Dedication to Sir Thomas Havelock 
relationship was the determination or prediction of the three ship-form parameters for some 
arbitrary ship. Actually, the resistance relationship gives quite good agreement with 
experiments when experimentally determined ship-form parameters are used. 
Apparently, in view of the shortcomings of the semiempirical approach and Sir Thomas’ 
rediscovery of Michell’s work, he abandoned this track and resorted to obtaining a solution 
to the basic formulation of wave resistance that was put forth by Michell in 1898 and which 
still forms the basis of all modern theoretical analyses of ship wave resistance. Michell’s 
formulation is based on the representation of the fluid velocity in terms of a potential func- 
tion which is built up of the sum of simple harmonic functions in the coordinates of the 
system and is coupled with several rather idealistic boundary conditions. These boundary 
conditions specify a slender-body ship characterized by small slopes in both the water-line 
and draft planes. The theory also requires that the wave slopes be small and does not 
allow changes of ship attitude. 
Sir Thomas, over the period from 1920 to 1930, investigated the representation of ship 
bodies in terms of discrete and continuous source-sink or doublet distributions along the 
centerline plane of the ship and the ramifications and results of such an approach to the 
evaluation of Michell’s integral. He was able to investigate the effects of straight or hollow 
bow lines, variations of entrance and beam for constant displacement, effect of parallel 
middle bodies, effect of finite draft, effects of relatively blunt and fine sterns on wave 
interference, and the variation of wave profile properties with systematic changes in ship 
form among other items important to practical ship design. In this work, he was the first to 
analytically determine and describe the influence of changes in water line shape on the 
wave resistance. 
The wave resistance curves Havelock obtained as a function of Froude number have all 
of the characteristics of those obtained from ship model experiments. The location of the 
characteristic humps and hollows are depicted extremely well but their amplitudes are exag- 
gerated in the low Froude number range (below 0.3). The agreement of the calculated 
resistance is excellent in cases of ship forms (especially “Michell ships”) which are 
described by simple functions but relatively poor for actual ship forms. 
In the 1930’s and 1940’s, Professor Havelock directed his efforts mainly toward the 
calculation of the wave profiles generated by two-dimensional and three-dimensional bodies 
as represented by source-sink or normal doublet distributions. He also derived relation- 
ships for and computed the wave drag of such bodies in terms of the energy and work in 
the waves. 
Included in his work during this period, Havelock initiated the idea of accounting for 
the boundary layer effects in a real fluid by modifying the source strength function by a 
reduction factor which would vary with the form of the ship and with the Reynolds number. 
He made calculations for both two-dimensional and three-dimensional bodies and found the 
reduction factor had no significant effect on the bow wave but it did reduce the wave height 
along the side of the ship, particularly near the stern. He also investigated the effect of a 
modification of the lines of the ship in the stern region and found this device has the 
greatest influence on the wave resistance at low Froude numbers where there was greatest 
disagreement between theoretical and measured results. However, there still existed appre- 
ciable discrepancies between measured and theoretical curves in the low Froude number 
range. The effect of the modification was found to be insignificant at high Froude numbers. 
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