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Terramechanics and off-road mobility

Limiting cone index, tracked vehicle

Cone index the soil must have for a tracked vehicle to keep moving, from its weight and track geometry.

Ref: TER-26
Rev: v1
Field: Terramechanics and off-road mobility
Result: CI_L,track [kPa]

C I_{L,track} = \frac{1.63 W}{2 n b c_{a} \sqrt{p_{t} d}}

The lecture’s limiting cone index for a tracked vehicle is CI_L = 1.63 W/(2n b c_a √(p_t d)), with n the number of stations or axles per side, so N_w = 2n. It is the cone index the soil must have for the vehicle to keep moving. The lecture’s symbol e for the link area ratio is written c_a here, consistent with its worked example. These are empirical correlations, not guaranteed pass or fail predictions for every soil and pass count. W is the total weight in kN.

Cone index the soil must have for a tracked vehicle to keep moving, from its weight and track geometry. It is an empirical correlation, so it points to the likely outcome, not a guaranteed pass or fail.

Calculator

Solve for

CI_L,trackLimiting cone indexComputed

kPa

WVehicle weight

1001,500

nRoad-wheel stations per side

212

bTrack width

0.251

c_aLink area ratio

0.51

p_tTrack pitch

0.080.3

dRoad-wheel diameter

0.31.2

Limiting cone index in psi57.16 psi
Mean maximum pressure for the same vehicle (N_w = 2n)304.7 kPa
Ratio CI_L/MMP1.294

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.

Limiting cone index (kPa) current value 394.1 kPa

nRoad-wheel stations per sideKey driver

1971,180

WVehicle weight

61.8927

bTrack width

236946

c_aLink area ratio

370741

dRoad-wheel diameter

322644

p_tTrack pitch

314607

The lecture vehicle needs a soil cone index of 394.1 kPa (57.16 psi). It is 1.63/1.26 = 1.294 times the MMP of 304.7 kPa, so CI_L follows MMP in proportion.
A soil with a remoulded cone index of 240 kPa, as in the remoulded cone index entry, falls short of 394.1 kPa. This is a go or no-go screening method, not a precise prediction.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (kPa)	Local step	Change in result
n Road-wheel stations per side	2 to 12	197.1	1,182	985.3	+1	−14.3 %
W Vehicle weight	100 to 1,500 kN	61.77	926.6	864.8	+10%	+10 %
b Track width	0.25 to 1 m	236.5	945.9	709.4	+10%	−9.09 %
c_a Link area ratio	0.5 to 1	370.5	740.9	370.5	+10%	−9.09 %
d Road-wheel diameter	0.3 to 1.2 m	321.8	643.6	321.8	+10%	−4.65 %
p_t Track pitch	0.08 to 0.3 m	313.6	607.4	293.7	+10%	−4.65 %

Sweep of Vehicle weight

Vehicle weight (kN)	Limiting cone index (kPa)
100	61.77
275	169.9
450	278
625	386.1
800	494.2
975	602.3
1,150	710.4
1,325	818.5
1,500	926.6

Sweep one variable

Vary

Limiting cone index (kPa)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

CI_L,track

Limiting cone index

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 the limiting cone index in proportion. Raising it by 10 % (to 701.8) moves the result by +10 %, from 394.1 to 433.5 kPa.

Road-wheel stations per side

· typical 2 to 12

The number of road-wheel stations on each side, a whole number. Lowers the limiting cone index in inverse proportion. Raising it by 1 (to 7) moves the result by −14.3 %, from 394.1 to 337.8 kPa.

Track width

m · typical 0.25 to 1

The width of each track, in m. Lowers the limiting cone index in inverse proportion. Raising it by 10 % (to 0.66) moves the result by −9.09 %, from 394.1 to 358.3 kPa.

c_a

Link area ratio

· typical 0.5 to 1

The link area ratio, between 0.5 and 1. Lowers the limiting cone index in inverse proportion. Raising it by 0.02 (to 0.96) moves the result by −2.08 %, from 394.1 to 385.9 kPa.

p_t

Track pitch

m · typical 0.08 to 0.3

The track pitch, in m. Lowers the limiting cone index with the square root of the pitch. Raising it by 10 % (to 0.209) moves the result by −4.65 %, from 394.1 to 375.8 kPa.

Road-wheel diameter

m · typical 0.3 to 1.2

The road-wheel diameter, in m. Lowers the limiting cone index with the square root of the diameter. Raising it by 10 % (to 0.88) moves the result by −4.65 %, from 394.1 to 375.8 kPa.

Worked example with the values above

Numerator: 1.63 W = 1.63 × 638 = 1,040 kN.
Denominator: 2n b c_a √(p_td) = 12 × 0.6 × 0.94 × √(0.19 × 0.8) = 2.639.
CI_L = 394.1 kPa.

Assumptions and limits

A tracked vehicle on fine-grained soil, with the lecture’s correlation constant 1.63.
Consistent units: kN and m give kPa.

Common mistakes

Using the total station count in place of the per-side count n.
Comparing a result in kPa against a soil strength in psi.

Statistics and uncertainty

Like MMP, the limiting cone index is an empirical correlation; treat results within ±10 % as equal. Soil moisture, pass count and slope change the real limit, so use the result as a screen.

Where it is used

Comparing the soil strength a vehicle needs with that measured on the route.
Screening vehicle options for a soft-ground route.

Maths you need

Cone index: penetrometer resistance of soil
Mean maximum pressure: peak pressure under road wheels

Related formulas

Practise this formula