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Surface, slope and truck
The tyres can push with at most friction times the normal force. On a slope the normal force falls as cos(theta) while the downhill pull grows as sin(theta).
Gearing
Model checks
The science
What is modelled
A vehicle on a slope with Coulomb tyre friction, rolling resistance, air drag and a governed engine. Tyre force is capped at mu times the normal force, which is the physical reason a muddy hill stops a truck.
Equations
- Normal force
N = m g cos(theta); grip limitmu N; slope pullm g sin(theta). - Passive acceleration
a = g (sin(theta) - mu cos(theta)); climb limit neartheta = atan(mu). - Static tip angle
atan(track/2 / h); suspension periodT = 2 pi sqrt(m/k).
Checks run in the page
- Block on a slope and the friction angle.
- Traction-limited acceleration with unlimited drive.
- Static tip angle of the track and height.
- Spring-mass period by numerical integration.
Honest simplifications
A reduced model: one lumped friction coefficient (no sinking, tyre pressure or soil deformation), a straight climb only, fixed gearing and an invented engine curve. Not a vehicle-safety tool.
What to try
- Press Wet mud: the grip limit drops below the slope pull and the truck stalls.
- Press Rain squall: friction and rolling resistance both worsen.
- Switch to high gear: less drive force, so it stalls on a lower slope.