Three toy off-road cars traced from marker drawings (drawings by a young child). The paper cars had no wheels, so you give them some: pick a wheel size, grip and suspension, then drive up hills, over bumps and across a tilting slope. Built from a Blender 5.2 model, run by a small vehicle-physics engine.
The silhouette and colours of each 3D body come straight from the photo of the drawing. Wheels, axles and glass are modelled in Blender.
Blue: speed (full scale 30 m/s). Amber: wheel slip (0 to 100 %). Green: suspension compression (plus or minus 15 cm). Last 12 seconds.
Runs the same engine without graphics and compares it with closed-form formulas: the tilt angle at which the car tips over, and the steepest slope a four-wheel-drive car can climb on a given grip.
A wheel can only push the car with the grip between tyre and ground. The most push a tyre can give is the friction force, grip times how hard the ground presses on the tyre. Slippery mud or ice has a small grip number, so the car cannot push much.
On a slope the car's weight pulls it back down the hill by m g sin(slope). The ground presses the tyres with m g cos(slope). With all four wheels pushing, the car just keeps going when mu cos(slope) is bigger than sin(slope):
Three things can stop the car: the tyres slip (grip), the engine is too weak (torque T at wheels of radius r), or the nose lifts and the car flips backwards (b is the distance from the centre of mass to the rear wheels, h_cg its height). The smallest of the three wins, and the panel tells you which.
A tall, narrow car tips more easily. On a sideways slope it starts to roll when the line straight down from its centre of mass leaves the wheels. That happens at
Lowering the centre of mass or widening the track makes the car safer. Soft springs let the body lean, which lowers the real tipping angle a little. If the tyres slip before the car tips (grip below tan of the angle), it slides instead.
A bigger wheel meets a step at a gentler angle. As a rule of thumb a normally gripping wheel can roll over a step lower than its radius (r greater than h). With very sticky tyres the corner can grab and lift a little higher, so the engine's measured limit is slightly above r here.
Each wheel hangs on a spring (force k times the squeeze) and a damper (force c times the speed of squeezing). The spring holds the car up and the damper stops it bouncing forever. Squashed springs press the tyre harder, which is why the ground grip changes over bumps.
The car is one rigid body on four spring-loaded wheels; tyres use a simple friction-circle model (total grip force never above mu x N); air drag is a single number; wheels are thin discs rolling on a smooth surface. Four-wheel drive splits torque equally. The body is a solid block shaped like the drawing. Numbers are for a toy-scale car about 4 m long. The silhouette comes from a photo, so the proportions are the child's, not an engineer's. These toy cars are not based on any real vehicle or brand.
Keys: W / Up = gas, S / Down = brake and reverse, A D / Left Right = steer, Space = parking brake, R = reset, C = camera. Drag on the 3D view to look around.