HeylandCircle: A Computational Framework for the Geometric Reconstruction of the Heyland Circle Diagram

Abstract

The Heyland circle diagram is a classical graphical tool for representing the steady-state behavior of induction machines using no-load and blocked-rotor test data. While widely used in alternating-current machinery texts, the diagram is typically presented as a hand-constructed aid and lacks a standardized computational formulation. This paper presents HeylandCircle, a computational framework that reconstructs the classical Heyland circle diagram directly from standard test parameters. The framework formalizes the traditional geometric construction as a deterministic, reproducible sequence of geometric operations, establishing a clear mapping between measured data, fixed geometric objects, and steady-state operating points. Quantities such as power factor, slip, output power, torque, and efficiency are obtained through explicit geometric relationships on the constructed diagram. Validation using a representative textbook example demonstrates close agreement with classical results. The framework provides a computational realization of the traditional Heyland diagram suitable for instruction, analysis, and systematic extension.