You misread Gerble’s post. He said “statics,” as opposed to dynamics. Your first-order-estimate of the rider - unicycle system was done with static equations, while the problem at hand involves dynamics.
Your statement about “everything” being solvable with scientific reasoning is only accurate in cases when every variable about the problem is either controlled or measurable. In the case of a uni rider doing a hop, there are other first- and second- order variables that you do not take into account in your analysis.
Your reasoning only stands to demonstrate that you do not have a full grasp of the problem at hand. The energy calculation you’ve made assumes that the motion of the unicyclist is completely reversible, ignoring the second law of thermodynamics. Energy is lost due to friction, drag, compression, etc.
Actually, to claim that equipment makes a difference based on an arguement of handwaving, generalization and pontification is foolish. What kind of difference are you looking for? What is this “more control” you’re talking about? Maybe, what, a 1% difference in dynamics? That’s not “more”… I claim any of the “mores” you’re barking about are washed out by statistical fluctuations in the rider’s performance and I dare you to prove otherwise. (Edit: there is no such thing as “all else being equal” in this problem)
If I could pedal grab onto a planter box with a 12 lb. unicycle and also with a 15 lb. unicycle, what’s the difference? If Gerble could rolling hop onto a loading dock with the same two unicycles, what’s the difference? If Joe Schmoe enters a unicycle high-jump contest and clears the bar by 1" on a 12 lb. unicycle but only clears it by 3/4" on a 15 lb. unicycle, what’s the difference? Insignificant… just like everyone’s scientific arguements.
You can argue physics until you’re blue in the face, but the proof is in the rider… the unicycle ain’t going to hop itself.
P.S. If you’re still hell-bent on being a “weight weenie” then read this thread and let us know how your new ultra-light unicycle helped you hop 1/4" higher.