Much has been written about the height of waves, and as we approached the southern limit of our course and headed to the east, well below the parallel of Cape Horn, we got the full benefit of those constant westerly winds that blow around the world. Here the heaviest straight line gales are to be met with and the great fetch of deep water helps to produce magnificent waves of the first magnitude.
Lecky, in his "Wrinkles," a book no sailor should be without, and a book no lover of the sea who likes to "be up" on things nautical should neglect to read, quotes Mr. Thomas Stevenson as the authority for an empirical formula that approximates the possible maximum height of waves, the same being considered as a function of the "fetch."
This is given as a matter of interest, for working it backward it shows how tremendous the sea spaces through which the rollers that followed us had their being. The Stevenson formula is as follows:
Height of wave in feet equals the square root of the "fetch" in nautical miles multiplied by the constant 1.5.
Or, backward: the distance a wave has come equals its height, divided by 1.5, and the quotient squared.
As the wind increased in strength the waves mounted until immense billows were formed that measured from 50 to 60 feet in a vertical line from hollow to crest. This was easily determined by mounting the shrouds and watching until the ship was in the trough, then noting the height of eye on a level with the wave crests. In reversing the Stevenson formula we find that for a 60-foot wave a fetch of at least 1,600 miles is necessary.[8]
[8] Dr. G. Schott, as the result of studying the form and height of sea waves, claims that under a moderate breeze their velocity was 24.6 feet per second, or 16.8 miles per hour, which is about the speed of a modern sailing vessel. (Some speed!) As the wind rises, the size and speed of the waves increase. In a strong breeze their length rises to 260 feet and their speed reaches 36.0 to 36.4 feet per second. Waves the period of which is 9 seconds, the length 400 or 425 feet, and the speed 28 nautical miles per hour, are produced only in storms. During a southeast storm in the southern Atlantic, Dr. Schott measured waves 690 feet long, and this was not a maximum; for in latitude 28 degrees south and longitude 39 degrees west, he observed waves of fifteen seconds' period, which were 1,150 feet long with a velocity of 78.7 feet per second, or 46-1/8 nautical miles per hour. Dr. Schott does not think that the maximum height of the waves is very great. Some observers have estimated it at 30 or 40 feet in a wind the force of which is represented by 11 on the Beaufort scale (the highest number of which is 12); and Dr. Schott's maximum is 32 feet. He believes that in great tempests waves of more than 60 feet are rare, and even those of 50 feet are exceptional. In the ordinary trade winds the height is 5 or 6 feet. The ratio of height to length is about 1:33 in a moderate wind, 1:18 in a strong wind, 1:17 in a storm; from which it follows that the inclination of the waves is respectively about 6, 10, and 11 degrees. The ratio to the height of the waves to the force of the wind varies greatly.--_Scientific American._