is shown by a line. The range where the bow of the model was submerged is also shown in Figures 9 and 11.

The Speed Reductions for the three models are given in

Figures 14, 15, and 16 as a function of wave steepness. The

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-

15-water condition. The reduction is calculated as the ratio of velocity in waves to the velocity in still water. The thrust was kept constant for each line and was equal to the thrust which re-suits in the indicated Froude number in stili water. The figures demonstrate that the velocity reduction in waves is higher for lower still-water velocities.

Figures 17 to 20 compare the speed reduction for the three different models. Each of the figures is gïven for a different Froude number (NF)O. The figures indicate that for the narrow and wide models the speed is reduced by approximately the same ratio for both of the models. For the parent form the speed re-duction seems to be somewhat higher.

VI. SOME THEORETICAL CONSIDERATIONS

Kreitner (Reference 4) suggested that the additional resis-tance in waves is mainly due to the reflection of waves, Havelock

(Reference 5) did not agree and demonstrated that the drifting force due to the wave reflection was very small. He proposed a theory where the additional resistance arose from the phase dif-ference between the ship motion and the excitation of the waves

(Reference 6). Hanaoka (Reference 7) introduced a theory for the condition that the ship is forced to oscillate in still water.

In this theory he showed that the resistance is considerably in-creased due to the forced heaving and pitchIng of the ship.

Maruo (Reference 8) based his calculations on Lagally's formula and computed the mean value for the horizontal force. For a simple ship going head-on into waves he derived the

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follow--

16-ing formula for the added resistance:

RQ = K(w) pgH2

BL

He divided the coefficient K(w) into components which are directly related to the motions, such as heaving and pitching, and to

phase relationships between the motions and the excitation. One

additional component includes the direct effect of the reflec-tion of sea waves. The effect of surge is considered to be small and so disregarded. From his calculations he drew the following conclusions:

The excess resistance is independent of the still-water resistance.

The additional resistance is proportional to the square of the wave height, provided that the linear theory is valid for the ship oscillation.

The pitching motion has a dominating effect upon the resistance increase.

The direct effect of the reflection of sea waves is comparatively small.

The maximum increase of the added resistance occurs at a slightly higher speed than that for pitch synchronism,

if the natural pitching period is longer than the natural heaving period.

Maruo points out also a possible application of the theory for long-crested irregular waves with fixed direction. It is

usually accepted that the continuous spectrum of the wave energy may be replaced by a finite number of components and the Fourier

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The results indicate that the added-resistance coefficient depends upon the beam of the ship, the Froude number, and the steepness of the waves. On the average, the added re-sistance seems to increase as the 1.2 power of the wave

height for the narrow model, as approximately the 1.75 power of wave height for the intermediate model and as the 1.80 power of wave height for the wide model.

For lower lower speeds, increasing the wave height has a considerable effect on the added resistance. The effect seems to be at a minimum for Froude number equal to 0.15 and then increases somewhat with increasing speed.

In waves of considerable steepness, there are several speed ranges where increased thrust would not result in an increase

-

17-integral of the water surface could be approximated by a Fourier series of a finite number of terms. We can then practically

ob-tain the mean value of the resistance by taking sufficiently long intervals.

All the above mentioned theories are based upon the linear

theory. There may be objections about the assumptions. On the other hand, however, it seems to be almost hopeless to consider the application of non-linear theory to this problem. If we

examine carefully the terms which should be omitted and those which should be taken into account, we may still be able to use the linearized theory to obtain a satisfactory approximate solu-tion for the problem of added resistance of a ship in waves.

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-f8-in speed until the thrust exceeds a critical value. Then the speed jumps suddenly by a considerable amount. At the new speed the cycle is repeated again. The speeds between these particular ranges cannot be achieved in actual tests. The

most pronounced of these speed ranges is close to the cri-tical value where the speed of the waves which are generated by the oscillating ship is 4 times the speed of the advancing ship and where, according to Havelock, the damping moment goes to infinity.

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B - Beam of the model

Bp - Beam of the parent form

Ct - Total resistance coefficient

P/2

S v2

C0 - Added resistance due to the oncoming waves

Ca = Ct - Co

E - Bow emergence in ft from forward perpendicular NOMENC LATURE

g - Acceleration of gravity ft

sec2

H - Wave height from trough to crest in feet

L - Waterline length of the model in feet

01

-

Refers to still water condition

subscripts

wJ - Refers to the condition in waves

NF -

Froude number

NF

qL

NRe - Reynolds number

R0

-

Added resistance due to the oncoming waves

R0 -

Still water resistance

- The total resistance in waves

T - Wave period in seconds

Te - Period of wave encounter - the time interval the ship encounters two successive wave crests in seconds

V

-

Velocity in ft/sec

V - Velocity in knots

V= 1.689V

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-19-NOMENCLATURE (cont.)

Z - Double amplitude of heaving

9

-

Double amplitude of pitching

X - Wave length - distance crest to crest in feet

il - Kinematic viscosity ft2 sec.

P

-

Density of water lbs sec2

ft4

H 27T

-

Maximum wave slope

-2 X

W -

Frequency w 27r T We Frequency of encounter We 27T Te

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-20-Sibul, O. J. and Reichert, G.

"Ship Resistance in Uniform Waves as a Function of Wave Steepness", University of California, 1ER Series 61,

Issue 14.

Havelock, T. H.

"The Effect of Speed of Advance Upon the Damping of Heave and Pitch", Quarterly Transactions of the Institute of Naval Architecture, London, Vol. 100, No. 2, April 1958, Golovato, P.

"A Study of the Forces and Moments on a Surface Ship Per-foritiing Heaving Oscillations", David Taylor Model Basin, Report No. 1074, August 1956.

Kreitner, H., TINA 81 (1939).

Havelock, T. H., Proc. Roy. Soc. 175 (1940). Havelock, T. H., Phil. Mag. 33 (1942).

Hanaoka, T., Journal of Zosen Kioka, 94, (1954).

Maruo, H.

"The Excess Resistance of a Ship in Rough Seas", Interna-tional Shipbuilding Progress, Vol. 4, No. 34, June 1957.

REFERENCES

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-.--

-0-050 0074 o-426 ¡054 ¡-78? 0141 29-lO 00640-0360-0700-06(01940.,/; 4-543 4-3 4-0 0-80-30-00044 0-460-43 03 3 0, ¡60 -0-0-710

-n-

-o'- -s'-#55 0-092 o-458 i-irs ¡-sar 0,56 25-26 0-072 00 0-0740-403 0144 0-IlS 4-3 4-2 4-3 s-7 8-6 7-055 045 0-45 044 0-25 33 -1,--16$ 0686 -.0, .11 _00_ 0,60 011O 0490 ¡502 2200 O-174 2093 COOl 005200700-0700-nl o-110 4-440 4-0 S-7 8-4 7-7 0-43 o-Sl o-44 0-40 0-lO 4 -o--¡62 -,0-0-671 -'1--1 -,0 0-65 0-530 0-320 ¡.414 2-390 O-109 255 0030 00450-074 0-060 0-502 0-lOO 4-2 3-3 4.3 3.7 0.5 72 o-43 059 g-4 037 0-0 4 -0-/65 -6'-0-660

-"

-o,-0-70 0-543 0-555 ¡-484 2308 O-198 ¡3-Il 0-e3S0-0-0l 0-070 0-0670-09 0-00 4-2 3-9 4-0 3-6 8-2 75 0-46 040043 0-30 0-0 4

-o-/64 -'o-0-646 -00- -1,-- -o'-0-75 O-160 0590 ¡57) 3.657 0.210 76/0 o.OS00135007jo.oS4o.lj, oo344 39 43 3-1 3-1 700.450-350-420-36 00 4 -0-165 -0'-OSSI _00_ _00_ __/_ 8-80 0/00 0620 ¡-676 2-852 0-225 /6-75 o-01 006/ 0-0440.03 0097 Ai 3.5 0-6 32 77 67 042 056 048035 0-0 4 ,,b1s 066 -o--000 -70 0-542 00684 0/0 -O-015 -o-032 -o-0017 o-054 0.048 0049 0045 0-03 0-095 5-0 S'O 4-0 43 ¡00 95 030 03? 04$ 039 0/0 0 -o-167 -s,-0-965

-"

-,,- -oi-o-55 o-070 O-150 o-oSO o-755 o-Oli! /00722 0-03900520-341 0-5430.006 6095 34 4.9 5-2 4-8 :0-3 67 os, o-29 042 0-40 0-5 fr, 148 -0-_ 0904 - 'O_ !, 71 -0-20 0-008 0 ¡92 0-290 0 490 0-0387 077-26 0060 0056 20570406 0,57 0034 69 6.3 6-7 6-3 536 526 040 0-27 056 052 03 ¡ -o-¡49

-o- o-893 -s-

-'o-0-25 O-010 0-240 ¡7509 0-522 00412 035-23 01/SO 00700.003 0-0649493 ''56 6-0 63 60 5.5 ISO il-6 056 o-460-5204$ 0-4 3 176 -a-5-087 -'o- -o'--0, 8-30 O-010 0-290 0-837 0-570 0-0450 ¡9333 o-1180-084 0075 0-062 0-055 olS 6-0 5-3 6-I 54 ¡2-6 Il-3 0-4.2 043 0-52 0-46 0-3 1fr4 171 0-885

-,,- -e,--0-35 0-011 0-359 0-565 0613 o-0484 /91-So o-080 .006 0/07 200 2-1,5,057 4: 4-0 60 47 13-i 93 097 044 0.50 039 85 2

-0-/72 -° 0-672

-o'-

-n- -o-o-40 0-OiS 0-387 0-399 0-674 o-0532 00-72 0.100 0-000 o-006 0007 0-033 0-567 5.4 4-7 54 4-0 ¡00 95 054 0-43 0-44 o.s 1-3 .2 -.0-173 -00--o-SOI

-'o-

-I'- -Jo-0-43 0-025 o-425 o-642 /085 0-0656 78-24 0-093 0055 0-0117 l-056 0,34 0-090 72 63 75 6-6 ¡45 ¡SI 0-3e 0-07 0-59 0-54 #6 -24 -$-174 -* 0853 __b0

--/'

050 0-024 0-476 0-634 ¡-Oil 00063 69-93 0-073 o-0030037 .048 osSo 004 7-2 04 7-2 65 ¡44 52-9 0-86 0-30 0-39 953 07 3 -0 /75 -'s o-802

-'o- -o,-

-s-o-SS 8-029 O-521 0.682 l-155 0-0910 8495 o-045 2-058 0-095 0051 O-100 0104 6-4 f-7 7-3 57 :3-8 ¡i-4 o-SS 0-11 0-57 0-47 0-7 3i

-¡76 -Oo-15765

-'7--l"

- n-o-60 ¡3-045 0-555 o-870 i-470 o-lis 55-65 0-085 0_07. -.04 0075 0.169 0553 5-4 50 5-5 35 ¡09 ¡6-5 0-49 0-40 0-45 042 o-5 4 /77 -01- 0761 -0.--05- -,,-0-65 0-050 0-400 0550 /-538 0-021 55-89 0-08 0-070 .000 4-070 0140 0040 5-0 4.7 5-3 3-4 /63 18-1 149 1-43 0-45 04/ 4-4 4 178 -.4--0-736 0,-. -'_O 0 0-70 0-065 0.635 012 ¡770 O-155 47.08 0084 7057 0-086 0763 0147 0405 5,0 4.3 34 5-d ¡04 05 I-4g 0-9 043 os 0-4 4*o ¡79 -0 0-739 00 - 11 _.50_ 0-75 0.070 0600 032 5770 O-140 46-63 0070 0062 0-01? 0007 0-'6S 0/30 5-2 43 5-3 49 ¡0-5 9-4 o-46 0-38 049 0-59 7-5 4k8 ' -¡80 -o-0-7:3 -0'-_11 -'il-080 0-090 O-710 5-$42 l-964 O-155 39-80 0070 o-039 0-094o-077 o-iO.4 0136 4-6 4-0 5.4 49 10-0 09 0-48 0-40 0.41 006 0.5 416 -1--10$ -0- 0-700 -o,-*- -o,---085 O-100 0-700 ¡239 2.094 o-065 '7-06 9070 o-057 0053 0-070 0163 0-147 5-3 3-3 52 47 ¡0-3 06 o-48 0-37 0-43 0-35 il-1 4/6

(29)

TRACK FOR THE SUOCARRIAGE SUBCARR tAGE . -SURGING J1 J, HEAV I N G TOW L I N E P I TC H I N G

PIVOT AT CENTER OF GRAVITY

LINEAR BALL BEARINGS

_-GUIDE RODS

r'11.. 0.075'

CONSTANT SPEED OF THE CARRIAGE DIFFERENTIAL PULLEY

-ARRANGEMENT FOR CONSTANT

THRUST TOWING

c51

WEIGHT FOR CONSTANT THRUST

(30)

LO 0..7

0.6

0.5

0.4

0.3

0.2

0.I

o o

0.02 0.04 0.06

0.08 0 I

0.12 0.14 0.16 0.18 0.2 0.22

0.24 0.26 0.28

0.3

0.32 0.34 0.36

FROUDE NUMBER

TOTAL RESISTANCE

OF THE MODEL IN

5.0 FEET WAVES

(X/LI.00)

I

B/Bp

0.75 I

I>

.

H0.342'

13

H0. 79'

57

/

/

'I

_

U

4 ¡

- 4

ST I L TURBULENCE L - WAT ST I L L- W A TE R O UT TURBULENCE STIMULATION STIMULATION WI T H E R WI 1H

(31)

U) LO 0.9 0.8 0.7 w

o

z0.6

I- w 0.4 0.3 0. cf o o 0.02 0.04 0.06 0.08 0.10 0.12 014 0.16 0.18

0.0 0.22

0.24

0.26 0.28

0.30 032 034 FROUDE NUMBER

TOTAL RESISTANCE OF THE 5 FOOT

SHIP MODEL IN WAVES

OF VARIOUS HEIGHTS AS A FUNCTION OF

FROUDE NUMBER 11 11±: J-H =0.342 -'0.267

J1:!6P4uí1

o.2I7o.i79

I

L

J.

WITH STIMULATION LENCE STMTUION STILL TURBULENCE WI ER -.

-_-I=i-.

i

_I

I

(32)

LO 91 0.7 0.6 0.5

04

0.3 0.2 0_I O o 0.02

0.04 0.06 0.08

0.1 0.12 0.14 0.16

0.18 0.2

0.22

0.24 0.26 0,28 0.30 0.32 0.34 0.36

FROUDE NUMBER

TOTAL RESISTANCE OF THE MODEL IN

5.0 FEET WAVES

(>y=

1.00)

H i j

0.342'

B/Bp

1.25

s

.11

H=0.217'

H0I7I'

si

H 0.157'

1*

£

X//.

__

__

-j

-V

--

UI'

.__ll

_

u-______ ST I L TU R B TURBULENCE ST I L L- WAT E R WI T STIMULATION H L - WATE R WITHOUT U L E N C E ST I M U L AT I ON 0.9 u, 0.8

(33)

X

REYNOLDS NUMBER

NRe

'U'.,

STILLWATER RESISTANCE COEFFICIENTS

FIG. 5

9 8 7 6

:

3 2

-B/Br

L25 LOO

o/Br

B/Bo.75

i

ITTC 1957 LINE 5 7 8 9 5 2 3

(34)

200

40

20

4 2

0.8

OE6

0.5

o

0.05

0.10

0.15

OE2

FROUDE NUMBER

a'

I t I

L

B/Bp075

I'

\%

\\\

H

xx

IHO3 42'

*

I H = O.267' t 'o H O.217

.

xx

-k

oI

'S'.' > 3

II

H

ADDED RESISTANCE COEFFICIENT DUE TO

THE ONCOMING WAVES

FIG. 6

0.25

OE3

loo

80

60

o

Io

X

o

6

(35)

40

200

100

80

60

40

20

o

L) 8 6 4 2

I-0

0.8

0.05

OJO

0.15

OE20

FROUDE NUMBER

0.25

0.30

0.35

B/Bp

= LOO

'

'P

' \

'J.

\

\

\

\

H =0.342'

V

=0.267'

H = 0.217' H 0. 157

.'

H=O.073

H=0

qj:o.o..

o

ADDED RESISTANCE COEFFICIENT DUE

(36)

300

200

lOO

80

60

40

20

o

8 6

4

2

0.8

0.6

B/Br

= L25

..

\

'

I I

J \

'I

\

.t

____________________________________________________ .

N

I!!

1

I

!

!.!I

s

s I s

ADDED RESISTANCE COEFFICIENT DUE

TO THE ONCOMING WAVES

FIG. 8

0.05

0.10

0J5

0.20

0.25

0.30

0.35

(37)

200

40

20 4 2 001 0.015 0.02

0.03 0.04

0.06 0.08 010

H/X

ADDED RESISTANCE COEFFICIENT AS A

FUNCTION 0F WAVE STEEPNESS

H/X

FIG. 9

liii!

FA

'

1

I'1

TJJ

V

AI

,4EiII

4l

IIrg

j4i

RANGE EMERGENCE OF 60W 0

ill

rnÑu

°ìdVM wi

WTo

I°__

Pi_iIIIU

IIIIII

_r

O

°AIII

Ii,

RANGE GETS WHERE

r.

11111

SUBMERGED BOW

r

Nillill

r

lOO

80

60

Ca X IO 8 6

(38)

300 200

I00

80

60 40 Ca X

30

20

Io

8 6 4 3 2 0.01 0.015 OE02 0.03 0.04 0.06 0.08 0.10 H IX

ADDED RESISTANCE COEFFICIENT AS A

FUNCTION OF WAVE STEEPNESS H/X

FIG. IO B/Br = LOO 4)

1i1

II

ir)iI

rTIiUUhI

Á..AFiiRIIII

141Ml

'All'il

.virAr4un

°

D

V4F' -111111

viii

o. 'b / o. ,,

/

/

(39)

200

20 6 4 2 FIG. II B/Br = .25 J 4 o

-LINE OF BOW EMERGENCE MAXIMUM

MV'

A

r

i

___!iiiti

VaIWAWA

4.,

"r"

;AIIIV__

IUMIIrAA

r-é'

.

M

RANGE EMERGENCE OF 80W 4

r AU!áII

AVA!4!i1

A

U

VI

11111

4V1IUIII

p

vr

0.01 0.015 0.02

0.03 0.04

0.06 0.08 0.10

H/X

ADDED RESISTANCE COEFFICIENT AS A

FUNCTION OF WAVE STEEPNESS H/X

100

80

60

40

30 C0x

Io

(40)

C

F-z

u

z

o

Q-X

w

2.3

2.2

2.1

2.0

L9

1.8 1.7

L6

L5

L4

1.3

.2

I.'

I-0

FIG. 12 Mf

______

NF O.t5

W7KAd

'7

/(

0J5

1.0

1.25

B/Bp

(41)

2.6

25

24

2.3 2.2 2.1

2.0

C

'.9

I-.

2,8

uJ

-z

ol.7

G-X

I.6

'.5

-4

'.3

1.2 I. I 1.0

o

B X =

0.07

Bp = = 1.25

I_00

-5 2 4 6 8

ai

2 4 6 8

0.2

2

FROUDE NUMBER

4 6 8

0.3

EXPONENT

n AS A FUNCTION OF FROUDE NUMBER

(42)

0.

a

0.

0.01

0.02

0.03

0.04

H/X

0.05

SPEED REDUCTION AS A

FUNCTION

0F WAVE STEEPNESS

0.06

FIG 14

0.07'

B/Bp

0.75

o

>

>

0.2

Ui

0.08

(43)

w

-J -J

I-(J)

z

o

w

w

Q-(J)

o

(n

w

>

z

o

w

w

0

0.06

o

0.01

0.01

s FIG. 15

-lv

'-v

(NFr) O.30

B/Br = 1.00

D

(NFr)O.l5

£

.

.

D D V o

THE FROUDE NUMBERS ARE

FOR STILL-WATER CONDITIONS.

GIVEN

SPEED REDUCTION AS A FUNCTION

0F WAVE STEEPNESS

.

002

0.03

0.04

0.05

0.06

0.07

1.0

0.8

0.04

0.02

0.6

0.4

0.2

o

>

)

0.I

0.08

(44)

o

>

1.0

0.8

OE6

0.4

0.2

O.'

0.0

0.0

0.0

0.01

0.02

0.03

0.04

H/X

0.05

SPEED REDUCTION AS A FUNCTION

0F WAVE STEEPNESS

0.06

0.

FIG. $6

B/Bp

L25

Sa D

xo

(4, D

o

A

o

o

(45)

LO 0.8 0.5 0.4 0.3 LO 0.8 o

(n>

uJ > 0.2

o

uJ uJ Q-UD 0.1 0.08 0.06 0.04 0.02 001 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 H /x

SPEED REDUCTION AS A FUNCTION OF WAVE STEEPNESS AND BEAM OF THE MODEL FOR STILL-WATER.

FIG. 17 & 18

I___

I

FOR STILL WATER

FROUDE NUMBER (NF)O02O

FIG. 18 0.2

\

\\

\

0,1

\o\

\

\Q_

\

0.O8

-0.06

.0,,

\

O.O4\ FOR STILL-WATER

FROUDE NUMBER (NF)OO.I5

\

\\

\

\

\

\

\

\

\

FIG. 17 0.6 uJ uJ Q-CI)

o

0.4

I

(46)

z

LO

0.8

0.6

0.4

0.3

Q

w

-w

Q-0.8

o

o>

(ID> 0.6

uJ

>

0.4

o

w

w

a-

0.3

(1)

o

0.2

O.'

SPEED REDUCTION AS A FUNCTION OF WAVE STEEPNESS

AND BEAM OF THE MODEL

FIG 196 20

1.25 FROUDE

FOR STILL-WATER

NUMBER (NF)O=O..3O x B /B p = 0.75

FIG.20

B/B=

0.2

.

.00

0.15

0.I

o FOR .STILL-WATER

FROUDE NUMBER (NF)0O.25 B/Bp

I .25

B/Bp 0.75

FIG. 19

B/BpI.00

(47)

-J &? 0.20 uJ L) 0.16

z

w 0.12 Q: 0.08

004

0.4 o Q: 0.3 Q: * 2 D

o

8 6 40 5 w

o

Ui (D

Q:3

lu

i

D

(nl

o

o NF BOW EMERGENC BOW S

o--E UB MERGENCE NF 2 4 6 8 0.1 2 4 6 8

02

2

MOTIONS AND RESISTANCE IN UNIFORM WAVES

4 6 8 0.3 FIG. 21

B/B='.25

H/X=O.0434 HO2I7FT. X/L=I.00 X=5.00FT. I

I.

PITCH HEAVE I NF '3 o NF 0.2 I' 0.1 o 1000 8 6 4 1.2 1.0 0.8 - 0.6

I

0.4 NJ 0.2 o 0.6

Cytaty

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