A global analysis of relativistic heavy-ion collisions is proposed which entails a measurement of the momentum of all emitted particles. The resultant thrust is a measure of final-state momentum flow and provides information on the global dynamics governing the collisions. This proposal is tested with a relativistic hydrodynamic model for collisions of equal-mass nuclei. The angle at which the thrust, or maximal directed momentum flow, occurs is O° CM for grazing collisions and increases monotonically to 90° CM for central collisions. Experimental observation of this dramatic behaviour would imply a mean free path much less than the size of the colliding nuclei.