Determining optimal pacing strategy for the track cycling individual pursuit event with a fixed energy mathematical model

Powering Toward Los Angeles: Comparing Power Output and Pacing Approach Between Maximal 2000- and 1500-m On-Water Racing in Elite Rowers

PURPOSE

To compare power output and pacing between maximal 1500- and 2000-m on-water rowing performances.

METHODS

Twenty-six (female n = 4, male n = 22) international rowers, across 6 boat classes, completed maximal 1500- and 2000-m on-water races, separated by 24 to 48 hours. Crew combinations and seat orders remained consistent between races. Peach PowerLine instrumentation measured power output and stroke rate. Differences in completion time, mean power output (MPO), percentage prognostic velocity (PPV; percentage of world record velocity in each boat class), stroke rate, and pacing variance were assessed using linear mixed modeling.

RESULTS

Compared with 2000-m, completion times were 90.4 (6.1) seconds shorter over 1500 m (-24.7% [0.7%]). Both MPO (P = .255, ηp2=.06) and PPV (P = .340, ηp2=.18) were not different between distances. Broadly, crews adopted a reverse-J-shaped pacing across both distances, demonstrating a reduced variance over 1500 m (P = .035, ηp2=.62). Percentage change in MPO from 2000 to 1500 m demonstrated a strong negative association with pacing variance over 1500 m (R2 = .74, P = .027).

CONCLUSIONS

International rowing crews did not increase MPO or PPV when racing maximally over 1500 m compared to 2000 m. Comparable strategies were adopted over both distances, with less variance in pacing observed over 1500 m. The crews that demonstrated greater increases in MPO over the shorter race employed a flatter pacing strategy. To improve 1500-m on-water performance, rowers may need to adopt a more even pacing approach.

Numerical optimization of pacing strategy in cross-country skiing based on Gauss pseudo-spectral method

In cross-country skiing competitions, the choice of pacing strategy is of decisive significance to athletes' performance. A reasonable pacing strategy is essential for athletes to improve their performance. In this paper, the mathematical models of cross-country skiing simulation and pacing optimization are established, including motion model, athlete power output model, and optimization model. The actual competition data of a Chinese athlete in Guyangshu 1.5 km track was compared with the model simulation results. The whole process time error is less than 3%, which verifies the accuracy of the motion and power output model. Gauss pseudo-spectral method is applied to the optimization model. By changing the distribution of athletes' power output, the racing time is minimized under the condition that the total energy output remains unchanged. Compared with the pacing strategy before optimization, the optimized racing time was shortened by 12.6 s, which verifies the effectiveness of the optimization model. Optimized results show that in the first significant uphill section, a recommendation is to use a more conservative strategy, while in the latter half of uphill sections the power output should be increased.

Measurements of roll, steering, and the far-field wake in track cycling

A series of measurements taken with two instrumented track bicycles in a velodrome are presented. The bicycle wheel speed, cadence, roll angle, steering angle, power, and airspeed are recorded. The experimentally-measured values are compared to existing theoretical models of roll and steering angles. The accuracy of the roll angle calculations is dependent on the fidelity of the modelled cyclist path and decreases for higher riding speeds. Experimental measurements of the steering angle show a reasonable agreement to theoretical calculations, albeit with reduced steering angles on the bends at higher speeds. There is also seen an increasing steering angle oscillation within each pedal cycle with increasing bicycle velocity which may influence a cyclist’s rolling resistance and the aerodynamic flow around the bicycle’s front end. Observations are made of changes in the flow field ahead of the bicycle due to the presence of other riders on the track, showing an effective tailwind of up to 0.7 m/s. The measured power shows a decrease at the bend entry due to the changing roll angle. Data presented in this paper provides new insights and can help to provide a validation of values used in existing track cycling analytic models.

Qualitative Video Analysis of Track-Cycling Team Pursuit in World-Class Athletes

Context: Track-cycling team pursuit (TP) is a highly technical effort involving 4 athletes completing 4 km from a standing start, often in less than 240 s. Transitions between athletes leading the team are obviously of utmost importance. Purpose: To perform qualitative video analyses of transitions of world-class athletes in TP competitions. Methods: Videos captured at 100 Hz were recorded for 77 races (including 96 different athletes) in 5 international track-cycling competitions (eg, UCI World Cups and World Championships) and analyzed for the 12 best teams in the UCI Track Cycling TP Olympic ranking. During TP, 1013 transitions were evaluated individually to extract quantitative (eg, average lead time, transition number, length, duration, height in the curve) and qualitative (quality of transition start, quality of return at the back of the team, distance between third and returning rider score) variables. Determination of correlation coefficients between extracted variables and end time allowed assessment of relationships between variables and relevance of the video analyses. Results: Overall quality of transitions and end time were significantly correlated (r = .35, P = .002). Similarly, transition distance (r = .26, P = .02) and duration (r = .35, P = .002) were positively correlated with end time. Conversely, no relationship was observed between transition number, average lead time, or height reached in the curve and end time. Conclusion: Video analysis of TP races highlights the importance of quality transitions between riders, with preferably swift and short relays rather than longer lead times for faster race times.

The individual time trial as an optimal control problem

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.