On the evaluation of sea spectra based on measured ship motions

On the Evaluation of Sea Spectra based on

Measured Ship Motions

August ₁₉₇₂

by K4t suyo sh 2Takekuma

take shi) Takahashi

Resistance and Propulsion Research Laboratory, Nagasaki rrec}jcal Institute,

Mitsubishi Heavy Industries, _Ltd.

Technische Hogeschool

DeRt

On the evaluation of sea spectra based on the measured ship motions.

by Katsuyoshi Takekuma Takeshi Takahashi

Summary

Statistical prediction of the behavior of a ship in waves by use of some typical sea spectra, such as, ISSC spectra, has been a common practice

for ship design and operation. The experimental proof of it, however, has

not been given yet because of the lack of accurate ship borne wave recorders. An attempt was made to solve this problem regarding a ship as a kind of wave recorder which is used through the calibration of response amplitude

characteristics. As the results, power spectral density of waves with

which a ship encounters at sea, could be successfully calculated under the assumption of linear superposition.

The usefulness of this method was confirmed by analyzing some sea data of two high speed container ships.

i Introduction

Theoretical investigation of seakeeping qualities has been largely advanced for these several years by the use of a high speed digital computer

and newly developed instruments. It has been a common practice for ship

design and operation to predict behaviors of a ship in waves by use of some typical sea spectra and response amplitude characteristics.

However, the experimental proof of the statistical prediction has been postponed, because of the lack of accurate ship borne wave recorders,

except such a few examples as given by Aertssen and van Sluys.

The advancement of stucLy on the correlation between sea data and model results is, therefore, not always satisfactory in comparison with other studies on seakeeping qualitiee, and many sea data have been

stored for long years without further analysis.

At present, the development of wave measuring equipment with good accuracy is regarded as one of the most important and difficult problem

in the investigations of' seakeeping qualities.

As one of the methods io solve the above mentioned problem, an attempt was made to obtain the significant wave heights and periods from

the records of ship motion in waves, under the assumption of linear

superposition which has been already used for the prediction of behavior

of hjps at sea. Since the accuracy of linear superposition and the

theoretical response amplitude characteristics of pitching motion at heading sea have been examined before hand by model tests, authors chose the pitching motion as the referential ship motion.

Regarding a ship as a kind of wave recorder which is used through the calibration of response amplitude characteristics, the spectra of waves, with which a ship encounterB at sea, can be successfully obtained. This method can be called "Reverse Operational Method of Sea Spectrum." The usefulness of this method was confirmed by analyzing some sea data of two high speed container ships, i.e., the Hakone Maru and the Kamakura

Mani.

2 Reverse operational method of sea spectrum

The spectra of short crested waves with which a ship encounters

can be evaluated theoretically from the response amplitude characteristics in regular waves and the power spectral density of measured ship motion under the assumption of linear superposition which is the same as used

in the prediction of the behavior of a ship at sea. The co-ordinate system is shown in Fig.l. Then

=J *

4Vs

cose

_/

et)1J cos5c

(i)

where

[cw)2J ; Power spectral density of wave

Power spectral density of pitching motion obtained from sea data

Response amplitude characteristics in regular wave obtained from theoretical calculation or model tests. Ship' s advance speed

Acceleration of gravity

e ; Encounter angle of ship's course and mean direction of

We

; Frequency of encounter observed or board

W

; Frequency of wave motion obtained b the following

formula at heading sea

W = -i

₊

J

I

4e/2VscO$9/

(2)

; Angle between direction of elemental wave and mean

direction of waves

Various mean wave heights and periods are also evaluated from the wave spectra thus obtained through the same methods as the prediction of behavior of ship motions.

Eq. (i) and (2), however, can be applied in only such cases as

encounter angle being smaller than 60 degrees.

3 Analysis of the sea data of the Hakone Maru

Seakeeping trials of the Hakone Maru, single screw high speed container ship operated between Japan and U.S.Pacific coast, were

performed in January ₁₉₇₁ by the 108th Research Commfttee of the

Ship-building Research Association of Japan. Principal particulars of the

Hakone Maru are shown in Table 1. Measurements of pitch, roll, yaw and

three vertical accelerations were carried out during North Pacific crossings. Power spectral density of waves with which she encountered during

North Pacific crossings were calculated by the proposed method mentioned

in the previous section. Some examples are shown in Fig.2

The power spectral density of waves obtained above is not in good

agreement with typical sea spectra, for instance, ISSC spectra or

Neuxnanns spectra as shown in Fig.2. Sometimes considerably large

differences can be seen. Where, ISSC spectra corresponds to the

significant wave height and period evaluated from the power spectral

density of waves obtained by the proposed method and Neuman's _spectra

corresponds to the measured wind speed.

However, the good coincidence le observed between the measured ship motions and the predicted ones obtained by the use of ISSC sea

spectra as shown in Fig.3. _{The agreement between significant wave}

heights and periods of thus obtained power spectral density of _waves

and mean wave heights and periods which were observed by one of authors on board is comparatively good as shown in Fig.4, considering the accuracy

Thus, it may be concluded that _{power spectral density of waves}

obtained by the proposed method using the sea data of _{pitching motion}

cari be applied to practical use with enough accuracy.

Aertssen and van Sluys reported _{in their paper that coincidence}

of

response amplitude characteristics of _{longitudinal ship motions which}

were obtained by theoretical calculation,

model tests in regular waves and evaluation from the records of ship motions and waves at sea is

considerably good. _{This may also support the applicability of the}

proposed method.

4 Application to sea data of the Kamakura _{Maru (1)}

(On evaluation of _{sea spectra and comparison of measured and predicted}

ship motions)

Seakeeping trials of the Kamakura Maru, twin screw container ship operated between Japan and Europe via Panama Canal, were performed in her

maiden voyage by Kobe shipyard, Mitsubishi eavy Industries Ltd.

Principal particulars of the Karnakura Maru are shown in Table 1. Measurements of ship motions various acceleration, pressure variations on hull surface and stresses at various locations were

carried out during North Pacific crossing. Fig.4 includs also the

comparison of the evaluated significant wave heights and the observed ones for ttKamakura Maru".

In this case, however _{it is regrettable that mean wave heights}

and pirads etc. which _{are to be compared with the calculated values}

could not be observed at the _{same time as the measurements of ship}

motions, because of the limitation on the number of items to be measured. Therefore, the comparison was made between the measured ship motions and the predicted ones obtained by the use of ISSC sea spectra agreement of both is comparatively good as shown in Fig.3.

5 Application to sea data of the Kamakura Maru (2)

(Further investigation on sea data of pressure variations)

An attempt was made also for comparison _{of sea data of pressure}

variations and. predicted ones obtained through _{the same method mentioned}

in the previous sections.

Fig.5 shows the results of comparison. _{In Fig.5, it is seen that}

spectra varies to a considerable existent, the agreement being good in

some cases and bad in other cases. In order to exasine the reason of

discrepancy, the prediction was made on two typical examples by the use

of the sea spectra evaluated by the proposed method instead of ISSC sea

spectra. The results are shown in Fig.6 and

_7.

Exp. No. 6-C is the

typical one where the remarkable difference exists between sea data and predicted one by the use of ISSC sea spectra, while exp. No. 5-B is another

typical one where good coincidence exists between them.

The prediction by the use of evaluated sea spectra yields a better

agreement than by ISSC sea spectra. Even in an extreme case of exp.

No. 6-C -the agreement is some what similer to the case of exp. No. 5-B,

as shown in Fig.2. _{The explanation for this results is given as follows.}

The response of pressure variation to wave components with high frequency

is more sensitive than that of ship motions as compared in Fig.6 and

_7.

The accuracy of prediction is much influenced with the difference of _sea

spectra which is used for the calculation. In the case of exp. No. 6-C,

considerable difference exists between the evaluated sea spectra and ISSC sea spectra which corresponds to the evaluated significant wave height, especially in high frequency zone.

In the case of exp. No. 5-B, -the evaluated sea spectra coincides well with ISSC sea spectra.

Therefore, it may be possible to obtain a good coincidence between the pressure variation observed at sea and predicted by calculation for

other cases by use of the reverse operational method. Further analysis

is now underway.

From the above examination, it may be that pressure variation can

be predicted by the use of following empirical formula without a terms due to sea waves.

where

{

(w?]

; Power spectral density of pressure variation

Response amplitude characteristics of pressure variation

/'i

[w)2]

=

\ [B(L)e_z)2Jcos,Z

e-g]

coX

()

6 Conclusion

Through the examination on sea data of two high speed container ships, the following conclusions are obtained.

(i) Regarding a ship as a kind of wave recorder, power spectral

density of waves with which a ship encounters can be calculated by the use of sea data of pitching motion and response amplitude

characteristics under the assumption of linear superposition. This

method can be called "Reverse Operational Method of Sea Spectrum". The usefulness of the method was successfully confirmed by the examples given by the authors.

(2) Pressure variation on ship hull can be also predicted with good

accuracy by the use of the above evaluated sea spectra. The accuracy

of its prediction is influenced by the accuracy of power spectral density of waves especially at high frequency zone.

Acknowl edgernent

The authors express their gratitude to Dr. Taniguchi, the director and manager of Nagasaki Technical Institute, MIII, to Dr. K. Watanab, the assistant manager of the same, arid to Dr. H. Fujii, the manager of Sea Keeping and Manoeuvre Research Laboratoty for their instruction and encouragement.

They thank also Mr. Hirai who was in charge of numerical calculation and other members of Nagasaki Experimental Tank for their assistance.

References

Aertsen.G and van Sliys. M. F

Service performance and sea keeping trials on large container ship

RINA

₁₉₇₂

Tuckey. John W

The sampling theory power spectrum estimates

Symposium on applications of autocorrelation analysis to physical

problems. Woods Hole, Mass., June 13-14 1949

Canham, H. J. S, and Cartwright, D. E., Goodrich, G. J., and Hogben, Sea.keeping trials on O.W.S. Weather reporter.

Lpp Bm dm Cb L/B B/d DW Number of Containers (20') Typ of 1]ngine MC H xRPM Service Speed Ship Owner Bu i ide r

Table i _{Principal particulars}

Ship _{"Ha.kone Maru"}

"Kamaku ra Maru" 175. orn 26.Om

iS.5m

95

24,777t 0.558 6.720 2.735 16, 3yJt 752 Diesel 27,8OOBHPil5RPM 22. 6Kfl0t8 NYK ruir Kobe 245.

322m

24. 12. 0m 58,058t 0.590 7.598 2.68 35, 396e 1,838 Th rhine 40000SHPi 35RPMX2 26.4KnotB NYK 1'IMI Kobe

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