#
Recommendations for Measuring Tennis Racket Parameters^{ †}

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}, and the Transverse MOI about the end of the other was 0.0576 kg·m

^{2}. Three operators ran each test twice, resulting in a total of six for each MOI. Polar MOI was measured as 0.00190 kg·m

^{2}and Transverse MOI ranged from 0.0567 to 0.0577 kg·m

^{2}(mean value 0.0570 kg·m

^{2}), indicating similar agreement to theoretical values and the accuracy results reported by Spurr et al. [9] (mean within 2%). Attempts were made to measure MOI with the sensor, by attaching it to the rods and then applying an FFT to the signal (accelerometer & gyroscope) to predict the frequency of oscillation, but initial results indicated that this was less accurate and more time-consuming than using the stopwatch.

_{T}) in our Pendulum technique, models were investigated to determine their suitability for predicting Transverse MOI from racket dimensions, mass and COM location [10,11]. The simplest approach is to model the racket as a beam [10] (Figure 1b).

_{f}

_{2}was assumed to equal l

_{f}

_{4}(from int. & ext. head length), so m

_{f}

_{2}equaled m

_{f}

_{4.}As the mass of all sections sum to the racket mass, their values can be obtained using:

## 3. Results

^{2}. Figure 2b–d shows that Transverse MOI was predicted well by all the models. All models were well correlated with the data (all R

^{2}> 0.934), with trendline gradients close to 1, and low intercept and root mean squared error (RMSE) values (Figure 2b–d). When a threshold of ±5% was introduced, fifteen rackets were out of this range for the two-section beam, reducing to twelve for the five-section beam (three of them being made of wood out of a total of eight wooden rackets) and only five (included in the fifteen of the two-section beam) for the unequal two-section beam. The maximum error was 9.5% for the two-section beam, 7.4% for the unequal two-section beam and 7.7% for the five-section beam. When the threshold was decreased to ±3%, the five-section beam was still consistent for seventy-five rackets, against sixty-five for the unequal-two section beam and only fifty-nine for the two-section beam. The Stepwise Linear Regression model indicated that mass (partial correlation (pC) = 0.941), COM location (pC = 0.864), racket length (pC = 0.492), and head width (pC = 0.245) all significantly contributed to Transverse MOI (R

^{2}= 0.936, p < 0.001), although removing head width did not have much of an effect on the model overall (R

^{2}= 0.930, p < 0.001).

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Transverse versus Lateral MOI, experimental Transverse MOI versus; (

**b**) two-section beam; (

**c**) unequal two-section beam and (

**d**) five-section beam.

Property Type | Details | Method |
---|---|---|

Manufacturer | Name, racket name & model, date, material/s ^{1} | - |

Geometric | Length ^{3}, depth ^{2,4}, head length/width (ext. & int.)^{3}, grip length ^{3}/circ ^{2,3}. | Measuring tape, calipers |

Dynamic | Frequency of the first bending mode | Modal analysis with accelerometer |

Inertial | Mass ^{5}, COM from butt ^{3}, Transverse, Lateral and Polar MOI | Scales, angle iron/measuring tape, Simple Pendulum and Bifilar Suspension |

String | Diameter ^{4}, material ^{1}, no. main/cross strings | Calipers |

^{1}As available,

^{2}Max./min., mean reported, resolution of:

^{3}1 mm using measuring tape;

^{4}0.1 mm using calipers; and

^{5}1 g using scales

Length | Head Length | Head Width | Frame Depth | Grip | |||||
---|---|---|---|---|---|---|---|---|---|

External | Internal | External | Internal | Max. | Min. | Length | Circumference | ||

Max. | Min. | ||||||||

0.69 ± 0.02 | 0.35 ± 0.03 | 0.33 ± 0.03 | 0.26 ± 0.02 | 0.24 ± 0.02 | 0.02 ± 0.00 | 0.02 ± 0.01 | 0.19 ± 0.01 | 0.14 ± 0.00 | 0.11 ± 0.00 |

0.66–0.81 | 0.30–0.49 | 0.27–0.46 | 0.22–0.31 | 0.20–0.29 | 0.01–0.04 | 0.01–0.03 | 0.15–0.24 | 0.12–0.15 | 0.10–0.13 |

Mass (kg) | COM (m) | Transverse MOI (kg·m^{2}) | Lateral MOI (kg·m^{2}) | Polar MOI (kg·m^{2}) | String Diameter (mm) | No. Main | No. Cross | Frequency (Hz) |
---|---|---|---|---|---|---|---|---|

0.32 ± 0.04 | 0.34 ± 0.02 | 0.051 ± 0.005 | 0.053 ± 0.005 | 0.00135 ± 0.00019 | 1.3 ± 0.1 | 16 ± 1 | 19 ± 1 | 144 ± 30 |

0.22–0.40 | 0.30–0.43 | 0.041–0.069 | 0.042–0.071 | 0.00091–0.00182 | 1.1–1.6 | 14–20 | 15–22 | 98–242 |

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## Share and Cite

**MDPI and ACS Style**

Allen, T.; Grant, R.; Sullivan, M.; Taraborrelli, L.; Choppin, S.; Spurr, J.; Haake, S.
Recommendations for Measuring Tennis Racket Parameters. *Proceedings* **2018**, *2*, 263.
https://doi.org/10.3390/proceedings2060263

**AMA Style**

Allen T, Grant R, Sullivan M, Taraborrelli L, Choppin S, Spurr J, Haake S.
Recommendations for Measuring Tennis Racket Parameters. *Proceedings*. 2018; 2(6):263.
https://doi.org/10.3390/proceedings2060263

**Chicago/Turabian Style**

Allen, Tom, Robyn Grant, Matthew Sullivan, Luca Taraborrelli, Simon Choppin, James Spurr, and Steve Haake.
2018. "Recommendations for Measuring Tennis Racket Parameters" *Proceedings* 2, no. 6: 263.
https://doi.org/10.3390/proceedings2060263