Scaling for speed on the water
  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. 
Joseph L. McCauley
physics.pop-ph