Pressure on the outer hull of aeroplane on theoretical emergency landing

I'm trying to figure out the proper way to calculate the pressure on the hull of aeroplane when landing on water.

Let's say the horizontal velocity of plane is $$1000$$ km/h and it starts free-falling from $$10$$ km.

First I though it can be calculated simply:

$$p = \rho_{\substack{H_2O}} \cdot v^2 / 2$$

This would result roughly $$p = 5\cdot 10^8\, \mathrm{Pa}$$.

However I think I'm using a 'wrong' velocity, since the plane is also free-falling from the sky. I'd think that since plane velocity from the free-fall depends on gravity, the initial altitude of the plane must also matter.

• Are you asking about an emergency landing or a free fall into water with the wings broken off? These are very different things. – noah Feb 23 at 17:21
• This is a very complicated problem that requires more specification. If the wings are still present, your aircraft is not effectively in free-fall because the wings are generating lift as the aircraft moves forward with some velocity. What you have calculated is the dynamic pressure of an object moving at the corresponding speed. – GodotMisogi Feb 23 at 18:02
• GodotMisogi and noah thanks for the comments, those things never really occured my mind! I guess freefall without wings is the screnario I'm looking for. – MarikH Feb 23 at 19:16