Proceedings of the 16th International Ship Stability Workshop, 5-7 June 2017, Belgrade, Serbia 1

Linear Seakeeping High Sea State Applicability

Timothy C. Smith, Naval Surface Warfare Center Carderock Division, timothy.c.smith1@navy.mil

Kevin M. Silva, Naval Surface Warfare Center Carderock Division, kevin.m.silva1@navy.mil

ABSTRACT

The small motion assumption of linear seakeeping codes is well known. The validity of this assumption is investigated by comparisons with a body exact non-linear seakeeping code over a range of significant wave height. A metric based on relative motion is proposed to quantify the validity of the assumption and indicate up to what point linear seakeeping is appropriate.

Keywords: Linear Seakeeping; numerical simulations.

1. INTRODUCTION

Despite the advent of relatively computationally fast non-linear time domain seakeeping programs, there is still some use for linear strip-theory seakeeping programs. Frequency domain programs can produce seakeeping predictions for many speeds, relative wave headings, and seaways in seconds of computation. This is especially useful for including seakeeping in early design analysis of alternatives and calculating mission operability. Time histories based on linear response amplitude operators (RAOs) are also fast to compute and provide representative motions for ship system design/evaluation.

The main assumptions of linear strip-theory seakeeping codes are well known. The first is that calculations are preformed about the mean undisturbed waterline. Hydrostatics, radiation, diffraction, and incident wave forces are all calculated on the submerged portion of the hull at the mean undisturbed waterline. This is also stated as a “wall sided” and “small motion” assumptions. These descriptions explain in a physical sense what using the mean undisturbed waterline to define the submerged hull actually means. “Wall sided” indicates that the hydrostatic properties are not changing as the ship moves. “Small motion” indicates that the submerged geometry used for radiation, diffraction, and incident wave force calculations can be considered constant. O’Dea and Walden (1985) examined linear seakeeping with respect to bow flare and wave steepness.

The other main assumption of linear strip-theory seakeeping relates to the independence of the two dimensional strips. The strips are assumed to be independent but in actuality flow from one will influence flow from strips further aft. As a result low speed strip-theory is limited to Froude numbers less than 0.3-0.35. Higher speed strip-theories have been formulated. This paper does not address the validity of using low speed strip-theory above Froude numbers of 0.3-0.35.

Lastly, as a direct result of having a constant submerged volume, the equations of motion can be solved for a unit wave height and linearly scaled to higher wave heights. This is most obviously seen with heavily damped heave and pitch motion. However, roll has non-linear damping and most linear seakeeping programs have some iterative or computational scheme to account for this and do not scale roll linearly with wave height.

However, seakeeping predictions in very small waves, where linear seakeeping assumptions are valid, are not very useful. Fortunately, the assumptions can be stretched and produce useful results at wave heights of interest. This paper discusses a metric to identify when the linear seakeeping assumptions are more than stretched but broken.

2. COMPARISON APPROACH

The validity of linear scaling of results will be determined by comparing linear strip theory results with non-linear time domain results for the same hull form, loading condition, and seaways. Heave,

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Proceedings

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Proceedings

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Proceedings

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CABILITY

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onsiderationthe validitynges of wate

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ute motions. rms of rela0th highest,

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using points and baselinect to incidentket parallel mng some of te critical dism the mean s decidedly n

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Proceedings

a probability bilities at boferences. Os and less dheight. Rol10% differet.

hreshold valfference, ane all inter-relet independeint location 2% differencts sets the thher destroyeof a forwar

0.14, the diffresponse is lints and accassociated pr

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0.14 for theow seas are Other headindifference in ll shows mor

ence at 2.0 n

lue to excnd relative ated and accently. So tak

as the fowce bewteen hreshold proer-like hull rd relative m

fference betwess than 2%ceptable difrobabilities.

elative motion Fr=0.21 and he

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at bow and sead seas (0 deg

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ure 11: Probaeeding half the

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CONCLUS

This study plicability ootions were ng SMP95 ghts, a singl

otions were ects were aan square of

obability of tical distanceplicability oedictions. Teds to be ems to detertistics such

ovide more d

ne 2017, Belgra

bility of relative draft at Fr=0

bility of relative draft at Fr=0

SIONS

proposed aof linear scalculated fand LAMP

e speed, andcompared to

apparent andf the motions

the relative was proposof linear sThis approaxpanded to

rmine generaas average

discrimination

rade, Serbia

ive motion at b0.21 and bow se

ive motion at b0.21 and follow

a metric to strip-theory for DTMB P for a rangd multiple heo see where

d important s. A metric bve motion esed to define strip-theory ach shows p

other speeral applicabi

of 1/10th hon than root m

5

bow and sterneas (60 deg).

bow and sternwing seas (180

quantify theseakeeping.

model 5415ge of waveadings. Thee non-linearto the root

based on theexceeding athe range ofseakeeping

promise butds and hullility. Otherhighest maymean square

n

n 0

e .

5 e e r t e a f g t l r y e

Proceedings of the 16th International Ship Stability Workshop, 5-7 June 2017, Belgrade, Serbia 6

statistic. Additionally, there may be some complementary metric based on variation in waterplane area that would improve selection of critical distance.

6. ACKNOWLEDGEMENTS

The author would like to thank the many who discussed the idea and provided invaluable computational support. Mr. Robert “Tom” Waters provided a rough idea of the relative motion metric. Mr. Andrew Silver first used the probability of keel emergence in a systematic way in 2016. Mr. Kenneth Weems provided the description of LAMP and the input files for the LAMP calculations.

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