Originally Posted by PeteHski

Okay, just for fun I made a very simple spreadsheet to calculate average power required to accelerate a bike from a standstill to a given speed.

So my simple bike model:-

Static mass m = 85 kg
Rotating Mass (wheels and tyres) mw = 3 kg

Initial speed u = 0
Final speed v = 11 m/s (40 kph)
Acceleration a = 0.75 m/s/s
Time taken t = 14.7 s

Kinetic Energy of static mass = 0.5 x m x v^2 = 5143J
Kinetic Energy of rotating mass = m x v^2 = 363J (Simplification with 100% of rotating mass at the tyre radius)
Kinetic Energy total = 5506J

Av Power total = KE/t = 375W
Av Power for total rotating mass = 25W (6.67% of total power)

If I saved 1 kg from the rotating mass (i.e. 33% - a very large and likely very expensive saving):-

KE static = 5143J
KE rotating = 242J
KE total = 5385J

Av Power total = 367W - saving of 8.3W (2.2%) over baseline:-

If I saved 1 kg from the static mass (a free trip to the toilet or a couple of weeks not eating junk food):-

KE static = 5082J
KE rotating = 363J
KE total = 5445J

Av Power total = 371 W - saving of 4.1W (1.1%) over baseline

So with my simplified model (worst case rotating mass ENTIRELY at the tyre outer radius), I save an absolute maximum of 4W (1 kg rotating vs 1 kg static mass) over an acceleration from 0-40 kph at 375W. Also consider that this calculation doesn't include additional power required to overcome air resistance or rolling resistance. It is only the power required to accelerate the mass.

Notes:

1. This is all my own working out using the appropriate equations with real world parameter values. So no 13 kg wheels made out of solid aluminium.
2. The simplifications and values are intended to maximise the effect of rotational inertia i.e. high acceleration, large mass saving and maximised wheel MOI.