A Note on Wave Resistance Theory: 
transverse and diverging waves 
Sir Thomas Havelock, Newcastle 
I wish to associate myself with this tribute to Professor 
Weinblum for his distinguished work in Ship Hydrodynamics, 
and I should like to add also that I am greatly indebted to 
him personally. This is my excuse for a few remarks on a 
certain aspect of wave resistance theory, though I have nothing 
new to add; the particular point is no doubt chiefly of theore- 
tical interest, but it happens to have come to my notice again 
recently. 
Considering an ideal frictionless liquid, the only resistance 
to the motion of a solid is the wave resistance, and it is 
obviously the horizontal resultant of the fluid pressures on the 
solid. Another method is to calculate the propagation of 
energy outwards in the wave motion, and so deduce the cor- 
responding resistance. These two methods give the same 
result, provided the calculations are made to the same degree 
of approximation in each case. It may be noted that, in gene- 
ral, this involves obtaining the velocity potential to a higher 
Schiffstechnik Bd. 4 — 1957 — Heft 20 
stage of approximation for the resultant pressure calculation 
than for the wave-energy method. The energy method was 
used at first only for two-dimensional problems, as for 
instance the motion of a submerged circular cylinder; this 
was because there was available the well-known connection 
between energy transfer and group velocity for straight- 
crested plane waves. For three-dimensional problems, such as 
a submerged sphere, the resistance was found at first by the 
resultant pressure method. Subsequently I gave a theorem 
for the energy transfer in a ship wave pattern and its appli- 
cation to the calculation of wave resistance (Proc. Roy. Soe. A, 
1932). This was done by considering control planes at great 
distances before and behind the moving solid, and calculat- 
ing the rate of work and the transfer of energy across these 
planes. If Ox is in the direction of motion of the solid, 0 being 
a moving origin, we assume that the surface elevation € at 
a great distance to the rear approximates to a form which 
can be expressed by 
= (YL co 
615 
