Experimental seakeeping trials on the italian frigate Sagittario

ARCHIE

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CENTRO PER GL STUDI DI TECNICA NAVALE C E T E N . s. p. a.

4

Experimental seakeeping trials on the Italian Frigate "SAGITTARIO" (Lupo Class)

B.Chil Report no

1109

Genoa, November

1980

_?CV/0O15

12b.v

Tech

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Introduction

On March 21st 1979 CETENA carried out high speed seakeeping trials on the Italian Frigate "Sagittario" (Lupo Class) on request arid on behalf of the Italian Navy. The test campaign performed in the Ligurian Sea was organized within the context of an important initiative by Mariconavarini, with the

aim to collect full scale experimental data on the seaworthiness of the ships. The tests were performed in the following trim and displacement conditions:

106.0 m. B ll.98m. TAV 3.60 m. T 3.68 m. 2310 tons Trials modalities

Fig. 1 is showing the ship's course and the mean sea direction during these tests. Please note that the sea trial Was cared un in eight phases, five of which were each characterized by a different heading angle, while repeat

ing, during the last three phases, the tes with the beam,how and quartering sea, to check the efficiency of the stabilizing fins.

The tests were performed at a speed of 30 and 20 knots. The results reported in this paper refer to the speed of 30 knots only since the environmental conditions during the 20 knots test changed so much as to annul the signific ance of a comparison between the results of the tests.

Seakeeping Test Instruments

The instruments taken on board are iliListrated in fig.2 directly deived _from ref./l/ showing the technical particulars of this equipment in detail.

The quantities mesaured during these trials are listed below: - the ship's speed (R:aydist)

- power and rp.m. (CETENA torquorneter)

- angular motion of the ship (RMS stabilized platform) - vertical acceleration at C.G. (RMS stabilized platform)

- vertical acceleration at bow and stern (KISTLER accelerometer) - slamming stress (Micron Measurement strain gauges)

= relative bow/sea surface motion (SEPA height sensor) - wave height (DATAWELL waverider buoy).

Analysis of the resulting measures

All above mentioned quantities were magnetic tape recorded; the time series f the motions and accelerations were frequency analyzed with the aid _{of a} Fist Fourier Analyzer to determine the _{response spectra to be correlated} with the spectrum of the sea. It has thus been possible to derive the trans fer functions for the vaious quantities _{at different heading angles.}

Dtrting this stage, special care was given to the relative bow/sea surface motion sinal (SEPA) which pei'mitted to obtain the sea spectrum after its

suitable correction by the angular motiori of the ship. More in detail: after having fixed an inertial tern, oriented as shown in fig. 3, having its origin in the ship's center of gravity and moving at the semé speed as the ship, it became possible to drefine the ship's linear motions _{along the}

three axes of the tern as well as the angular one yaw çb , pitch 8 and roll respectively as three subsequent Eulerian rotations.

In this way, the tern (x', y', z'.). integral with the ship, obtained after the three rotations is mathematically linked to the system of inertial axes

(x, y, z) through the matrix relation:

Therefore a ship point of öordinates Q , Q) with respect of the center

of gravity in the system integral with the sip,when

it

has only angular mo tions,will be subject to a shifting vector P. the coordinates of which in the

inertial term (z., y, z) can be expressed as follows:

P.x

Py Q (3)

Pz Qz

in which

M1

is th inverse matrix of 1 as expressed by the relation (2). When assuming in first approximation that. the yaw angle is zero (this assum tion being justified by the fact that the ship virtually maintained the same course during the trial), the vertical coordinate of the vector P can be ex pressed by the relation:

-seri9

Qx +

cos9 senç Q -'- cos9 co Q

which in our case can be reduced as follows, due to.the fact that. the SEPA transducer is positioned along the ship's plane of symmetry (Qy 0):

-sen9 Q

- cosO cos5e, Qz (5)

If the ship is heaving in addition to its rolling and pitchiig,. the SEPA ultrasonic sensor will measure the quantity R, resulting from the following

relation: .

-whei considering the sea elevation , the previOus signal will be reduced by

the-ame amount so that the- trend of the wave contour (t) as a function of tithé can be exp±essed by the following formula:

- (t) R(t) + z(t)

P(t)-

Q

or more explicitly: . . .

-- _{(t) = R(t)}

+

Z(t) - Qxsen

0(t) _{+ Qz} {cos 8(t) cos

ci(t)i}

(7)

COSO

-cos

sen4

senç sen

ccs4i

s'en

+cos

sençb cos9 -sen9

senO cos4i cosço cosØ +sëntp sene ser4 seng cosO

sen9 cos

-sen cosg

-lcoEç

sen9 seriçb cosç cosO

(2)

)Ct _x y, z, y z (1)

in which the matrix M is expressed in terms of the three rotations s foJ, lows

However, one more problem must be solved due to the fact that the instrumen tation on board allows for measuring R(t), 0(t) and ç0(t) whereas the heav ing signal can only be theasured through its acceleration (t). A solution might be possible through a double integration in the time domain of the ac celeration signal. Since the initial conditions are unknown, this can be oh viated by assuming an average zero value for the vertical motion and for its derivatives with respect to the time.

But as our interests are mainly geared towards spectral characteristics of the sea rather than towards wave height as a function of time, we preferred to operate in he frequency domain to derive tbe sea spectrum from the relation: S C we) S

( w) + S(

We) + 2 CzR (

W)

₍₈₎ in which and Sp are respectively representing the heave spectrum and the corrected relative vertical motion Rc(t) resulting from the relation:

R3(t) R(t) - Qxsen 0(t) + Q {cos 0(t)cos p(t) - l (9.)

and with CzR the cross spectrum between z(t) and Rc(t).

Since the spectrum SAA of (t) and the cross spect'um CAR between (t) and R(t) can be easily bälculated, the spectra related to heave motion. z(t) can be expressed by the relations:

( cue) _°e)

CzR ( w)

_{j2 CAR}

(

W)

so that (8) can bewritten as follows

C we) SRR (

(2))

AA(°e

2

C0e2 CAR (

W)

(10)

This will give us immediate information on the energy contents of the sea

and hence, to determine the wave parameters such as for instance the signific ant wave height, whereas the frequency parameters such as the modal or mean period will require an additional operation Since the sea spectra.were deny ed as a function of the encountet' frequency we.

During this trial, the ship is indeed travelling at a certain speed V and ata certain heading angle14 with respect to the direction of the wave propagation.

To determine the sea spectrum as a function of its absolute frequency it _will be necessary to. perform a frequency mapping. Conversion of the spectrum

versus encounter frequency into an absolute frequency spectrum is based tpon energy considerations the energy content of the sea spectrum remains capstant whatever its rèpresantatioti in abScissa

S(we)dweS(w)dw

. . (12) or in other words t. :. S ( ' _{) S} (

W)

(1

-2wV

cos1a) . (13)

-4-Display of the results'

The table 1 includes the findings of th various trials steps in terms of si nificant amplitude of the ship's,motions arid accelerations, as well as regard ing the significant sea heights as well as mean RPM, power and speed.

Fig. 4 shods the sea spectra as a function of the absolute frequency establish ed with the methbdolo described above during the phase 1, 3. 4, 7 and 8 .of

Table 1. In view of the poor reliabilityof the data i'egurding beam seas, only the spectra of the steps 1, 4 arid 8 are reported in fig.. 5 for comparison with the spectrum derived from wave elevation measUred by mean of the wave rider buoy. The figures 6 thru 11 are showing respectively the roll, pitch and barycentric vertical acceleration response spectra as well as heave, ver tical accelerations at bow and stern measured during the phases with head, bow and beam seas.

The figures 12 thru 15 are featuring in the same order, the response amplitu de operators of the ship motions and vertical accelerations at'the C.G. for the trial steps with head and bow seas except for fig. 12 regarding roll, where only bow sea values are reported. These figure are also reporting the theoretical response amplitude operators obtained by the SCOSTF computer pro gram used by CETENA based. upon the strip theory.

Conclusions

Fig. 5 clearly shows that the values measured by the waverider buoy are in agreement with those obtained by the system installed on board except rorsome differences at peak frequency when the ship is running with seas from the forward quadrant.

We have however planned to repeat this experimental campaign which should en able us to make comparisons and to obviate the poor frequency resolution of the sea spectrum measured with the waverider buoy, due to frequent iriterrup' tions of the transmitted signal because of the negative environmental condS. tions.

As to following and quartering seas, the on board system can't be used to de termine the sea spectrum since there is no one to one relation between the en counter and the absolute frequency, nor it is possible to get information on the wave height from such data because of the "shadow".phenomena caused by :the hull at the wave elevation measuring point. As already said before, no

agreement was achieved with beam seas (step n°3 and n°7 of the trial) regard ing significant sea amplitudes (see table ri° 1) and spectra distributions (fig. 4) so that a further and more thorough study of this problem will be necessary and other tests to check the validity of the wave-height recording

system used on board of the ship.

Finally, as to the response amplitude operators of the various motions and accelerations, an overall satisfactory agreement was, found between the ex perimental and the theoretical findings., when taking into account' the errors. due: to a lack of knowledge about the short-crestedness of. the sea.

THeonly exception concerns the response operator of roll wh.ich theoretical values overestimated the experimental ones. In our opinion, this.is due to the inadequate theoretical approach which only considers the purely linear phenomenon.

wlgnts

The Author wants to thank Comm. C.F. Timossiq the Chief Eng'±néer C.0 Ven, and the whole crew for their determinant cooperation during the installation of the instruments on board and during the measuring campaign..

References

/1/ B.Chilô "Description of an instrumentation package to recOrd L.Mantellato seakeeping full. scale data"

STEP I SEA DIflECTION FINS P.P.M. POWER SPEED

SIGNIIICANT AMPLITUDE SEA

SIGNIFICANT I.IEIGWT OL1 ' PITCfl VERT.ACC.

VET. A.

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VERT. ACC., a U1VE

[hp].

['knots].

.[deg]

[deg]

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[m/sec2]

[rn]

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1.59 0.41 2.01

2 QUAftTERING 221 .

3t000

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0.39 1.94 5 _FOLLOWING 11 _?20 3b000 0.6 2.17 0.41 0.45 0.95 0.61 0.43 '1.42 6 QU'A'TERING ON' 220 54700 294 : 0.25 0.30 0.49 0.38 0.18 1.00 7 bEAM _{219 34900 29.8 2.11 0.43 0.50 1.14} ' 0.67 0.35 1.26 8 BOW 212 36000 29.9 0.94 O8'O 1.13 3.59 ' .1.45 ' 0.57 , 2.10 I..I.I I, I TABLE I

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