It is fuel efficient to minimize the relative distance between vehicles to achievea maximum reduction in air drag. However, the relative distance can only be reduced to acertain extent without endangering a collision. Factors such as the vehicle velocity, the relativevelocity, and the characteristics of the vehicle ahead has a strong impact on what minimumrelative distance can be obtained. In this paper, we utilize optimal control and game theory toestablish safety criteria for heavy duty vehicle platooning applications. The derived results showthat a minimum relative distance of 1.2m can be obtained for two identical vehicles withoutendangering a collision, assuming that there is no delay present in the feedback system. If aworst case delay is present in the system, a minimum relative distance is deduced based uponthe vehicle’s maximum deceleration ability. The relative distance can be reduced if the followervehicle has a greater overall braking capability, which suggests that vehicle heterogeneity andorder has substantial impact. The findings are verified by simulations and the main conclusion isthat the relative distance utilized in commercial applications today can be reduced significantlywith a suitable advanced cruise control system.