Skiing
Calculation of the speed of a skier by kinematic analysis
Author:
Title 4
Learning objectives :
This activity allows students to analyze the speed of a skier during an Olympic descent. It develops the ability to decompose a velocity vector and to understand the challenges of kinematic analysis.
Concepts covered
Velocity vectors; Orthogonal component analysis; Pythagorean theorem; Board sports; Visual Perspectives
What students will do :
The student uses the FizziQ Kinematic Study module to analyze a video of a skier competing. After calibrating the scale and pointing out the successive positions of the skier, the student analyzes the horizontal and vertical components of the speed then calculates the real speed by combining these two components to compare it to that displayed in the video.
What is required :
Smartphone or tablet with the FizziQ application; Olympic Games 'Downhill' video accessible via FizziQ resources; FizziQ experience notebook
Scientific background :
The kinematic analysis of a skier in Olympic downhill allows us to explore several concepts of mechanics applied to high-level sport. The skier moves in three-dimensional space, but traditional video analysis captures this movement in two dimensions. The video, generally taken from the side, makes it possible to measure two orthogonal components of the speed: Vx (horizontal) and Vy (vertical). The real speed V is the norm of the speed vector, calculated according to the Pythagorean theorem: V = √(Vx² + Vy²). This distinction is crucial because the horizontal component alone significantly underestimates the skier's actual speed. For a slope of 30°, ignoring the vertical component can lead to an underestimate of 15%. When pointing, the choice of a marker on the skier is decisive: the helmet generally provides a clearly visible point representative of the center of mass. Points like skis or feet follow more complex trajectories due to technical movements. The discrepancies between the measured speed and that displayed in the video can be explained by several factors: 1) Perspective effects: the camera is never perfectly perpendicular to the trajectory; 2) The official radar measures instantaneous speed while video analysis calculates an average speed between two positions; 3) The accuracy of the scale calibration directly influences the results. The speeds in alpine skiing are impressive: 110-120 km/h downhill, and up to 160 km/h in speed skiing. At these speeds, aerodynamic forces become preponderant, hence the importance of the "egg" position adopted by skiers to minimize drag.