Library / Terramechanics and off-road mobility / TER-25
Terramechanics and off-road mobility
Effect of weight and track width on MMP
How the mean maximum pressure changes when the vehicle weight and track width change and everything else stays the same.
- Ref
- TER-25
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- MMPnew/MMPold
With everything else fixed, the mean maximum pressure is proportional to the weight and inversely proportional to the track width: MMPnew/MMPold = (Wnew/Wold)(bold/bnew). To keep the same MMP after adding weight, widen the track in proportion: bnew = boldWnew/Wold. The relation drops the wheel count, pitch and diameter because they cancel between the old and new vehicle only if they do not change.
How the mean maximum pressure changes when the vehicle weight and track width change and everything else stays the same. Pressure rises in proportion to weight and falls in proportion to width.
Calculator
- Track width that keeps MMP unchanged, boldWnew/Wold0.6583 m
- Change in MMP1.278 %
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.
- Adding 62 kN (9.72 %) while widening the track from 0.6 to 0.65 m changes MMP by 1.28 %. To hold MMP exactly, the track would need to be 0.6583 m wide.
- Without the wider track the same extra weight would raise MMP by 9.72 %, which for the lecture vehicle (304.7 kPa) is about 29.6 kPa.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| Wold Original weight | 100 to 1,500 kN | 0.4308 | 6.462 | 6.031 | +10% | −9.09 % |
| Wnew New weight | 100 to 1,500 kN | 0.1447 | 2.17 | 2.026 | +10% | +10 % |
| bnew New track width | 0.25 to 1 m | 0.6583 | 2.633 | 1.975 | +10% | −9.09 % |
| bold Original track width | 0.25 to 1 m | 0.422 | 1.688 | 1.266 | +10% | +10 % |
Sweep of New weight
| New weight (kN) | Pressure ratio |
|---|---|
| 100 | 0.1447 |
| 275 | 0.3979 |
| 450 | 0.6511 |
| 625 | 0.9043 |
| 800 | 1.157 |
| 975 | 1.411 |
| 1,150 | 1.664 |
| 1,325 | 1.917 |
| 1,500 | 2.17 |
Sweep one variable
Variables and how each one contributes
Pressure ratio
What the equation gives you. Everything else feeds it.
Original weight
The weight of the original vehicle, in kN. Lowers the ratio in inverse proportion. Raising it by 10 % (to 701.8) moves the result by −9.09 %, from 1.013 to 0.9207.
New weight
The weight of the new or up-armoured vehicle, in kN. Raises the ratio in proportion. Raising it by 10 % (to 770) moves the result by +10 %, from 1.013 to 1.114.
Original track width
The track width of the original vehicle, in m. Raises the ratio in proportion. Raising it by 10 % (to 0.66) moves the result by +10 %, from 1.013 to 1.114.
New track width
The track width of the new vehicle, in m. Lowers the ratio in inverse proportion. Raising it by 10 % (to 0.715) moves the result by −9.09 %, from 1.013 to 0.9207.
Worked example with the values above
- Weight ratio: Wnew/Wold = 700/638 = 1.097.
- Width ratio: bold/bnew = 0.6/0.65 = 0.9231.
- MMP ratio = 1.013.
Assumptions and limits
- Wheel count, track pitch, link area ratio and road-wheel diameter unchanged.
- Weight and track width in the same units for old and new.
Common mistakes
- Using the formula when the wheel count or pitch changes as well.
- Mixing the weights of one track and a full vehicle.
Statistics and uncertainty
MMP-based mobility indices are only good to about 10 %, so a computed change of less than that is within the uncertainty of the method. A wider track has side effects on turning resistance and ground clearance not captured here.
Where it is used
- Seeing how much extra track width an up-armoured vehicle needs.
- Comparing the pressure effect of a weight change with a track width change.
Maths you need
- Proportionality: doubling weight doubles the pressure
- Mean maximum pressure: peak pressure under road wheels