As can be readily determined from Kutta-Joukowski & calculation of The Magnus Effect, removing the rotational element from a marine shaft greatly reduces Lift, Drag and the horse power required to generate them. Enclosing the shaft in a stationary casing then can be calculated as straight forward drag based upon presented area of the appendage. This can be determined by viewing a standard NACA Foil or fin section which is the elliptical result of a cross section through a shaft at the angle of incidence (shaft angle) of the fluid stream. A chart of drag factors for standard NACA foil series is shown below:
|NACA Series||Drag Co-efficients
(< 2 Degrees of incidence)
The total drag on a fin or foil comes from two major components, induced drag (drag generated by lift) and profile drag (drag created by the shape and size of the foil). These two major drag components can be thought of as “active” and “passive” drag. Then, within “passive” or profile drag, there are two further components, drag due to the cross-section being presented to the incident flow, and wetted surface area drag due to the friction drag of the surface of the foil.
The passive drag components are present in both the enclosed as well as conventional exposed shaft systems. It is worthy of note however that the Magnus effect is more detrimental to the performance and power losses created by a spinning exposed shaft in a conventional system due to the presence of both “active”, “passive” and “vortex” drag, than can be calculated for a non-rotating enclosed system, which only exhibits “passive” drag elements.
For every action there exists an equal and opposite reaction, simply put, the generation of lift, friction, and drag requires an equal input of energy to overcome itself.
Similarly, each cutlass style bearing within the shaft system adds an additional 3% of lost energy, plus more losses associated with stuffing boxes and shaft seals averaging approximately 2%. Extrapolation of the formulae defining the Magnus effect in a series, shows an increase relative to lift and velocity, therefore total shaft horse power losses can range from 6% to more than 10% after all the components are added together.