How Do You Calculate the Power Produced by a Pendulum-Driven Flywheel?

[BurnIt0017]

Hi, a pendulum drives a flywheel using a over run clutch so the flywheel will only spin in one direction.
The length of the pendulum is 2.5 meters and the bob weight is 25 kilograms. It is a rigid pendulum.
The flywheel diameter is 4 meters. 4.5 kilogram weights are placed at 60 degree intervals around the out side edge of the flywheel.
The flywheel and pendulum are on the shaft.
If the pendulum is dropped from 2 meters above the ground how much power is created at the center shaft for the first period of the pendulum?

I am asking for assistance to me find the formulas that will help describe this device.

I will have the prototype fabricated in a few days.

https://www.youtube.com/watch?v=OqV_VHz5BKo

 

[Simon Bridge]

You already have the equations that describe it - it is damped harmonic motion ... you know the equations for gravity and the spring - set up the free body diagrams.

Note:
- you can rig the coupling so the flywheel is pushed in the same direction on the backswing too.
- you are basically transferring energy from the downswing to the flywheel - even in the ideal zero-friction case, the pendulum swings less and less until it stops, or, in the case the coupling works both ways, some equilibrium has been reached.

 

[russ_watters]

Gravitational potential energy is just mgh. You gave us m and h, so you can easily calculate the available energy. How much gets transferred on the first swing is tougher. Half would be a reasonable guess, but getting closer requires calculating the flywheel moment of inertia and combining the equations of motion of the flywheel and pendulum which isn't all that easy.

 

[Dale]

In your system there are three places for energy. Gravitational PE of the pendulum $-mgr\;cos(\theta)$, kinetic energy of the pendulum $1/2 \; m (r \dot{\theta})^2$, and kinetic energy of the flywheel $1/2 \; I \omega^2$. You can calculate the moment of inertia, I, using the formulas here:
http://en.wikipedia.org/wiki/List_of_moments_of_inertia

How much is transferred the first stroke depends on how much of the pendulum KE is removed and put into the flywheel. Without further details it cannot be calculated. Probably the easiest way would be to simply measure it.

 

[Simon Bridge]

I think the diagram is showing that the flywheel turns at the same speed as the pendulum for half the stroke, and free-wheels for the other half ... it also has a spring which is anticipated to be needed to stop the pendulum at the start position - perhaps OP thinks that the return stroke will go farther than this?

The video included appears to show a home-made trapped-roller clutch.

I think it should be possible to do some back-of envelope work for an idealized situation.

The design does call for a small, regular, input to keep it going ... I've seen a number of clever feedback systems with solenoids and pendulums used in clocks. Perhaps that's the idea here?

 

[mfb]

I think the diagram is showing that the flywheel turns at the same speed as the pendulum for half the stroke, and free-wheels for the other half

I came to the same conclusion.
Therefore, only the first downwards motion will accelerate the flywheel. Afterwards, the flywheel velocity is the same as the maximal pendulum frequency (neglecting friction here), so we have a free pendulum and a flywheel at a constant speed. This is easy to analyze with energy conservation.

 

[russ_watters]

Oh, good point: since the speeds are equal, the starting PE and final combined KE must be the same. So all of the energy transfer happens On the first stroke. So that makes the calc easier: just set initial PE equal to final KE and solve.

 

[BurnIt0017]

Hi, I started fabrication. I am hoping to do some basic testing in a few days.
Thank you for the help.

 

[BurnIt0017]

https://www.youtube.com/watch?v=HN4mBojjI_Q

Hi, video of manually operating dual pendulum driving a flywheel. Once the flywheel is moving the pendulum keeps the flywheel moving without much effort.

Should the weights on the flywheel be place toward the center or toward the outer diameter for the greatest mechanical advantage to the drive the center shaft?

 

[Simon Bridge]

Should the weights on the flywheel be place toward the center or toward the outer diameter for the greatest mechanical advantage to the drive the center shaft?

I have a feeling it may be six of one and a half-dozen of the other ... treat it in terms of energy rather than force: the higher the moment of inertia, the more energy gets stored for a particular frequency ... which means that the flywheel will take longer to slow down, but, when slow enough to engage the pendulum, it will draw more energy per stroke.

You realize the pendulum is acting as a reservoir that keeps topping up the flywheel right?

 

[BurnIt0017]

Hi, I was not happy with the test results of the pendulum driving the flywheel using a overrun clutch. I am changing the project to a rotative beam engine. I have completed the beam fabrication, should the beam end be placed directly above the flywheel crank or is there a better position that will provide any mechanical advantage? Suggestions welcome.

http://www.youtube.com/watch?v=9olEqWGldvo

video of flywheel and crank

 

[Mech_Engineer]

I'm afraid to ask, but what application is this little project for?

 

[BurnIt0017]

http://www.youtube.com/watch?v=Cpp5_yU99dQ

Hi, I have been working on VAWT project but I live in a low wind area. No wind no power. I watched a few videos on youtube of some projects trying to use pendulums to make a motor. So I am trying to fabricate a rotative beam engine that is powered by a pendulum to operate a generator. The challenge will be to setup the system to use as little input power as possible.

 

[Simon Bridge]

You realize that the pendulum cannot "power" anything except in the sense that it can act as a store of energy? You won't be able to get any more energy out of the generator that you put into the initial state of the pendulum... anything else between the pendulum and the generator just reduces the output... so there doesn't seem to be any point to this?

* that " rotative beam engine" (your link) appears to be a simple (rimless) spoked wheel with a hand-crank (and something at the other end). Compare with:
http://en.wikipedia.org/wiki/Beam_engine#Rotative_beam_engines
... a rotative beam engine is a kind of beam engine which is a kind of steam engine... though the beam+pump can be driven by other sources of energy.

* The "dual pendulum" is, in fact, physically, just a single pendulum ... i.e. the behavior is the same as a single pendulum that is shorter, with twice the mass.

* The load test went pretty much as I'd thought - the flywheel was heavily loaded so it quickly ran out of energy ... needing the pendulum to top it up. The pendulum would have lost energy quite quickly too and the whole lot comes to rest when that runs out unless you have some other input.

 

[BurnIt0017]

https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=-1n-C5o8fZ0

http://www.youtube.com/watch?v=-1n-C5o8fZ0

Hi, thanks for info. This is a learning experience and I am not sure what I will use for the input power to keep the pendulum moving.

 

[russ_watters]

Let me be clear: do you understand that the output energy of the generator cannot continuously exceed the input energy driving the pendulum? Or alternately stated: the pendulum cannot add energy to the system?

 

[Simon Bridge]

Hi, thanks for info. This is a learning experience and I am not sure what I will use for the input power to keep the pendulum moving.

The youtube video looks like a scam - don't buy into it.
The operation of the device is, at best, being misrepresented - if I am generous I would say that the designer does not understand what it does.

You need to take a hard look at your designe and ask what role the pendulum plays in the operation of the task.
If you think it is a source of energy, any energy, you are doing it wrong.

AFAICT, F uses the pendulum as an almost-return-device reminiscent of free-energy devices, and raises many of the same red flags in his descriptions.
Since it is only almost-return, you have to keep pushing it. The energy in the pushing is, at best, no less for the mediation of the pendulum than if you'd done the work by direct lifting. What it [the entire machine] does do is spread the work over a longer time, and engage maybe a different muscle-set, than many other designes.

 

[BurnIt0017]

http://www.animatedengines.com/watt.html

Hi, the first attempt produced poor results. I am altering the project to a rotative beam engine. I plan to replace the steam piston with a pendulum and place weights on just one side of the flywheel. It will still require a energy input to keep the pendulum oscillating but it may produce better results. Suggestion welcome.

 

[mfb]

better results

How do you measure "better"?
How do you define "good", if you have no idea where your power comes from and how good you can transfer it to the pendulum?

 

[BurnIt0017]

https://www.youtube.com/watch?v=



Hi, I completed the rotative beam. I plan to use a small DC electric motor to power the input. The output will drive a three phase AC generator. I can measure the current at the input and the output.

 

[russ_watters]

Burnit, I must insist that you answer my direct questions if you want this thread to continue. PF is not a blog site and it is not a crackpot site.

 

[Simon Bridge]

Burnit, I must insist that you answer my direct questions if you want this thread to continue. PF is not a blog site and it is not a crackpot site.

Seconded.