WAVE RESISTANCE THEORY AND APPLICATION 23 
In regard to the effect of viscosity upon wave- 
making, some attempts have been made to allow 
for this, but no adequate theory has yet been pro- 
vided. It is well known that at low speeds we do 
not observe the oscillations in the resistance curve 
indicated by theory for a frictionless liquid and 
due to interference between bow and stern waves; 
in fact, the wave resistance is due very largely to 
the bow and entrance only, the effect of viscosity 
being to reduce the wave-making properties of 
the stern. We may begin then simply by intro- 
ducing an empirical reduction factor into the 
calculations, and for simplicity this factor was 
taken as constant and operative over the whole 
of the rear half of the model. This idea was im- 
proved by Wigley and made more useful from a 
practical point of view; comparing calculated 
and observed results for a large number of models, 
Wigley deduced a simple expression for such a re- 
duction factor and for its dependence upon veloc- 
ity. When we remember other considerations 
which have not been taken into account, it must 
be admitted that this viscosity correction prob- 
ably includes other effects than those due to 
viscosity alone; nevertheless it serves a very use- 
ful purpose. The difference made by this correc- 
tion can be seen in the curves of Figs. 6 and 7. 
The latter diagram illustrates a promising field of 
application of the theory as it stands at present; 
although it is not possible to give with sufficient 
certainty absolute values of the resistance, yet it 
is within reach to forecast differences made in the 
resistance curves for two models of a series with 
small variations in form. However, for a satis- 
factory account of viscous effects it will be neces- 
sary to link up wave theory and boundary layer 
theory. Starting with a much simplified concep- 
tion, consider a ship of streamline form with its 
boundary layer over the surface and becoming 
of any appreciable thickness only near the stern. 
The displacement thickness of the layer gives 
some measure of the amount by which the stream 
lines of the flow are displaced outwards; suppose 
then that we take the effective form of the ship 
for wave-making as the actual form increased by 
the displacement thickness of the boundary layer. 
Some calculations were made on these lines 
recently; but, needless to say, it was not possible 
to deal with actual boundary-layer structure. 
What was done was to make small modifications 
of the lines near the stern such as might reason- 
ably be ascribed to boundary layer effect, the 
main point being that these modifications were 
confined to quite a small region near the stern. 
The purpose of the calculations was to illustrate 
the possible effect of such boundary-layer modi- 
fications of the form and to see if they were suf- 
ficient to eliminate the excessive resistance oscilla- 
tions at low speed given by theory for a friction- 
less liquid, while at the same time not materially 
affecting values at high speeds. 
Figs. 12 and 13 show some of the results, with 
the modified forms and the corresponding re- 
sistance curves. They agree fairly well with the 
anticipated effect, except that the hollow at a 
Froude number of about 0.34 still remains too 
pronounced; but the latter is a persistent dis- 
agreement between calculated and observed re- 
sults for which some other explanation must be 
found. 
OSTRO 7 ONS Ol O75 O25 OP 
Scale of fav//gL 
Fic. 12 
0.18 0.26 034 0.42 0.50 
Scale of f=v/VgL 
Fic. 13 
573 
