Finding optimum angular velocity of own designed KERS

[kang_smith]

I am doing a university project related with designing KERS.
I am stuck in finding out the max ω(optimum angular velocity) of the flywheel that store max E(kinetic energy).

The information i got is:

Eq. 1: E= 1/2 mr^2 ω^2
Eq. 5: E= Emax (1-s^2) s = ω,min/ω,max
By looking at Eq. 1, running at low speed will not have much kinetic energy, thus have less turning cycle and not much electricity can be generated.
In contrast, by looking at Eq. 5, lowering the ω,min will actually have greater useful energy.

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In theory the higher the angular velocity the better. This would require less inertia to store the same amount of energy, thus reducing the overall weight and packaging requirements.

However, the higher the angular velocity, the more stress you put into the flywheel due to centrifugal forces (each shape of flywheel out of a set material will have a angular velocity at which it will rip itself apart). Also, the higher the flywheel revs, the more difficult (and bigger) the transmission between flywheel and output shaft will be due to the high gear ratios. A high ratio transmission including some sort of CVT will have various power losses due to friction; and most of these losses tend to increase as revs go up.