Maximizing KE in flywheel energy storage system (KERPS)

[caddy5384]

Homework Statement

Describe and explain some of the design features of a flywheel in order for it to store
maximum energy. Your answer should include consideration of the flywheel’s shape,
the material from which it is made and its design for high angular speeds.

Homework Equations

KE=Iω²/2
T=Iα
Angular momentum=Iω
I=∑mr²

The Attempt at a Solution

The only part I do not understand about the question is that the answer states that high density material is preferred to increase the mass of the flywheel.

What I am thinking is that, to maximize the kinetic energy of the flywheel, mass of the flywheel must be low because of the conservation of angular momentum.

Since kinetic energy is Iω²/2, an increase in ω results in a greater increase in kinetic energy. Also, since angular momentum is conserved, I must be low for ω to be big.

Since I=∑mr², mass must be low for I to be low.

What did I get wrong?

Any help would be appreciated.

 

[rude man]

Since KE = Iω²/2 you want to maximize I and ω. What maximizes I? What is I for a cylindrically shaped mass of radius R? Look it up or calculate it from I = ∑mr².


I think you misunderstand. Angular momentum conservation does not enter the picture. You will be draining energy from the flywheel as you make use of its stored energy, for example drivng a generator driving an electric load.

 

[BvU]

Hello Caddy, and welcome to PF.
Want to point your attention to this angular momentum thing: the idea of such a flywheel is that you store energy by making it spin as fast as possible without it flying apart. That requires angular acceleration, so actually increasing the angular momentum. Certainly no conservation of angular momentum in that phase !

 

[haruspex]

I agree, of course, with the responses above.
Beyond that, the shape is an interesting question. You need to consider the trade-off between two principal modes of failure. What do you think might happen to a flywheel if you spin it too fast?

 

[NascentOxygen]

Beyond that, the shape is an interesting question. You need to consider the trade-off between two principal modes of failure. What do you think might happen to a flywheel if you spin it too fast?

Or if you slow it down too fast ...

 

[BvU]

Well, caddy, thanks for bringing this subject up again from under thick layers of dust (at least in my brain...). You must be young, curious and eager to learn for sure, so I wonder why you didn't google beyond flywheel (which features $E_k={1\over 2}I\omega^2$ as its first relationship, but just a few lines down brings in the mucho importante $\sigma_t$) and also looked at flywheel energy storage !?

Paraphrasing what MacBeth said a long time ago: Read on, MacDuff !

@Haru (and somewhat spoiling for caddy -- oh great mentoring spirit up there in the cloud, forgive me my getting carried away --): I knew about the tensile strength and your two modes question raised my curiosity as to which is the second. Imbalance springs to mind, but for introductory physics that looks awkward: depends on application, implementation and what not (see the link).


Slightly related personal experience: long ago Club of Rome triggered all kinds of applied physics initiatives and one could do further studies into environmental physics, energy storage (yes, flywheels among other even more exotic things) and such. Not being very engaged and a lot more rightist than now, I declined to continue in that direction: it looked short-lived and dead-end to me. Just a year later I was impressed beyond description, placing my foot on a thumping block of bumping concrete the size of a house at CERN. On the block, a huge motor/generator -- flywheel combination to even out the power consumption of the Proton Synchrotron. Which is now 55 years old and still at the core of the business there.

Further reading: e.g. PJ Janse van Rensburg MSc thesis 2011. I was impressed! But somehow cruelly felt relieved reading Beacon Power had to file for bankruptcy in the same year...(they were saved, though). So I should admit that long ago I was wrong and it still is a relevant and viable subject.


Oh, and: what is KERPS ?

 

[caddy5384]

Thank you for the help. I understand the question now.

KERPS: kinetic energy recovery system in cars

My guess to the questions above:

When it spins too fast, there will be a bigger frictional force.. Energy will be lost quickly.

When you slow it down to fast, Torque is too huge and breaks the components. (?)

 

[AlephZero]

When it spins too fast, there will be a bigger frictional force.. Energy will be lost quickly.

If you tie a stone to a piece of string and whirl it around fast enough to break the string, do you think the cause is "a bigger frictional force?"

The biggest "friction force" on a high speed flywheel would probably air resistance, but you can get rid of that by running the flywheel in a vacuum.

When you slow it down to fast, Torque is too huge and breaks the components. (?)

That is true, but unless you want to recover all the KE very quickly (e.g. in a fraction of a second) for some reason, it's probably not a big problem in real life.

 

[haruspex]

When it spins too fast, there will be a bigger frictional force..

No, I'm thinking of the internal forces in the flywheel.
Consider the flywheel as made of a lot of blocks connected with strings. For simplicity, there are just radial strings and tangential strings. What determines the load on a tangential string at a certain position? What about the radial strings?