CENTRIFUGAL VERTICLE SPIRAL WHEEL.

The basics of this design, uses a pair of smaller spirals (slave spirals), The force applied by a mass, on the downward/outward ramps utilize centrifugal force, to rotate the main wheel frame with excess power.
the spirals in this version are Archimedean spirals, similar to MT 43, they expel 4 loads outwards as the spiral turns 360 degrees " one every 90 degrees".
( a 1 kg ball on this 1 meter radius constant ramp spiral is the same force as a 1 kg weight on a cord wrapped around 15.915 radius pulley "excluding the cord weight and friction).
A larger spiral with a 2.2 meter radius (the master spiral) is used to resupply the balls or (fluid).

The wheel would be horizontal, so that the system does not need a 2.2 meter spiral to keep the flow continuing in the slave spirals.

The calculations below are based on a vertical wheel.

The pair of the 2 meter diameter slave spirals, are attached to the main rotational wheel frame at a distance of 1 meter from the center axle.

The slave spirals turn in opposite directions, in this version they turn 2 times the speed of the main wheel frame.(gearing can be changed for different rotation ratios).
the slave spirals are connected to each other on the wheel frame by gears, one of these slave spirals central gears, connects to a stationary central sun gear.
the slave spiral gear rotates around the stationary sun gear.
The calculations below are based on the slave spirals turning 720 degrees on the wheel frame when the main wheel turns 360 degrees.
each spiral would eject 8 balls per revolution of the wheel.

First calculated a reference speed of 1G on a horizontal wheel in which the mass is at 1 meter from the center axle.

a mass at 1 meter distance from the axle = 1G when the wheel turns 29.91 rpm.

step 2: work out the centrifugal forces on a 1 kg mass when wheel speed doubles.
29.91 rpm = 1G
1 kg = 1kg

29.91 x 2 = 59.82 rpm
1 kg = 4kg

59.82 x 2 = 119.64 rpm
1 kg = 16kg

119.64 x 2 =239.28 rpm
1 kg = 64kg

If the wheel speed is at 59.82 rpm, the 1 kg mass, at 1 meter from the center main wheel axle has a mass of 4 kg. (on a horizontal wheel)

It takes 1.003 seconds to lift each ball at 59.82 rpm.

to lift 1 kg 1 meter in 1.003 seconds = 9.777 watts (slave spiral)
16 * 9.777 = 156.435 watts.

to lift 1 kg 2.2 meters in 1.003 seconds = 21.509 watts. (master spiral)
16 * 20.532 watts = 344.158 watts.

The slave spirals mass is at 4G, It actually increases as it travels down the spiral, it exits at 2 meters from the main wheel center axle.
4* 156.435 watts = 625.742 watts
the balls enter at 1 meter distance form the wheels centeral axle, but exit at 2 meters from the main wheel center axle. so the force when it exits is twice that of the entry point. if 150 cm was the average output the slave spirals output = 938.614 watts.

The slave spirals turn 720 degrees on the main wheel frame, when the main wheel turns 360 degrees.
The wheel now gets 2 * the torque.
The main wheel output =1,877.228 watts.

Power needed to lift the 16 balls = 344.158 watts.
output power of the main wheel = 1,877.228 watts.
output to input ratio = 5.454 to 1.

if the wheel still turns at the same rpm and the spirals are geared to turn 4 times the main wheel speed, this output ratio also doubles.
Ratio would be about 11 to 1.
if the wheel speed doubles, the ratio also increases.

The horizontal system would have a better input output ratio, due to either using a siphon system or a vertical spiral that has a smaller diameter, as it would not need to lift the fluid as high compared to the vertical system.

Is the math's correct ?
If it is, the system has great potential to self rotate with plenty of excess power to turn external systems.

Note: could not animate either balls or fluid traveling through the spirals.