You haven't added any power by swinging the handlebar. And if your legs are already pushing as hard as they can against the pedals, then increasing the load they have to fight against will only slow down your cadence while adding no power.
Adding to what Ed said above, what we have in 'boom swinging' not unlike oval chainrings... which you don't believe in too, right
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But Ed tried Rotors and got pretty astounding results if you ask me. I actually have a set as well myself, but I cannot fit them to my bent... I'll need to test them objectively to see whether they work for me with power meter (at least on a trainer) and maybe have them shortened which is no small feat because they are heavily CNCed.
Remember, that unlike with a linear drive, using pedals results in a continuously variable leverage ratio where in some points extra pressure is extremely advantageous, and in others - completely useless, and speed/force of your muscle contraction is complex function with certain optimums + there is muscle synergies to consider! And again, this is not motivated reasoning - we are trying to explain data we seem to have (like in case on Ed and rotor cranks - I presume that Rotor cranks is not an investment significant enough to go to such length to justify it), not trying to arrive to a favourable conclusion, and conclusion is 'seems plausible, more research is needed'.
Personally, marketing 'boom swinging' in particular as something that can grand you huge, DF-like spring powers may be a bit misleading, but I don't think Cruzbike go as far. In fact, as you well know, real sprinting power comes from fast twitch muscle requirement at high cadence, and track spinters generate their nearly 4 HP of watts while sitting and spinning huge cadences - and not just because their bikes are geared pretty low and rocking the bike with, like, 300 Hz is likely impossible, but it certainly *feels* *somewhat* advantageous. Untill we have a real model of what is going on (with clearly defined causes and effects) I'm trying to keep an open mind.
P.S. 'Road bike geometry' *is* pure marketing, and here I indeed have models and concrete proof in terms of prototypes, but admittedly 'looking good and familiar' on an ad might help them sell more bikes that geometry that works better in practice but looks weird...
Plus, like I said on other forums, if your bike is sufficiently controlled in all conditions for you, improving on it is useless and may compromise other aspects (even if those aspects are "just" aesthetics). What I'm a bit peeved at is that models that are not intended for high performance and geared for 'accessibility' in general can massively benefit from much steeper steering angles and would not appeal to 'dyed in the wool DF racer' anyway, so bending over backwards in that area is useless anyway.