8 feet diameter stainless steel water wheel - need help for PMA/PMG Sizing

Good morning, I came accross this site when looking for information on waterwheel and power.
When we designed the water wheel we calculated that it would produce around 3hp. Now that its time to order the PMA/PMG I am being asked about the power rate, forces/toque all all of those things.
This is what I calculated/came up with so far:
Wheel diameter is 8 feet
Wheel width is 2 feet
RPMs at no load = 27, the water barely fills the buckets...
An engineer looked at the numbers and told us that at 100% efficiency he estimated 3.48HP and or 682 lb.-ft. at the shaft

The speed of water is at least 12' per second at the channel by the times it reaches the wheel, we must confirm this, but the guess is conservative.

you can see the youtube videos here:


https://youtu.be/iTzqOrC3v3s



I can increase the water speed by diverting the water directly as soon as it enters the spillway, right not, the water is going down on the center of it and then turns to the channel.

Water flow is at least 5-10 galons per second on the low season, when it rains it goes up tremendously , its incredible because we are in a valley.

I am thinking a 2kw PMA/G, attached is the quotes that I got, but honestly its confusing...

hoping that someone could help us somehow... we did everything in house by researching and learning, but now we got to the PMA/PMG and we are stuck...

Thanks
Nuno

Hi Nuno;   Welcome to Permies!
That is a very nice water wheel you have, I'm jealous!  
If I may ask, what is your goal ?  
Power for a home ? Or is this a school project?  

I'm no engineer , just a micro hydro guy, but your numbers look rpm dependent.
You should be able to gear the PMA to any reasonable rpm you want?
How were you thinking of driving the PMA ? With a direct flex drive coupler? Or with gears and a chain?
By your engineers numbers, it sounds like you have significant toque.
Give us some more information and we might be able to help you make your choice.

thomas rubino wrote:Hi Nuno;   Welcome to Permies!
That is a very nice water wheel you have, I'm jealous!  
If I may ask, what is your goal ?  
Power for a home ? Or is this a school project?  

I'm no engineer , just a micro hydro guy, but your numbers look rpm dependent.
You should be able to gear the PMA to any reasonable rpm you want?
How were you thinking of driving the PMA ? With a direct flex drive coupler? Or with gears and a chain?
By your engineers numbers, it sounds like you have significant toque.
Give us some more information and we might be able to help you make your choice.

This is mostly for fun, its a private project, but we do intend to run a pound water fountain/jet and a couple of LED lights from it.
We just want to be able to take the most out of it.
We will be using belt/pulley system to increase the speed.
Not sure if we can reverse a speed reducer, to make it a speed increaser.
Any ideas on how to get the speed up would be welcome.

Well the fact your not wanting to make huge amount of power makes this easier.
A PMA and a standard auto alternator are normally similar in size.
I would experiment with different size pulleys from the wheel to a practice alternator.  
Get your rpms close and then choose what PMA fits your needs best.
Of course, an alternator (PMA or regular) will spin slower when produsing power.

Hopefully you can get the rpms up enough to use a higher rpm PMA and lower your upfront costs.

EDIT)  Your plan of using belts for a drive system rather than chain could be problematical.  When they get wet they may want to stretch on you and slip. Chain drive is foolproof.

Also is this power going to a battery bank ? Or are you hoping to run directly off of the alt ?  I assumed we were talking D.C. power, are you thinking A.C.?

thomas rubino wrote:Well the fact your not wanting to make huge amount of power makes this easier.
A PMA and a standard auto alternator are normally similar in size.
I would experiment with different size pulleys from the wheel to a practice alternator.  
Get your rpms close and then choose what PMA fits your needs best.
Of course, an alternator (PMA or regular) will spin slower when produsing power.

Hopefully you can get the rpms up enough to use a higher rpm PMA and lower your upfront costs.

EDIT)  Your plan of using belts for a drive system rather than chain could be problematical.  When they get wet they may want to stretch on you and slip. Chain drive is foolproof.

Also is this power going to a battery bank ? Or are you hoping to run directly off of the alt ?  I assumed we were talking D.C. power, are you thinking A.C.?

The idea is to produce the most power possible - we think that 2KW is about right...looking for advice on this.
We wanted to produce AC power that we could use directly. We purchased a North Star Belt Driven Generator that has built in power stabilizer and plugs (attached) but it needs between 3480-3780 RPM, and we are having a hard time figuring out how to increase the speed to this amount 140:1, and the problem is that we do not know how much it would slow down on a load, any advice on how to?
We will make a small housing for gears, PMA/generator to be as dry as possible.
I would like to use chain drive, it would be easier for me to build because we have a in-house plasma machine and I could build a 48" diameter sprocket to install in the axle to start, then a 40"... but I think it would make to much noise..., what do you think? see bellow:

https://geargenerator.com/#625,625,25,27,1,2,103611.69999998849,4,1,192,48,4,27,-90,0,0,0,0,0,0,16,4,4,27,-60,0,0,0,0,1,1,160,40,4,27,-60,0,0,0,0,2,0,13,3.25,4,27,-60,0,0,0,0,0,0,3,-428

Well you are certainly correct that a chain drive would be noisy.  An insulated cover would mitigate some of that noise. With your plasma cutter pulley production would be simplified.
Belt drive would be virtually silent, with the ambient noise from the stream.
Making A.C. directly is slightly harder as rpms must be within a certain limit.   D.C. would simply produce less power as the rpm's dropped.

Unfortunately I do not know any sure way to calculate the spin resistance when under load. Would your load remain constant? Or fluctuate with lighting needs?
I'm afraid you will need to experiment with rpms in the 4000 range in the hope you can maintain 3500-3600 under load.
Here is an idea. Use a small gas engine (they run at 3600) hook this to your PMG and apply your anticipated load. The engine will of course compensate to keep rpms at 3600, But you should get an idea by the amount of compensating you hear the engine do, how much draw (resistance) your PMG is creating.
I would build a dummy shaft that is the same diameter as your PMG shaft , fit it and the main shaft with pulley's . I realize that coming up with pulley's of the appropriate size is no doubt a  problem as well.
Spin it up and see what you get.
I know this is not the answer you were wanting. I just do not have the engineering skills to calculate what you need.
Please do give us an update (with photo's) as you progress.

thomas rubino wrote:Well you are certainly correct that a chain drive would be noisy.  An insulated cover would mitigate some of that noise. With your plasma cutter pulley production would be simplified.
Belt drive would be virtually silent, with the ambient noise from the stream.
Making A.C. directly is slightly harder as rpms must be within a certain limit.   D.C. would simply produce less power as the rpm's dropped.

Unfortunately I do not know any sure way to calculate the spin resistance when under load. Would your load remain constant? Or fluctuate with lighting needs?
I'm afraid you will need to experiment with rpms in the 4000 range in the hope you can maintain 3500-3600 under load.
Here is an idea. Use a small gas engine (they run at 3600) hook this to your PMG and apply your anticipated load. The engine will of course compensate to keep rpms at 3600, But you should get an idea by the amount of compensating you hear the engine do, how much draw (resistance) your PMG is creating.
I would build a dummy shaft that is the same diameter as your PMG shaft , fit it and the main shaft with pulley's . I realize that coming up with pulley's of the appropriate size is no doubt a  problem as well.
Spin it up and see what you get.
I know this is not the answer you were wanting. I just do not have the engineering skills to calculate what you need.
Please do give us an update (with photo's) as you progress.

is it possible to make a custom large pulley? I thought about two steel plates welded with a picket in between, half " down from the top of the larger plates and the belt would drive there, but these are V belts and I would not know how to make a V-Shape, only a Square U.

The only way I know to make a pulley for a V belt is with a lathe, taper the disk down.  Not a big deal for a small pulley... great big deal if your pulley is 48" .
Automotive belts have switched away from V belts to flat multi rib belts . It may be possible to fab pulleys for them in your shop.  However getting the length you need might be impossible.
In industrial applications smooth flat belts are commonly used. They would be easy to fab but slippage running an alternator could be a big deal with them.

hello from my personal experience, I would see the following solution: use the circumference of the wheel, which under load will turn around half the number of laps
ideal would be laser-cut stainless steel sectors in order to have a large toothed gear for a motorcycle type chain (also stainless steel) in order to connect via a twin pulley of the correct diameter to have a 1:50 multiplication
the pin could be long up beyond the wall to be connected to the generator

at this point a 500/600 rpm three-phase brushless servomotor that can be easily found
then an ELC circuit will be needed to stabilize the output voltage in case of off grid
while if you put on the grid, an MPPT grid tie inverter solves easily by straightening and leveling the three phases in order to have from 300 to 700 volts dc
for your knowledge you can see on youtube here
[youtube]https://www.youtube.com/watch?v=w16StyKLkvA&t=190s
[/youtube][youtube]udos46[/youtube]