The Concept of Optimal Dynamic Pedalling Rate and Its Application to Power Output and Fatigue in Track Cycling Sprinters-A Case Study

Abstract

Sprint races in track cycling are characterised by maximal power requirements and high-power output over 15 to 75 s. As competition rules limit the athlete to a single gear, the choice of gear ratio has considerable impact on performance. Traditionally, a gear favouring short start times and rapid acceleration, i.e., lower transmission ratios, was chosen. In recent years, track cyclists tended to choose higher gear ratios instead. Based on a review of the relevant literature, we aimed to provide an explanation for that increase in the gear ratio chosen and apply this to a 1000 m time trial. Race data with continuous measurements of crank force and velocity of an elite track cyclist were analysed retrospectively regarding the influence of the selected gear on power, cadence and resulting speed. For this purpose, time-dependent maximal force-velocity (F/v) profiles were used to describe changes in performance with increasing fatigue. By applying these profiles to a physical model of track cycling, theoretical power output, cadence and resulting speed were calculated for different scenarios. Based on previous research results, we assume a systematic and predictable decline in optimal cadence with increasing fatigue. The choice of higher gear ratios seems to be explained physiologically by the successive reduction in optimal cadence as fatigue sets in. Our approach indicates that average power output can be significantly increased by selecting a gear ratio that minimises the difference between the realised cadence and the time-dependent dynamic optimum. In view of the additional effects of the gear selection on acceleration and speed, gear selection should optimally meet the various requirements of the respective sprint event.

Keywords: force–velocity profile; optimisation; performance modelling; track cycling.

Figure 1

Development of gears by track cycling sprinters over the past 25 years, shown as deployment (i.e., distance cycled per revolution of the pedals), and resulting changes of mean pedalling rate. The values shown are the means for the 6 female and 10 male cyclists ranked highest in the flying 200 m at the world championships of the respective year.

Figure 2

Development of the time difference of the split times for the first and second 100 m of the fastest 6 female and 10 male athletes in the flying 200 m race at the world championships from 1998 to 2022. Traditionally, the split time of the first half has been much faster than the split time of the second half. From 2005 onwards, there is a sudden decrease in the difference between the split times for the first and second 100 m, especially for men.

Figure 3

Mean power output (P) for each revolution of the crank (black squares) and the corresponding pedalling rates (PR; black dots) and speeds (black triangles) in a 1000 m time trial by an elite track cyclist. The gear ratio of 3.87:1 (58/15) corresponded to a deployment of 8.12 m. In the race, the mean power was 918 W at a mean cadence of 126 rpm. The oscillating data is induced by the design of the racing velodrome.

Figure 4

Fatigue-free force–velocity profiles and power–velocity profiles of the athlete in standing (black) and seated positions (grey) calculated (black and grey squares) by linear and non-linear regression analysis. In standing position, F_max was 1932 N and PR_max amounted to 237 rpm with a corresponding slope of −8.15 N rpm⁻¹. In seated position, calculations yielded F_max = 1561 N, PR_max = 262 rpm and a slope of −5.95 N rpm⁻¹.

Figure 5

The F/v and P/v profiles of an elite track cyclist in the absence of fatigue (straight black line, standing position) and at the end of a 1000 m time trial (grey straight line, seated position). During the race, the maximal mean pedal force (F_max) decreased from 1932 N to 998 N, the maximal power output (P_max) from 2040 W to 745 W and the optimal pedalling rate (PR_opt) declined from 119 rpm (standing position) or 131 rpm (seated position) to 84 rpm. The triangles represent the raw data points of the current pedalling rate with corresponding power output every 10th second from the first to the last pedal revolution in chronological order.

Figure 6

Comparison of actual pedalling rate PR_i (grey dots) and actual power output P_i (black triangles) as percentage of the dynamic optimum of pedalling rate PR_opt,i and dynamic maximal power output P_max,i for each crank revolution i at its corresponding time t during the 1000 m time trial.

Figure 7

Pedalling rate (PR), power output (P) and speed (v) calculated for a gear ratio of (A) 3.87:1 (58/15) to rebuild the actual race, (B) 4.92:1 (59/12) to maximise mean power output, (C) 4.36:1 (61/14) to minimise finishing time over 1000 m and (D) 2.88:1 (49/17) to minimise finishing time over 250 m. Time-dependent power output, pedalling rates and resulting speeds were estimated applying our recently published mathematical approach to the raw data [2].