Now, let's say for the sake of argument we do this acceleration over a period of 10s, the extra power needed to accelerate the big-ring drive is 0.5W. This kind of acceleration needs quite a lot of input power, somewhere in the region of 1000W, and some old calculations I did using some long lost software indicated that the theoretical difference in chain absorbed power at 250W at 100rpm was about 1W when going from 40t to 60t, so we can hazard a reasonably informed guess that you're going to need something like an extra 2W to overcome the extra losses if you drive a 40t rather than a 52t at 1000W.
(I'm not a physics/maths person)
What's the situation then with a more appropriate example of the acceleration being done over 2s rather than 10s, bearing in mind the perceived advantages of small chainrings occur in the context of snap/jump. Would you be dividing the time by 5, therefore increasing the extra power needed by the same i.e. 10W to overcome drivetrain losses? Or even 0.5s / 40W? Sprints are decided in those kind of timescales if snap/jump is the deciding factor.
(I'm not a physics/maths person)
What's the situation then with a more appropriate example of the acceleration being done over 2s rather than 10s, bearing in mind the perceived advantages of small chainrings occur in the context of snap/jump. Would you be dividing the time by 5, therefore increasing the extra power needed by the same i.e. 10W to overcome drivetrain losses? Or even 0.5s / 40W? Sprints are decided in those kind of timescales if snap/jump is the deciding factor.
If the maths is wrong, sorry :/