A mathematical model for quantifying training.

A systems modelling approach has been used to quantify the dose-response nature of training. Considerable attention has been focused on the modelling process with little work on the determination of the training impulse (TRIMP) scores. Currently, the methods employed to calculate TRIMPs are subject to various limitations including the use of generic ordinal category or exponential weighting factors for higher exercise intensities. These weightings are necessary to prevent excessively high scores from long duration, low intensity bouts of exercise. We propose a new method to calculate TRIMP scores based upon a whole body bioenergetic model. Our method is individual specific, removing many of the previous limitations. Furthermore, this model could enable a greater comparison of continuous and interval training methods. This model takes into account the length of repetition(s), concentration of the interval session and mode of recovery. This approach, while requiring further research, offers a potential improvement in the accuracy of training load calculations.

External effects in the 400-m hurdles race.

A mathematical model based on a differential equation of motion is used to simulate the 400-m hurdles race for men and women. The model takes into account the hurdler's stride pattern, the hurdle clearance, and aerobic and anaerobic components of the propulsive force of the athlete, as well as the effects of wind resistance, altitude of the venue, and curvature of the track. The model is used to predict the effect on race times of different wind conditions and altitudes. The effect on race performance of the lane allocation and the efficiency of the hurdle clearance is also predicted. The most favorable wind conditions are shown to be a wind speed no greater than 2 m/s assisting the athlete in the back straight and around the second bend. The outside lane (lane 8) is shown to be considerably faster than the favored center lanes. In windless conditions, the advantage can be as much as 0.15 s for men and 0.12 s for women. It is shown that these values are greatly affected by the wind conditions.

The effect of track geometry on 200- and 400-m sprint running performance.

This study looked at how the geometry of the running track affects performances in the 200- and 400 m sprint running events. Although an athletics track must be designed with two parallel straights and two curved bends, the lengths of the straights and bends are not fixed and may vary within an approved set of limits. The bend can be semi-circular or a double-curve consisting of arcs of two different radii. A mathematical model was used to calculate the effect of track geometry on race times for six different track designs; three with semi-circular bends (encompassing the extremes of the permitted designs), and the three permitted double-curve designs. The calculations revealed substantial differences among the track designs. The time difference (in the inside lane) between the fastest and slowest tracks is about 0.1 s in the 200-m race and 0.2 s in the 400-m race. The time differential between the outside and inside lanes for a double-curve track can be up to 0.08 s greater than for a standard track with semi-circular bends.

The effects of wind and altitude in the 400-m sprint.

In this paper I use a mathematical model to simulate the effect of wind and altitude on men's and women's 4400-m race performances. Both wind speed and direction were altered to calculate the effect on the velocity profile and the final time of the sprinter. The simulation shows that for a constant wind velocity, changing the wind direction can produce a large variation in the race time and velocity profile. A wind of velocity 2 m x s(-1) is generally a disadvantage to the 400-m runner but this is not so for all wind directions. Constant winds blowing from some directions can provide favourable conditions for the one-lap runner. Differences between the running lanes can be reduced or exaggerated depending on the wind direction. For example, a wind blowing behind the runner in the back straight increases the advantage of lane 8 over lane 1. Wind conditions can change the velocity profile and in some circumstances produce a maximum velocity much later than is evident in windless conditions. Lower air density at altitude produces a time advantage of around 0.06 s for men (0.07 s for women) for each 500-m increase in elevation.