A quasi-steady theory is developed for the unsteady plane motion of ' seaplanes with high length-beam ratios and of shock-mounted, hydro-skis impacting on a water surface while undergoing pitching rotation. This theory is based on a dynamic-camber equivalent in which a pitching flat plate immersed in a stream is replaced instantaneously by a stationary cambered airfoil for which, similar fluid-particle trajectories exist at the boundary. Since experimental hydrodynamic data were unavailable for verification of the proposed theory/ comparisons are made with classical two- and three-dimensional linearized airfoil theory for steady and unsteady submerged motion and with a less exact method that neglects the rotational effect on the pressure distribution. The agreement with the two-dimensional unsteady oscillating airfoil theory is not very good because of the presence of a large unsteady circulation term but the three-dimensional comparisons, which include, in addition, some data on oscillating airfoils with aspect ratio of 2, indicate fair agreement. Upward pitching is seen to broaden the stagnation peak of the longitu¬dinal pressure distribution and decrease the instantaneous ratio of maximum to average pressure, whereas downward pitching yields the oppo-site result. From the comparison with the less exact method that neg¬lects rotational effects on the pressure distribution, it is deduced that the effects of rotation might be important for some practical narrow-hull impacts but the less exact theory could be used for the trimming shock-mounted hydro-skis considered. The loads predicted by the proposed theory for the trimming shock-mounted hydro-ski are less than those for the fixed-trim hydro-ski. The proposed theory might also be useful for calculations for a low-aspect-ratio pitching hydro¬foil. Applications of a cambered-airfoil theory to the determination of water-pressure distributions on hulls with curved-up bows are indi¬cated. Appendixes containing exact solutions for the pressure distri¬bution, load, and;moment on a cambered airfoil immersed in a stream at a finite angle of attack are included. Step-by-step computational pro¬cedures with data-sheet headings for application of the proposed theory to seaplane hulls with high length-beam ratios and shock-mounted hydro-skis impacting on a water surface and involving rotation in pitch are also given in an appendix.
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