Tracked Vehicle Mobility Lab: Ground Pressure, Soil Sinkage, Gradeability and Skid Steering

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p - sinkage - max slope -

Terrain

Vehicle (generic unarmed chassis)

The science

Physics teaching model. A generic, unarmed, museum-style tracked chassis used to explain civil and engineering terramechanics. Numbers are textbook-order, not data for any real vehicle.

Nominal ground pressure p = W / (2 b L) (two tracks, width b, ground-contact length L = 3.8 m, uniform pressure assumed).
Bekker pressure-sinkage p = (k_c/b + k_phi) z^n, so z = (p / (k_c/b + k_phi))^(1/n). Wider tracks lower p and raise the stiffness term k_c/b.
Compaction resistance (energy to make the rut) R_c = 2 b (k_c/b + k_phi) z^(n+1) / (n+1); internal/rolling resistance taken as 0.03 W cos a.
Maximum thrust (Mohr-Coulomb) H = c A + W cos a tan(phi), A = 2 b L. Slope limit: largest a with min(H, eta P / v) = R_c + R_int + W sin a. On firm ground with c = 0 and no resistance this reduces to tan a = tan phi. Shear-displacement (Janosi) curve is ignored.
Step: geometric ceiling = top of the front idler track (~1.0 m); the smooth-belt friction bound is the height where the idler-arc surface angle equals atan(mu). Real grousers/hull noses sit between the two. Trench: idealised, the front tip must reach the far edge while the centre of gravity is still over the near edge, so w_max = distance from front tip to CG.
Torsion bar: K = G J / l, J = pi d^4 / 32, wheel rate k = K / a^2 (arm length a), static deflection W_wheel / k, heave frequency f = sqrt(12 k / m_sprung) / 2pi.
Skid steering: R = (B/2)(1+rho)/(1-rho), rho = v_inner/v_outer; turning resistance moment M_r = mu_t W L / 4 with the empirical mu_t = mu_max / (0.925 + 0.15 R/B). Track forces F_o,i = R_f/2 +- M_r/B; power F_o v_o + F_i v_i.
Plate geometry: line-of-sight thickness t / cos(theta), theta measured from the plate normal. Pure geometry; this page makes no protection or penetration claims.