Discussion at Midwinter convention: The single-phase induction motor

V. Karapetoff: The problem treated by the author is quite old, and a complete absence of correlation with the work of previous investigators is rather deplorable. Thus, the whole set of papers and a voluminous discussion before the Institute in 1918 are entirely ignored, as well as the subsequent contributions to the theory of this class of machines. In 1921 I showed the equivalence of the two theories of the single-phase induction machine Journal, Vol. 40, page 640) and gave a new equivalent diagram, only one branch of which contains variable slip. A circular locus and a general-performance equation follow from this diagram directly. In Vol. 41 of the Transactions there is a paper by Mr. Kostko which to me only shows that elementary mathematics is inadequate to lead to a simple theory of the machine, on the basis of two oppositely revolving fields. Mr. Perkins´ paper shows that elementary mathematics is also inadequate in the cross-field theory. I hope, therefore, that this method of approach will now be definitely abandoned in favor of more advanced and shorter mathematical tools. In the Journal for 1923 (Vol. 42, page 1181) I indicated the use of the scalar product of vectors in the solution of problems on locus diagrams of electrical machinery. This new use of vector analysis has already proved to be quite fruitful in a derivation of the exact circle diagram of the polyphase induction motor, without inversion or long formulas. The next step is to try this method on the single-phase machine, preferably using the unified equivalent diagram mentioned above.