Hydroplaning Speed Calculator: Dynamic Aquaplaning Speed from Tyre Pressure
Find the speed at which a tyre starts to hydroplane from its inflation pressure with NASA’s 9√P rule (knots) for a rotating tyre and 7.7√P for a non-rotating tyre at touchdown, in knots, mph and km/h, with your speed margin, the risk at your water depth and a table by tyre pressure.
How it works
V_P (knots) = 9 × √P for a rotating tyre, P = tyre inflation pressure in psi (Horne and Dreher, NASA TN D-2056) · V_P (mph) = 10.35 × √P · V_P (non-rotating tyre, knots) ≈ 7.7 × √P · 1 kt = 1.1508 mph = 1.852 km/h · 1 bar = 14.504 psi
Dynamic hydroplaning happens when a tyre runs through standing water fast enough that the water cannot escape from under the footprint. The pressure of the water wedge rises with the square of speed, and when the lift it produces equals the load on the tyre, the tyre rides on the water and loses braking and steering. NASA researchers Walter Horne and Robert Dreher showed that the load per unit of footprint area is close to the inflation pressure and the lift coefficient about 0.7, which reduces the onset speed to about 9 times the square root of the tyre pressure in psi, in knots (10.35√P in mph). That is why lightly inflated tyres plane at surprisingly low speeds, while an airliner tyre at 200 psi holds on to about 127 kt. A tyre that is not rotating, such as an aircraft wheel at the moment of touchdown or a locked wheel, can keep planing down to a lower speed, about 7.7√P knots, so a firm touchdown that spins the wheels up quickly matters on a flooded runway. The formula needs water deeper than the tread grooves, roughly 2.5 mm (0.1 in) or more on a smooth surface; open tread and grooved or porous pavement raise the depth needed. Thinner films still cause viscous hydroplaning on smooth or rubber-coated surfaces at any speed. The result is a rule-of-thumb onset estimate, not a guarantee of grip below it.
Worked example
A jet with 120 psi main tyres hydroplanes at about 9 × √120 = 9 × 10.954 = 98.6 kt, which is 113 mph or 183 km/h. A tyre that is not spinning at touchdown can plane down to 7.7 × √120 = 84 kt. Touching down at 110 kt on 3 mm of water is 11 kt above the onset speed, so the risk is high: expect little braking until speed falls below about 99 kt. At 110 kt the onset would only reach your speed with a pressure of (110 ÷ 9)² = 149 psi.
Sources: Horne & Dreher, Phenomena of Pneumatic Tire Hydroplaning, NASA TN D-2056 (1963) · NASA Technical Reports Server: TN D-2056 record · Wikipedia: Aquaplaning (9√P, 7.7√P and car examples)
Frequently asked questions
At what speed does a car hydroplane?
With tyres at 35 psi the 10.35√P rule gives about 61 mph (98 km/h) in water deeper than the tread; at 30 psi it is about 57 mph. Worn tyres, under-inflation and deep puddles bring it lower, and NASA’s formula is only a rough guide for car tyres, so slow down well before that in heavy rain.
What is the 9√P rule for aircraft?
It estimates the dynamic hydroplaning speed in knots as 9 times the square root of the tyre pressure in psi. A light aircraft with 30 psi tyres can hydroplane at about 49 kt; an airliner with 200 psi tyres at about 127 kt. For a tyre that is not rotating, such as at touchdown, use 7.7√P.
Does tread depth change the hydroplaning speed?
The 9√P onset applies once water is deeper than the tread. Tread grooves let a tyre clear thinner films, so worn tyres plane in shallower water and in more conditions; tests of half-worn car tyres found aquaplaning about 3–4 mph earlier than with full tread.
What are viscous and reverted-rubber hydroplaning?
Viscous hydroplaning is loss of grip on a very thin film over a smooth surface, such as a rubber-coated touchdown zone or painted markings, and can happen at any speed. Reverted-rubber hydroplaning follows a long locked-wheel skid, when friction heat turns water to steam and melts the tyre surface.
How much water is needed to hydroplane?
Dynamic hydroplaning generally needs standing water deeper than the tread grooves, about 2.5 mm (0.1 in) or more on smooth tyres and pavement; NASA’s tests put the critical depth between about 0.1 and 0.4 in depending on tread and surface texture.
Related calculators
Planning aid using the NASA rule of thumb; it does not guarantee grip below the estimated speed. Not a substitute for the aircraft flight manual (AFM/POH), operator procedures or safe driving for the conditions.