Freedom-movement
Based on that second falcrum, here called rotor-axis (RA), the process of movements will have additional freedom.
Next position of a mass-point (MP) thus is not only determined by turning around the system-axis (SA), but also by direction and value of inertia of that mass in each moment.
Only if a pendulum does have more than one arm, thus inertia may contribute to speed and direction of movements.
The picture of ´Sling-effect´ above, here once more is shown.
Here however, only few positions (A to E) are drawn. Thick lines mark the position looked at, thin lines mark the previous position. From the last-but-one to the last position, inertia linearly is deduced (thick black line).
Positive combination of forces
Later on (at B) the pulling power necessary, will come right-angle towards the rotor-arm, while the old inertia-direction shows nearby parallel to the rotor-arm. But even here,
the resulting line of inertia and pulling power is longer than each of these two forces.
When the rotor did swing out even more (C), the vectors of both forces will be added.
A sling-unit practically will be a two-arm lever-gear or pendulumm (RT+RO), while a normal wheel will show but one lever-arm. Compared with a fix rotor-arm (like a spoke of a wheel), by two-arm sling-effect with less input of power, conciderable higher end-speed of a mass-point will be achieved.
At the begin of movement (A, resp. before A), the system has to pull (red thick line) and nearby same direction, given inertia will move the mass further on. Both movement vectorially will be added to the motion in toal (thick green line). That new motion will be faster than the old (speed of inertia) and will be fare above the power input of the system (only normal to the rotor-arm at a short lever arm).
So, after D, speed will no more be increased - so, here a throwing man should release the missile.
Later on (at E), inertial speed even will be reduced. The rotor of a sling-unit like this, so will stay at a ´lean-back´ position - like a whip normally will be curved backwards.
This will say, only at that phase of swinging-outwards, input forces of the system and these of inertia of a mass-point may be added vectorially to a motion of higher kinetic engery. At the relation of length of rotor-arm and rotor here, that phase will take about 180 degrees turning of the rotor-arm and a maximum turning of but 135 degrees by the rotor.
Free and / or fix
A free swinging pendulum afterwards will come to a status comparable with a normal wheel with fixed spokes (F). There, turning-speed and inertial-speed (resp. power) automatically are same, however inertia showing tangential outwards. Thus, the spoke has to do some work, must force a mass-point centripedally to its next position. This work however, will bring no more increasing of kinetic energy - thus, a fixed wheel is a ´dead´ system (while a spiral-track-system means ´life´.
The conciderations to Sling-effect above, brought the essential knowledge, that the ideal track of a free swinging pendulum, nearby perfectly can also be achieved by a fixed gear: by a rotor truning relatively backwards a quater. So, to a mechanical rotor-system, at the phase of swinging-out of mass, that addition of forces above also will be valid. So that high kinetic energy can be achieved by relativly low input power - cause additionally powered by (no-cost) inertia.
However, after that phase of swinging-outwards, also a rotor like this will come to a status like a fix wheel, will say, the mass-point again has to be pulled inwards. Felix Würth tries to earn the additional energy by finally slow-down of the system.
Consequenceseither but to use that positive swing-out-phase (so, the pendulum or rotor-arm may not make full turns, but must swing back),
or to reverse the relations of forces at the inward-pull-phase by an additionals, ´inverse´ pendulum.
Both will demand new principles of motions, which based at analyses of that crop circle picture, will bring quit new concepts of swinging systems.
Evert / 20.11.1999