Water wheel and hydroelectric power question

[Pinon1977]

Homework Statement

What type of water wheel is better: even or odd number of moment arms?

Relevant Equations

Not sure

So I'm trying to determine what the advantage would be using a even or odd number of moment arms respective to a water wheel and the torque that it can produce. Part of me wants to say that the odd number armsvwould be best because you would not have an equal opposing Force from the moment arm being utilized. Please see the sketch. As represented by the center line in the three arm waterwheel, there is nothing opposing the force ( Falling water) that's pushing down on the right side of the machine. However, as you seen the 4 arm water wheel, there is the continuation of the arm which, in my mind's eye, we cancel out some of the downward torquing effect. Maybe I'm way off base here.

 

[haruspex]

I would expect (given the design of the wheel in all other regards) there is an ideal number of blades, not necessarily odd or even.
What makes you think the parity matters? Is this an exercise given to you or just curiosity?

 

[phinds]

Why would either of those be better than a standard water wheel:

 

[Pinon1977]

I would expect (given the design of the wheel in all other regards) there is an ideal number of blades, not necessarily odd or even.
What makes you think the parity matters? Is this an exercise given to you or just curiosity?

It is an exercise I have given myself. I am going to build one of these configurations and I'm trying to figure out if there's any logic behind my hypothesis.

It just seems like there would be more have a propensity for the system to become overbalanced on one side or the other with an odd number of moment arms.

Now that I'm thinking about it every windmill that I've ever seen is that three blades on it. That may be for other reasons rather than to work. I'm not sure.

 

[Pinon1977]

Why would either of those be better than a standard water wheel:
View attachment 328282

Good question and good point. I am in search of a new design configuration that would be more efficient than the aforementioned the design.

 

[haruspex]

seems like there would be more have a propensity for the system to become overbalanced on one side or the other with an odd number of moment arms.

So long as the paddles are evenly spaced, it will be perfectly balanced regardless of the number.

 

[haruspex]

Good question and good point. I am in search of a new design configuration that would be more efficient than the aforementioned the design.

There are many designs for different situations.
https://www.alternative-energy-tutorials.com/hydro-energy/waterwheel-design.html
https://en.wikipedia.org/wiki/Pelton_wheel

 

[BvU]

every windmill that I've ever seen

and boy, have we got a lot of those. For centuries already

Seems the French have them too

$\$

 

[phinds]

I'm not sure windmills are a good argument for 4 blades. A modern windmill has 3. I assume that if 4 were more efficient, they would have 4. The thing to keep in mind is that windmills catch wind in ALL of the blades at the same time. Water wheels do not so they are not fundamentally the same at all.

EDIT: Ah, I see. The 4-wheel configuration was simply a response to the OP's statement that they all have 3, not a claim that it was a better design.

 

[Tom.G]

IIRC, the odd number of blades is to avoid (un)balance problems that can result in a mechanical resonance with an even number of blades.

Probably the historic windmills didn't go fast enough for that problem to occur.

Cheers,
Tom

 

[haruspex]

IIRC, the odd number of blades is to avoid (un)balance problems that can result in a mechanical resonance with an even number of blades.

Probably the historic windmills didn't go fast enough for that problem to occur.

Cheers,
Tom

Interesting possibility… but that would make a prime number even better, no? E.g. 7 better than 9.

 

[jbriggs444]

Interesting possibility… but that would make a prime number even better, no? E.g. 7 better than 9.

Especially for cicada powered hamster wheels.

 

[berkeman]

I am in search of a new design configuration that would be more efficient than the aforementioned the design.

Have you seen the efficiency numbers in the Wikipedia article for different kinds of waterwheels? It looks like the most efficient are the "overshot" and "backshot" configurations with lots of slots like the picture @phinds posted:

https://en.wikipedia.org/wiki/Water_wheel