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Kinematic analysis of the flight phase of the Nordic combined and ski jump on a large hill (HS-134 m) during the 2009 Nordic World Ski Championships

Svoboda Z., Janura M., Cabell L., Janurova E.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 1

19-25

EN

The purpose of this study was to assess the execution of the flight phase in the Nordic combined (NC) among three groups of competitors, representing different skill levels, and to compare them with three groups of ski jumpers (SJs). Thirty NC and thirty SJ competitors, who performed ski jumps on an HS-134 m jumping hill, were divided into three subgroups based on jump length execution. Two-dimensional (2-D) kinematic data were collected from the lower extremities, trunks, and skis of the competitors. The SJ group had a smaller lower extremity angle ( p < 0.05), which results in the larger center of mass anterior movement ( p < 0.05) in comparison to the NC competitors. The NC competitors achieved jump lengths comparable to those of the SJ competitors by having significantly higher in-run velocities.

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A power function profile of a ski jumping in-run hill

Zanevskyy I.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 4

3-10

EN

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.

3

Optymalizacja profilu najazdu skoczni narciarskiej

Struk R., Palej R.

Czasopismo Techniczne. Mechanika

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2004

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R. 101, z. 5-M

363--370

PL

Niniejsza praca dotyczy zagadnienia optymalnego kształtowania zarysu najazdu skoczni narciarskiej. W pracy określono funkcję celu oraz ograniczenia równościowe i nierównościowe na zmienną decyzyjną. Problem optymalizacji sprowadzono do rozwiązania nieliniowego równania różniczkowego drugiego rzędu. W celu wyznaczania rozwiązań dopuszczalnych, cechujących się liniową zależnością promienia krzywizny, zastosowano metodę strzałów wykorzystującą wielomian interpolacyjny. W pracy pokazano, że istnieje możliwość obniżenia sił bezwładności działających na skoczka nawet o 35% w stosunku do istniejących rozwiązań.

EN

The paper deals with optimization problem of ski jumping inrun profile. The decision variable and the objective function, as well as equality and inequality constraints have been formulated. The optimization problem involves nonlinear second order differential equation. The shooting method was applied to obtain feasible solutions characterized by linear dependency of radius of curvature. The inertia force acting on ski jumper during sliding down can be reduced up to 35% for the optimum inrun profile.