Rolling Resistance Equation: Determine at 20 mph

[Aerstz]

Homework Statement

Determine an equation for rolling resistance for a wheeled vehicle @20 mph.

Homework Equations

(1) Drr = Crr * g * m * V

The Attempt at a Solution

(2) Drr = Crr * g * m

My real question: is velocity a valid part of the rolling resistance equation where speeds are slow (~20 mph)? I would like to check this with you because an equation I used in the past (1) includes velocity, yet other equations I found neglect it - most seem to neglect it. Are the two equations above over-simplified; do they have practical worth? Thanks.

 

[PhanthomJay]

Well your first equation can't be correct because the units are not consistent. The rolling resistance force can be approximated by D = Crr*m*g, where Crr is the dimensionless coefficient of rolling resistance which is a function of many factors, including speed, but speed is often neglected at the lower velocities. Even at higher speeds, the coefficient might change from say 0.010 at speeds up to say 20 km/hr to 0.015 at 100 km/hr. Just to give you an order of magnitude.







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[Aerstz]

Thank you for your clarification. I can now trust in equation (2).

 

[PhanthomJay]

I should have noted that eq 2 is for level surfaces and where the weight and normal forces are equal. In general, D = Crr N, where N is the normal force on the wheel.

 

[Aerstz]

Understood. Thanks again.