# Research on a Simplified Estimation Method for Wheel Rolling Resistance on Unpaved Runways
## 2 Theory and Methods
### Parameter Determination Based on Field Tests  
The determination of parameters requires the relationship between tire rolling resistance and the mass of the test object. Considering factors such as the repeatability of the tests, cost, and operational complexity, [PERSON] [32] proposed using an aircraft load-simulating vehicle to simulate wheel rolling resistance, which has been validated for its accuracy. Therefore, this study employs an aircraft load-simulating vehicle for field tests. The test vehicle is equipped with five wheels, one of which is the main load-bearing wheel with standard tire pressure. During the test, tractors are placed at both ends of the load-simulating vehicle to ensure stable forward movement. Strain gauges are installed on the main load-bearing wheel to measure the rolling resistance. The testing process is shown in Figure 4. Due to limitations in the test site and conditions, the experiment is designed with three load levels--80 kN, 100 kN, and 120 kN--corresponding to the load on the main load-bearing wheel. The unpaved runway consists of well-compacted clay soil with a compaction degree of over 90% and good surface regularity, with zero longitudinal slope. The test section is 20 m long, and the tractor advances the aircraft load-simulating vehicle at a speed of 10 km/h. The sampling frequency for measuring rolling resistance is set at 10 Hz, yielding approximately 80 valid data points per test. Each load condition is tested four times. The 10 Hz sampling frequency was selected primarily because it is the maximum sampling rate supported by the specific sensors employed in the measurement system. Crucially, this frequency has been demonstrated to be sufficient for capturing the continuity and essential characteristics of rolling resistance data on soil runways [33]. After processing the resistance data obtained from the aircraft load-simulating vehicle tests to remove outliers, the variation of resistance over time is plotted, as shown in Figure 5.  
Figure 4: Field tests with aircraft load-simulating vehicle. The key data from each group are summarized in Table 3.  
The data acquired at a 10 Hz sampling frequency exhibit excellent continuity in graphical representations. On soil surfaces with 90% compaction density, maximum rolling resistance values reach 7.2 kN, 9.82 kN, and 12.23 kN under 80 kN, 100 kN, and 120 kN loader weights, respectively. While minimum resistance values show no consistent pattern, the measured resistance fluctuates significantly around central values across all loading conditions, with oscillation amplitudes expanding as loads increase. These fluctuations span 0-8 kN, predominantly concentrating between 2-8 kN. Average resistance values demonstrate a progressive increase from 3.27 kN (80 kN load) to 4.42 kN (100 kN) and 5.73 kN (120 kN), accompanied by reduced standard deviations at higher loads, indicating enhanced stability under greater vertical loading. Figure 5: Variation of rolling resistance under different vertical loads. The preceding analysis inferred that the wheel rolling resistance is correlated with the vertical load. Additionally, the wheel rolling resistance averages under various vertical loads were obtained from the aircraft load simulation tests using a loading vehicle. The following section will utilize these data to conduct curve-fitting to explore the underlying relationship. The allometric function \(y=\alpha x^{b}\), consistent with the theoretical framework of the simplified resistance model, was selected for its inherent compatibility with observed soil mechanics behavior. This functional form enables simultaneous determination of the scaling coefficient \(A\) and the deformation exponent \(n\) through regression analysis of field test data. Soils in loess regions were categorized into clay soils, while existing studies propose \(n=0.5\) (\(N=1.5\)) as a representative sinkage index for clay soils [20; 21; 22].