R&A Rules Limited
andUnited States Golf Association

PROTOCOL FOR MEASURING THE MOMENT OF INERTIA OF
GOLF CLUBHEADSTPX3005
Rev. 2.0
1 December 2020

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Revision

Date

Details of Revision

1.0Jun-2005

Original published version.

2.0

1-Dec-2020

Updated references to The Equipment Rules. Reformatted
step numbering and section titles to be consistent with otherprotocols. Eliminated requirement for use of Microsoft Excel
spreadsheet and equipment specificity.

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1 Scope
This protocol describes the methods used to determine the clubhead moment of inertia ofwoods to the Equipment Rules, Part 2, Section 4b (i), as administered by R&A Rules Ltd. (TheR&A) and the United States Golf Association (USGA).

2 Test Protocol
2.1 Measurementa. Using a calibrated mass balance or equivalent, measure and record the mass of theclubhead.
b. Measure the moment of inertia of the clubhead about the vertical axis of the clubhead
orientated at a 60° lie angle, See Figure 1.

Figure 1: Clubhead mounted such that the axis of rotation is parallel to the vertical axis of the clubhead.

i.
ii.

Measure the moment of inertia about the centre of mass of the clubhead in thisorientation.
If the position of the centre of mass is unknown, or if measurement of themoment of inertia is impracticable, see Appendix, 4)3 Determination of Conformance Status
If the moment of inertia of the clubhead about its centre of mass exceeds 5,900 g-cm² plus atest tolerance, the clubhead does not conform to the Equipment Rules, Part 2, Section 4b (i).
Appropriate screening methods may be applied.

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4 Appendix: Moment of Inertia Calculations, Unknown Centre ofMassFigure 2: Measurement of the moment of inertia of a club head, unknown centre of mass.

In the case that the position of the centre of mass is unknown, or if measurement of the momentof inertia is impracticable:
a. Measure the moment of inertia of the clubhead about the vertical axis of the clubhead
orientated at a 60° lie angle, with the club at a known position.
b. Measure the distance between the axis of rotation and a known point on the clubhead.
This distance should be expressed in Cartesian coordinates on a plane normal to theaxis of rotation. The origin of this plane should be the axis of rotation.
c. Repeat the moment of inertia measurement (step a.) eight further times varying thedistance between the axis of rotation and the known point on the clubhead.
i.
Note that the orientation of the clubhead relative to the axis of rotation should bekept constant.
d. Using the parallel axis theorem, calculate the moment of inertia of the clubhead about its
centre of mass.
The parallel axis theorem may be expressed as:
𝐼𝐼

𝑚𝑑(1)

where m is the total mass of the body and d is the distance from the center of mass to the axis ofrotation. In a Cartesian coordinate system, this may be rearranged to show:
𝐼𝐼

𝑚𝑑𝐼𝑚𝑥𝑥𝑦𝑦(2)This may be generalized for a collection of measurements j:
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𝐼𝐼𝑚 𝑥𝑥𝑦𝑦(3)It can be shown that this may be expressed as:
𝐟𝐊𝐱

(4)

where:𝐟𝐼⎧
⎪𝑚
⎪𝐼
⎪
𝑚
⎨
⎪
⎪⎪𝐼
⎩𝑚𝑥𝑥.
.
.
𝑥𝑦 ⎫⎪⎪𝑦 ⎪⎬⎪⎪⎪𝑦 ⎭,𝐊1
⎡⎢𝑚
⎢1
⎢𝑚⎢⎢⎢
⎢1
⎣𝑚𝑥𝑥𝑥.
.
.

2𝑥𝑦2𝑥𝑦2𝑥𝑦2𝑦 ⎤⎥2𝑦 ⎥⎥⎥,⎥⎥⎥
2𝑦 ⎦𝐱𝐼𝑥𝑦

For multiple points (n>3), this system may be solved to arrive at a least-squares solution by useof the pseudo inverse of the K matrix:
𝐱𝐊𝐓 𝐊

𝟏𝐊𝐓𝐟(5)

An iterative solution is required such that initial guesses of 𝑥 and 𝑦 are inserted into K and asolution is found with the iteration scheme converging in two iterations.

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