Bias according to lane assignment has long been recognized in athletics (e.g. Jain 1980
). This may be due to both biomechanical and psychological factors. One mechanical factor proposed as a limitation to sprint performance is the force experienced by the limbs during stance (Weyand et al. 2000
). On running around an appropriately banked bend, sprinters effectively experience an increase in body weight (but not mass), as ground reaction forces are required both to overcome gravity and provide the centripetal acceleration (). If limb force and certain kinematic factors are constrained (see below), the increases in force requirement on sprinting around a bend result in a decrease in sprint speed, with sprints around tighter bends being slowed to greater extents.
Figure 1 A representation of the modelled changes made on sprinting around a bend. When sprinting along the straight, the average forces from both left and right (L and R) legs have to be sufficient to oppose gravity (a, dark grey); on running around a bend ( (more ...) Greene & McMahon (1979)
and Greene (1985)
provide an analysis of running around bends from first principles, with the goal of making as few simplifying assumptions as possible. Such an approach provides support for the constant limb force concept with data from both sprinting amateur runners (Greene 1985
), and mice turning tight corners (Walter 2003
): stance time, and hence duty factor (the proportion of stride time the foot spends in contact with the ground), increases on bends, and reduced sprint speeds are observed. In contrast, the constant force hypothesis fails for Greyhounds (Usherwood & Wilson 2005
): Greyhounds experience greatly increased limb forces when racing around bends; duty factor and speed are not altered to compensate for the increased net force requirements.
We develop an analysis to determine whether the performance of elite human athletes trained to run around banked bends of relatively tight radii is consistent with the constant limb force hypothesis. Are Greyhounds special, or can constraints to limb force be avoided in specialized humans? Using the constant force hypothesis and two kinematic assumptions (see below) we make use of the 2004 Olympic Games as inputs to predict the results of the World Indoor Championships from the same year. This analysis is particularly timely as the indoor 200
m discipline has subsequently been abandoned by the IAAF because of the extreme bias observed according to lane assignment.
Our model is similar to previous analyses in that it is based on the assumptions that neither limb forces nor the distance travelled during stance (Lstance
) vary with sprinting around bends of different radii. The constant Lstance
assumption is broadly supported by a range of empirical data (Cavagna et al. 1976
; Greene & McMahon 1979
; Greene 1985
; Weyand et al. 2000
). Our model deviates subtly from that of Greene (1985)
in that we assume protraction time—the time taken to swing the leg forwards (tswing
) between each stance period for that leg—to be constant, rather than assuming a constant stride frequency. In order to keep stride frequency constant after an increase in stance time due to sprinting around a bend, tswing
would have to reduce—the limb protraction velocity would have to increase. Instead, we assume that the leg is protracted at maximum velocity under all conditions, keeping tswing
constant and allowing stride frequency to vary slightly. While this development does add a further empirical term to the model, we feel the assumption to be more justifiable, and maximally performing sprinters of a range of standards achieve very similar values for tswing
(Weyand et al. 2000
), so there is little added complexity.