On Vibratory Forces induced on the Rudder behind a Propeller

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This paper deals with the theoretical investigation into the vibratory forces induced on the rudder behind a propeller.<BR>It is shown that the induced velocity in the position of the rudder is almost the same as that far behind a propeller. Therefore, we can adopt the induced velocity far behind a propeller as the circumstances of the rudder. This induced velocity can be obtained by representing the circulation distribution for the propeller with the linear combination of modified Bessel functions.<BR>Since the reduced frequency of the rudder is considerably large, the inductions of oscillating pressure distribution on the rudder are limited in extremely near field of itself. In addition, the oscillating velocity induced by the propeller is concentrated in narrow region near the tip of the propeller. Accordingly, we can treat the rudder as the oscillating wing with low aspect ratio. Then, the problem is reduced to an integral equation. This integral equation has the analytical solution, therefore, the vibratory forces induced on the rudder can be obtained without difficulty.<BR>Calculations are made for the rudder of aspect ratio 2 in the position of O. 5 D behind Troost B 4-55 propeller.
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