Body center of mass trajectory shows how race walkers elude Froude law

Froude number, Fr = v^2/gl (where v is the speed of progression (m/s), g is gravity acceleration (9.81m/s^2), l is the leg length (m)) is used to compare dynamic similar gait (Alexander, 1989). Fr=1 defines the maximal speed value for pendulum-like locomotion such us walking. Race Walking is an Olympic discipline, which is supposed to be the fastest expression of walking. Assuming athletes’ leg length = 1m, the maximal speed according to “Froude Law” is 3.13m/s much lower than race pace (20km: 4.16m/s; 50km: 3.61m/s). Alexander (1984) suggested a possible explanation of this discrepancy by differences in kinematic: he suggested that the straight knee at heel strike and the back movements would maximise the radius of the inverted pendular motion. The aim of the study was to analyse the race walkers’ Body Center of Mass (BCoM) pattern in order to find how they elude the “Froude Law”. Methods 16 Athletes race-walked on a treadmill at incremental speed 2.77-4.72m/s at a step of 0.138m/s every minute. Kinematic acquisitions were made by 8 Vicon 1.3Mp Cameras at 300Hz. The mathematical description of the BCoM pattern was done with 10 harmonics Fourier Analysis and Lissajous Contour as explain by Minetti and co-workers (2011) with a custom-written software in LabVIEW (National Instrument, USA). Results Athletes’ leg length average 0.93±0.04m, which allowed for a theoretical (Fr=1) maximal speed of 3.02m/s. The Lissajous Contour of the BCoM during race walking showed a characteristic pattern different both from walking and running: during single support BCoM reached the lowest position, while it is highest during double support. At velocity ≤ 4.4m/s two forward ‘protrusions’ were present in the lowest part of contour. Discussion The pattern of race walkers’ BCoM was found to be dynamically opposite when compared to walking. In fact, during the single support phase of normal walking, BCoM shows the lowest speed and reaches the highest point of a contour resembling a circumference arc, as in an inverted pendulum. Also, the forward ‘protrusions’ of race walk contours indicate that speed increases in the middle of the support phase. This confirms that race walk rules constraint to adopt a trajectory different from walking but, by deviating from a circle arc, there is no issue of extending the radius. Although a variation of walking, race walking is not a pendulum-like gait, thus it does not undergo the “Froude Law”. References Alexander RM. (1984). American Scientist. 72. 348-354. Alexander RM. (1989). Physiol Rev. 69. 1199-1227. Minetti AE, Cisotti C, Mian O. (2011). J Biomech, 44, 1471-77