Derivation aside (if you like I’ll provide one), the following should give you some feel for the amount of deceleration that is possible. The formula is approximate,
(Change in forward velocity of wave-form) = (1/2) * square-root(g / h) * (change in water depth h),
where g is 32 ft per sec squared. If we measure everything in feet and seconds, the formula approximates to,
(Change in forward velocity of wave-form) = 2.8 square-root(1/ h) (change in water depth, h)
So, for a gradual bar, going from a depth of 10 to 9 foot (in one second), the above gives a change in the velocity of the wave of -.89 ft/sec. ( about -0.6 mph)
But for a more rapid change, going from a depth of 10 to 5 foot (in one second), the above gives a change in the velocity of the wave of -4.5 ft/sec. ( about -3 mph)
In the first case, the change would appear virtually imperceptible to the observer, and maybe surfer too. But in the second case such a deceleration is unlikely to go unnoticed by the surfer, or at least felt by the surfer. Whether or not he realizes that the wave is decelerating is another matter.
Under more extreme cases when the wave runs over a deep ledge, or reef the wave can almost appear as if it stopped and simply 'jacked". (Please consider keeping this in mind the next time you or you see someone upon take off seem to loose all contact with the face - or be seemingly ‘launched’.)
That said, I’ll like to take a small degression.
Implications for design.
The amount of deceleration, as mentioned in my post “The Decelerating Wave-Form”, is different for different regions of the wave - greatest near the curl, less so out on the shoulder. Which suggests there is a transition from greater to less, moving from curl to shoulder. It then follows that if you’re moving transversely across the face, that different sections of your rail are also experiencing different decelerations. In particular, if your tail is closest to the curl, the forward wetted rail (farthest from the curl) is experiencing less of a deceleration than the tail section of the rail (and tail itself).
But as also mentioned in the post “The Decelerating Wave-form”, the upward flow on the wave-face is also different, this time greatest in the curl region. So it follows that this upward flow is also different in the tail region than on the more forward regions of the rail.
I won’t continue with this here as its not the topic of the post, but it did seem to be an opportunity to offer up some numbers and introduce design into the discussion, though admittedly, probably unnecessarily. There’s also the other fact that a total of zero people have actually read my post “Rails Plane” (which probably should be telling me more than I care to take from it). But when you start putting this all together in the context of design, you wind up with a curious approach to rail design. based on what is actually happening. That rails can operate as hulls, but require an asymmetric treatment -i.e. an asymmetric hull approach. Which was going to be a follow up post to “Rails Plane”, which would have likely met with the same faith as the original post, so I thought I mention it here - totally selfish, my apologies.