Gyroscopic Water Wave Energy Converters

[JTC]

Say I have a disk spinning in a buoy. Let me say the spin axis is vertical to the flat surface of the buoy (or sea if there were no waves).

Now along comes a wave (that will induce a "precession" of the disk/buoy. The axis of this precession is from "starboard to port."

This would induce (due to the gyroscopic effect) an angular velocity of that rotor disk, about an axis that goes from bow to stern.

So let me assume I can do a very simple, back of envelope (assuming all is at the center of mass), calculation to calculate the induced angular velocity from the mass, geometry, etc.

How do I get as similar "quick and dirty" estimation of the power generated?

You see, the issue is that I do not know how generators work.

I do know that Power = Torque * angular velocity.

I just found the angular velocity

Do I simply add to my formula a "hypothetical" torque that would STOP the rotation? And assume that this torque times the rotation rate without the torque is an estimation of the generated power?

But this makes no sense because Power = Torque times the angular velocity it rotates. Here, I would be applying a torque to COUNTER the angular velocity.

I am not looking for anything complicated. I have tried to read the on-line sources. But I cannot frame this problem in my head (or even try to read the sources), until I figure out how to estimate the power.

(And yes, i am aware there is induced yaw, pitch, roll due to ONE gyro, but let's keep this simple... In THIS context, HOW do I estimate the generated power? How does a generator work?)

 

[anorlunda]

You don't need to care how a generator works. Just assume that it is a 100% efficient converter of mechanical power to electric power.

What makes the disc spin? What keeps it spinning as you take energy out?

 

[JTC]

You don't need to care how a generator works. Just assume that it is a 100% efficient converter of mechanical power to electric power.

What makes the disc spin? What keeps it spinning as you take energy out?

No, you have missed my point. I DO CARE (for that is the VERY question I asked) -- but just a bit for the sake of a general and simplified understanding.

As I mentioned, I am NOT concerned with the power needed to get it spinning. It is spinning.

I am concerned with an OVERVIEW -- a SIMPLIFIED GENERALIZATION -- of a ball park on how to compute the power generated (NOT the average power).

My question states the issue clearly.

The waves induce the precession of a spinning disk and this, in turn, induces an angular velocity.

How would I model the power? By the angular velocity TIMES the moment that would have stopped the angular velocity?

 

[berkeman]

No, you have missed my point. I DO CARE (for that is the VERY question I asked) -- but just a bit for the sake of a general and simplified understanding.

As I mentioned, I am NOT concerned with the power needed to get it spinning. It is spinning.

I am concerned with an OVERVIEW -- a SIMPLIFIED GENERALIZATION -- of a ball park on how to compute the power generated (NOT the average power).

Please do not yell in all capital letters. It is against the PF forum rules. Thank you.

The waves induce the precession of a spinning disk and this, in turn, induces an angular velocity.

I see how the wave tilts the buoy and that generates a torque on the gyroscope inside the buoy which causes it to precess. But I'm not seeing how this is supposed to affect the angular velocity of the gyroscope. Can you show us the equations you are using to calculate that effect?

Also, It seems like this scheme for trying to extract some of the energy from passing water waves is not very efficient. It does not use the up-down motion of the wave to extract some energy. I would think there is a fair amount more energy to be extracted from the up-down motion of the water waves on the tethered buoy, compared to trying to extract some of the energy from the changing tilt on the wave surfaces...

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

 

[CWatters]

I think the OP is saying that the wave will try and tip the axis in one plane ( port/starboard) but the gyro will force it to tip in the fore and aft plane. The angular velocity he's talking about is in the fore/aft plane not the rotational plane of the gyro.

That said I agree with post #2. Why not assume that 100% of the energy in the wave is captured?

PS Not enough information is provided to calculate the actual efficiency.

 

[anorlunda]

Power=torque times speed.

mechanical 1 foot pound per second = electrical 1.36 watts

That's all you need to estimate the power.

 

[JTC]

Sorry for CAPS... It was not intended to shout, but to emphasize. I won't do it again (after that one just now)

As for whether it is efficient -- I did not ask that.

As for power estimation - I do know the equation that Power = Torque times speed.

But none of that is my question.

The fact is that the gyroscopic effect will induce the angular velocity (I gave all the axes in my original post).

Others are doing this:


There are many if you google it.

The equation (barring geometry and center of mass and dual mass system) =
Moment = Moment of Inertia * precessoin rate * spin rate.

But without the moment, it is free to rotate.

But I am not interested in arguing the efficiency.

The question is simple: how does one estimate the power? Yes, I know that P = T * angular speed.

But there is an angular speed when it is free to rotate.

What Torque do I use to "complete" the equation P = T * angular speed?

 

[JTC]

And here is a paper

http://porto.polito.it/2562362/1/PhD_Thesis_BRACCO_withjudices.pdf

The same thing always happens...

They reduce the dynamics to a simplified equation that relates
induced Torque to induce angular velocity.
(They use all the parameters about mass and moment of inertia and geometry and bearings, etc.)

But it is one equation.

So if there is no torque then you get free rotation.
But how do you estimate the power using P = T * angular rate?

The only thing I can guess is that the assess the free rotation.
The apply a moment to stop it.
And use the product to get the varying power.

 

[anorlunda]

And here is a paper

http://porto.polito.it/2562362/1/PhD_Thesis_BRACCO_withjudices.pdf

The same thing always happens...

They reduce the dynamics to a simplified equation that relates
induced Torque to induce angular velocity.
(They use all the parameters about mass and moment of inertia and geometry and bearings, etc.)

But it is one equation.

So if there is no torque then you get free rotation.
But how do you estimate the power using P = T * angular rate?

The only thing I can guess is that the assess the free rotation.
The apply a moment to stop it.
And use the product to get the varying power.

They do more than than torque. On pages 16-17 of the paper they calculate the power. It is laid out step by step. Equation 2.19 is the derived equation for power. And by the way, they did that before even mentioning a generator. But if you insist on understanding how the generator works, the paper even includes the equations for that.

What more do you want from us?

 

[russ_watters]

@JTC, you're missing the point here. You're asking how much power a certain recovery method can achieve without taking into account the efficiency, which means the recovery method is irrelevant to the question. What you need is the input energy, which is a function of the size of the waves and buoy and frequency of oscillation.

 

[JTC]

@JTC, you're missing the point here. You're asking how much power a certain recovery method can achieve without taking into account the efficiency, which means the recovery method is irrelevant to the question. What you need is the input energy, which is a function of the size of the waves and buoy and frequency of oscillation.

Russ, I am aware of that. It is specifically mentioned in the papers. There are models to take that into account and I get it.

The only thing I do not get is how this thing works to even get a starting point.

Here... assuming we have a gyro, we get

Moment= Moment of Inertia * Precession times spin.

And these three quantities form a right handed system (which is why I defined the axes in my original post).

If one does not restrict with a moment, one gets rotation.

So as an upper limit model, what is the power?

These papers just multiply the moment times the angular velocity.

 

[russ_watters]

Ok, so then your question appears to be "how does this method of energy recovery work?", not "how much energy can it recover?"

 

[JTC]

Ok, so then your question appears to be "how does this method of energy recovery work?", not "how much energy can it recover?"

(I promised earlier that I would not use caps, but now I must): YES!

That is exactly what I need to know

Assuming one has an equation that relates the "prescribed" spin and precession rates (these are now given), along with all necessary parameters,
this final equation (assuming negligible yaw), will provide the angular velocity.

How does one gain an upper limit approximation for the generated power?

If I do not restrict (apply a torque) to the axle, I get the angular velocity.
If I totally restrict the angular velocity, I get a torque.

But I can't get both.

Yet the papers do it.

I would imagine that if in addition, I applied a torque, i would get a modified angular velocity.

But these papers just multiply the two terms as an upper limit to the generated power -- and that confuses me.

So this means I do not know how to "capture" the angular velocity in a generator.

 

[JTC]

Ok, so then your question appears to be "how does this method of energy recovery work?", not "how much energy can it recover?"

Let me try this...

I can obtain an equation like the following:

f(moment_on_the_axle, angular_velocity, all_other_stuff_is_given) = 0

But this is one equation for the two things I must multiply to get an expression for the upper limit approximatoin to the power.

 

[CWatters]

Ive not read the paper (can't access it) but...

If you have a mass that has been set rotating (by a wave or whatever) then it contains energy = 0.5 * I * ω². If you know that this energy can be extracted and replaced with a frequency F (perhaps dependant on the frequency of the waves) then you can calculate the average power that is available to be extracted... P=E*F

 

[CWatters]

You can also use the equations of motion to work out the torque required to extract all the energy in a given time. Eg first calculate the required angular deceleration to stop it rotating in the required time, then torque equals moment of inertia * angular acceleration.