What math are you talking about? The only math I saw was in the comparison of paddling work to work lifting a boat. Not particularly relevant, to my way of thinking, but not flawed (except for comparing the work of the paddle, which is simplistic and not correct).
On the other hand, the description of the difference in paddling a 14 ft vs. a 17 ft hull being dependent on the distance the water must be pushed out of the way and how long it takes to do so is just kooky talk - which is to say it is definitely not correct. The drag numbers tell the whole story - they incorporate the effect of the hull having to push the water out of the way, form drag, wave drag, friction drag, etc.
PS - about the paddle calculation - I call it simplistic because it doesn't take into account the rotational movement and weight distribution of the paddle.
Do you not understand why drag matters? I'm sure you do, otherwise you would be paddling around an old door or a telephone pole. Perhaps you don't find it interesting - so be it, but there's no reason to imply that we're wasting time and energy.
Length vs Resistance graph Here is a graph showing the Kaper resistance of a boat design of different lengths with the same displacement. Computer generated hull, then the software changed the length of the hull, keeping all other aspects the similar. Obviously when the length changed other factors change too but they are minor. I don’t think it is possible to change ONLY the length. But this is about as close as you can get to that.
You can see short has the advantage till about 4 mph then the longer boats start to have the advantage. Of course this doesn’t mean these are pratical boats. Matter of fact the 13’ foot is rather unstable. So in the real world, it would be wider and mostly likely slower than this chart shows. The purpose of this was to see what happens when the length changed and you can clearly see the effects. There was no attempt to make the boats practical.
