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i've seen some old flywheel powered toy cars and i'm wondering could that be scaled up to work on a pedal car so that it spins up while you're pedalling and then have it engage by lever or something to assist pedal power over bumps and stuff or just give it a boost on the flat? also most flywheels seem to be mounted vertically, is there any reason not to mount one horizontally as i think it would fit into the pedal car better that way?

oh and assuming i'm limited to a certain weight would a small flywheel with an evenly distributed weight or a wider flywheel with most of the weight on the outside edge maintain its spin for longer?

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There are a number of complications to using a flywheel for energy storage, and I think the Wikipedia page titled, "Flywheel energy storage", covers several, but not all, of them.

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

The equation for stored kinetic energy, in a spinning flywheel, is a good place to start:

U = 0.5*J*(omega)^2 [equation 1]

where U is stored energy, omega is angular speed,

and J is this thing called, "moment of inertia",

For a solid disc, spinning about its center, mass evenly distributed throughout the disc,

J=0.5*M*R^2 [equation 2a, disc]

For a ring, spinning about its center, with all the mass on the edge,

J=1.0*M*R^2 [equation 2b, ring]

So maybe that answers one of your questions, the one about how to best distribute the mass of a flywheel. Answer: a spinning ring, with all its mass on its edge, increases stored energy by a factor of 2, compared to a solid disc, with same mass, moving at same angular speed.

Angular speed, omega, is what I am going to write about next.

By the way, your intuition might be telling you that a flywheel has to be massive, to effectively store lots of energy, but that is not true.

As we have seen from the equations so far, total energy stored is proportional to the flywheel's mass, and proportional to the square of its angular speed.

The square law thing is a big deal. If you can spin the wheel twice as fast, you store four times the energy. Ten times as fast, gives a hundred times the energy!

So that kind of explains the way the pros are doing it. They're not really concerned about how massive the flywheel is. Their game is to build a flywheel with exceptional tensile strength, and then spin it as fast as it can be spun, without ripping itself apart.

I think this quote, from the Wiki article, kind of exemplifies, this spin-it-fast approach,

composites, suspended by magnetic bearings, and spinning at speeds from
20,000 to over 50,000 rpm in a vacuum enclosure.[2] Such flywheels can
come up to speed in a matter of minutes – reaching their energy capacity
much more quickly than some other forms of storage."

Yeah. Vacuum enclosure. Magnetic bearings. High strength composites. Ridiculous angular speed.

This kind of brings me to my next point, which is friction losses. That's one of the things that Wiki article mostly fails to mention, that will be a be a big deal for the kind of thing you're contemplating, basically a scaled up version of a toy car made to run on a table top.

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

These NASA peeps have seemingly slipped the surly bonds of mechanical friction, with their magnetic bearings, plus vacuum enclosure, plus electromagnetic coupling, to move the energy in and out.

However, for your application, if you are truly considering mechanical bearings, plus some kind of mechanical clutch for coupling/decoupling to/from the flywheel, then friction losses are probably going to be a big deal.

It might be the kind of thing where you spend way more energy trying to pump the flywheel, than you ever practically get back from it, on those occasions when you want some "assist" or "boost".

It would be kind of like a business that always loses money. That's good for tax purposes, but not good for making a living.

Actually, thinking in that direction, a human powered machine, that loses energy in a profligate way, might be good for physical exercise for the human, but maybe not so good as practical transportation, like a typical bicycle.

Also did I mention, flywheels store angular momentum as well as energy? It gives this kind of kind of, "gyroscope effect". The flywheel wants to stay oriented in the same direction, and that can sometimes be a problem for transportation applications. Sometimes. For a bicycle, or motorcycle, the angular momentum in the wheels actually helps keep the bike stable, although it makes turns a little more difficult. The Wiki article mentions this briefly, under the heading, "Effects of angular momentum in vehicles"

Comes down to mass and rotational speed.
A toy car is light and the flywheel in comparison make the majority of the weight.
Take a push bike on a straight and get it to a certain speed.
The energy you need to provide with your legs to maintain the speed is the smae your flywheel would have to provide.

A multi geared flywheel that is kept at very high speeds will provide more energy for longer than a slow turning wheel - with same mass and dimensions.
Of course more energy is required to get it to that high speed.
Upscaling a toy car to something real with a driver would mean to have a flywheel of over 200kg.
And with that weight comes to problem of moving it.
There might be little to no overall gain for you unless your ride always starts on top of a hill.