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Most nodes of ad-hoc wireless networks are battery-powered, therefore energy efficiency is an important concern in ad-hoc networks. Most transmission and energy consumption models in ad-hoc wireless networks assume an ideal physical layer model, where the probability of the packet being received by the neighbour is 100% once the neighbour node is within the transmission range of the transmitter. In this paper, we investigate the Rayleigh fading and Lognormal fading scenarios to derive the optimal transmission range in ad-hoc wireless networks. In this paper, based on the hop-by-hop retransmissions (HHRs) model, where a packet is retransmitted between two nodes until it is received and acknowledged correctly, the relationship between expected energy consumption and the distance between two nodes is derived in the two-node model. In an equal-hop end-to-end multihop transmission model, the relationship between the total expected energy consumption, the range of each hop, and the transmission power of each node is derived and analysed. It is shown that the minimum energy consumption can be achieved by adjusting both the transmission power and the range of each hop. Furthermore, based on a one hop model, an efficiency function is proposed based on the one hop progress and one hop energy consumption. The relationship between expected one hop energy consumption, the range of the hop, and the nodes transmission power has been derived and the results show that, these two relationships derived through different methods are the same, which validates the relationship.