The properties of the distribution factor of armature windings

In many problems the resultant of a number of equal and equally spaced vectors is required in terms of their simple scalar sum. This relation is usually expressed in the form of a ratio f(¿) = sin ¿/q sin (¿/q), where q is the number of vectors spaced over an angle 20. The vectors may be those of the electromotive or the magnetomotive force of the coils of an armature winding; the quantity f(¿) is then called the distribution factor, and is of frequent occurrence in the theory and design of armature windings. The object of this paper is to discuss the principal mathematical properties of the distribution factor, and to give a complete series of curves exhibiting these properties in a form suitable for practical application.