The Thin Line: The Hybrid Model Bringing Power Measurement to Every Indoor Cyclist

Abstract

The Thin Line: The Hybrid Model Bringing Power Measurement to Every Indoor Cyclist presents the Hybrid Linear Regression Model (HLRM)—a scientifically grounded yet human-centred solution for estimating cycling power without a physical power meter. Designed for accessibility, the HLRM leverages widely available inputs—heart rate, cadence, body weight, and reference power—to deliver real-time power estimates in watts with a standard error of approximately ±4.8 W. Developed from empirical data collected across 40 participants (ages 38–84) and refined through robust statistical methods inspired by Huber’s (1964) theory of robust estimation, the model incorporates both linear and quadratic physiological components to reflect the non-linear relationship between effort and power output. By integrating heuristic physiological insights with rigorous regression techniques—including variable simplification, centering, and outlier resistance—the HLRM achieves both high accuracy and interpretability. Validated in real-world conditions and optimized for smartphone-based applications, the model enables cyclists to access performance metrics such as power, energy expenditure, and training zones using only basic sensors. While limitations include dependence on heart-rate sensor fidelity and optimal performance near 80 RPM, the HLRM represents a significant step toward democratizing performance science. More than a computational tool, it embodies a vision of ethical innovation—where precision meets inclusivity, and every pedal stroke becomes a measurable, meaningful act of human energy.