The aim of the research was to find a function of the curvilinear segment profile which could make possible to avoid an instantaneous increasing of a curvature and to replace a circle arc segment on the in-run of a ski jump without any correction of the angles of inclination and the length of the straight-line segments. The methods of analytical geometry and trigonometry were used to calculate an optimal in-run hill profile. There were two fundamental conditions of the model: smooth borders between a curvilinear segment and straight-line segments of an in-run hill and concave of the curvilinear segment. Within the framework of this model, the problem has been solved with a reasonable precision. Four functions of a curvilinear segment profile of the in-run hill were investigated: circle arc, inclined quadratic parabola, inclined cubic parabola, and power function. The application of a power function to the in-run profile satisfies equal conditions for replacing a circle arc segment. Geometrical parameters of 38 modern ski jumps were investigated using the methods proposed.
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