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Depends on your path round the velodrome, doesn't it? If you're managing a steady speed round the track and not going up and down the banking, the only difference is going to be in the initial work of accelerating up to speed.
I would have thought that on a track it was the reduced rolling resistance of lightweight tubes that made the greater difference (and wouldn't they have used tubs?). Rolling resistance is also a function of load on the tyre, but a 50g difference is going to be an infinitesimal effect at track pressures.
(Edit - beaten to it by Tester)
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If you're managing a steady speed round the track and not going up and down the banking
There's an interesting thing here for more advanced maths illustration. Leaving the inner tubes aside, because they are nothing like a simple change of mass, let's say the initial sample bike comes in at 6.75kg. To pass scrutineering, you buy a 50g slug of Tungsten and glue it inside one of the frame tubes. On a pursuit bike, where do you glue it to maximise the benefit?
Thanks for replying. I’m trying to work out the energy impact of using normal inner tubes vs. light weight inner tubes (combined weight difference of 50g) on, e.g., Campenaerts’ hour record of 55km. It’s for illustrative purposes rather than a formal inquiry, so don’t need to overly complicate it.
Edit- what I’ve done so far:
W=F*d
W=(m*a)d . I’m not sure how to work out or around the acceleration.
W=[m(v-v0/t)]d
W=[.05kg(15.28m/s-0m/s /3600s)55000m
W=[.05kg(.004244m/s^2)]55000m
W=.000212N*55000m
W=11.66J
...?