Wheel sinkage follows the classic Bekker pressure–sinkage relation used in real planetary-rover terramechanics: p = (kc/b + kphi)·z^n, where kc is the cohesive modulus and kphi the frictional modulus of the regolith, b the wheel width and n the sinkage exponent (n = 1 here). Integrating this under a rigid wheel of diameter D carrying load W gives the static sinkage depth:
z0 = [ 3W / ( (3-n)(kc + b·kphi)·sqrt(D) ) ]^(2/(2n+1))
kc and kphi are scaled from the cohesion and friction-angle sliders relative to Apollo-era lunar-regolith Bekker baselines (kc0 ≈ 1.4 kN/m², kphi0 ≈ 820 kN/m³ at c0 = 1 kPa, φ0 = 30°), so raising cohesion stiffens the cohesive term and raising friction angle stiffens the frictional term — both reduce sinkage, matching real soil-mechanics behaviour.
Motion (compaction) resistance is the work done pushing the wheel down into the sinkage bowl, Rc = (kc + b·kphi)·z0²/2. Maximum shear traction comes from Mohr–Coulomb failure under the contact patch (length lc ≈ sqrt(D·z0)): Fmax = b·lc·c + W·tan(φ). Net drawbar pull is Fmax − Rc — if it goes negative the wheel spins in place instead of moving the rover.
The slope panel applies the infinite-slope stability check at a reference depth of 0.5 m: FS = tan(φ)/tan(β) + c/(γ·z·sinβ·cosβ), with unit weight γ = ρ·g. FS < 1 means the slope fails; for cohesionless regolith this reduces to comparing the slope angle directly against the angle of repose (≈ the friction angle).
- Left pane — wheel cross-section sunk to depth z0 in the regolith, load arrow and sinkage bowl to scale.
- Top-right pane — the Bekker pressure–sinkage curve p(z), with the working point at (z0, p0) marked.
- Bottom-right pane — slope-stability diagram comparing the chosen slope angle to the friction angle / angle of repose.