# Radius vs speed for flywheel energy storage

If I understand the formula correctly, the equation for kinetic energy of a flywheel is $$mw^2r^2$$ whereas the formula for "centrifugal force" is $$mw^2r$$.

So how come so much focus is on the speed of flywheels if you could get 4x the power with only 2x the strain by doubling the radius?

• How about the space required? And the bursting forces... – user207455 Jun 25 at 8:15
• @SolarMike Grid sotrage doesnt really need to worry about space. Also how would bursting forces be a problem? Nothing is packing inside anything else – P.Lord Jun 25 at 8:24
• Have a search for "kinetic energy storage" and see what you find... – user207455 Jun 25 at 8:25
• Yeah, no references to bursting forces and space requirements for portabpe use but not grid storage. I think you may be confused – P.Lord Jun 25 at 8:37
• I’m not confused, you don’t mention grid storage in your question and I know how kinetic energy storage works and it has been used on buses... So I’m happy where I am, I tried to help you by giving you some hints on what to search for to help your google-fu but.... – user207455 Jun 25 at 9:12

While the kinetic energy scales with $$r^2$$, so does the material requirement. This means the kinetic energy storage only increases linearly with the amount of material. On the other hand running your flywheel faster increases kinetic energy storage for free (as long as you don't reach the stress limit). This means to keep cost low you always run your flywheel at maximum speed (for its radius). Then you either increase the flywheels radius or the amount of flywheels until you meet your required energy capacity. In both cases stored energy scales linearly with material requirement.
• @P.Lord The energy capacity increases only by $r^2$ if you keep $\omega$ constant. But if your flywheel is already running at maximum speed, increasing $r$ while keeping $\omega$ constant will rip it apart. Therefore if you further increase $r$ you have to decrease $\omega$, to not rip it apart. The result is that the energy capacity only increases proportional to the mass $m$ for any flywheel. For a ring shaped flywheel that means $E\propto r$, for a disc shaped flywheel $E\propto r^2$. – Azzinoth Jun 25 at 16:35