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Tyre
Pressure and groove depth set the onset speed. Vehicle mass changes only the footprint size.
Road and water
A wet strip of chosen depth, start and length lies across the lane.
Driving
Entry speed, reaction time and brake demand. ABS decides what happens when demand exceeds grip.
Camera
Layers
Quality
Model checks
The science
What hydroplaning is
A tyre on a wet road must push the water out of its footprint. Below a certain speed the tread grooves and the squeezed film drain it fast enough and rubber touches asphalt. When the water cannot escape quickly enough, a wedge of water builds up ahead of the tyre and its pressure carries part of the wheel load: the tyre rides on a film and friction collapses.
Dynamic pressure of the wedge
Water of density rho = 1000 kg/m3 brought to rest at the leading edge produces a stagnation pressure q = rho v^2 / 2. The wedge transmits only part of it to the footprint: p_wedge = Cw q S, where S (0 to 1) says how much of the film the tread cannot drain. The share of the footprint lifted off the road is phi = min(1, Cw S q / p), with p the inflation pressure (contact pressure is close to p). Full hydroplaning is phi = 1:
v_hp = sqrt( 2 p / (rho Cw S) )
The coefficient Cw = 0.64 is calibrated so that a deep film (S about 1) reproduces the NASA/Horne spin-up result v_hp = 9 sqrt(p[psi]) knots: for 32 psi (220 kPa) about 94 km/h. Vehicle mass does not appear: a heavier car has a larger footprint but the same contact pressure, so the onset speed is set by tyre pressure, not weight.
Tread drainage
Grooves can swallow a film up to about kappa d_g (kappa = 0.6, groove depth d_g). The film in excess, h_e = max(0, h - kappa d_g), forms the wedge, and S = h_e / (h_e + h0) with h0 = 0.25 mm. A deep tread therefore delays hydroplaning in shallow water; in water deeper than the grooves every tyre is close to S = 1.
Friction and braking
The friction coefficient blends the wet-road grip with the film: mu = mu_wet (1 - phi) + 0.05 phi, with mu_wet = mu0 (1 - 0.3 min(1, h/1 mm)). Braking deceleration is a = min(demand * mu0 * g, mu g) with ABS; without ABS a demand above the available grip locks the wheels and the sliding coefficient is taken as 0.85 mu. The stopping distance is s = v t_r + integral v dv / a; on a dry road with constant mu it reduces to v t_r + v^2 / (2 mu g).
Footprint area
One tyre carries m g / 4, so the contact patch area is A = m g / (4 p); a lower pressure gives a longer patch (and a lower v_hp), which is why under-inflated tyres hydroplane earlier.
Honest simplifications
This is a lumped teaching model, not a computational fluid-structure simulation of a real tyre. Real hydroplaning depends on tread pattern, rubber stiffness, road macrotexture, film depth distribution, cornering and steering; the film factor S, kappa and the friction law are simple fits chosen to reproduce the Horne speed at deep water and the known trends (shallower grooves, lower pressure, deeper water = earlier loss of grip). Aerodynamic and rolling drag, weight transfer and tyre heating are ignored; the wheel spin-down shown in 3D is purely visual. Never use this as a safety rule: slow down in heavy rain.
What to try
- Load Healthy tyres, shallow water, then Bald tyres, flooded lane: watch the blue wedge grow on the footprint plate and the stop get longer on graph 3.
- Drop the pressure to 140 kPa and see the hydroplaning speed move left on graph 1.
- Increase the mass: the patch gets bigger but the hydroplaning speed does not change.
- Switch ABS off and press the full brake: the wheels lock and the stop is longer even on a dry road.
- Use Coasting through a puddle to see lift without braking: the car only wobbles when the lifted fraction passes about 55 %.