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Off-road mobility calculator

Will a tracked or wheeled vehicle get across soft ground? Pick a vehicle and a soil and compare three standard prediction methods side by side: mean maximum pressure (MMP), the WES vehicle cone index (VCI) used in the NATO Reference Mobility Model, and Bekker–Coulomb terramechanics. See each go or no-go with the working shown, find where the methods disagree, and practise predicting the answer. Maclaurin’s limiting cone index is there as an optional fourth.

About the data. All vehicle and soil figures here are representative values from open sources, assembled for teaching. A name such as “Challenger 2 class” means the row is modelled on a vehicle of that kind. It is not necessarily the actual data for that vehicle, and not a performance claim. Soil figures are representative of a type of ground on a given day, not of any site. Overwrite any value with your own data in the custom rows.

Passes required
Methods to show

Data basis. Vehicle: Open-source figures for a vehicle of this class. Soil: Published Bekker parameter set.

    Unanimous GO

    Tracked IFV, 25.7 t (Warrior class) on Lean clay (WES), one pass.

    All three main methods say GO. Check the margins below before treating that as safe: a thin margin on a soil that varies with the weather is not much comfort.

    For the strength-based methods, Maclaurin asks for the strongest soil (39.4 lbf/in²) and MMP for the weakest (20.2 lbf/in²), a ratio of 1.95. Compare that spread with the scatter in a real cone index reading, which is often 20 per cent or more.

    The same vehicle on the same soil, by each method. Strengths are in lbf/in².
    MethodWhat it answersStrength neededSoil strengthMarginVerdict
    MMP (one pass)Pressure under the worst-loaded point, bridged to a soil strength20.1655.8435.7 GO
    VCI (one pass)Minimum rating cone index for that many passes20.4755.8435.4 GO
    Bekker–CoulombWhether thrust beats resistance without bellying out––drawbar pull 326 kN GO

    Method by method

    Mean maximum pressure (MMP)

    GO

    The pressure under the most heavily loaded point of the running gear, turned into the weakest soil the vehicle can cross. Confidence in this branch (tracked): Verified

    210 kN/m²MMP70.27 kN/m²nominal pressure2.99×MMP / nominal20.16 lbf/in²soil strength needed55.84 lbf/in²soil strength

    Margin 35.7 lbf/in². Against the planning guideline of 150 kN/m² for a single pass on wet fine-grained soil the vehicle is outside the envelope (margin -60 kN/m²).

    Show the working
    1. Weight W = m g = 25.7 t × 9.81 = 252.12 kN.
    2. MMP = 1.26 W / (2 n b e √(p d)) = 1.26 × 252.12 / (2 × 6 × 0.46 × 0.9 × √(0.152 × 0.61)) = 209.99 kN/m².
    3. Bridge to a soil strength: VCI1 = 0.096 × MMP = 20.159 lbf/in².
    4. Soil strength used: rating cone index (RCI = CI × RI) = 55.838 lbf/in². Margin = 35.68 lbf/in², so the verdict is GO.

    Watch out: MMP contains no soil property. The step from pressure to soil strength is an empirical bridge with mixed units, and the one-pass bridge is the weaker of the two.

    WES vehicle cone index (VCI)

    GO

    A dimensionless mobility index from the running gear, converted into the minimum rating cone index the soil must have. This is the method underneath NRMM. Confidence in this branch (tracked): Verified

    69.96mobility index20.47 lbf/in²VCI, one pass55.84 lbf/in²soil strength35.4 lbf/in²margin
    Show the working
    1. Convert to imperial units: W = 56678.2 lbf.
    2. Factors: contact pressure 10.19, weight 1.2, traction element 0.181, grouser or chains 1, bogie or wheel load 4.359, clearance 1.929, engine 1, transmission 1.
    3. MI = ((CPF × WF) / (TEF × GF) + WLF − CF) × EF × TF = 69.959.
    4. VCI1 = 20.473 lbf/in² and VCI50 = 47.719 lbf/in². This case uses the single-pass value.
    5. Soil strength used: rating cone index (RCI = CI × RI) = 55.838 lbf/in². Margin = 35.36, so the verdict is GO.

    Watch out: It is a curve fitted to a finite set of vehicles. Far outside that set the equation still returns a number, which is why the tool flags the mobility index range.

    Bekker–Coulomb terramechanics

    GO

    A soil-mechanics model. It asks whether the soil can supply more thrust than the vehicle meets in resistance, and whether the vehicle sinks until it bellies out. Confidence in this branch (tracked): Representative

    1.01e-7 msinkage2.07e-7×sinkage / clearance339 kNmaximum soil thrust12.61 kNmotion resistance326.4 kNdrawbar pull1.29drawbar pull / weight

    Predicted steepest slope on this soil before traction runs out, ignoring engine power: about 22.3 (rise over run).

    01833660.10.20.30.40.50.6 Resistance 12.6 kNThrust at the slip shown Slip, ikN
    Show the working
    1. Mean contact pressure p = W / A = 252.12 / 3.588 = 70.27 kN/m².
    2. Thrust (Coulomb, Micklethwait): H = A c + W tan φ = 247.2 + 91.76 = 338.98 kN.
    3. Sinkage (Bekker): z = (p / (kc/b + kφ))^(1/n) = 1.013e-7 m, which is 2.07e-7 times the ground clearance.
    4. Compaction resistance Rc = b (kc/b + kφ) zn+1 / (n+1), summed over the running gear = 0.000005458 kN. Internal resistance = 0.05 W = 12.61 kN. Total R = 12.606 kN.
    5. Drawbar pull = H − R = 326.37 kN. The verdict is GO.

    Watch out: Sinkage is the most sensitive output, and it depends on soil parameters that need a bevameter test and change with moisture. Bulldozing resistance is not modelled, so drawbar pull at large sinkage will be optimistic.

    All vehicle and soil figures here are representative values from open sources, assembled for teaching. A name such as “Challenger 2 class” means the row is modelled on a vehicle of that kind. It is not necessarily the actual data for that vehicle, and not a performance claim. Soil figures are representative of a type of ground on a given day, not of any site. Overwrite any value with your own data in the custom rows.

    How to read the results

    Read the verdicts across, not down. When all methods agree you have a robust answer. When they split, the split is information: the methods were built from different data and ask different questions. MMP asks how hard the vehicle presses. VCI asks what soil strength the vehicle needs for a given number of passes. Bekker–Coulomb asks whether the soil can supply enough thrust, and how far the vehicle sinks.

    Margins matter more than the verdict. A cone index measured on a given day has real scatter, often 20 per cent or more, so a GO with a thin margin is a close call, not a guarantee.

    Limits. The tool has no obstacle, slope-change, vegetation or layered-soil model, carries no uncertainty, treats the vehicle load as evenly shared and gives results to more figures than the methods justify. It is for learning how the methods behave and compare, not for acceptance or operational decisions.

    Related tools and pages: all tools, mean maximum pressure, remoulded cone index, drawbar pull and bearing capacity of clay.