44 



WAVES 



crest. But the angle along 15 feet of the steepest part of the curve 

 of a wave of this same height only 50 feet long would average about 

 20°, contrasted with about 12° on a direct line from bottom of trough 

 to top of crest (fig. 10) . 



lO to 1 wave ( BC = 1/5AC ) 

 Angle BAC = about 12° 

 Angle BAC = about 20° 



Figure 10. — Profile of a wave of trochoid form, 10 feet high and 100 feet long 

 from crest to crest, to show the angle at which a boat, 30 feet long, would be 

 pitched upward on the steepest part of the crest. 



Thus, a small boat would be pitched upward at about three times 

 as steep an angle as it mounted the crest of the shorter wave than of 

 the longer, whereas the slope would be only twice as steep in the one 

 case as in the other if it depended solely on the linear dimensions of 

 the wave. It is largely because of this relationship between length, 

 curvature, and slope that relatively short waves — even if well-rounded 

 — may cause small craft to pitch so sharply, and that a "chop" is so 

 proverbially uncomfortable for small-boat navigation. 



A trochoid approaches a sine curve in shape if its height is small 

 relative to its length. But the crests become narrower and the troughs 

 relatively longer if the height is large, relative to the length (i. e., if 

 the wave is steeper). If the ratio of length to height decreases to as 

 little as about 7:1 (steepness about 0.014) so that the angle at the 

 crest increases to about 120°, the wave becomes unstable ( fig. 11) . And 



Figure 11. — Theoretical profile of steepest possible wave, according to Stokes 

 and Michell. (After Sverdrup, Johnson, and Fleming.) 



when the crests approach this angle of instability, they tend to be- 

 come cycloid in form and therefore very much steeper toward the top, 

 as anyone can see who watches the seas in stormy weather. Waves 

 cannot continue to advance in this shape, but break at the crests, 

 thus losing in height and consequently in steepness as described on 

 page 19. 



Very few actual measurements have been made of the profiles of 

 waves. But considerable material is available for such, from pub- 

 lished stereophotograms. And these show that the crests of high, 



