Library / Automotive and vehicle dynamics / VEH-30
Automotive and vehicle dynamics
Static rollover threshold
The lateral acceleration, in g, at which an ideal rigid vehicle lifts its inside wheels, equal to half the track width divided by the centre of gravity height.
- Ref
- VEH-30
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- ay,lift/g [g]
t is the track width and h the height of the centre of gravity. For a rigid vehicle with a centred centre of gravity, the inside wheels lift when the overturning moment m ay h equals the restoring moment m g t/2, giving ay/g = t/(2h). The same ratio gives the tangent of the side slope at which the vehicle would tip. It is a quasi-static estimate: suspension roll, tyre deflection, soil sinkage and load shift all make rollover happen earlier. On a slope, sliding starts first if the friction coefficient is below this value.
The lateral acceleration, in g, at which an ideal rigid vehicle lifts its inside wheels, equal to half the track width divided by the centre of gravity height. The same ratio gives the side slope on which it would tip.
Calculator
- Tipping side slope angle, tan⁻¹(t / 2h)55.49 °
- Tipping side slope as a percentage, 100 t / 2h145.5 %
- Lateral acceleration at wheel lift14.27 m/s²
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A car with t = 1.6 m and h = 0.55 m would lift its wheels at 1.455 g, more than tyres can supply on tarmac (about 1 g), so it slides before it rolls. A tall vehicle with h = 1.0 m reaches it at only 0.8 g, a truck with t = 2.0 m and h = 1.5 m at 0.6667 g.
- When the friction coefficient is greater than this ratio the vehicle rolls instead of sliding. This is the case for trucks on dry roads, and for military vehicles with a high centre of gravity on rough ground, where kerbs and soft shoulders trip vehicles at lower accelerations.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (g) | Local step | Change in result |
|---|---|---|---|---|---|---|
| t Track width | 1.2 to 3 m | 1.091 | 2.727 | 1.636 | +10% | +10 % |
| h Centre of gravity height | 0.4 to 2 m | 0.4 | 2 | 1.6 | +10% | −9.09 % |
Sweep of Centre of gravity height
| Centre of gravity height (m) | Rollover threshold (g) |
|---|---|
| 0.4 | 2 |
| 0.6 | 1.333 |
| 0.8 | 1 |
| 1 | 0.8 |
| 1.2 | 0.6667 |
| 1.4 | 0.5714 |
| 1.6 | 0.5 |
| 1.8 | 0.4444 |
| 2 | 0.4 |
Sweep one variable
Variables and how each one contributes
Rollover threshold
What the equation gives you. Everything else feeds it.
Track width
The track width, in m: the distance between the left and right wheel contact centres. Directly proportional: a wider vehicle is much harder to roll. Raising it by 10 % (to 1.76) moves the result by +10 %, from 1.455 to 1.6 g.
Centre of gravity height
The height of the centre of gravity above the ground, in m. Inversely proportional: a taller or top-heavy load is the most common cause of rollover. Raising it by 10 % (to 0.605) moves the result by −9.09 %, from 1.455 to 1.322 g.
Worked example with the values above
- Half the track: t / 2 = 1.6 / 2 = 0.8 m.
- Ratio to the centre of gravity height: (t / 2) / h = 0.8 / 0.55 = 1.455.
- ay,lift / g = 1.455 g, and the tipping slope is tan⁻¹(1.455) = 55.49°.
Assumptions and limits
- A rigid vehicle with a laterally centred centre of gravity and no suspension deflection or tyre or soil deflection.
- Quasi-static loading on a flat surface (or a side slope), with enough friction to prevent sliding.
Common mistakes
- Using the full track width instead of half the track width, which doubles the threshold.
- Treating the result as a guaranteed safe limit. Suspension roll and dynamic effects make the real threshold lower.
Statistics and uncertainty
The ratio of t to h is sensitive to the height of the centre of gravity, which is known to 5 to 10 % and moves with load, so the threshold is uncertain by the same amount. Suspension roll typically lowers the real threshold by 10 to 20 %, and dynamic effects, such as sudden steering inputs, can lower it a lot more. Treat the value as an upper bound.
Where it is used
- Comparing the rollover risk of cars, trucks and military vehicles.
- Setting safe side-slope limits for vehicles on rough or sloping ground.
Maths you need
- Moments: overturning and restoring moments
- Slope angle: tan of an angle as a percentage grade