Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf

By A. J. Cochran; M. R. Farrally | Go to book overview

44

Experimental determination of inertia ellipsoids

S.H. Johnson

Lehigh University, Bethlehem, Pennsylvania, USA

Abstract

This paper presents a method for measuring the elements of the inertia matrix of an irregular rigid body like a golf-club head by use of a simple pendular device. The examples demonstrate the use of the inertia ellipsoid as a means for visualizing and interpreting inertia properties.

1 Introduction

Indirectly, the rules of golf require that clubheads be rigid bodies. As such, the contribution of the club to an impact with a ball is controlled by the face shape, the location of the face relative to the center of mass, the frictional properties of the face, the clubhead mass and the inertia matrix. The inertia matrix represents the dynamic consequences of the arrangement of the clubhead mass. The ellipsoid of inertia is a graphical way to portray an inertia matrix.

The following body axis system is used here:

z-axis: centerline of the hosel

xy-plane: plane of the hosel end

x-axis: a line in the xy plane parallel to the face

y-axis: completes a righthanded coordinate system

The origin of this xyz axis system is at the center of the hosel end. With this axis system, the coordinates of the center of mass will normally be three positive numbers.

An apparatus for determining the coordinates of the center of mass is shown in the photograph, Figure 1. A transverse rod is attached to the device shown and a hanging weight is moved along the rod until static balance is achieved. This allows calculation of the distance from the pivot line to the center of mass. The process is repeated for two mutually perpendicular orientations.

Science and Golf II: Proceedings of the World Scientific Congress of Golf. Edited by A.J. Cochran and M.R. Farrally. Published in 1994 by E & FN Spon, London. ISBN 0 419 18790 1

-290-

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