Windmills and Power Generation

[JTC]

I tried yesterday with the gyro and did not make myself clear. So let me try with a windmill, please.

I look at a windmill and I see the blades are spinning. Thus, the shaft axis has an angular velocity.
I can ballpark and check the angular velocity with my eyes.

I want a ballpark approximation on the power being generated.

But I am NOT concerned with efficiency or electricity.

I do know that P = Torque * angular velocity. = T * w

I know (see) the angular velocity.

Someone tells me that that windmill is known to generate Power, P.

So my question is: where is the torque, what is generating it? How does this generator work? Does the generator apply a REVERSE torque on the axis of the windmill (reverse to the angular velocity), such that the product of T and w is negative and is this an estimate of the power generated?

Again, I do not care about electricity or efficiency of wind capture.

I want to use this formula -- P = T w -- to estimate the power generated, but I do NOT see where the T is coming from.

Please do not tell me to look at the electrical wiring of a generator. I want to SHIELD myself from the electricity and the wind and put a black box around this problem and get a simple approximation using P = Tw

Somehow, there must be a Torque and it must be supplied by the generator. Or do I assume that there is a Torque from the windmill? But there cannot be a Torque because the angular velocity is constant. Unless the generator supplies a resisting torque through friction. I just don't understand how this works.

 

[stockzahn]

To make the windmill's wheel spin you need forces acting on the blades in the rotation plane. These forces are acting over the entire surface of the blades, but you could sum them up and imagine one force acting in one point of each blade. These forces multiplied with the distance from the shaft yields the torque $T$.

$$T=F\cdot l$$

Now, if you start rotating the rotor of the generator, due to electrical induction current is produced, which generates a magnetic field. This magnetic field tries to stop the rotor's motion - if the rotor stops, no current will be produced anymore. If the torque generated by the wind is as strong as the decelerating torque of the magnetic field, the windmill spins with constant speed producing constant current. If you want to produce more current, the magnetic field increases and you also need more wind (a higher torque) to keep the windmill spinning.

 

[stockzahn]

Sorry, I hit the "post" button before I was finished. Here the end of my last post:

Now, if you start rotating the rotor of the generator, due to electrical induction current is produced, which generates a magnetic field. This magnetic field tries to stop the rotor's motion - if the rotor stops, no current will be produced anymore. If the torque generated by the wind is as strong as the decelerating torque of the magnetic field, the windmill spins with constant speed producing constant current. If you want to produce more current, the magnetic field increases and you also need more wind (a higher torque) to keep the windmill spinning.

 

[JTC]

Sorry, I hit the "post" button before I was finished. Here the end of my last post:

Now, if you start rotating the rotor of the generator, due to electrical induction current is produced, which generates a magnetic field. This magnetic field tries to stop the rotor's motion - if the rotor stops, no current will be produced anymore. If the torque generated by the wind is as strong as the decelerating torque of the magnetic field, the windmill spins with constant speed producing constant current. If you want to produce more current, the magnetic field increases and you also need more wind (a higher torque) to keep the windmill spinning.

And that is what I wanted to hear last night.

Thank you.

I know I must appear stupid, but I need to read this from someone.

May I ask you, please, to review last night's post on the gyroscope and confirm that the same issue applies?

 

[JTC]

So then, can I assume, focusing on the windmill and ignoring all sorts of friction loses, the following...
Somehow the wind makes the blades spin at some angular velocity.

When I buy a generator to put into the windmill, my interest (as a first year engineering student, not an advanced engineer who is aware of complexity), is: what resisting torque does the generator supply?

Then, on the back of an envelope, I multiply that torque against the angular velocity of the blades to get a ball park upper limit estimation of the power generated?

 

[stockzahn]

May I ask you, please, to review last night's post on the gyroscope and confirm that the same issue applies?

I didn't go through all posts, so I'm not sure if I get what exactly the question is. If you want to know how a generator works I recommend to read about electrical machines (I suppose in the internet you will find more information, than you need for that, for "windmills" asynchronous machines are used). The output power of a generator can be calculated by multiplying current and voltage ($P=U\cdot I$). I'm not an electrical engineer, but I think the voltage depends on the number of coils in the machine and the current on the magnetic field (whether produced by permanent magnets or electromagnets, depending on the machine). This electrical power again must be the product of the torque generated by the magnetic force and a distance to the shaft, and the angular velocity.

However, the electrical power you can generate and also the angular speed the generator is working at should be in the description of the generator. If you don't use a gearbox to change the angular speed, you directly can calculate the torque the generator is designed to work at. With different gears you can adapt the angular speed and therefore change the torque on the generator. Or the other way around: If you know the torque and the angular speed produced by the windmill, you have to find a probate generator or you have to add a gear box to adapt it.

 

[JTC]

I didn't go through all posts, so I'm not sure if I get what exactly the question is. If you want to know how a generator works I recommend to read about electrical machines (I suppose in the internet you will find more information, than you need for that, for "windmills" asynchronous machines are used). The output power of a generator can be calculated by multiplying current and voltage ($P=U\cdot I$). I'm not an electrical engineer, but I think the voltage depends on the number of coils in the machine and the current on the magnetic field (whether produced by permanent magnets or electromagnets, depending on the machine). This electrical power again must be the product of the torque generated by the magnetic force and a distance to the shaft, and the angular velocity.

However, the electrical power you can generate and also the angular speed the generator is working at should be in the description of the generator. If you don't use a gearbox to change the angular speed, you directly can calculate the torque the generator is designed to work at. With different gears you can adapt the angular speed and therefore change the torque on the generator. Or the other way around: If you know the torque and the angular speed produced by the windmill, you have to find a probate generator or you have to add a gear box to adapt it.

This is just wonderful. Thank you very much.

For me, the important part is that now I know what I don't know.

I have an approximate theoretical box around my understanding and can now start scaffolding as I read more.

I just needed to hear this put in a framework of simplicity.

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