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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

Solve for
kN
1001,500
kN
1001,500
m
0.251
m
0.251
  • 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.

Pressure ratio () current value 1.013
WoldOriginal weightKey driver
0.4316.46
WnewNew weight
0.1452.17
bnewNew track width
0.6582.63
boldOriginal track width
0.4221.69
  • 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

VariableTypical rangeLowest resultHighest resultSwing ()Local stepChange in result
Wold Original weight100 to 1,500 kN0.43086.4626.031+10%−9.09 %
Wnew New weight100 to 1,500 kN0.14472.172.026+10%+10 %
bnew New track width0.25 to 1 m0.65832.6331.975+10%−9.09 %
bold Original track width0.25 to 1 m0.4221.6881.266+10%+10 %

Sweep of New weight

New weight (kN)Pressure ratio
1000.1447
2750.3979
4500.6511
6250.9043
8001.157
9751.411
1,1501.664
1,3251.917
1,5002.17

Sweep one variable

Pressure ratio ()Hover, touch, or use the arrow keys on the chart
00.511.52 200400600800100012001400 New weight (kN) now 1.013

Variables and how each one contributes

MMPnew/MMPold

Pressure ratio

Result ·

What the equation gives you. Everything else feeds it.

Wold

Original weight

kN · typical 100 to 1,500

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.

Wnew

New weight

kN · typical 100 to 1,500

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.

bold

Original track width

m · typical 0.25 to 1

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.

bnew

New track width

m · typical 0.25 to 1

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

  1. Weight ratio: Wnew/Wold = 700/638 = 1.097.
  2. Width ratio: bold/bnew = 0.6/0.65 = 0.9231.
  3. 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

Related formulas

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