Estimating the relationship between heart rate and power output for short term cycling exercises

In this paper, we statistically analyze a dataset of performance diagnostics of 1940 subjects to examine the influence of different physical characteristics on the relationship between heart rate and power output. Five characteristics - the cyclist's height, weight, age, sex and fitness level - were identified as parameters for the model. Next, we divide the dataset into different subsets according to the statistical analysis and modify formulas found in the literature to estimate the maximum heart rate as well as the maximum power output for each group. Then, we derive formulas from the dataset to estimate the heart rate and power output at the individual anaerobic threshold (IAT) as well as the heart rate at low workload. A linear curve between these points describes the immediate relationship between heart rate and power. We compared the results of the adapted formulas to the results of the original formulas for experimental data of 15 subjects. The adapted formulas show better results in terms of mean absolute error (MAE) and sum of squared residuals (SSR) for estimating the maximum power output, but no improvement in estimating the maximum heart rate. The heart rate at IAT is predicted with a MAE of 9 beats per minute (bpm) and heart rate for low intensity with a MAE of 13 bpm. Power at the IAT is predicted with a MAE of 22 Watts.