  Dimensional analysis combined with limited experimental data for the
performance of fully submerged propellers have been available since the 1950s.
I present two new scale-free hydrodynamic predictions for the relative
performance of both submerged and surface-piercing propellers. Larger p/D
(pitch to diameter ratio) are more favorable for peak peopeller efficiency and
higher speeds; lower p/D are more favorable for carrying loads at low speeds.
This conflicts with the common advice to swing as large a diameter as slowly as
possible but diameter D has dimensions while p/D is dimensionless, and useful
hydrodynamic recommendations must be given in terms of dimensionless variables.
For the surface piercing case I compare my scaling predictions with empirical
data using a single case in each class as a baseline. One scaling law allows
propeller diameter to be predicted from an established baseline where shaft hp
and shaft RPM are the variables. The second prediction is inferred from Froude
nr. scaling and allows boat speed to be predicted based on shaft horsepower
(shp) and weight, given a known baseline in the same class of drag coefficient.
I also discuss the existing available data on surface piercing propellers and
compare the data with both typical competition data and speed records. In the
context of the p/D ratio I discuss the limits on both too high and too low gear
ratios. I state for the first time a basic requirement for setting the leading
edge camber of surface piercing propellers for optimal acceleration and top
speed. I end by using the basic hydrodynamic ideas of circulation conservation
and vortex stretching to provide a qualitative picture via the tip vortices of
the physics of blade ventilation in surface piercing.
