Vehicle detection sensitivity formulas for multi-turn rectangular loops

This paper describes the derivation and application of a formula to calculate the vehicle detection sensitivity of a multi-turn, rectangular loop of round wire. The effect on detection sensitivity of reinforcing steel mesh in the pavement and "lead in" cable inductance is also considered. The loop is installed in the roadway pavement and connected to roadside detection electronics by a transmission line, "lead in", cable. When a vehicle passes over the loop, Eddy currents induced in the vehicle undercarriage cause a decrease in loop inductance which is sensed by the detector electronics. The multi-turn rectangular loop is modeled as a number of series connected, single-turn, rectangular loops which exhibit mutual coupling between each other. This loop is the primary of an air core transformer with two secondary windings comprised of shorted turns simulating the vehicle undercarriage and reinforcing steel mesh. The derived formulas are used to calculate tables of vehicle detection sensitivity versus loop turns, loop size, wire size, vehicle undercarriage height, etc.