Library / Terramechanics and off-road mobility / TER-08
Terramechanics and off-road mobility
Mean ground pressure of a tracked vehicle
Average pressure under a tracked vehicle on level ground, assuming two equal rectangular track footprints.
- Ref
- TER-08
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- p̄ [kPa]
The weight m g is carried on two equal rectangular track footprints, each of width bc and length ℓc on the ground. The nominal pressure is the weight divided by the total contact area 2 bc ℓc, on level terrain with the weight evenly distributed. It does not represent the higher local pressure under the road wheels, and the real contact length on soft ground is greater than the length of the flat track. The result is in kPa.
Average pressure under a tracked vehicle on level ground, assuming two equal rectangular track footprints. It is the first number to check when judging whether a vehicle will float on soft terrain.
Calculator
- Total contact area, 2 bc ℓc4 m²
- Vehicle weight, m g196.2 kN
- Pressure in psi7.114 psi
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 on two 0.5 m wide tracks, 4 m long, presses on the ground at 49.05 kPa (7.11 psi). Main battle tanks are typically 80 to 100 kPa, and light vehicles built for soft ground 20 to 40 kPa.
- Lengthening the contact to 5 m lowers the pressure to 39.24 kPa, a gain of 20 %. Soft snow and peat carry only 10 to 30 kPa, so they need large, light vehicles.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Vehicle mass | 5,000 to 70,000 kg | 12.26 | 171.7 | 159.4 | +10% | +10 % |
| bc Width of each track | 0.25 to 1.2 m | 20.44 | 98.1 | 77.66 | +10% | −9.09 % |
| ℓc Track length in contact with the ground | 2 to 7 m | 28.03 | 98.1 | 70.07 | +10% | −9.09 % |
Sweep of Track length in contact with the ground
| Track length in contact with the ground (m) | Mean ground pressure (kPa) |
|---|---|
| 2 | 98.1 |
| 2.625 | 74.74 |
| 3.25 | 60.37 |
| 3.875 | 50.63 |
| 4.5 | 43.6 |
| 5.125 | 38.28 |
| 5.75 | 34.12 |
| 6.375 | 30.78 |
| 7 | 28.03 |
Sweep one variable
Variables and how each one contributes
Mean ground pressure
What the equation gives you. Everything else feeds it.
Vehicle mass
The vehicle mass, in kg. Directly proportional: a heavier vehicle presses harder. Raising it by 10 % (to 22,000) moves the result by +10 %, from 49.05 to 53.95 kPa.
Width of each track
The width of each track, in m. Inversely proportional: wider tracks spread the load. This is the cheapest way to improve flotation. Raising it by 10 % (to 0.55) moves the result by −9.09 %, from 49.05 to 44.59 kPa.
Track length in contact with the ground
The length of each track in contact with the ground, in m. Inversely proportional: longer tracks spread the load, but they also make turning harder. Raising it by 10 % (to 4.4) moves the result by −9.09 %, from 49.05 to 44.59 kPa.
Worked example with the values above
- Weight: m g = 20,000 × 9.81 = 196,200 N.
- Contact area: 2 bc ℓc = 2 × 0.5 × 4 = 4 m².
- p̄ = 196,200 / 4 = 49,050 Pa = 49.05 kPa.
Assumptions and limits
- Two equal rectangular track footprints on level ground, with the weight carried evenly along them.
- No sinkage, no load transfer by acceleration or slope, and a rigid track.
Common mistakes
- Using the width of the vehicle in place of the width of a single track.
- Forgetting to take both tracks: the area is 2 bc ℓc.
Statistics and uncertainty
The mass and the track dimensions are known to 1 to 2 %, so the nominal pressure is good to about 3 %. The real pressure is far less certain. Under the road wheels the peaks are two to four times the mean, the load is not spread evenly along the track, and sinkage lengthens the contact patch. The nominal figure is for comparison between vehicles, not a prediction of the pressure at a point.
Where it is used
- Comparing the flotation of tracked and wheeled vehicles on mud, snow and sand.
- The first screening check of whether a vehicle can cross soft ground.
Maths you need
- Pressure: force divided by area
- Weight: m g