  Granular surfaces subjected to forces due to rolling wheels develop ripples
above a critical speed. The resulting pattern, known as "washboard" or
"corrugated" road, is common on dry, unpaved roads. We investigated this
phenomenon theoretically and experimentally, using laboratory-scale apparatus
and beds of dry sand. A thick layer of sand on a circular track was forced by a
rolling wheel on an arm whose weight and moment of inertia could be varied. We
compared the ripples made by the rolling wheel to those made using a simple
inclined plow blade. We investigated the dependence of the critical speed on
various parameters, and describe a scaling argument which leads to a
dimensionless ratio, analogous to the hydrodynamic Froude number, which
controls the instability. This represents the crossover between conservative,
dynamic forces and dissipative, static forces. Above onset, wheel-driven
ripples move in the direction of motion of the wheel, but plow-driven ripples
move in the reverse direction for a narrow range of Froude numbers.
