# Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental

#### 2.2. Data Analysis

#### 2.3. Mathematical Modelling (Sagittal Plane)

- ${A}^{*},{B}^{*},{C}^{*},{D}^{*},{E}^{*},{G}^{*}$ = centre of mass segments A, B, C, D, E and G, respectively
- ${\ell}_{A},{\ell}_{B},{\ell}_{C},{\ell}_{D},{\ell}_{E},{\ell}_{G}$ = length of segments
- ${\rho}_{A},{\rho}_{B},{\rho}_{C},{\rho}_{D},{\rho}_{E},{\rho}_{G}$ = distances of centre of mass from their proximal ends
- ${\hat{n}}_{1},{\hat{n}}_{2},{\hat{n}}_{3},{\hat{a}}_{1},{\hat{a}}_{2},{\hat{a}}_{3},{\hat{b}}_{1},{\hat{b}}_{2},{\hat{b}}_{3},{\hat{c}}_{1},{\hat{c}}_{2},{\hat{c}}_{3},{\hat{d}}_{1},{\hat{d}}_{2},{\hat{d}}_{3},{\hat{e}}_{1},{\hat{e}}_{2},{\hat{e}}_{3},{\hat{g}}_{1},{\hat{g}}_{2},{\hat{g}}_{3}$ = mutually orthogonal unit
- ${\tau}_{N/A},{\tau}_{A/B},{\tau}_{B/C},{\tau}_{C/D},{\tau}_{D/E},{\tau}_{E/G}$ = torque of each joints

^{*}. The linear accelerations at the centre of mass ${A}^{*},{B}^{*},{C}^{*},{D}^{*},{E}^{*}$ and G

^{*}referring to the reference frame N are given as follows,

_{i}is obtained as,

_{iR}with i = 1, 2, 3, 4, 5, 6 represents first, second, third, fourth, fifth and sixth value of generalised active force. Meanwhile the values of ${m}_{A},{m}_{B},{m}_{C},{m}_{D},{m}_{E}$ and ${m}_{G}$ are the mass of each segment of the body A, B, C, D, E and G. Value $\overrightarrow{F}$ is the action force and g is the value of gravity. Meanwhile, the generalised inertial forces are obtained as,

$\overrightarrow{T}$: | Vector of applied torque |

M: | Mass matrix |

$\stackrel{\xb7\xb7}{\mathrm{Q}}$: | Angular acceleration vector |

$\overrightarrow{\mathrm{G}}$: | Vector of moments from gravitational forces |

$\overrightarrow{E}$: | Vector of moments from external forces |

## 3. Results

_{5}(rad) from professional parachutist data has been chosen to identify the percentage error. The error value percentage is calculated, and we found that the experimental data are acceptable and reliable to be used in this study since the percentage error are relatively small.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Extension and flexion joint of (

**a**) arm, (

**b**) ankle, (

**c**) elbow, (

**d**) shoulder and knee, (

**e**) hip.

**Figure 4.**(

**a**) Two-link kinematics open-chain representing the whole body in the sagittal plane. (

**b**) A free-body diagram that shows force acting at every body segment.

Joint | Phase | Joint Movement Direction |
---|---|---|

Arm | Preparation to land | Extension (−) |

Foot strike | Extension (−) | |

Elbow | Preparation to land | Flexion (+) |

Foot strike | Flexion (+) | |

Shoulder | Preparation to land | Flexion (+) |

Foot strike | Flexion (+) | |

Hip | Preparation to land | Flexion (+) |

Foot strike | Flexion (+) | |

Knee | Preparation to land | Flexion (+) |

Foot strike | Flexion (+) | |

Ankle | Preparation to land | Plantar Flexion (−) |

Foot strike | Dorsiflexion (+) |

**Table 2.**The meanSD, maximum and minimum value of professional and amateur parachutists at the event of foot strike.

Professional | Amateurs | |||||
---|---|---|---|---|---|---|

Variable | Mean ± SD | Max | Min | Mean ± SD | Max | Min |

Torque (Nm) | ||||||

Wrist | −384.73 ± 26.95 | −751.32 | −1590.02 | 212.05 ± 78.67 | 2809.92 | −4627.90 |

Elbow | 158.76 ± 38.86 | 656.97 | −134.27 | 494.07 ± 94.61 | 3318.81 | −3185.36 |

Shoulder | 177.78 ± 48.47 | 300.03 | 153.52 | 160.42 ± 66.56 | 3074.12 | −4236.73 |

Hip | 50.44 ± 19.82 | 65.23 | 51.35 | −22.62 ± 19.75 | 710.43 | −968.52 |

Knee | 49.34 ± 18.73 | 93.99 | 61.08 | 42.00 ± 23.23 | 123.57 | −187.37 |

Ankle | −24.30 ± −3.15 | −26.75 | −51.42 | 11.43 ± −8.37 | 87.62 | −57.96 |

**Table 3.**Estimation percentage relative error ε

_{r}on knee angle for the professional parachutist between Runge-Kutta analysis r and experimental result s.

Frame | Runge-Kutta (Rad) (r) | Experimental Result (Rad)(s) | ${\mathit{\epsilon}}_{\mathit{r}}=\left|\frac{\mathit{r}-\mathit{s}}{\mathit{s}}\right|\times 100\mathit{\%}$ |
---|---|---|---|

1 | 1.90437 | 1.89949 | 0.25691% |

2 | 1.98698 | 1.99188 | 0.24596% |

3 | 1.74827 | 1.75034 | 0.11842% |

4 | 1.79565 | 1.79817 | 0.14016% |

5 | 2.07085 | 2.06973 | 0.05394% |

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**MDPI and ACS Style**

Aziz, S.; Rambely, A.S.; Gan, K.B.; Wan Din, W.R.
Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method. *Mathematics* **2020**, *8*, 917.
https://doi.org/10.3390/math8060917

**AMA Style**

Aziz S, Rambely AS, Gan KB, Wan Din WR.
Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method. *Mathematics*. 2020; 8(6):917.
https://doi.org/10.3390/math8060917

**Chicago/Turabian Style**

Aziz, Syazwana, Azmin Sham Rambely, Kok Beng Gan, and Wan Rozita Wan Din.
2020. "Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method" *Mathematics* 8, no. 6: 917.
https://doi.org/10.3390/math8060917