Overlapping Paddled Wheels

Question

I am trying to create two paddled wheels overlapping each other alternately. Figure looks something like this.

And the rotation phases would be like:

Since the position of those paddles are a little bit off, though I'm not an engineer of anything, I knew the balance will also a bit off. Correct me if I'm wrong.

What I am thinking is to add additional paddle of maybe 1/3 of the 3 main paddles. I want it shorter since I don't want it to get involve in the interactions of 3 main paddles between those 2 wheels. This will serve as a compensation to balance out the rotation of the wheels.

Can anyone give me a formula to calculate where should I put the compensation paddle and the length & weight of it to balance out everything?

PS: I'm not an engineer of anything so I'm not sure if this design is possible and will work in the real world. I am just trying to experiment with something.

EDIT: These are the problems that I wanted to be solve:

1. Unbalanced Mass Distribution: If the paddles are not evenly spaced or are angled differently, they can cause an imbalance. This imbalance can lead to vibrations, uneven wear, or strain on the wheel and its bearings.

2. Centrifugal Force: When a wheel rotates, the centrifugal force acts on the paddles. If the paddles are at different angles, the forces might not be evenly distributed, potentially causing wobbling or instability.

3. Torque Imbalance: Paddles at different angles can create varying amounts of torque as the wheel rotates. This could affect the performance of the wheel and any attached mechanisms, particularly if precision is important.

4. Dynamic Imbalance: As the wheel rotates, any imbalance in paddle positioning can result in dynamic imbalances, leading to further issues like shaking or difficulty in maintaining a steady rotation.

Possible Solution: Implementing Compensating Paddles

1. Placement:

• Opposite Main Paddles: Place compensating paddles directly opposite the main paddles. This helps balance the wheel by distributing forces evenly.
• Calculated Positions: Alternatively, place them at specific angles based on the main paddles' positions. For example, if the main paddles are at 0°, 120°, and 250°, place compensating paddles at angles where they can effectively counterbalance the forces.

2. Length and Size:

• Short Length: Making them shorter ensures they do not interfere with the operation of the main paddles. Their primary function is to add balance rather than interact with the main components.
• Weight: Ensure the weight of the compensating paddles is sufficient to counterbalance the imbalances but not so large that it affects the overall performance of the wheel.

Sample figure with compensating paddles:

How can I calculate for the position, length and weight of compensating paddles?

Answer 1

First: You can't have three paddles that alternate above and below just by an offset of angle. You would have to have a complex gearing system that constantly changes the relative speed of rotation. Call the paddles A,B and C.

A - above
B - below
C - above
A _ ????. A is designed to be above - but sequence requires it to be below.

You would need an even number of paddles.

Second: Why would you want to have the paddles alternate above and below? Unless you have some very compelling reasoning for that, why not just set all the blades at $120^o$ separation and leave it a that? Save a lot of trouble.

Third: You can do this with four paddles. Unless the rpm is very high you won't need to worry about vibration, load etc. Think of the paddles on a paddle steamer, most of the paddles are out of the water with no load. Those in the water have varying loads depending how deep they are in the water. Of course, these wheels turn very slowly. Whatever it is that the paddles you are designing are to do the load on the paddles, and therefore the axles, will vary as they rotate. Don't see the value in trying to balance the loads with additional small paddles.

Almost all machines that are converting rotating motion to linear motion or vice versa have loads that are not balanced around the axle during any one cycle. In the extreme example of an ICE like as in an automobile engine you do need to have balancing because of the tremendous force at one moment at one position during ignition/expansion. This will not be the case with any type of paddle wheel motor/generator. There is no sudden increase in load.