Heavy Crawler on Dune Sand

What is modelled

Soft ground yields under a track: the pressure needed to sink a plate grows as a power of the depth (Bekker). The track sinks until that pressure equals the weight per area, and pushing the machine forward keeps compacting the sand in front of it, which costs a resistance. The tracks can push on the ground only as much as the sand can be sheared (Mohr-Coulomb), and the shear stress builds up with the slip displacement. The drawbar pull is what is left of the thrust after the compaction and slope resistances.

Equations

• Pressure p = (kc/b + kφ) zn, so the sinkage is z = (p / k)1/n with p = W / (2 b L).
• Compaction resistance Rc = 2 b k zn+1 / (n+1).
• Thrust H = Hmax [1 − (K / iL)(1 − e−iL/K)], Hmax = 2 b L c + W tan φ.
• Drawbar pull DP = H − Rc − W sin θ.

Checks run in the page

• Sinkage by bisection against the closed form.
• Simpson integral of pressure over depth against its closed form.
• Shear stress summed along the track against the thrust formula.
• Slip at 90 % of the thrust limit by bisection against a scan.

Honest simplifications

The track is treated as a rigid flat plate of its full length, the sand constants are typical dry-sand values scaled by a firmness factor, the shear modulus K is fixed at 2.5 cm, the load is spread evenly and speed effects, bulldozing and track pitching are ignored. Real terramechanics uses measured soil data and a more detailed track model.

• Press Very heavy and watch the drawbar pull fall.
• Press Wide long tracks and compare the sinkage.
• Press Dune slope and read the climbable slope.