How large a wave would be generated from a 50 mph wind, with a 1420 mile fetch, over a 69 hour period be?

Question

How large a wave would be generated from a 50 mph wind, with a 1420 mile fetch, over a 69 hour period be?

Answer 1

A wind of that force would mean a Beaufort force 9 severe gale. The average wave height would then be perhaps 7 meters after 8 to 10 hours of constant force.

The thing is: wave height are very much depending of the depth and eventual current. Wind against current creates deep high waves. Shallow water also increase the height of the waves.

I have myself experience in 1975 in a depth of about 30 meter, in a mini-submarine, that a sea of only two meters is still felt at the bottom.

Your fetch of 1420 miles is more than enough to see a well formed train of waves. Your period of 69 hours is also more than sufficient. But in real life, you will never see the wind blowing at a force 9 for 69 hours in the same direction. The fear of seafarers is exactly when the barometer starts to climb again and the wind veers as the cold front is passing. Then the waves crosses, creating freak waves that can be twice the height of the average.

For your information, the usual calculation of the speed of waves in free water is the square root of their lenght in feet, multiplied by 1.34 gives the speed in knots. That's what yacht designers use to calculate the so-called displacement speed a.k.a the hump. At that speed, a vessel pushes a bow wave and pulls a stern wave. To exceed that and come to planning speed, it needs to climb the bow wave, something that requires power and hull shape aimed at that.