Library / Terramechanics and off-road mobility / TER-19
Terramechanics and off-road mobility
Idealised track steering resistance
Resisting yaw moment when a tracked vehicle pivots on the spot, assuming uniform pressure and fully developed sideways (Coulomb) sliding of both tracks.
- Ref
- TER-19
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- Mres [kN·m]
μy is the lateral friction coefficient of the track on the ground, W the total weight and ℓc the track contact length. For symmetric pivoting with uniform pressure over two equal rectangular tracks and fully developed lateral Coulomb sliding, the resisting yaw moment has the magnitude μy W ℓc/4. The moment balance for the vehicle is Iz ṙ = (B/2)(HR − HL) − Mres, so the steering thrust difference must exceed Mres to start the turn. Soft soil and turns of finite radius need a distributed shear model.
Resisting yaw moment when a tracked vehicle pivots on the spot, assuming uniform pressure and fully developed sideways (Coulomb) sliding of both tracks. It is the moment the track thrust difference must overcome.
Calculator
- Resisting moment in newton-metres98,000 N·m
- Moment relative to weight times length, Mres / (W ℓc)0.125
- Thrust difference needed for a 2 m track spacing, 2Mres / B98 kN
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 20 t vehicle (196 kN) on tracks 4 m long, with μy = 0.5, needs a yaw moment of 98 kN·m to pivot. With a 2 m track spacing the two tracks must differ by 98 kN of thrust, about 50 % of the weight.
- Steering resistance rises with track length, so a vehicle with tracks of 5 m instead of 4 m needs 122.5 kN·m. This is why the length-to-width ratio of a tracked vehicle is kept below about 1.8 to 2: the longer it is, the harder it is to steer.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN·m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| W Total vehicle weight | 30 to 600 kN | 15 | 300 | 285 | +10% | +10 % |
| μy Lateral friction coefficient | 0.1 to 1 | 19.6 | 196 | 176.4 | +10% | +10 % |
| ℓc Track contact length | 2 to 7 m | 49 | 171.5 | 122.5 | +10% | +10 % |
Sweep of Track contact length
| Track contact length (m) | Steering resistance moment (kN·m) |
|---|---|
| 2 | 49 |
| 2.625 | 64.31 |
| 3.25 | 79.63 |
| 3.875 | 94.94 |
| 4.5 | 110.3 |
| 5.125 | 125.6 |
| 5.75 | 140.9 |
| 6.375 | 156.2 |
| 7 | 171.5 |
Sweep one variable
Variables and how each one contributes
Steering resistance moment
What the equation gives you. Everything else feeds it.
Lateral friction coefficient
The lateral friction coefficient of the track on the ground: about 0.4 to 0.9 on firm ground, and more for tracks with grousers. Directly proportional: a high-grip surface resists pivoting more. Raising it by 10 % (to 0.55) moves the result by +10 %, from 98 to 107.8 kN·m.
Total vehicle weight
The total weight of the vehicle, in kN. Directly proportional. Raising it by 10 % (to 215.6) moves the result by +10 %, from 98 to 107.8 kN·m.
Track contact length
The length of each track in contact with the ground, in m. Directly proportional: long tracks must be dragged sideways through more ground, which is why long tracked vehicles are hard to pivot. Raising it by 10 % (to 4.4) moves the result by +10 %, from 98 to 107.8 kN·m.
Worked example with the values above
- Weight times length: W ℓc = 196 × 4 = 784 kN·m.
- Multiply by the friction coefficient: μy W ℓc = 0.5 × 784 = 392 kN·m.
- Mres = 392 / 4 = 98 kN·m.
Assumptions and limits
- Symmetric pivot turn with uniform pressure over two equal rectangular tracks, and fully developed lateral Coulomb sliding.
- Firm ground without bulldozing or sinkage effects, with the weight evenly carried by the tracks.
Common mistakes
- Using the formula for a turn of large radius. It applies to the pivot turn, and a finite radius needs a smaller moment.
- Forgetting that the steering thrust difference acts at half the track spacing: the force needed is 2Mres / B.
Statistics and uncertainty
The lateral friction coefficient dominates the uncertainty: it varies by ±20 to 40 % with the surface, vegetation and the soil tendency to build up in front of the track side, and it changes during a turn. The pressure distribution is also not uniform. The calculated moment is therefore best treated as an estimate within a factor of 1.5, adequate to size the steering drive but not to predict a particular turn.
Where it is used
- Sizing steering drive power and judging whether a heavy tracked vehicle can pivot on a given surface.
- Comparing track length–width proportions for manoeuvrability.
Maths you need
- Coulomb friction: sliding friction force μ N
- Moment of a distributed force: integrating force × distance