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The static and dynamic stiffness behaviour of composite golf shafts and their constituent materials

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Abstract

Golf shafts are normally characterised using static or quasi-static tests, yet the golf swing itself is dynamic. The purpose of this research was to determine whether stiffness properties obtained from these tests can be used when modelling the dynamic behaviour of golf shafts made from carbon fibre reinforced polymer (CFRP). Three shafts, matched for all properties except shaft flex, were subjected to human swing testing by 12 skillful players whilst strains were recorded. Peak principal strains as well as strain rates increased as shaft flex decreased (p < 0.001). CFRP flat panels with lay-ups similar to those contained in the shafts were constructed and tested statically and at strain rates between 10−4 and 4 s−1. Some level of strain-rate dependency was found for these panels, but only for strain rates exceeding those seen during a swing, which suggests that static material tests are appropriate for measuring the dynamic stiffness of golf shafts.

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Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. R&A Rules Ltd, 6 Pilmour Links, St Andrews, Fife, KY16 9JG, UK

    Nils F. Betzler, Stuart A. Monk & Steve R. Otto

  2. Sports Materials Research Group, School of Metallurgy and Materials, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    Carl Slater & Martin Strangwood

  3. Sport and Exercise Sciences Research Institute, University of Ulster, Shore Road, Newtownabbey, BT37 0QB, UK

    Eric S. Wallace

Authors
  1. Nils F. Betzler
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  2. Carl Slater
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  3. Martin Strangwood
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  4. Stuart A. Monk
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  5. Steve R. Otto
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  6. Eric S. Wallace
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Corresponding author

Correspondence to Nils F. Betzler.

Appendix

Appendix

Based on the definitions provided in Fig. 8, it is possible to find the following relationship between measured and principal strain:

$$ \varepsilon_{{{\text{a}}/{\text{b}}}} = \varepsilon \cdot \cos \left( {\varphi_{\varepsilon } - \varphi_{\text{a/b}} } \right), $$
(3)

where ε a/b is the magnitude of the strain at positions a or b (μm/m), ε is the magnitude of the principal strain (μm/m), φ ε is the orientation of the principal strain (rad), and φ a/b is the orientation of positions a and b (rad).

Fig. 8
figure 8

Shaft cross-section with nomenclature for principal strain calculation

Full size image

Rearranging (3) yields:

$$ \varphi_{\varepsilon } = \arctan \left( {\frac{{\varepsilon_{\text{b}} \cos \left( {\varphi_{\text{a}} } \right) - \varepsilon_{\text{a}} \cos \left( {\varphi_{\text{b}} } \right)}}{{\varepsilon_{\text{a}} \sin \left( {\varphi_{\text{b}} } \right) - \varepsilon_{\text{b}} \sin \left( {\varphi_{\text{a}} } \right)}}} \right). $$
(4)

It is further possible to calculate the principal strain for any given output from the two strain gauges at positions a and b from Eq. (3):

$$ \varepsilon = 0.5\;\left( {\frac{{\varepsilon_{\text{a}} }}{{\cos \left( {\varphi_{\text{e}} - \varphi_{\text{a}} } \right)}} + \frac{{\varepsilon_{\text{b}} }}{{\cos \left( {\varphi_{\text{e}} - \varphi_{\text{b}} } \right)}}} \right). $$
(5)

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Betzler, N.F., Slater, C., Strangwood, M. et al. The static and dynamic stiffness behaviour of composite golf shafts and their constituent materials. Sports Eng 14, 27 (2011). https://doi.org/10.1007/s12283-011-0068-1

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