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Hello MrVibrating,
So it seems. This logic is irrefutable, until it is.Working backwards from first principles (deductive logic), is the only possible route to a solution; the only way out of the '1+1=3 ?' conundrum.
Moderator: scott
So it seems. This logic is irrefutable, until it is.Working backwards from first principles (deductive logic), is the only possible route to a solution; the only way out of the '1+1=3 ?' conundrum.
in a round-about way, yes. Also, the tests aren't a SIM. I no longer use wm2d. I do my own maths. Feeds my delusions. :)Is it just me or are you actually getting mechanisms that are increasing speed on their own? I know it's a sim, but well done on the ideas. Cool stuff!
MrVibrating wrote: ↑Sun Nov 05, 2023 4:37 pm Spent some time this morning investigating which type of mechanism may be optimal for kiiking under CF, as opposed to gravity.
Under gravity, the simplest solution reduces to a balanced variable moment of inertia, plus an unbalanced weight:
However the counter angular momenta of these swings seems likely to interfere with smooth application of OB torque from the OB mechanism.
One obvious problem may be the counter-momenta from swinging these weights in the first place - clearly, if a linked pair swing in the same angular direction each phase, their combined counter-momenta will have a significant effect on accelerating and decelerating the wheel. But even with counterposed angular directions, there's still hefty exchanges of angular momentum:
From a 1 rad/s push-start and then left to coast, speed almost halves from the swings' MoI variation.
An additional issue is that in order to optimise the excursion / stroke length under CF force, the radius of these weighted vMoI's needs to be half the wheel radius; this in turn means that as the weights swing upwards, they may begin to encroach on the center, where CF diminishes potentially to zero. All else being equal, this is likely to result in chaotic sync between multiple sets of swinging members as the system attempts to relax into its max-MoI, min-KE state:
With two pairs of counterposed swings the RPM's are more stabilised, but one pair ends up hogging more momentum than the other.
It looks like things could be stabilised further by gearing the two pairs to force sync; besides, these are just passive swings without vMoI's - actively pumping them, and then harnessing the resulting inertial torques to accelerate the rolling OB system, will add another layer of regulation.
However there are many different ways of 'kiiking', which simply reduces to controlling I/O ±G-time symmetry; spending more time under gravity's constant acceleration than deceleration per cycle, albeit reactionlessly; without applying force or torque to an external inertia or ground.
One alternative method could be to attach a weight with a high MoI to the edge of the wheel via a motor, then, as the wheel lowers the OB weight, spin it up so that the counter-torque slows the descent, increasing positive G-time. When rising again decelerate or brake it, thus accelerating the lifting phase and cutting negative G-time. The weight's spin thus oscillates, spinning and braking as it rises and falls, and causing the wheel to gain momentum from G*t each GPE cycle. Here's what that looks like:
So from a 1 rad/s push-start, all further momentum is gained from G*t, via this up vs down time asymmetry. That's all kiiking really is - performing some workload to purchase momentum from G*t, in an otherwise closed system of interacting masses. 'Kiiking' = 'gaining statorless momentum'.
But what works well under real gravity isn't necessarily optimal when operating under CF force; hence why i suspect kiiking with a linear action may be the way to go here:
This seems objectively better, insofar as eliminating the unnecessary angular component of the weight's motion. A single vMoI could be cranking two or more masses in and out on opposite sides of the wheel, and with two such sets for a total of four weights, the two shared vMoI's could counter-rotate, further minimising stray counter angular momenta from interfering with the rolling OB operation.
So the next problem to be solved is the issue of a ratchet and pawl mechanism; suffice to say i don't intend to model the clunky vagaries of a real one, so much as to simulate a simplified one-way bearing - a conditional constraint that clutches when torqued in one direction, and slips in the other. Once that's sussed i'll be ready to string together a complete mechanism, using inertial torques from pumping CF swings to progressively accelerate the OB system..
They're demonstrating different means of gaining momentum - from gravity and time, in an otherwise-closed system of interacting masses. In other words, this is only possible because gravity's there - otherwise, N1 would apply; all else being equal, you cannot alter net system momentum via the internal expenditure of work. Momentum of a closed system's constant, unless acted upon by an externally-applied force. But even then, N2 would apply - F=mA - implicitly precluding unilateral forces and hence implying some other external inertia against which to apply that force; N3 thus applies and this 'external' inertia is really internal and part of your new, larger closed system. Hence this ability to source or sink momentum from or to gravity and time, while a trivial trick we all learn on the park swings as toddlers, is actually an interesting edge-case scenario in the laws of motion. For similar reasons, OB torque is, in and of itself, dangerously close to a kind of reactionless torque. Again, a reactionless rise in momentum has the potential to be OU; throw a 1 kg projectile at 1 m/s without recoil while coasting on skates at 1 m/s and you've created 1.5 J of free energy. Unfortunately for us, G-time and thus the amount of acceleration and thus momentum gained per cycle decreases inversely to RPM under basic over-balancing schemes, and it is these diminishing momentum returns per GPE lift with rising RPM that effectively enforces CoE in these systems. Hence the goal of regulating per-cycle momentum gains independently of wheel speed.
We all know it isn't that simple. The swinging weight has to be decoupled from the weight it lifts. When it actuates the other weight to lift it, it loses energy and doesn't rotate as far, requiring itself to be lifted to a reset position.We know a fast moving mass has zero weight at the top of the arch.
It is believed the bottom mass to be double it's weight. By the nature of it's swing.