# Research on a Simplified Estimation Method for Wheel Rolling Resistance on Unpaved Runways
## 1 Introduction  
During aircraft operations on unpaved runways, the rolling resistance encountered by the wheels significantly impacts runway length determination, a critical issue that has long attracted scholarly attention. Theoretical calculations of wheel rolling resistance rely on studies of wheel-soil interactions. Scholars have proposed various theoretical models and experimental approaches to address this challenge, primarily categorized into empirical, semi-empirical, and numerical simulation methods.  
A classic example of the empirical method is the Cone Index approach developed by the U.S. Army Corps of Engineers during World War II, which provides soil strength data for wheel resistance calculations [1, 2]. However, its applicability is highly limited to specific vehicles and terrains. The semi-empirical method, integrating theoretical analysis with experimental validation, has gained broader acceptance in modeling wheel-soil interactions [3, 4]. A key model in this category is the pressure-sinkage model. [PERSON] first proposed the rigid wheel sinkage theory [5], but its applicability was restricted to passive wheels and performed poorly for driven wheels. [PERSON] advanced this field by developing the widely recognized Bekker model [6] through extensive experimentation and theoretical analysis, which laid the foundation for subsequent pressure-sinkage models. Numerical simulations have also evolved into a mature framework with advancements in computational technology. For instance, [PERSON] et al. established a 3D finite elementmodel for pneumatic wheels to simulate rolling resistance, deriving a universal formula for predicting wheel resistance under varying speeds and wheel pressures [7].  
In terms of experimental research, the U.S. military conducted full-scale aircraft tests to investigate wheel resistance. In the 1990s, to address the inability of existing standards to predict braking and turning behaviors of large transport aircraft on arid or semi-arid unpaved surfaces, the U.S. Army performed takeoff and landing trials with C-17 aircraft on semi-prepared runways, developing a model to predict ground taxiing behavior under such conditions [8]. In 2009, runway condition readings (RCR), runway friction coefficients (RFF and \(\mu\)), and deceleration resistance were estimated by correlating C-17 stopping performance on concrete runways with soil-specific landing conditions and friction measurements, enabling landing rollout assessments [9]. While full-scale tests offer high accuracy, their exorbitant costs and logistical complexity hinder practical implementation. [PERSON] et al. designed a portable measurement system for evaluating rolling and braking friction coefficients on grassy airfields [10; 11; 12], yet their findings lacked generalizability due to limited test scales. It is worth noting that operational frameworks for paved/contaminated runways distinguish between braking traction (e.g., Runway Condition Report, RCR) and comprehensive resistance including unbraked wheel drag (e.g., Runway Condition Code, RSC under ICAO's Global Reporting Format (GRF)) [13; 14]. While this study focuses on fundamental wheel-soil interactions on dry, unpaved runways, future extensions to contaminated conditions (e.g., wet soil, snow) would require integrating RSC-based contaminant parameters to account for additional drag forces during takeoff acceleration [14; 15].  
This study adopts a theoretical approach. By analyzing wheel-soil interaction models, a resistance calculation equation is derived. A simplified estimation method is then established through global sensitivity analysis of resistance-influencing parameters. Field tests in loess regions were conducted to calibrate the simplified parameters, yielding an empirical formula for wheel resistance on loess-based unpaved runways. The formula's accuracy is validated, providing a practical tool for resistance estimation in loess regions and a methodological reference for other terrains.