The recent discussions about the loss of the Bounty and statements by her captain that she had previously survived 70 foot waves make the subject of wave height perception timely.
Here is a graph showing the wave heights that can be expected in various conditions:
You can see that 70 foot waves are rather improbable. We certainly would have heard about the storm that produced them if the Bounty had been in them. Because of their circular flow, hurricanes don’t actually produce extremely large waves but large and confused waves. Waves larger than 50 feet only occur in deep water in a couple parts of the globe where very strong winds blow in the same direction for days at a time.
Waves always look higher than they are and there are two reasons for this:
A lot of people looking at waves are nervous and scared.
This one is rooted in physics and explains how even an experienced mariner can report something shown to be so improbable by the graph above.
We first have to look at a little known aspect of wave physics. Imagine a vessel which sits flat on the surface of the water and rolls little such as a raft or an inner tube. Mount a tripod on this float with a plumb bob and watch it go over a very smooth swell. The plumb bob will not move but will continue pointing to the same place on the raft as it would in flat water. There are even wave tank movies of a plumb bob pointing straight up inside the curl of a breaking wave when the float is carried to the top.
Take a cup of water and swing it around with your arm so that you can keep the water from sloshing out. Once you have learned to do this so that the water stays in the cup even when momentarily inverted, watch the path your hand takes and you will see that it almost perfectly represents the path of an object being carried up into the curl of a breaking wave.
So, the down that you perceive in waves tends to be towards the surface of the water under you and not towards the center of the earth. It is the confusion in the brain that this effect causes which is at the heart of seasickness.
In a large and perfect wave, your perception of “down” as a reference point for estimating the height of the wave will therefore be like this:
You can see the difference between the height that you would report and the height that a device such as a weather buoy would report.
Most vessels roll and this further scrambles up the “down” perception. The way that you got your sea legs was by your brain learning to sort out the changes in “down” caused by the rolling motion and filtering out those motion effects. However, it does this primarily using the water surface as a reference. Once it thinks it knows where “down” is, it’s happy. When the waves get large enough that people ask themselves how big they are, the effect shown in the diagram above begins to effect perceptions and waves generally appear to be about twice as high as the actual vertical distance from trough to crest.