The author examined the nature of the resistance of bilge keels by the towing experiments of thin plates and ship-models fitted with bilge keels, and the following general conclusions were obtained:
(1) The amount of resistance of bilge keels moving through water parallel to the stream lines is smaller than that of thin plates having the same nature of surface and area calculated by Professor Hiraga's formula. From this fact, it appears that the“corner effect”, so to call, is existing at the joining parts of the bilge keels to the plates.
(2) Taking the above-mentioned “corner effect”into account, the frictional resistance of bilge keels having sharp edges can be expressed by the following formula:-
(
R-f)
t°=
KS(1+<2
L'x/
S-4
Ly/
S)
V1.90(ν
t°/ν
15°)
•165……(1)
where (
R-f)
t°……Frictional resistance of bilge keel at
t° C in kg.,
K……Coefficient of frictional resistance depending upon the nature of surface,
=.04577 for polished metal surfaces,
=.04857 for painted surfaces,
S……The area of bilge keel in m
2.,
L……The length of bilge keel in m.,
L'……The length of bilge keel excluding the aft round-up portion of it,
x……Edge effect in m, taking from Prof. Hiraga's paper,
y……Corner effect in m, depending upon the breadth of bilge keel as shown in Fig. 6,
V……Towing speed in knots,
ν
15°……Kinematic viscosity in m
2×sec
-1 at 15°C
ν
t°……Kinematic viscosity in m
2×sec
-1 at t°C.
(3) The amount of the corner effect depends upon the breadth of bilge keel and it is independent of the sectional form, length and speed,
(4) For bilge keels fitted to ship-models, the frictional resistance calculated by the formula (1) amounts to about 97% of the measured increase of resistance due to bilge keels.
View full abstract