THE WAVE GENERATED BY A FINE SHIP BOW 
T. Francis Ogilvie 
Untverstty of Michigan 
Ann Arbor, Michtgan, U.S.A. 
ABSTRACT 
The flow field near the bow of a ship has some cha- 
racteristics of a high-Froude-number problem, even 
if ship speed is moderate. Some of these features 
can be predicted by slender-body theory if the usual 
assumptions of that theory are modified in the bow 
region to allow for the occurrence of longitudinal rates 
of change greater than normally assumed, Analytic- 
al results are derived for the case of a fine wedge- 
shaped bow, in which case a universal curve can be 
drawn for the shape of the bow wave on the hull, re- 
gardless of speed, draft, or entrance angle (all with- 
inlimits, of course), The lengths must be nondimen- 
sionalized by the quantity (HU2/g)' °| where H is 
the draft, U is ship speed, and g is the gravita- 
tion constant. Itis shown how this mathematical mo- 
del matches with the usual slender-body model and 
how it eliminates certain of the objectionable features 
of the latter, with only minor complications. Some 
experimental resultsare shown which generally con- 
firm the predictions, 
I. INTRODUCTION 
The Froude number can be taken as a rough measure of the 
relative magnitude of inertial forces with respect to gravitational 
forces in the interior of a fluid region, In the usual problem of ship 
hydrodynamics, neither of these forces dominates the other in the 
overall picture, and this fact is recognized in the custom of treating 
Froude number as a quantity which is O(1) ase -+0, where € is the 
small parameter that provides the reference for ordering all quantities 
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