..on 2nd thoughts, isn't it a 50% accumulator? So 2-cycs to unity, 3 to 133%..
And MoI's obviously supposed to be kg/m² (kg-m²-rad/s is momentum). Whatevs. The same input workload buys the same amount of momentum for the same energy each cycle, in spite of rising RPM's, so plotting that flat trace across RPM's, the rotKE is inevitably going to intersect it after n cycles, and keep on climbing.. The no. of cycles to unity appears to be a function of the sum of the MoI ratio, so for 1:1 = 2 cycs, with a 50% per-cycle efficiency accumulator, for 2:1 = 3 cycs @ 33%, 3:1 = 4 cycs @ 25% etc. Suffice to say if real, it ain't dolphin-friendly.. but does it even work? On Thu, Jun 6, 2019 at 6:12 AM Vibrator ! <[email protected]> wrote: > Magic Roundabout > > > You're standing on the edge of a turntable, holding a heavy flywheel in > your hands. > > Beginning with both axes parallel, spin that baby up.. > > ..then rotate its axis 90° into the perpendicular plane. This exerts a > precessional torque, which is earthed through the turntable's rigid axis, > having no effect upon its current balance of momentum.. > > ..now brake away that counter-momentum in your hands, earthing the lot.. > > ..you're now stood on the edge of a rotating turntable, holding a > stationary flywheel.. > > ..flip it back to parallel and repeat the cycle.. > > > Simplifying, assume equal MoI's for both axes (ie. 1 kg-m²-rad/s each). > > Both the per-cycle input torque * angle and the resulting momentum yield > appear to be RPM-invariant; that is, the input energy cost of momentum > appears to be constant / invariant to system speed, whereas its rotational > KE is obviously squaring up.. > > For example, 10 purchases of 1 kg-m²-rad/s at 1 J each costs a total of 10 > J (this includes dissipating half the input energy per cycle). Yet 10 > kg-m²-rad/s divided by two 1 kg-m² MoI's gives them 5 rad/s each, and so > 12.5 J each, 25 J total. > > Using two equal MoI's, we find a 75% net loss after the first cycle, 50% > following the second cycle, 25% at the third.. we hit unity at the fourth > cycle, and 125% of unity at the fifth.. and efficiency keep rising by that > same 25% per cycle as we accumulate ever-more 'unilateral' momentum, at > fixed cost, its KE value squaring with rising velocity.. > > > Only thought this up 24 hrs ago but barely slept since.. where am i going > wrong? It's too simple! > >
