The 9√P rule
Walter Horne’s NASA work in the early 1960s showed that a rotating pneumatic tire can ride up on a water film at a speed that scales with the square root of inflation pressure:
Vdynamic (kt) = 9 × √P with P in psi
That is the same statement as 10.35 × √P in miles per hour. For a locked or non-rotating tire the coefficient is lower, typically written
Vlocked (kt) = 7.7 × √P
A 32 psi light-airplane tire therefore has a dynamic hydroplaning speed of about 51 kt, and a locked-wheel speed of about 44 kt. A 200 psi transport tire is around 127 kt rotating.
Assumptions
The formula is for a standing water film deep enough to lift the footprint. It does not model viscous hydroplaning in a thin film, reverted-rubber hydroplaning from a skid, groove or tread drainage, or a crowned, textured runway. Touching down at or above the rotating-tire speed, then braking so the wheel stops, can put you into the lower locked-wheel regime. FAA material on wet and contaminated runways emphasizes a firm, on-speed landing and avoiding a late flare that keeps the airplane in the hydroplaning band.
Sources
NASA TN D-2056 (Horne & Dreher, 1963) and later NASA hydroplaning reports; FAA Pilot’s Handbook of Aeronautical Knowledge (tires, hydroplaning); FAA Airplane Flying Handbook (wet-runway landing); AC 91-79A, Mitigating the Risks of a Runway Overrun Upon Landing. For takeoff and landing distance corrections, see the takeoff / landing distance calculator.
Frequently asked questions
Is 9√P in knots or miles per hour?
The coefficient 9 is for pressure in psi and speed in knots. In mph the same relation is 10.35√P. This page reports both.
Why is the locked-wheel speed lower?
Once the tire has stopped rotating, the mechanism is different and the speed at which a water film can support the wheel is lower. The usual planning figure is 7.7√P knots. A skid after touchdown can put you into that regime.
Can I land faster than 9√P on a wet runway?
The figure is an estimate, not a hard limit, but landing well above it on standing water raises the chance of dynamic hydroplaning. Use the POH wet-runway data, a firm on-speed landing, and the runway length you actually have.