The paper deals with the problem of mathematical modelling a curvilinear segment of a ski jumping in-run hill. The aim of the research was to find the profile which makes the take-off action easier for a ski jumper. The value of the normal reaction acting on the sportsman at the point bordering on the take-off table is smaller than the value of this force at the same point for the existing ski jumping hills. Additionally, a reaction at the point of contact the straight and curvilinear segments should be the same. To obtain such the profile, the simplified model was taken into account and appropriate differential equation with exceeded number of boundary conditions is derived. To solve this non-classical boundary-value problem Kansa method is employed. In the proposed model, sliding down the sought curve, a value of centripetal acceleration increases from zero and reaches a maximum at the end of this curve. Taking into account geometrical parameters of two polish ski jumping hills in Bystra, we can obtain the modified profile without the inflexion point, which fulfills all required conditions. The results obtained were verified taking into account an equation of motion, which contains all the forces acting on the jumper during the descent.
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