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3 DISTRIBUTION /AVAILABILITY OF REPORT 



Approved for public release; 

 distribution is unlimited. 



4 PERFORMING ORGANIZATION REPORT NUMBER(S) 



DTNSRDC-86/058 



5 MONITORING ORGANIZATION REPORT NUMBER(S) 



6a NAME OF PERFORMING ORGANIZATION 



David Taylor Naval Ship 

 R&D Center 



6b OFFICE SYMBOL 

 (If applicable) 

 Code 1542 



7a NAME OF MONITORING ORGANIZATION 



6c ADDRESS (C/ty, State, and ZIP Code) 

 Bethesda, MD 20084-5000 



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 ORGANIZATION 



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61152N 



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ZR02301 



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ZR0230101 



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11 IITLE (Include Security Classification) 



Analytical Approximation for Steady Ship Waves at Low Froude Numbers 



12 PfRSOrvjAL AUTHOR{S) 



Noblesse, Francis 



Ha TYPE OF REPORT 



Final 



13b TIME COVERED 

 FROM TO 



4 DATE OF REPORT (Year. Month, Day) 



1986 September 



15 PAGE COUNT 

 24 



'6 SUPPLEMENTARY NOTATION 



COSATI COOES 



18 SUBJECT TERMS (Continue on reverse if necessary and identi^ by block number) 

 Ship Kelvin Wake 



Waves Low Speed 



Wave Pattern Low Froude Number 



1? ABSTRACT {Continue on reverse if necessary and identify by block number) 



A simple analytical relationship between a ship-hull form and its steady far-field 

 Kelvin wake is obtained by considering the low-Froude-number limit of the Neumann-Kelvin 

 theory. In particular, this relationship predicts the occurrence of a sharp peak in the 

 amplitude of the waves in the far-field Kelvin wake at an angle, a, from the ship track 

 that is smaller than the Kelvin-cusp angle of 19°l/2 for a hull form which has a small 

 region of flare and is wall sided elsewhere, if the Froude number is sufficiently small. 

 An explicit relationship between the angle, (|), between the ship track and the tangent to 

 the ship mean waterline in the region of flare and the corresponding wave-peak angle a 

 in the Kelvin wake is obtained. For instance, this relationship predicts the occurrence 

 of a sharp peak in wave amplitude at an angle a in the Kelvin wake equal to 14 for a hull 

 having a small region of flare within which the waterline-tangent angle <^ is approximately 



(Continued) 



20 Distribution /AVAILABILITY of abstract 



H JMCLASSlFIED/UNLIMITEO D SAME AS RPT 



Ddtic users 



■JAME OF RESPONSIBLE INDIVIDUAL 



Francis Noblesse 



21 ABSTRACT SECURITY CLASSIFICATION 



UNCLASSIFIED. 



22b TELEPHONE (/nc/ude Area Code) 



(301) 227-1856 



22c OFFICE SYMBOL 



Code 1542 



DD FORM 1473, 84 MAR 



83 APR edition may be used until exhausted 

 All other editions are obsolete 



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