Evaluating and advancing scaling methods for reliable wheel mobility prediction in low-gravity environments

Abstract

Predicting wheel mobility in low-gravity environments through Earth-based gravity tests offers a practical alternative to expensive parabolic flights and computationally intensive numerical simulations. However, an optimal scaling method for varying wheel speeds remains unidentified. This study systematically evaluated three scaling methods — Granular Scaling Laws (GSL), reduced-weight tests, and equal-mass tests — using Discrete Element Method simulations at three wheel angular velocities ($\pi /10$, $\pi$, and $2\pi$ rad/s). The methods were assessed based on their accuracy in predicting horizontal velocity, slip ratio, sinkage, and power consumption under free-driving conditions. GSL maintained errors below 5% across all conditions, while the equal-mass test showed velocity-dependent degradation with errors reaching 234% at high speeds. The reduced-weight test underestimated sinkage by over 100%, risking vehicle immobilization. An analytical framework employing an inertial number was developed to quantify soil flow characteristics, facilitating a comprehensive comparative analysis of the scaling methods. This analysis revealed that the equal-mass test inadequately captured dynamic flow phenomena, accounting for its velocity-dependent degradation. Conversely, GSL accurately reproduced soil flow characteristics under all conditions, enabling precise mobility predictions over a broad velocity range. These findings establish GSL as the most accurate and practical scaling approach for extraterrestrial rover mobility design and analysis.