Page 240 - Introduction to Naval Architecture

PROPULSION 225

As required this gives thrust in the units of force and the various
expressions in brackets are non-dimensional, fi is a function of
advance coefficient and is likely to be important. f% is a function of
Reynolds' number. Whilst relevant to the drag on the propeller
blades due to viscous effects its influence is likely to be small in
comparison with the other dynamic forces acting. It is therefore
neglected at this stage. f s is a function of Froude number and is
concerned with gravity effects. Unless the propeller is acting close to
a free surface where waves may be created, or is being tested behind
a hull, it too can be ignored.
Hence for deeply immersed propellers in the non-cavitating condi-
tion, the expression for thrust reduces to:

For two geometrically similar propellers, operating at the same
advance coefficient the expression in the brackets will be the same
for both. Hence using subscripts 1 and 2 to denote the two
propellers:

If it is necessary to take Froude number into account:

To satisfy both Froude number and advance coefficient:

where A is the ratio of the linear dimensions.
Since ND/V a is constant:

Thus for dynamic similarity the model propeller must rotate faster than
the corresponding ship propeller in the inverse ratio of the square root
of the linear dimensions.