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The transmission range that achieves the most economical use of energy in wireless ad hoc networks is studied for uniformly distributed network nodes. By assuming the existence of forwarding neighbors and the knowledge of their locations, the average per-hop packet progress for a transmission range that is universal for all nodes is derived. This progress is then used to identify the optimal per-hop transmission range that gives the maximal energy efficiency. Equipped with this analytical result, the relation between the most energy-economical transmission range and the node density, as well as the path-loss exponent, is numerically investigated. It is observed that when the path-loss exponent is high (such as four), the optimal transmission ranges are almost identical over the range of node densities that we studied. However, when the path-loss exponent is only two, the optimal transmission range decreases noticeably as the node density increases. Simulation results also confirm the optimality of the per-hop transmission range that we found analytically.