Here i'm zooming in on a two-cycle run, again omitting the first cycle to preclude any startup noise, beginning the measurement from the start of the second cycle at the frame below:
The energy results of that single cycle are as follows:
iKE = 1431.87368072
fKE = 1491.90812646
dKE = +60.03444574
kPt = 56.99851084
fPt = -34.50538244
net in = 56.99851084
net out = 94.53982818
diff = +37.54131734
CoP = 1.66
Immediately it becomes apparent that when using the other method, controlling the actuator for 'velocity', this smooths over the sharp dyke in that saw-tooth transition.
Thus it appears that the 'more conservative' result was actually due to a lazier reaction from the actuator, the latency inherent to controlling the actuator's velocity rather than its specific length.
The gain is thus not refuted by the counter-example as it's simply skidding over the gainful torque transition, missing the opportunity. Controlling for 'length' produces this more-immediate response, tracing a more-detailed interaction.
Let's examine each stage of the flywheel interaction in respect of the kiiking action it's responding to. It's basically a four-stroke cycle - spin up, spin down, then repeat in the opposite angular direction.
Remember, the spin-up code on the weight motor controls for 'velocity', using the sine of the secondary armature angle as a multiplier for the target spin-up speed, such that it reaches a maximum of '1' at 9 o' clock and '-1' at 3 o' clock, fading smoothly up and down from '0' at the 12 and 6 o' clock positions. The target speed is
relative, hence the applied acceleration is shared between the absolute velocities of the weight and secondary armature.
So here's the first stroke:
The weight motor is performing work spinning up the weight, and so applying the counter-torque that's resisting the weight's fall under CF force, slowing its descent and so increasing its time spent under this G-force's constant acceleration, boosting the drop's effective momentum yield.
In parallel to this action however, the flywheel actuator begins the cycle mid-way through an
output stroke - it's in the process of extending the flywheel's MoI, braking it against some source of positive torque whilst harvesting KE into PE..
Since the weight's distance from the central axis is increasing, it must be applying negative inertial torque, which would require the flywheel to accelerate in response, so whatever the source of this positive torque it is more powerful that the negative torque corresponding to the widening MoI.
Yet this torque is also in the same direction that the weight is being spun up - the counter-torque from which is in the opposite direction, albeit now being sunk to CF force and time.
There is only one remaining moment that could account for this positive torque component: the weight's orbital axis, ie. the kiiking (green) axis; the counter-torque from spinning it up is also decelerating its orbital velocity, and so the positive torque being countered and harvested by the flywheel actuator during this stroke can only be the counter-torque corresponding to this orbital deceleration.
In effect, the gainful interaction begins in the process of harvesting part of the previous cycle's energy gain (or priming energy, whichever precedes).
So we've identified part of where our positive torque's originating..
in the previous cycle. The area under the curve below the zero line is PE in the bag.
Let's go on to stroke 2:
On the left side we see the weight decelerating back to stationary relative to the secondary armature. This recoups much of its KE back into PE, whilst transferring its axial AM into orbital AM on the kiiking axis.
On the right side we again see more harvesting of flywheel KE into PE as the weight reaches maximum extension having expended all of its CF-PE. Again it's notable that this increase in MoI on the primary axis
hasn't required countering by a positive torque from an MoI retraction on the flywheel, its actuator instead extending to brake against a more-powerful
positive torque, harvesting more PE.
Since the kiiking axis is now accelerating and in the same direction as the primary armature, the source of
this positive torque can only be the counter-torque from de-spinning the weight.
Moving on to stroke 3:
The weight motor is back under positive load, spinning the weight up the other way. The resulting counter-torque is accelerating the lifting phase, reducing the dwell time under the G-force's constant deceleration and so minimising the momentum being shed back where it came from.
Again however, instead of seeing the flywheel actuator extending to counter the MoI retraction from the inbound weight, it initially retracts, adding positive rather than negative inertial torque - again, apparently the ice-skater effect is being overpowered by the counter-torque from spinning up the weight..
..only after this spin-up phase completes, its counter-torque ceasing, does the flywheel MoI begin extending in response to the narrowing MoI on the primary armature, ending the stroke with more harvesting of PE.
On to the final stroke:
The final de-spin recoups further PE on the weight motor, the counter-torque from deceleration of the kiiking axis / secondary armature once again overpowering the inertial torque from the retracting MoI on the primary armature, hence the flywheel actuator pulling its MoI back in, until the weight's de-spun and the positive inertial torque from its retraction is finally felt and countered, delving into that last scoop of KE to PE from orbital braking torque that begins the subsequent cycle.
This might not be the most accurate or exhaustive of analyses but the gist of it seems to be that at every step, the mechanism is operating consistently - some of the PE gain on the central axis (active flywheel
or motogen, since these results seem to corroborate those) is being harvested from axial counter-torques, others from orbital, seemingly flipping between them in opposite quadrants.
A juggling act of axial and orbital counter-momenta thus seems to be key to the gain mechanism, as indicated by earlier analyses.
The foundation of the energy asymmetry is the divergent inertial reference frame generated by the I/O ±dp/dt asymmetry; making momentum (and thus energy) from inertia a game of differentials.
The most concise root of understanding remains the internal FoR, equivalent to kiiking under gravity: we have an
ideally time-constant rate of exchange of momentum, here provided by an actively-regulated G-force in the form of CF force, and a
time-asymmetric inbound versus outbound ±dp/dt with corresponding non-cancelling yields, accumulating under conditions of inertial isolation from the environment as an effectively unilateral acceleration of the FoR of the input-energy workload, the KE gain equal to the half-square of the inertia times the 'velocity' component of the anomalous momentum delta. Yup,
that old cliché.
I guess the next thing to do is probably go back to using the motogen - doing it this way is just masochism if unnecessary - checking off the internal reactions in the same way whilst tabbing up the energy evolution. I honestly expected the active flywheel to circumvent some bug in the motogen metrology but instead we're seeing independent corroboration of a consistent effect.. the initial impression of a tendency towards unity an inadvertent result of the laggy flywheel actuator control code failing to replicate the instantaneous responsiveness of the motogen.
What sufficiently-responsive active constraints are showing is that there's a physically-consistent chain of causality throughout the interaction. Nothing is bugging out. CoE is broken, because CoAM is.
