# Research on a Simplified Estimation Method for Wheel Rolling Resistance on Unpaved Runways
## 3 Conclusions  
Based on an analytical evaluation of pressure-sinkage models in terramechanics, the Bekker formulation was selected to derive a theoretical equation for wheel rolling resistance. A global sensitivity analysis of the model parameters led to the development of a simplified resistance equation. Field experiments under vertical loads of 80 kN, 100 kN, and 120 kN provided empirical resistance values, enabling calibration of the simplified equation. Six candidate equations with adjusted power exponents were generated to evaluate predictive robustness. Finally, the accuracy of the proposed formulation was validated by incorporating resistance estimates into takeoff roll distance calculations for a transport aircraft. Key findings include:  
1. The Bekker-derived resistance equation demonstrates superior practicality due to its parametric simplicity and strong correlation with measured resistance values. Its ability to balance theoretical rigor with operational measurability makes it the optimal choice for resistance prediction in unpaved surface operations.
2. Among six primary parameters influencing rolling resistance, vertical load \(W\) and soil sinkage index \(n\) emerge as dominant factors. When soil conditions are fixed (e.g., at a specific airfield), \(W\) becomes the sole critical operational variable. This insight justifies the simplified power-law formulation \(F=Am^{N}\), which preserves essential nonlinear characteristics while simplifying the parameters compared to the original model.
3. Application of the calibrated equation (\(N=1.39\)) to takeoff performance analysis yielded a roll distance prediction of 937 m, deviating by 148 m (13.7%) from theoretical benchmarks. The 13.7% deviation falls within acceptable limits for preliminary engineering assessments, thereby confirming the model's utility in real-world scenarios such as rapidly constructing unpaved runways after emergency events like earthquakes to promptly deliver disaster relief supplies to affected areas.  
While demonstrating sufficient accuracy for cohesive soils, the model requires validation across granular soil types. Subsequent research should integrate dynamic sinkage effects and moisture-dependent parameter variations to enhance universal applicability.  
Conceptualization, P.G., X.C., and Z.W.; methodology, P.G., X.C., and Z.W.; validation, P.G. and X.C.; formal analysis, P.G. and Z.W.; investigation, P.G.; writing--original draft preparation, P.G. and X.C.; writing--review and editing, P.G. and X.C.; visualization, Z.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request. The data are not publicly available due to privacy concerns.  
**Conflicts of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.