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Conventional high-speed linear induction motors designed to operate from a 50 Hz supply possess large leakage reactances. This is because of the large end-winding-overhang/core-width ratio. The resulting poor power-factor performance of these machines may be improved by incorporating the primary end windings into the main magnetic circuit of the machine. Difficulties in construction and low airgap flux density point to the use of airgap windings. A mathematical model is developed, and verified against practical test results, to give the complete electrical and mechanical performance of axial-flux linear machines with 2-dimensional conductor distribution and airgap windings. The treatment makes no assumptions about input current balance. Any number of serially connected coil groups, energised from independent voltage sources, are considered. The model is also suitable for predicting the performance of conventional linear machines and in this case gives improved estimates over previous single-dimensional analyses. The model is used to predict the performance of two equivalent high-speed designs. These results show an improved power factor over a conventional design for an airgap-wound machine with a minimum of coil overhang.