The Optimal Road Grade Design for Minimizing Ground Vehicle Energy Consumption

Reducing energy consumption of ground vehicles is a paramount pursuit in academia and industry. Even though the road infrastructural has a significant influence on vehicular fuel consumption, the majority of the R&D efforts are dedicated to improving vehicles. Little investigation has been made in the optimal design of the road infrastructure to minimize the total fuel consumption of all vehicles running on it. This paper focuses on this overlooked design problem and the design parameters of the optimal road infrastructure is the profile of road grade angle between two fixed points. We assume that all vehicles on the road follow a given acceleration profile between the two given points. The mean value of the energy consumptions of all vehicles running on the road is defined as the objective function. The optimization problem is solved both analytically by Pontryagin’s minimum principle and numerically by dynamic programming. The two solutions agree well. A large number of Monte Carlo simulations show that the vehicles driving on the road with the optimal road grade consume up to 31.7% less energy than on a flat road. Finally, a rough cost analysis justifies the economic advantage of building the optimal road profile.