Thank you so much for your thoughtful reply. I really appreciate you bringing physics to your explanation. As a physics minor, I’m actually a bit embarrased I didnt think it all the way through.
(chuckling) Thaks for the kind words- I was once a tutor, several subjects including physics. And once started, it never leaves ya. In any event-
My thinking was very shallow just imagining a shock load to the leash plug from the leash pulling back from the attached rider at an angle more than 45 degrees relative to the board. You thought it all the way through with the spring constant (k) reducing the Impulse = F*(deltat) = F(kdeltax)deltat. Furthermore, the force of tension in the leash more often than not is being applied close to parallel with the board. All of these things factor in. Another thing I didn’t consider that the board and rider generally fall in the same direction, Newtons first law. It’s rarely the case the full force of the wave grabs the board and takes off while the rider is at rest underwater. And also even if that were the case, as you mentioned the elasticity of the leash would factor in and and the leash pulling parallel to the board would factor in.
Well, if you think of the leash as a simple spring or something elastic, it kinda jumps at you.
Now, springs are modelled as a straight linear function, but really when you get to the liimit of the stretch it has, elastic limit if you like, the force per unit extension goes up, in fact K for a lot of things is a function of X, consider say a bow or something like that. F=kX^n, perhaps. But you can just go with F=Kx for a given F, work off a table or whatever.
And, you don’t want to overcomplicate anything either. All you want to consider is the board relative to a fixed point for this particular problem. The water pushing it away makes for a certain force on the board and there ya go. Now-
The first and only time I’ve broken a leash happened with a longboard and the context is very telling. I was riding a 10’ Takayama Model T glassed to the hilt with a drill box leash plug that went through the whole board and the knot was tied off in the fin box. I’m not seeing the entire fin box getting yanked through the board as a probable outcome, in contrast with a shortboard with a cup plug The thing feels like it is 30 lbs carrying it down the beach. Anyway, I was paddling back out one day and punched through one wave and continued on when a really fast wave right behind it was jacking up and getting ready to pitch right on my head. The last thing I wanted was to have a lip detonate on my head with that heavy 10’ board so I threw it away from me (no one was around, surfing alone). I dove underwater after I threw the board. That wave grabbed the board and took off like I had my leash tied to a dump truck. That leash broke like it was made of fishing line. The shock load of it was way too much since I was basically at rest underwater and the board was accelerated very fast in a short period of time. So with I = F*(deltat) = (ma)(delta*t), the mass (m) of the 10’ log being way more thank a potato chip short board comparably and probably a larger acceleration due to the larger volume for the waves to act on the board and pull on it, the impulse spikes big time.
Umm, I wouldn’t be all that concerned with the mass of the board. The area of it, the water resistance, yeah, definitely. You have, in the case of a 10’ board, a whole lot of area, which the wave takes and whoosh, there ya go. And yes, a lot more area and resistance than a short board.
On the other hand, lets say you stood on a 10 meter diving board with the very same surfboard and attached the leash to something and threw it down, like a spear, as hard as you could. Film it,or video it, see how much extension of the leash you get and how long it takes to where it’s starting to stretch the leash- v=vnought plus gt. Or, if you like, a bucket of something that weighs the same as the board. Same deal. It’s a momentum problem. f=mv.
Now, experiment 2. If you take, say, a fishing scale or similar. attach the leash at one end to something solid and start pulling backwards. Start recording what force it takes to stretch the leash a given distance. Give you an idea what it takes to stretch the thing a typical distance.
I don’t think the leash was snapped, by the way. Stretched to it’s limit fast, yeah. May have had a nick in it too. And it snapped.
I realize I’m geeking out here, but it’s fun. I’m sure there are several other factors that could be explored, but you captured the essence of it. Thank you again for the break down. I guess I was just so fixated on this cup plug being being blasted by a leash pulling back on it, I figured it shouldn’t stand a chance of staying in. But that is a lame excuse for not thinking it through. Sorry for being lazy, I don’t know what the hell is wrong with me.
Heh- it is really easy to overthink something. Among my many faults, it is. But don’t look at it like a physicist, it’s an engineering problem, good approximations are fine, a little testing and measuring and see what you can draw from it all. ‘Surf science’ is a bunch of handwaving, after all.
Have fun
doc…