Example screen shot used to estimate the runners’ position as a function of time.
Schematic illustration of the main procedure for estimating the runners’ positions: Two known parallel lines, orthogonal to the track, are extended to find the horizon crossing point for each frame. Auxilliary lines are drawn from onto the track, corresponding to each of the runners’ current positions. The positions are read off from the rail. This method was used in the second half of the race. In the first half, in which there were strong camera perspective effects, other methods were also used. See the text for details.
Estimated position (top), speed (middle), and acceleration (bottom) for Bolt (solid curves) and Thompson (dashed-dotted curves) as a function of time. Actual distance measurements are indicated in the top panel with error bars. Gray bands indicate the 68% confidence regions for the spline estimators as estimated by Monte Carlo simulations.
(a) Comparison of real and projected distance profiles at the end of the race. The point where the profiles cross the horizontal line is the new world record for a given scenario; (b) is a zoomed version of (a). The dashed line shows the first scenario, and the dotted line shows the second scenario; the actual trajectory, is shown as a solid line. For comparison, Thompson’s trajectory is indicated by a dashed-dotted line.
Photo montage showing Bolt’s position relative to his competitors for the real (left Bolt) and projected (right Bolt) world records.
Compilation of distance (m) versus time (s) for Usain Bolt and Richard Thompson in the dash at Beijing 2008. The data for the second and last rows are not real observations, but ensure sensible boundary conditions for the smooth spline. The second row ensures zero starting velocity, and the last row gives a smooth acceleration at the finishing line. The data for are taken from the known starting position and therefore have zero uncertainty, and the data for and are taken from a high-resolution picture of the finish. These times are not read from the screen clock, but are adopted from official sources. Zero uncertainties are assigned to these points.
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