The mass of the air surrounding a moving belt leads to a number of forces normal to the belt: hydrodynamically induced inertia, Coriolis force, and centrifugal force. These forces act in concert with those generated by the belt’s own inertia to govern out-of-plane dynamics. Their effect is to reduce stability and limit the safe running speed. These detrimental consequences can be reduced through management of the air flow around the belt. An analysis of the governing partial differential equations is presented; experiments on the aerodynamic interaction terms are reported; and a numerical simulation method for belt dynamics is outlined.