Library / Terramechanics and off-road mobility / TER-49
Terramechanics and off-road mobility
Individual track thrusts for prescribed force and yaw moment
Left track thrust needed to deliver a total longitudinal ground force F and a leftward yaw moment Mz, from the track centre-line spacing B.
- Ref
- TER-49
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- HL [N]
A skid-steered vehicle must deliver a total thrust F and a yaw moment Mz with its two tracks. Taking forces forward and the lever arm as half the track spacing B/2, F = HL + HR and Mz = (B/2)(HR − HL), so HL = F/2 − Mz/B and HR = F/2 + Mz/B. The demanded moment must include the soil’s own steering resistance, which can be much larger than the geometric moment.
Left track thrust needed to deliver a total longitudinal ground force F and a leftward yaw moment Mz, from the track centre-line spacing B. The right thrust F/2 + Mz/B is in the derived rows. Include soil steering resistance in the demanded moment and check each result against available traction.
Calculator
- Right track thrust, F/2 + Mz/B6,500 N
- Thrust difference between the tracks, 2Mz/B3,000 N
- Sum of the two thrusts (equals F)10,000 N
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.
- The left track must give 3,500 N and the right track 6,500 N, a difference of 3,000 N that steers the vehicle.
- The tracks must also stay within the available traction: the larger one is 65 % of the total thrust, so if that exceeds the soil limit the vehicle cannot turn as demanded.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| F Required total thrust | −100,000 to 100,000 N | −51,500 | 48,500 | 100,000 | +4000 N | +57.1 % |
| Mz Required yaw moment (left positive) | −50,000 to 50,000 N m | −20,000 | 30,000 | 50,000 | +2000 N m | −28.6 % |
| B Track centre-line spacing | 0.5 to 5 m | −1,000 | 4,400 | 5,400 | +10% | +3.9 % |
Sweep of Required yaw moment (left positive)
| Required yaw moment (left positive) (N m) | Left track thrust (N) |
|---|---|
| −50,000 | 30,000 |
| −37,500 | 23,750 |
| −25,000 | 17,500 |
| −12,500 | 11,250 |
| 0 | 5,000 |
| 12,500 | −1,250 |
| 25,000 | −7,500 |
| 37,500 | −13,750 |
| 50,000 | −20,000 |
Sweep one variable
Variables and how each one contributes
Left track thrust
What the equation gives you. Everything else feeds it.
Required total thrust
The required total thrust, in N. Raises both track thrusts equally, by F/2 each. Raising it by 10 % (to 11,000) moves the result by +14.3 %, from 3,500 to 4,000 N.
Required yaw moment (left positive)
The required yaw moment, left positive, in N m. Lowers the left thrust and raises the right thrust, in proportion to 1/B. Raising it by 10 % (to 3,300) moves the result by −4.29 %, from 3,500 to 3,350 N.
Track centre-line spacing
The centre-line spacing of the tracks, in m. A wider spacing needs a smaller thrust difference for the same moment. Raising it by 10 % (to 2.2) moves the result by +3.9 %, from 3,500 to 3,636 N.
Worked example with the values above
- Common part: F/2 = 10,000 / 2 = 5,000 N.
- Steering part: Mz/B = 3,000 / 2 = 1,500 N.
- HL = F/2 − Mz/B = 5,000 − 1,500 = 3,500 N.
Assumptions and limits
- A rigid, flat track patch or cone in homogeneous soil, with a linear pressure profile where stated.
- Constant soil strength and deformation length over the test, and the same rate and cone for comparisons.
Common mistakes
- Using the linear pressure formula beyond the one-sixth limit on the load offset.
- Mixing the left and right sign convention for yaw moment.
- Including rod friction in the cone force.
Statistics and uncertainty
Pressure cells and penetrometers carry 5 % to 10 % uncertainty, and the penetration or shear work depends on rate and soil state. Compare only tests run under the same conditions.
Where it is used
- Checking track pressure distribution, thrust sharing and steering demand.
- Comparing soil strength and shear energy between test beds.
Maths you need
- Linear pressure distribution: p = W/A (1 ± 6e/L)
- Work as an integral: W = ∫ F dz
- Moment balance: the sum of moments about the vehicle centre is zero