A tractor drive tire of overall unloaded diameter $d = 1.40\text{ m}$ and section width $b = 0.45\text{ m}$ carries a dynamic vertical wheel load of $W = 12.0\text{ kN}$. The tilled soil has a cone index of $CI = 800\text{ kPa}$ ($800\text{ kN/m}^2$). According to the Wismer & Luth traction model, the dimensionless wheel numeric (mobility number $C_n = \frac{CI \cdot b \cdot d}{W}$) is ________ (answer in integer).
Answer Key:
42
Step-by-Step Solution & Explanation
The dimensionless wheel numeric $C_n$ in the Wismer & Luth model is:
$C_n = \frac{CI \cdot b \cdot d}{W}$
Given $CI = 800\text{ kN/m}^2$, $b = 0.45\text{ m}$, $d = 1.40\text{ m}$, and $W = 12.0\text{ kN}$:
$C_n = \frac{800 \times 0.45 \times 1.40}{12.0} = \frac{504}{12.0} = 42$