Water wheel and hydroelectric power question

  • Thread starter Pinon1977
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In summary, the conversation discusses the advantages of using an even or odd number of moment arms in a water wheel and the torque it can produce. The individual believes that an odd number of arms would be better due to the lack of equal opposing force, but others argue that as long as the paddles are evenly spaced, the wheel will be balanced regardless of the number of arms. The conversation also touches on the history and design of windmills and their relation to water wheels. Overall, there is no clear consensus on the ideal number of blades for a water wheel and it ultimately depends on the specific design and situation. The individual is conducting this research as an exercise and is interested in finding a more efficient design.
  • #1
Pinon1977
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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.
 

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  • #2
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?
 
  • #3
Why would either of those be better than a standard water wheel:
1687498594588.png
 
  • #4
haruspex said:
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.
 
  • #5
phinds said:
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.
 
  • #6
Pinon1977 said:
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.
 
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  • #8
Pinon1977 said:
every windmill that I've ever seen
1687511562021.png
and boy, have we got a lot of those. For centuries already :smile:

Seems the French have them too

1687511744193.png

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  • #9
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.
1687523177449.png


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.
 
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  • #10
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
 
  • #11
Tom.G said:
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.
 
  • #12
haruspex said:
Interesting possibility… but that would make a prime number even better, no? E.g. 7 better than 9.
Especially for cicada powered hamster wheels.
 
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  • #13
Pinon1977 said:
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

1687797375682.png
 
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