Rolling Resistance Calculator

Rolling resistance arises primarily from the imperfect elasticity of the rolling material and the supporting surface, causing deformation as the wheel moves. The core equations governing this phenomenon are:

• Normal Force ($N$): $N = m \times g$, where $m$ is mass and $g$ is acceleration due to gravity.
• Coefficient of Rolling Resistance ($C$): Derived either via presets or directly through $C = c_{roll} / r$, where $c_{roll}$ is the rolling coefficient and $r$ is the wheel radius.
• Rolling Resistance Force ($F_{rr}$): $F_{rr} = C \times N$.

Consider a heavy cart with a mass ($m$) of 200 kilograms moving under standard Earth gravity ($g = 9.81\text{ m/s}^2$). First, calculate the normal force: $N = 200 \times 9.81 = 1962\text{ Newtons}$. Next, assume a rolling resistance coefficient ($C$) of 0.02, which is typical for pneumatic tires on asphalt. Multiplying these values together ($F_{rr} = 0.02 \times 1962$), we find the rolling resistance force is 39.24 Newtons. This means the cart constantly combats a 39.24 N retarding force while rolling.

To ensure high accuracy in your mechanical and physical models, keep these tips in mind:

• Verify Unit Consistency: Always ensure mass is in kilograms, acceleration in meters per second squared, and radii in meters to yield force in Newtons.
• Account for Surface Variability: Rolling coefficients change dramatically between dry concrete, wet asphalt, and soft soil; select presets carefully or measure empirical values when precision is critical.
• Speed and Deformation: Remember that at very high speeds, additional phenomena like air hysteresis and aerodynamic drag supersede basic rolling resistance.