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Investigating the Influence of Shaft Balance Point on Clubhead Speed: A Simulation Study^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Shaft Modeling

^{3}, which is comparable to the densities reported by Betzler et al. for sheets of carbon fiber-reinforced polymer used in the construction of golf shafts [11]. The wall thicknesses of shafts B and C were varied linearly from 0.5 to 1.5 and 1.5 to 0.5 mm, respectively, such that their average wall thickness was 1 mm.

^{2}, which is representative of a regular-flex shaft [4]. For shafts B and C, the elastic moduli were varied along the shaft to generate the same bending stiffness profile as shaft A. The shear moduli were set to half the elastic moduli, such that the torsional stiffness $GJ$ of each shaft was equal to the bending stiffness $EI$. Figure 1 plots the inner radius, cross-sectional area, area moment of inertia, and elastic modulus profiles for each shaft. The vertical lines in the radius plot indicate the center of mass position of each shaft. Fourth-order polynomials were fit to $A\left(x\right)$, $I\left(x\right)$, $E\left(x\right)$, and $G\left(x\right)$ to parametrize the analytical shaft model [10].

#### 2.2. Golfer Model

#### 2.3. Golf Swing Optimization

## 3. Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The inner radius, cross-sectional area, area moment of inertia, and elastic modulus profiles for each shaft design. The vertical lines in the radius plot indicate the center of mass positions of each shaft. Best viewed in color.

**Figure 2.**(

**a**) Box plot of the 100 clubhead speeds using each shaft; (

**b**) mean clubhead speed leading up to impact; (

**c**) mean lag deflection during the period of max lag deflection; (

**d**) mean kick velocity leading up to impact.

**Table 1.**Shaft design parameters. All shafts have a length of 1.105 m, total mass of 65 g, and average stiffness (bending $EI$ and torsional $GJ$ ) of 50 Nm

^{2}.

Shaft | ${\mathit{t}}_{1}\left(\mathbf{mm}\right)$ | ${\mathit{t}}_{2}\left(\mathbf{mm}\right)$ | ${\mathit{x}}_{\mathit{C}\mathit{M}}\left(\mathbf{m}\right)$ | ${\mathit{I}}_{\mathit{b}}(\mathbf{g}-{\mathbf{m}}^{2})$ | $\mathit{\rho}$ |
---|---|---|---|---|---|

A | 1 | 0 | 0.5064 | 23.17 | 1.561 |

B | 0.5 | 1 | 0.6143 | 31.10 | 1.897 |

C | 1.5 | -1 | 0.4264 | 17.58 | 1.508 |

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**MDPI and ACS Style**

McNally, W.; McPhee, J.
Investigating the Influence of Shaft Balance Point on Clubhead Speed: A Simulation Study. *Proceedings* **2020**, *49*, 156.
https://doi.org/10.3390/proceedings2020049156

**AMA Style**

McNally W, McPhee J.
Investigating the Influence of Shaft Balance Point on Clubhead Speed: A Simulation Study. *Proceedings*. 2020; 49(1):156.
https://doi.org/10.3390/proceedings2020049156

**Chicago/Turabian Style**

McNally, William, and John McPhee.
2020. "Investigating the Influence of Shaft Balance Point on Clubhead Speed: A Simulation Study" *Proceedings* 49, no. 1: 156.
https://doi.org/10.3390/proceedings2020049156