Comparisons of theory with experiment for ship rolling in oblique seas

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COMPARISONS OF THEORY WITH EXPERIMENT FOR SHIP ROLLING IN OBLIQUE SEAS

by

R. T. SCHNITKE 4

Defence Research Establishment Atlantic Dartmouth, Nova Scotia, Canada

ABSTRACT

A computer program to predict ship roll, yaw and sway motions in oblique seas has recently been developed at DREA, based on strip theory with strict account taken of the circulatory and viscous damping effects of hull appendages. Predictions are compared with experimental data from regular wave tests with a fully appended self-propelled frigate model. The effects of varying forward speed, heading to the sea, metacentric height and bilge keel configuration are examined. Agreement between theory and experiment is good.

L

INTRODUCTION

Over the past two decades, considerable success has been achieved in the theoretical prediction of ship heave and pitch motions. Computer programs to perform such predictions are now in common use, and a large number of correlation studies have shown that the accuracy of the absolute motion predictions is generally very

satisfac-tory. For lateral plane motions, however, of which by far the most important is roll,

the situation is much different. Although several programs exist which predict roll, sway and yaw by purely theoretical means, for example Reference 1, correlation studies2 have shown that errors in roll prediction are generally significant, particularly for high speed warship hull forms. As to sway and yaw, correlation studies have been very few and inconclusive.

The fundamental reason for the discrepancies reported in correlation studies is that programs suc1 as Reference 1 generally make inaccurate estimates of roll damp-ing, especially at hirer speeds. Experience with these programs has led to the widely held belief that the roll damping prediction problem is so complex and

non-linear as to be theoretically intractable. In keeping with this philosophy, cer-tain computer programs3 require that the roll damping coefficient be input by the user. Model test programs specifically dedicated to the experimental determination of roll damping are fairly common.

The failure of Reference 1 to make accurate predictions of roll damping may be traced to an inadequate treatment of hull appendages, and in particular to the failure to include the effects of dynamic lift on such appendages as rudders, skegs and propeller shaft brackets. The theory used in the present paper includes these effects and consequently produces good estimates of both roll damping and roll response.

GENERAL DESCRIPTION OF THEORY

The mathematical model used herein for ship lateral motions in oblique seas has basically four facets:

1) Strip theory for computing hull added nass, wavemaking damping and exciting forces.

general form:

(-w2A. + iwB. + C. )n = F.

kk

k jk jk 3

Lifting surface contributions to damping and exciting forces.

Viscous roll damping, principally from bilge keels.

Hull circulatory effects.

The equations for coupled sway, roll and yaw response are written in the

j = 2,4,6

where w is frequency of encounter and the subscripts 2, 4 and 6 refer to sway, roll and yaw, respectively. A.k and B.k are the added mass and damping coefficients, Cjk are the restoring coefficients, and F are the exciting forces and moments. These coefficients are ascribed the general form:

A.

=A11 +A'

Bk

.k+B

+B

where superscript H denotes hull coefficients derived from strip theory, superscript F signifies contributions due to appendages (foils) such as rudders and fins, and

superscript C denotes hull circulatory terms.

For B44, the roll damping coefficient, there is an additional term, B4, the viscous roll damping coefficient. This takes account of the viscous resistance to rolling of bilge keels, skeg, hull, rudder and other appendages.

Detailed expressions for the terms on the right hand side of the above equations are given in Reference 4. Basically, the H-terms are derived from Reference 5, the F-terms from Reference 6, and the C-terms from Reference 7. The viscous

contribution to roll damping is estimated using the data of References 8, 9 and lo.

3. COMPARISON OF THEORY WITH EXPERIMENT

Theoretical predictions are now compared with experimental data from regular wave tests with a fully-appended self-propelled frigate model at the seakeeping basin of the David Taylor Naval Ship Research and Development Center2. This was a compre-hensive experimental program in which metacentric height, bilge keel configuration, heading and forward speed were systematically varied. Two different bilge keels were used (designated BK1 and BK3) and three metacentric heights (GM1, GM2 and GM3). Some details are given below.

Length between perpendiculars 18.182 ft

Beam 2.156 ft

Draft .716 ft

Block coefficient .485

Prismatic coefficient .604

Metacentric height designation % of bean

GM1 12.1

GM2 9.0

GM3 6.1

Bilge keel Area in % of Length in

designation wetted area % of LBP

BK1 2.34 29.6

BK3 1.00 17.0

Figures 1 and 2 show the effect on roll response of varying sea direction at low and high Froude numbers, respectively. Figures 3, 4 and 5 show the effect of varying metacentric height and bilge keel configuration at low Froude number in bow

seas and high Froude number in beam seas. Finally, Figure 6 presents data showing the influence of metacentric height on roll response in quartering seas at low Froude

r

Agreement between theory and experiment is generally good. The following points are especially worthy of mention:

The considerable variation in roll response with heading to the sea is resonably well predicted, both at low and high speed.

Predictions of peak response are generally good, indicating good estimation of roll damping.

Theory correctly predicts a substantial reduction in roll response as speed increases. This decrease is mainly due to the twin rudders, which contribute significantly to roll damping at high speed.

The dramatic increase in roll response in quartering seas as metacentric height is reduced is very well predicted. This is of considerable practical importance, since the GM3 case is representative of the metacentric height/beam ratio at which frigates and destroyers commonly operate.

4. CONCLUSION

Fairly extensive comparisons of predicted and measured roll response for a frigate model show generally good agreement at all headings to the sea. This suggests that the theory of Reference 4 yields predictions of sufficient accuracy for prelim-inary design purposes.

NOTATION

A. added mass coefficient

jk

Bik damping coefficient

Cik restoring coefficient

F. exciting force or moment

GM metacentric height

i

II

heading angle relative to sea direction

(rO O

head seas, 180 following seas)

n2 sway

n4 roll

n6 yaw

w frequency of encounter

C superscript denoting hull circulation

F superscript denoting foil contribution

0 2 30 2 3 WAVE LENGTH/SHIP LENGTH I. FRIGATE MODEL,HEADING EFFECT, F.I5,BK1 GM1

-THEORY TEST -THEORY TEST G3 -THEORY TEST 2 3

WAVE LENGTH/SHIP LENGTH

2. FRIGATE MODEL,HEADING EFFECT, F3 .46,BK, GM,

0 0 I 2 3

WAVE LENGTH/SHIP LENGTH

3. FRIGATE MODEL,GM EFFECT, F2 .15,60W SEAS

539 >4 -J -J 02 a-GM THEORY TEST GM2 _GM3 I 2

30

WAVE LENGTH/SHIP LENGTH

4. FRIGATE MODEL, GM EFFECT, F3 .46

BEAM SEAS, BK1

O I 2

30

5. FRIGATE MODEL,GM EFFECT, F3 .46 BEAM SEAS, BK3 o -THEORY TEST GM3 $ I5O° I 35 4 w a-GM, 92 CI) 2 3 w 9O W a- GMr BK' _GM 5K3 $ I5O 35 I 2

30

WAVE LENGTH/ SHIP LENGTH

6. FRIGATE MODEL,GM EFFECT, F3 r .15

QUARTERING SEAS

-THEORY

TEST GM3

REFERENCES

Myers, W. G., Sheridan, D. J. and Salvesen, N.: "Manual NSRDC Ship-Motion and Sea-Load Computer Program". NSRDC Report 3376, February 1975.

Baitis, A. E. and Wermter, R.: "A Summary of Oblique Sea Experiments Conducted at the Naval Ship Research and Development Center". 13th International Towing Tank Conference, 1972.

Raf f, A. I.: "Program SCORES - Ship Structural Response in Waves". Ship

Structure Committee Report No. SSC 230-1972.

Schmitke, R. T.: "Prediction of Ship Roll, Sway and Yaw Motions in Oblique Waves", DREA Report 77/4, June 1977.

Salvesen, N., Tuck, E. O., and Faltinsen, O.: "Ship Motions and Sea Loads'. Trans., SNANE, Vol. 78, 1970.

Sehmitke, R. T.: "Prediction of Wave-Induced Motions for Hullborne Hydrofoils". J. Hydronautics, 1977.

Comstrock, J. P. (Ed): "Principles of Naval Architecture". SNAME, 1967.

Kato, H.: "Effect of Bilge Keels on the Rolling of Ships:. Memories of the Defence Academy, Japan, Vol. 4, 1966.

Tanaka, N.: "A Study on the Bilge Keels (Part 4 - On the Eddy-Making Resistance to the Rolling of a Ship Hull):. Society of Naval Architects

of Japan, Vol. 109, 1960.

Kato, H.: "On the Frictional Resistance to the Roll of Ships". Society of Naval Architects of Japan, Vol. 102, 1958.