Library / Terramechanics and off-road mobility / TER-06
Terramechanics and off-road mobility
Breakover angle
The sharpest ridge crest a vehicle can straddle before its belly touches, for a symmetric crest with point contacts at the two axles.
- Ref
- TER-06
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- β [°]
hc is the ground clearance at the midpoint between the axles and L is the wheelbase. Treating the two axle contacts as point supports on a sharp, symmetric crest, the vehicle just touches the ridge when the two ground slopes each have tan(β/2) = 2hc/L. The breakover angle β is the full angle between them, in degrees. It is the largest crest angle the vehicle can straddle; a sharper crest will ground the belly. It uses the static clearance and ignores suspension travel and tyre deflection.
The sharpest ridge crest a vehicle can straddle before its belly touches, for a symmetric crest with point contacts at the two axles. It depends on the midpoint ground clearance and the wheelbase.
Calculator
- Half-angle, β / 216.7 °
- Slope of each side of the crest, 2hc / L30 %
- Clearance needed for a 30° breakover, (L / 2) tan 15°0.4019 m
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 vehicle with 0.45 m of mid-body clearance and a 3 m wheelbase can straddle a crest of 33.4°. Stretching the wheelbase to 4 m lowers it to 25.36°.
- Breakover is why short wheelbase vehicles are favoured for rough terrain, and why raising the suspension helps: lifting the underbody by 5 cm gives 36.87°.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (°) | Local step | Change in result |
|---|---|---|---|---|---|---|
| hc Ground clearance at the midpoint between the axles | 0.15 to 1 m | 11.42 | 67.38 | 55.96 | +10% | +3.13 ° |
| L Wheelbase | 1.5 to 8 m | 12.84 | 61.93 | 49.09 | +10% | −2.89 ° |
Sweep of Wheelbase
| Wheelbase (m) | Breakover angle (°) |
|---|---|
| 1.5 | 61.93 |
| 2.313 | 42.53 |
| 3.125 | 32.13 |
| 3.938 | 25.75 |
| 4.75 | 21.46 |
| 5.563 | 18.38 |
| 6.375 | 16.07 |
| 7.188 | 14.27 |
| 8 | 12.84 |
Sweep one variable
Variables and how each one contributes
Breakover angle
What the equation gives you. Everything else feeds it.
Ground clearance at the midpoint between the axles
The ground clearance at the midpoint between the axles, in m: the lowest point of the underbody there. Raises the angle: more underbody clearance clears a sharper crest. Raising it by 10 % (to 0.495) moves the result by +9.36 %, from 33.4 to 36.53 °.
Wheelbase
The wheelbase, in m. Lowers the angle: a longer wheelbase bridges the crest less well, which is why long vehicles ground out more easily. Raising it by 10 % (to 3.3) moves the result by −8.65 %, from 33.4 to 30.51 °.
Worked example with the values above
- Ratio: 2hc / L = 2 × 0.45 / 3 = 0.3.
- Half-angle: tan⁻¹(0.3) = 16.7°.
- β = 2 × 16.7° = 33.4°.
Assumptions and limits
- A rigid vehicle with point supports at the two axles on a sharp, symmetric crest.
- The lowest point of the underbody is at the midpoint between the axles, at the static ride height.
Common mistakes
- Using the ground clearance under the axles, not the lowest point at the midpoint.
- Quoting the half-angle as the breakover angle.
Statistics and uncertainty
The mid-body clearance is measured to a centimetre or two, so the angle is known to about 1°. As with approach angle, the load and suspension compression reduce the real clearance by 5 to 15 cm, so the practical angle can be 5° to 10° lower. The point-support assumption also overestimates the angle if the tyres are large, because the contact is spread over a patch.
Where it is used
- Predicting whether a vehicle grounds out on a crest, hump or rutted ground.
- Comparing vehicles and setting geometry requirements for off-road use.
Maths you need
- Trigonometry: tan⁻¹ of a ratio
- Geometry of a ridge: two slopes meeting at a crest