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Many articles on hydroplaning cite the following formula on the minimum speed necessary for hydroplaning to begin:

$$ 9 * \sqrt{\text{Tire Pressure}} = \text{Maximum Hydroplaning Speed} $$

Is this the correct formula to calculate knots groundspeed using PSI for tire pressure?

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The formula that you have mentioned is correct but with a slight alteration. The expression on the left-hand side of the equation should be equal to $\text{Minimum Hydroplaning speed}$, meaning that at or above this groundspeed, hydroplaning is possible. Therefore, the correct formula for an aircraft rotating wheel is: $$9\sqrt{\text{Tire Pressure [PSI]}}=\text{Minimum Hydroplaning speed [knots]}$$ or, with a different tire pressure unit: $$34\sqrt{\text{Tire Pressure [Bar]}}=\text{Minimum Hydroplaning speed [knots]}$$ In order for a tire to lift from the surface of the runway and hydroplane, certain conditions must be met. These are:

  1. The depth of the water on the runway must be greater than the depth of the tire tread. If this essential condition is not met, the hydroplaning cannot occur.
  2. The minimum hydroplaning speed is also dependent on whether an aircraft tire is rotating or non-rotating. The given formula is only valid for a rotating aircraft wheel (e.g. takeoff). If a wheel is not rotating (e.g. upon landing or locking up), a different formula is applicable: $$7.7\sqrt{\text{Tire Pressure [PSI]}}=\text{Minimum Hydroplaning speed [knots]}$$ If a wheel is not rotating - it is more prone to hydroplane. This makes sense because the grooves on the tire are no longer working effectively to expel the water from beneath the tire.
  3. The mentioned formula is Empirical, meaning that it is based on observations and not mathematically deduced from laws of physics. This is also why the dimension of the expression of the left-hand side is not equal to the dimension of the expression of the right-hand side of the equation for this formula. Notice that the measurement unit for one side of the equation is $\sqrt{\text{PSI}}$ and for the other side is $\text{knots}$

In order to avoid hydroplaning upon touchdown (non-rotating wheels), the crews are often instructed to perform the so-called "positive landing" - meaning that you don't make a gentle (smooth) touchdown, but instead, a firm contact to the runway surface so that you immediately penetrate a layer of standing water on the runway. The use of ground spoilers increases the weight on the wheels to more easily penetrate the layer of standing water and improves braking capabilities, so the use of ground spoilers in this kind of situation is definitely desirable. Light brake pressure is advised in order to not lock the wheels.

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  • $\begingroup$ I agree the formula provides for the speed above which brakes should not be applied when landing on a wet runway. In my sleepiness last night, I debated using minimum or maximum. I can see your reasoning. I reasoned from the pilot perspective as the minimum speed required for hydroplaning to start or maximum speed I want to press on the brakes. $\endgroup$
    – wbeard52
    May 4, 2023 at 0:46
  • $\begingroup$ Yes, it is the same thing, just a matter of perspective, I hope I answered your question well! $\endgroup$
    – Darjan
    May 4, 2023 at 13:25
  • $\begingroup$ I thought it was great. Do you have a reference for the information, though? $\endgroup$
    – wbeard52
    May 4, 2023 at 23:34
  • $\begingroup$ Sure. The majority of the information is from the ATPL Book 12 - Operational Procedures. You can check any ATPL Book 12 from any provider (former JAA versions, current EASA versions, CAE, Oxford and etc, they will all have the same topic discussed. Some will go into more detail and some in less). The information is mainly provided from Chapter 21 - Contaminated Runways, subsection - Aquaplaning (Hydroplaning). Part of the answer is also written from my experience. $\endgroup$
    – Darjan
    May 5, 2023 at 9:57
  • $\begingroup$ Great. Thanks. I appreciate the information. $\endgroup$
    – wbeard52
    May 5, 2023 at 13:33

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