Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T17:23:54.613Z Has data issue: false hasContentIssue false
  • English
  • Français

The wave resistance formula of J.H. Michell (1898) and Its significance to recent research in ship hydrodynamics

Published online by Cambridge University Press:  17 February 2009

E. O. Tuck
E. O. Tuck
Affiliation:
Applied Mathematics Department, University of Adelaide, S.A. 5001, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

John Henry Michell (1863–1940) published scientific papers only between 1890 and 1902, but included in his 23 papers from that short but productive period are some of the most important contributions ever made by an Australian mathematician. In this article I shall concentrate on the extraordinary 1898 paper “The wave resistance of a ship” Phil. Mag.(5) 45, 106–123. There are many reasons why this paper was an astounding achievement, but perhaps the most remarkable is that the resulting formula has not been improved upon to this day. In the computer age, many efforts have been made to do so, but with little success so far. The formula itself involves a triple integral of an integrand constructed from the offset data for the ship's hull, and even the task of evaluating this triple integral is not a trivial one on today's computers; another reason for admiration of Michell's own heroic hand-calculated numerical work in the 1890's. Lack of a routine algorithm for Michell's integral has inhibited its use by naval architects and ship hydrodynamic laboratories, and there has been a tendency for it to receive a bad press based on unfair comparisons, e.g. comparison of model experiments (themselves often suspect) with inaccurate computations or computations for the wrong hull, etc. The original integral is in fact quite reasonable as an engineering tool, and some new results confirming this are shown. Improvement beyond Michell is however needed in some important speed ranges, and indications are given of recent approaches that may be promising.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 4 , April 1989 , pp. 365 - 377
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bai, K. J. and McCarthy, J. H. (eds.), Proc. workshop on ship wave resistance computations, David W. Taylor N.S.R.D.C., Bethesda, Md., 11 1979.Google Scholar
[2]Birkhoff, G., Korvin-Kroukovsky, B.V. and Kotik, J., “Theory of the wave resistance of ships. Part 1: The significance of Michell's integral”, Trans. Soc. Nav. Architects Mar. Eng. 62 (1954) 359–371.Google Scholar
[3]Cherry, T. M., “J.H. Michell”, Australian dictionary of biography 10 (1986) 494–495.Google Scholar
[4]Doctors, L. J. and Beck, R. F., ‘Numerical aspects of the Neumann-Kelvin problem”, J. Ship Res. 31 (1987) 1–13.CrossRefGoogle Scholar
[5]Gertler, M., “A reanalysis of the original test data for the Taylor standard series”, David Taylor Model Basin Rep. 806 (1954).Google Scholar
[6]Graff, W., Kracht, A. and Weinblum, G., “Some extensions of D.W. Taylor's standard series”, Trans. Soc. Nav. Architects Mar. Eng. 72 (1964) 374.Google Scholar
[7]Havelock, T.H., “The collected papers of Sir Thomas Havelock”, edited by Wigley, C., Office of Naval Research, Washington D.C., 1963.Google Scholar
[8]Joukowski, N.E., “On the concomitant wave”, in Collected Works of N.E. Zhukovskii Vol. 2, pp. 712–745, Moscow, 1949 (in Russian).Google Scholar
[9]Maruo, H., “Evolution of the theory of slender ships” Weinblum Memorial Lecture, U.S. National Academy of Sciences, 04 1988.Google Scholar
[10]Newman, J.N., “The damping and wave resistance of a pitching and heaving ship”, J. Ship Res., 3 (1959) 1–19.CrossRefGoogle Scholar
[11]Radok, J.R.M. and Niedenfuhr, F.W., “The collected works of J.H. and A.G.M. Michell”, Noordhoff 1964.Google Scholar
[12]Sretenskii, L.N., “A theoretical investigation on wave resistance”, Trans. Tsent. Aero-Gidrodinam. Inst. 319 (1937) (in Russian).Google Scholar
[13]Tuck, E.O., “A systematic asymptotic expansion procedure for slender ships“’ J. Ship Res. 8 (1964) 15–23.CrossRefGoogle Scholar
[14]Tuck, E.O., “A strip theory for wave resistance”, 3rd Int. Workshop on Water Waves and Floating Bodies, Wood's Hole, Massachusetts, 04 1988.Google Scholar
[15]Tuck, E.O., “Wave resistance of thin ships and catamarans”, University of Adelaide, Applied Mathematics Rep. T8701, January 1987.Google Scholar
[16]Wehausen, J.V., “The wave resistance of ships”, Adv. in Appl. Mech. 13 (1973) 93–245.CrossRefGoogle Scholar
[17]Weinblum, G., “A systematic evaluation of Michell's integral”, David Taylor Model Basin Rep. 886 (1955).Google Scholar
[18]Wigley, W.C.S., “Ship wave resistance. A comparison of mathematical theory with experimental results”, Trans. Inst. Nav. Architects, 68 (1926) 124–137.Google Scholar