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Terramechanics and off-road mobility

Mean maximum pressure (MMP)

Peak ground pressure under the road wheels of a tracked vehicle, which is higher than the nominal pressure because the load is carried on the track under the wheels.

Ref: TER-24
Rev: v1
Field: Terramechanics and off-road mobility
Result: MMP [kPa]

M M P = \frac{1.26 W}{N_{w} b c_{a} \sqrt{p_{t} d}}

MMP = 1.26 W/(N_w b c_a √(p_t d)) is the peak pressure under the road wheels of a tracked vehicle, in kPa, with W the total weight in kN, b the track width in m, c_a the link area ratio, p_t the track pitch, d the road-wheel diameter and N_w the number of road-wheel stations across both tracks. For a single track use that track’s own load and its own station count: never combine the total vehicle load with one side’s wheel count. MMP and the nominal ground pressure (NGP = W/2bl) are both pressures, but they describe different things: do not apply MMP thresholds to NGP.

Peak ground pressure under the road wheels of a tracked vehicle, which is higher than the nominal pressure because the load is carried on the track under the wheels. It better predicts soft-ground performance than the nominal value.

Calculator

Solve for

MMPMean maximum pressureComputed

kPa

WVehicle weight

1001,500

N_wRoad-wheel stations, both tracks

424

bTrack width

0.251

c_aLink area ratio

0.51

p_tTrack pitch

0.080.3

dRoad-wheel diameter

0.31.2

VCI₁ = 0.096 MMP (one pass)29.25 psi
VCI₅₀ = 0.27 MMP (50 passes)82.26 psi
Weight per road-wheel station53.17 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.

Mean maximum pressure (kPa) current value 304.7 kPa

N_wRoad-wheel stations, both tracksKey driver

152914

WVehicle weight

47.8716

bTrack width

183731

c_aLink area ratio

286573

dRoad-wheel diameter

249498

p_tTrack pitch

242470

The lecture vehicle (638 kN, 12 stations, 0.60 m tracks) has an MMP of 304.7 kPa against a nominal ground pressure of 111 kPa for a 4.79 m contact length, a ratio of 2.745. The peak under the wheels is nearly three times the nominal average.
Widening the tracks to 0.65 m cuts MMP to 281.2 kPa, and adding two stations (14) gives 261.1 kPa.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (kPa)	Local step	Change in result
N_w Road-wheel stations, both tracks	4 to 24	152.3	914	761.6	+1	−7.69 %
W Vehicle weight	100 to 1,500 kN	47.75	716.3	668.5	+10%	+10 %
b Track width	0.25 to 1 m	182.8	731.2	548.4	+10%	−9.09 %
c_a Link area ratio	0.5 to 1	286.4	572.8	286.4	+10%	−9.09 %
d Road-wheel diameter	0.3 to 1.2 m	248.8	497.5	248.8	+10%	−4.65 %
p_t Track pitch	0.08 to 0.3 m	242.5	469.5	227.1	+10%	−4.65 %

Sweep of Vehicle weight

Vehicle weight (kN)	Mean maximum pressure (kPa)
100	47.75
275	131.3
450	214.9
625	298.4
800	382
975	465.6
1,150	549.1
1,325	632.7
1,500	716.3

Sweep one variable

Vary

Mean maximum pressure (kPa)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

MMP

Mean maximum pressure

Result · kPa

What the equation gives you. Everything else feeds it.

Vehicle weight

kN · typical 100 to 1,500

The total weight of the vehicle, in kN. Raises MMP in proportion. Raising it by 10 % (to 701.8) moves the result by +10 %, from 304.7 to 335.1 kPa.

N_w

Road-wheel stations, both tracks

· typical 4 to 24

The total number of road-wheel stations across both tracks, a whole number. Lowers MMP: more wheels share the load. Raising it by 2 (to 14) moves the result by −14.3 %, from 304.7 to 261.1 kPa.

Track width

m · typical 0.25 to 1

The width of each track, in m. Lowers MMP in inverse proportion. Raising it by 10 % (to 0.66) moves the result by −9.09 %, from 304.7 to 277 kPa.

c_a

Link area ratio

· typical 0.5 to 1

The link area ratio: the fraction of the track’s plan area occupied by its links, between 0.5 and 1. Lowers MMP in inverse proportion. Raising it by 0.02 (to 0.96) moves the result by −2.08 %, from 304.7 to 298.3 kPa.

p_t

Track pitch

m · typical 0.08 to 0.3

The track pitch, in m. Lowers MMP, but only with the square root of the pitch. Raising it by 10 % (to 0.209) moves the result by −4.65 %, from 304.7 to 290.5 kPa.

Road-wheel diameter

m · typical 0.3 to 1.2

The road-wheel diameter, in m. Lowers MMP, but only with the square root of the diameter. Raising it by 10 % (to 0.88) moves the result by −4.65 %, from 304.7 to 290.5 kPa.

Worked example with the values above

Numerator: 1.26 W = 1.26 × 638 = 803.9 kN.
Denominator: N_w b c_a √(p_td) = 12 × 0.6 × 0.94 × √(0.19 × 0.8) = 2.639.
MMP = 304.7 kPa.

Assumptions and limits

Total vehicle weight with the total number of road-wheel stations (or one track’s load with its own count).
A consistent set of units: kN, m, giving kPa.

Common mistakes

Mixing one track’s wheel count with the total vehicle load.
Applying MMP thresholds to the nominal ground pressure.

Statistics and uncertainty

MMP is an empirical index; its link to real soil performance scatters. Treat a difference of less than 10 % between two vehicles as no real difference. The inputs, especially the link area ratio and pitch, are usually known to a few per cent.

Where it is used

Comparing tracked vehicles for soft-ground mobility.
Feeding the VCI correlations for go or no-go screening.

Maths you need

Ground pressure: force over contact area
Square roots: pitch and wheel diameter

Related formulas

Practise this formula