What's your favourite gear ratio?

^Good shout!

It takes less energy to accelerate a 40/13 gear ratio from 0 to 120r.p.m. than it does a 52/17 ratio, that's an undisputed fact.

It's not undisputed, because I dispute it.

We can pretty much disregard the chainring and sprocket inertia, because the difference is tiny next to the inertia of the heavy chain. On the big ring, the chain has to go faster, so you definitely need to add more energy to that system to get it up to speed. However, the big ring system has higher efficiency, you can look up chain drive theory for yourself or you can take my word for it, but it's the case either way.

Now, the pcd of a 52t ring is 210mm, and 120rpm is 4π rad/s, so the eventual chain speed is 0.105×4π m/s, and the chain mass is about 0.4kg, so it's kinetic energy is
0.5×0.4×(0.105×4π)²=0.35J
We can simply scale for the little ring to get (40/52)²×0.35=0.20J

Of course, the big-ring system needs a greater length of chain, by about 12%, and that extra 50g of chain also need to be accelerated with the rest of the bike up to about 15m/s, so there is another 5J of energy to expend there, which swamps the 0.15J difference caused by the higher chain speed.

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.

Feel free to pick holes in my analysis, but at first pass it looks like you could never accelerate fast enough on a bicycle to make the drivetrain inertia matter, because the the excess friction losses are always running away from the tiny decrease in the energy needed to bring the drive up to speed, by a factor of about 4.

TLDR=? It's not a noticeable difference?

There you have it, and so the debate ends, on my part anyway. This will be my last entry on the subject ever, at leas in this thread.

Having said that, I sincerely hope that one day I'll get the opportunity to meet you guys and be able to show you my credentials, let alone the credentials of my coach. I have no doubt that you will all stand your ground regardless, but trust me, you will definitely be in for a surprise ;-)

I do not fault your credentials, just that something seemed off about the claims and that I would need someone smarter than I to explain it, and then someone less smart, but still smarter than I to translate it.

In other news, I did a 4km run on a 53/14 ratio this afternoon, well yesterday really I suppose. Flat, secluded from traffic, sun shining, full power all the way, fucking beautiful. For a brief moment there, I felt like I was braking the world record. Far from it in reality of course, but you lot and your maths can never take that feeling away from me.

There you have it, and so the debate ends, on my part anyway. This will be my last entry on the subject ever, at leas in this thread.

Having said that, I sincerely hope that one day I'll get the opportunity to meet you guys and be able to show you my credentials, let alone the credentials of my coach. I have no doubt that you will all stand your ground regardless, but trust me, you will definitely be in for a surprise ;-)

Are you Victoria Pendleton?

aicmfp

My maths can't, but I can ask why you were running with your bike.

My maths can barely sort out the right money for a pint.

record braking looser! > > > > >

^^If we ever do meet, please bring a transcript of this thread, or simply remind me to punch you in the face before we hit the bar.

Duly noted.

Anticlimax big style... What are we gonna argue about now?

Your secret identity?

If an anticlimax is failure to climax, what would returning said climax back from whence it came be? An unclimax? Declimax?

"Your secret identity?"

No more secret than yours... Mum?

http://24.media.tumblr.com/tumblr_m910fhAUa71qhdayio1_500.jpg

otter cums on self

I think this is returning the climax from whence it came, no?

In a slightly less direct method than I had in mind.

Ha!

Playground is about to shut... :-(

I sincerely hope that one day I'll get the opportunity to meet you guys and be able to show you my credentials, let alone the credentials of my coach.

You could be Tony Doyle and Alf Whiteway for all that it matters; cyclists, and perhaps particularly track cyclists, failed to grasp physics because they were bound up in superstition and tradition for decades.

Everything which is now being done on the track could have been done in 1950 if people had imported expertise from other fields at the time. We have CFD and FEA to make development quicker and perhaps cheaper, and we have some new materials which score some marginal gains, but in 1950 there were the low speed wind tunnels and sufficient available aerospace materials to make something the shape of a modern track bike with disc wheels. It wouldn't have been as stiff and light as today's all carbon fibre designs, but it would certainly have been faster than the then state-of-the-art round-tubed steel frames with high spoke-count low rim-depth wheels. It's not just about the bike either; we made what are by today's standards appalling errors in training and nutrition back in the olden days, sometimes because nobody knew better but equally because cycling coaches thought that the things which had worked in the past were still the best, even while the science was pointing in a different direction.

^This

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.

If the maths is wrong, sorry :/

We were talking about going from 0 to 120rpm, on Pro sprint gearing that's from a standing start to about 36mph. Nobody can do that in 2s. If they could, they would need to make about 5 times as much power in our example, so chain friction loss would be nearly 5 times as high (nearly, because only roller friction loss goes up with power, side plate friction is constant). Inertial effects remain the same in terms of energy, so reducing the time by a factor of 5 just increases the power needed by the same factor. So, assuming you can find somebody with the 5kW* burst needed (and the long chainstays required to get the required grip off the line and keep the front wheel somewhere hear the ground), the big ring drive needs an extra 2.5W to accelerate but loses about 8W less in friction compared wit the small-ring drive.

*This is simple scaling from my previous example, which turns out to be wrong by a factor of more than 2. The kinetic energy of a normal sized track sprinter (100kg including bike and clothing) at 36mph (16m/s) is 26kJ (ignoring the small additional inertia of the rotating parts), so he needs 2.6kW for 10s just to accelerate, plus a rising amount to overcome drag which will be of the order of 700W at full speed. We can disregard drag if we just deal with the first rotation of the crank, but that still places an upper bound on acceleration rate on 100" gearing of 12rpm/s, unless you can find a rider who can exceed the 26W/kg starting effort described.