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The flywheel research I see usually focuses on small, high-speed (thousands of RPM) flywheels, often with an emphasis on transportation-related applications. The largest rotating building in the world weighs 500,000 kg. According to my calculations, that mass rotating at 60 RPM would have a KE of several hundred kWh. Is that correct? If so, why are there no big and slow flywheels for utility-scale energy storage? What am I missing?

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    $\begingroup$ The KE of a rotating object depends on its moment of inertia, not just its mass. A large rotating ring will have far more KE than a narrow cylinder of the same mass rotating about its axis, for example. It's impossible to say how much KE is in a rotating building from just its mass and angular velocity, you'd also need to know its size, shape, and mass distribution (all of which contribute to the moment of inertia). $\endgroup$ Commented Nov 5, 2021 at 21:01
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    $\begingroup$ Because there are easier ways of producing "several hundred kWh". $\endgroup$
    – Solar Mike
    Commented Nov 5, 2021 at 21:20
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    $\begingroup$ I calculated that if your "several hundred kWh" was 500kWh, a cylinder with a radius of 19.1m would be required. Integration or a table is required to calculate internal stress from centripetal forces here. I was lazy so this engineeringtoolbox.com/… gave me 38.6Mpa if the material were steel. 250Mpa is listed as the yield strength of mild steel. The height if the cylinder was calculated to be...5.4 cm. so that is what the kind of device you are talking about would look like. $\endgroup$
    – DKNguyen
    Commented Nov 6, 2021 at 2:15
  • $\begingroup$ @DKNguyen that's good information, thanks! I was looking at concrete, and calculating that a cylinder with radius approx. 10m and height 13m and rotating at 120 RPM would have a mass of 10,000,000 kg and a KE of approx. 10 MWh. No idea if that is structurally possible with concrete. $\endgroup$
    – Phil Loden
    Commented Nov 6, 2021 at 8:13
  • $\begingroup$ They would be a very large waste of capital. $\endgroup$ Commented Nov 6, 2021 at 14:53

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What you are missing is that it is cheaper to increase the storage capacity of a flywheel by increasing its rotating speed than it is by making the flywheel bigger. This is the reason why (proposed) kinetic energy storage flywheels rotate at speeds high enough to generate stresses that are almost but not quite big enough to make the flywheel tear itself to pieces.

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    $\begingroup$ That reasoning seems to line up with my math in the comments. $\endgroup$
    – DKNguyen
    Commented Nov 6, 2021 at 2:23
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IMHO another you are missing is the practicalities of size and friction.

A 500000 kg disc is bound to be big and it needs special considerations for support, transportation, installation etc, thus making it impractical.

Additionally any practical application will have coulomb friction associated with it. However the thing is that coulomb friction is proportional to the weight. Thus increasing the weight increases the friction and the losses.


Arguably same thing can be said of viscous damping and high rotation. The main difference that the conditions to mitigate the losses are simpler in the case of viscous damping. E.g. vacuum chambers can be considered. For coulomb friction of a 500000 disc my mind goes toward technologies which are either exotic (magnetic levitation) and/or not invented yet (anti grav).

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  • $\begingroup$ The building I mentioned was using some kind of magnetic bearing, so I think you're right, something like maglev would be necessary. $\endgroup$
    – Phil Loden
    Commented Nov 6, 2021 at 8:14
  • $\begingroup$ @PhilLoden so how much power would your "maglev" bearing need? $\endgroup$
    – Solar Mike
    Commented Nov 6, 2021 at 13:00
  • $\begingroup$ Friction is proportional to weight, but so is inertia. F=umg and F=ma, so the deceleration due to friction is completely independent of the mass (for fixed m and g, a is proportional to u only). Two cars with the same tires and moving at the same speed have the same stopping distance regardless of their weight. A large flywheel is impractical, but not due to increased friction - friction slows a large flywheel at the exact same rate as a small one. $\endgroup$ Commented Nov 8, 2021 at 15:23
  • $\begingroup$ In a perfect (non deformable) world I would agree - although I would disagree with your example if you mean rolling resistance. However materials hit their limits as you increase the weight and deformations occur. At the end of the day, I haven't been able to put the same wheels on a loaded truck and a small passenger car and try to brake them from 50 mph and see if weight has a noticeable effect $\endgroup$
    – NMech
    Commented Nov 8, 2021 at 15:52
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Regarding energy storage, you really have to make a difference between power and energy.

For example, a laptop draws a few tens of watts peak, and a cordless drill draws several hundred of watts peak. So, from the same battery voltage, often around 18V, that's a few amps versus a few tens of amps.

Energy density is in Watt.hours/kilogram

Power density is in Watt/kilogram

You can also calculate it vs volume, vs cost, etc.

The laptop battery is optimized for maximum energy density so the laptop runs for a long time while reducing weight, at the expense of high power density: these cells will only be able to deliver a few amps.

The cordless drill battery is optimized for the opposite requirements, which mean maximum power density at the expense of energy density.

The results are very different chemistries, different costs, etc. Other factors like lifetime, number of cycles, cost, etc, are of course important too.

Now if you want to do energy recovery on braking in a vehicle, then you need an energy storage that can charge at very high power. A 12 ton bus going at 50 km/h has a kinetic energy of about 1.2MJ. If it stops in 5 seconds then that's an average power of 240 kW, which is quite large.

If you want to store the kinetic energy of that bus to reuse it when it accelerates again, then you need a system which can both absorb and release 240kW.

Lithium batteries have gone a long way, and now the high power density ones would definitely be able to do that on discharge, but when carging, they tend to be able to safely take a much lower power.

So, if the bus was fully electric, a battery pack sized for powering the bus and accelerating it from a stop to its nominal speed in the desired time would not be able to recover the full energy on braking, because its allowed safe power is much lower than its safe discharging power. If the bus is not electric but instead hybrid, then the battery is much smaller, which is even worse for recovery.

This is why these systems tend to use supercapacitors, flywheels, or pressure tanks, which have the advantage of huge and equal power density both on charge and discharge, plus almost unlimited number of cycles.

Drawbacks of these systems are mainly very low energy density, high cost of stored energy, and energy loss for flywheels. That's not a problem for a kinetic energy recovery system, which only has to store enough energy for one acceleration, and only for the duration of a bus stop. But it means these could never be used as a main battery.

Basically, it's only for pulse power requirements.

So you will find flywheels in utilities, when there is a need for short-term pulse power, for example to react quickly in case of a sudden increase in power demand while the generators take a bit more time to react.

However, if you want to store energy from solar panels to use at night, it's not cost-effective. Concentrated solar plants just store the heat, which is cheap. Other systems just use batteries. A popular option is to run a hydroelectric dam in reverse to store energy by pumping the water up.

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