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Terramechanics and off-road mobility
Terramechanics driving slip
Slip of a driven wheel on soil: zero when it rolls freely, rising to one when it spins without moving forward.
- Ref
- TER-14
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- s
U is the actual forward speed of the vehicle, Re the effective rolling radius and ω the wheel angular speed, so Reω is the speed the wheel would travel if it rolled without slip. The slip s is the fraction of the wheel surface speed that is lost: 0 for free rolling and 1 for a wheel spinning without any forward motion. This definition holds for forward driving with Reω > 0 and 0 ≤ s ≤ 1. It differs from the road-tyre slip ratio, which is bounded differently and is negative in braking.
Slip of a driven wheel on soil: zero when it rolls freely, rising to one when it spins without moving forward. This differs in sign and normalisation from the road-tyre slip ratio.
Calculator
- Slip in per cent20 %
- No-slip speed of the wheel surface, Re ω5 m/s
- Speed lost to slip, Re ω − U1 m/s
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 wheel of effective radius 0.5 m turning at 10 rad/s would roll 5 m/s without slip; the vehicle moves at 4 m/s, so the slip is 0.2 (20 %). On soft soil, working slips of 10 to 30 % are normal because the soil must shear to give thrust.
- If the vehicle stops while the wheels turn (U = 0) the slip is 1, a wheel spinning in a hole. The slip is what links the thrust to the soil, via the shear displacement j = s x along the contact.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| ω Wheel angular speed | 2 to 30 rad/s | −3 | 0.7333 | 3.733 | +10% | +36.4 % |
| U Forward speed | 0 to 10 m/s | −1 | 1 | 2 | +10% | −40 % |
| Re Effective rolling radius | 0.25 to 1 m | −0.6 | 0.6 | 1.2 | +10% | +36.4 % |
Sweep of Forward speed
| Forward speed (m/s) | Driving slip |
|---|---|
| 0 | 1 |
| 1.25 | 0.75 |
| 2.5 | 0.5 |
| 3.75 | 0.25 |
| 5 | 0 |
| 6.25 | −0.25 |
| 7.5 | −0.5 |
| 8.75 | −0.75 |
| 10 | −1 |
Sweep one variable
Variables and how each one contributes
Driving slip
What the equation gives you. Everything else feeds it.
Forward speed
The actual forward speed of the vehicle over the ground, in m/s. Lowers the slip. A faster actual speed at the same wheel speed means the wheel is slipping less. Raising it by 10 % (to 4.4) moves the result by −40 %, from 0.2 to 0.12.
Effective rolling radius
The effective rolling radius of the wheel, in m. Raises the no-slip speed Reω, and so the slip, because the vehicle is not moving faster. Raising it by 10 % (to 0.55) moves the result by +36.4 %, from 0.2 to 0.2727.
Wheel angular speed
The angular speed of the wheel, in rad/s. Raises the no-slip speed, and so the slip, in the same way as the radius. Raising it by 10 % (to 11) moves the result by +36.4 %, from 0.2 to 0.2727.
Worked example with the values above
- No-slip speed: Re ω = 0.5 × 10 = 5 m/s. The vehicle moves at U = 4 m/s.
- Ratio: U / (Re ω) = 4 / 5 = 0.8.
- s = 1 − 0.8 = 0.2 (20 %).
Assumptions and limits
- Forward driving at a steady speed with a fixed effective rolling radius, which on soft ground differs from the geometric radius.
- Re ω > 0 and the slip between 0 and 1.
Common mistakes
- Using the road-tyre slip ratio definition and sign in a soil model that expects this one.
- Using wheel odometry for the ground speed, which makes the slip appear to be zero.
Statistics and uncertainty
The slip is a small difference of two nearly equal speeds, so measurement errors are magnified: with 1 % errors in both the wheel speed and the ground speed, the slip at s = 0.1 is uncertain by about ±1.3 percentage points, i.e. ±13 % of itself. Ground speed over soft soil is hard to measure accurately (wheel odometry does not give it), so radar or GPS is used.
Where it is used
- Relating soil thrust to slip, and spotting wheelspin or track slip on soft ground.
- Calculating the speed lost to slip, and tractive efficiency.
Maths you need
- Rolling radius: speed = R ω
- Fractions and percentages: slip as a proportion