I need a relationship between energy and mobility (distance) to compute the energy consumption in mobile wireless sensor networks
Find the attachment
www.cs.binghamton.edu/~kang/teaching/cs526/mobility.pdf
If you are referring to "physical" mobility, then the energy greatly dependent on the mechanics that "moves" the sensor or the node. Based on the energy conservation principle the exerted energy to accelerate an object to a speed (v) should equal the kinetic energy that the object gains E=1/2 m v^2, that is in case of frictionless motion.
For your particular case, for an almost constant speed sensors I suggest to model the mobility energy as the following E_m = a * d +c, where (d) is the traveled distance in meters, (a) models the continuous friction losses in Joule per meter and (c) is the required kinetic energy.
thank you Akram Hourani for your intersting answer
but, i want to ask you if you have a real model for a real type of sensor node so that the values of (a) and (c) can be detemined
http://www.researchgate.net/publication/263856627_Effects_of_node_mobility_on_energy_balancing_in_wireless_networks
Article Effects of node mobility on energy balancing in wireless networks
For this question you have to find the path loss models. It differs from LOS to NLOS cases. IEEE 802.** have proposed some models for path loss which can help you to find the relation between the consumed power and distance for different frequencies.
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