Q:

Rolling resistance in relation to diameter

I am trying to determine the effects the radius of a wheel has on its ability to move across soft ground materials and have found the formula. Would this formula suggest that rolling resistance is inversely proportional to the radius of a wheel or am I missing an aspect of the rolling resistance coefficient? 
$F = \frac{CN}{r}$
$F$ is the rolling resistance
$C$ is the rolling resistance coefficient
$N$ is the weight of the load (normal force)
$r$ is the radius of the wheel 

A:

You are correct in assuming that the rolling resistance is inversely proportional to the radius of the wheel if the pressure on the wheels is same. The reason for this is that for the same inflation pressure a wheel with lower radius will have a higher proportion of deformation(become more flattened/less circular) than for a wheel with larger radius which will have lower proportion of deformation(as it is larger, with about the same amount of flattening due to same pressure, it will be more circular).
Thus higher proportion of deformation means greater friction/rolling resistance. Hence for the same pressure, rolling resistance is inversely proportional to radius of the wheel. 

