The spray sheets produced during vertical wedge impact and steady planing

Abstract

“Added mass” theory is usually employed in a momentum analysis. In connection with the vertical impact of a wedge, Pierson noted an anomaly when it is employed in an energy analysis, because the two approaches yielded different results. This led the writer to conjecture that the “difference” might be due to the energy dissipated in the spray sheets. The analysis which follows appears to support that conjecture, in that the size of the spray sheets so calculated is the same as those of Pierson's [(1950), The penetration of a fluid surface by a wedge. Stevens Institute of Technology Report No. 381 (July) (IAS paper FF-3)] numerical calculations. The theory predicts, for both vertical wedge impact at constant vertical velocity and for the steady high speed planing of a slender prismatic hull, that half the pressure drag energy ( Du o ) appears as kinetic energy in the spray sheets, the other half being absorbed by the downward deflection of the main body of water. This does not agree with the conclusions drawn from the experimental work of Latorre and Tamiya [(1975), An experimental technique for studying the planing boat spray. Proceedings of the Fourteenth International Towing Tank Conference, Ottawa, Canada, Vol. 4, pp. 562–571] and Latorre [(1983), Study of prismatic planing model spray and resistance components. J. Ship Res. 27, 187–196]. Nor does it agree with two-dimensional planing theory [summarized in ch. 3 of Payne [(1988), Design of High-speed Boats, Volume I: Planing. Fishergate, Inc., Annapolis, Maryland]] where all the energy appears in the spray sheet at very high Froude numbers. But the equal division of energy into spray and water deflection for slender surfaces was predicted for a high speed slender planing surface by both Wagner [(1932), Uber Stoss-und Gleitvorgänge an der Oberfläche von Flüssig-keiten.