# Quad-Bike Operational Instability

## Abstract

**:**

## 1. Introduction

- The trauma and death that occurs annually with QBs in Australia. In the period 2001–2010, there were 124 fatal QB-related incidents in Australia. Two-thirds of these fatalities occurred on farms, with about half involving roll-overs sideways (Lower et al.) [1].
- The circumstances of these incidents are as varied as the riders who experience them—anybody from mature adults with much experience but little formal rider education and varied intuition, to young and inexperienced although perhaps educated riders with ‘gung-ho’ attitudes.
- The failure of most QB manufacturers to provide any roll-over, tip-up or pitch-over protection. This is perhaps because the risk of instability is not seen as an inherent problem in the design and operation of most machines used in off-road environments. Rather, it is considered that the problems can be avoided, or at least mitigated, by seeking evolutionary modifications that would make the machine safer, and by providing more education and protective items for the rider.
- The need for the design and promotion of commercial Roll-over Protective Structures (ROPS) as part of the original design, as based on the well-established principle of energy absorption use within the structure to mitigate the impact and resulting trauma.
- The failure of Governments to mandate the fitting of ROPS. The wide diversity of opinions between the stake-holders leaves Governments unable, perhaps more on political than policy grounds, to mandate the fitting of ROPS to all (or most) QBs.

## 2. Quad Bikes as Off-Road Machines

## 3. QB Operation and Instability

## 4. Longitudinal Rearward Operational Instability

- static: the component of the weight down the slope;
- quasi-static: the rolling resistance of the wheels and any drawbar pull (the latter is not included here).

#### 4.1. Static Effects

_{g}) to the height of the CoG perpendicular to the ground surface (r, radius of the wheel + y

_{g}, the height of the CoG above the rear axle).

#### 4.2. Quasi-Static Effects

- the weight of the QB: ±30% for the eight work machines tested by UNSW as shown Table A1;
- the type of tyres;
- the condition (particularly the deformability) of the soil surface.

#### 4.3. Dynamic Effects

- a reactive moment on the chassis, arising from:
- ○
- a linear acceleration of the chassis up the slope;
- ○
- a rotational acceleration of the driving wheels.

- an impulse on the front wheels, perpendicular to the slope, having a moment about the rear axle.

_{g}

^{2}+ y

_{g}

^{2})] (which provides a measure of the moment of inertia about the rear axle,) gave a significant linear and highly correlated relationship between these two variables (correlation coefficient 0.98); this justifies the use of mass for this argument.

## 5. Lateral Instability

- (i)
- The component of the (static) weight down the slope, plus any (effectively quasi-static) forces through the CoG (such as the centrifugal ‘force’ during turning) and any dynamic inertial forces arising from sliding impact on a resisting object, must fall outside the base.
- (ii)
- The lateral force at the wheel/surface contact patch must not exceed the shearing strength (represented by tan γ, the ‘lateral coefficient’,) at that interface.

#### 5.1. Static and Quasi-Static Effects

_{g}), the angle of impending instability by rolling over (γ), represented by the upper wheels leaving the ground, is given by:

#### 5.2. Dynamic Effects

- an impulse (perpendicular to the surface) on the upper wheels;
- the inertial effect if the rotation of the QB is stopped when the lower wheels fall into a hole;
- the inertial effect if the QB is stopped while sliding sideways due to the quasi-static failure noted above.

_{g})

^{2}+ (t/2)

^{2}] (which provides a measure of the moment of inertia about the lower wheel ground contact points), gave a significant linear and highly correlated relationship (correlation coefficient 0.99) between these two variables; this justifies the use of mass for this argument.

## 6. General Instability

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Longitudinal Operational Instability

_{c}) that acts on it as a reaction to the moment on the wheels (M

_{w}). It is this former moment, and this moment alone, which tips the chassis of the QB over rearwards.

- static: the component of the weight down the slope;
- quasi-static: the rolling resistance of the wheels and any drawbar pull.

_{f}= 0

_{r}= W cos α’

_{w}= H . r + V

_{r}. x’

_{c}+ W sin α’. y

_{g}= W cos α’. x

_{g}

_{w}= M

_{c}

_{g}= W cos α’. x

_{g}

## Appendix B. Lateral Instability

## Appendix C

**Table A1.**Dimensional data for work Quad-Bikes—Adapted from Grzebieta et al. [2].

Make | Honda | Honda | Yamaha | Polaris | Suzuki | Kawasaki | Kymco | CF Moto |
---|---|---|---|---|---|---|---|---|

Model | Fourtrax TRX 250 | Foreman TRX 500 FM | Grizzly YFM450FAP | Sportsman 450HO | Kingquad 400ASI | KVF 300 | MXU300 | CF 500 |

Vehicle type | ATV—agric. | ATV—agric. | ATV—agric. | ATV—agric. | ATV—agric. | ATV—agric. | ATV—agric. | ATV—agric. |

Driven wheels | Rear | 4WD | 4WD | 4WD | Rear | Rear | Rear | 4WD |

Front track width | 795 | 930 | 860 | 1002 | 880 | 850 | 810 | 960 |

Rear track width | 775 | 925 | 860 | 954 | 900 | 830 | 780 | 860 |

Wheelbase | 1131 | 1281 | 1233 | 1283 | 1270 | 1165 | 1160 | 1290 |

Front cargo capacity, kg | 15 | 30 | 40 | 41 | 30 | 20 | 20 | 20 |

Rear cargo capacity, kg | 30 | 60 | 80 | 82 | 60 | 30 | 30 | 40 |

Max. vehicle payload, kg | 175 | 220 | 210 | 220 | 172 | 164 | 165 | 180 |

Unladen kerb mass, kg | 199 | 293 | 289.5 | 327 | 275.5 | 246 | 229 | 371.5 |

Distance unladen CoG behind front axle, mm | 568 | 608 | 571 | 657 | 615 | 554 | 570 | 606 |

Distance unladen CoG ahead rear axle, mm | 563 | 673 | 662 | 626 | 655 | 611 | 590 | 684 |

CoG height, mm | 436 | 528 | 496 | 533 | 510 | 494 | 492 | 554 |

## References

- Lower, T.; Pollock, K.; Herde, L. Australian quad bike fatalities: What is the economic cost? Aust. N. Z. J. Pub. Health
**2014**, 37, 173–178. [Google Scholar] [CrossRef] [PubMed] - Grzebieta, R.; Rechnitzer, G.; Simmons, K.; McIntosh, A. Final Project Summary Report: Quad Bike Performance Project Test Results, Conclusions, and Recommendations. Available online: http://www.tars.unsw.edu.au/research/Current/Quad-Bike_Safety/Reports/Final_Summary_Report4-QBPP_Test_Results_Concl_Recom_Jan-2015.pdf (accessed on 18 October 2016).
- Payne, P.C.J.; Fountaine, E.R. The Shear Strength of Top Soils; Tech. Memo. No 42; National Institute of Agricultural Engineering (Silsoe Research Institute): Bedford, UK, 1951. [Google Scholar]
- Macmillan, R.H. The Mechanics of Tractor—Implement Performance; Theory and Worked Examples: A Text Book for Students and Engineers. Available online: https://minerva-access.unimelb.edu.au/handle/11343/33718/ (accessed on 18 October 2016).
- Lock, J. Inquest into Nine (9) Deaths Caused by Quad Bike Accidents. Deputy State Coroner. Office of the State Coroner Findings of Inquest; Brisbane, Queensland, Australia. Available online: http://www.courts.qld.gov.au/__data/assets/pdf_file/0018/432306/cif-quadbikeaccidents-20150803.pdf (accessed on 18 October 2016).

**Figure 1.**Static rear longitudinal instability angles (shown as tan α) for the eight work Quad Bikes (QBs) and a range of typical traction coefficients (tan θ) for tyres on agricultural soils.

**Figure 2.**Plot of the slope as tan α verses stand-alone mass for work QBs in rear longitudinal instability.

**Figure 3.**Static lateral instability angles (shown as tan γ) for the eight work QBs, and a range of typical lateral traction coefficients (tan θ, assumed equal to the longitudinal values shown in Figure 1) for tyres on agricultural soils.

**Figure 4.**Static instability for rear longitudinal versus lateral directions for eight work QBs; two sets of data values at (0.78:1.25) coincide.

© 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Macmillan, R.H.
Quad-Bike Operational Instability. *Safety* **2017**, *3*, 15.
https://doi.org/10.3390/safety3020015

**AMA Style**

Macmillan RH.
Quad-Bike Operational Instability. *Safety*. 2017; 3(2):15.
https://doi.org/10.3390/safety3020015

**Chicago/Turabian Style**

Macmillan, Ross H.
2017. "Quad-Bike Operational Instability" *Safety* 3, no. 2: 15.
https://doi.org/10.3390/safety3020015