Thursday, January 21, 2010

drivetrain losses: running some numbers

I ran my model for two conditions. The first was for 290 watts @ 80 rpm, the other for 50 watts @ 90 rpm.

So what do we expect? At 290 watts @ 80 rpm, chain tension is relatively high. It gets harder to bend chains at higher tension, so reducing the amount of chain tension pays off. Lower chain tension comes from a bigger chainring. The crankset is a simple lever: force on the pedals is multiplied by the ratio of the crank length to the effective chainring radius, and that radius is proportional to the number of chainring teeth. Additionally the bending where it matters most, at the cog, is less in bigger front-rear combos.

On the other hand, at 50 watts, chain tension is small. The built-in tension, both from the chain hanging and from the force of the chain components against each other, still dominates. Here more compact gears gain benefit from moving the chain more slowly. Links bend less often at slower chain speed, so this pays off. And the bending where it matters most, at the pulleys, doesn't change with gear. So increased chain bending in smaller front-rear combos is less of an issue.

Here's some numbers. Don't worry too much about that 19.5 tooth cog.... it's just a model, so doesn't let the pragmatic requirement for integral tooth counts get in its way....
290 watts @ 80 rpm
28/14 w/ 12T pulleys: Ploss = 11.530 (3.976%)
30/15 w/ 12T pulleys: Ploss = 11.125 (3.836%)
32/16 w/ 12T pulleys: Ploss = 10.788 (3.720%)
34/17 w/ 12T pulleys: Ploss = 10.508 (3.623%)
36/18 w/ 12T pulleys: Ploss = 10.275 (3.543%)
39/19.5 w/ 12T pulleys: Ploss = 9.997 (3.447%)
42/21 w/ 12T pulleys: Ploss = 9.790 (3.376%)
44/22 w/ 12T pulleys: Ploss = 9.684 (3.339%)
46/23 w/ 12T pulleys: Ploss = 9.600 (3.310%)
48/24 w/ 12T pulleys: Ploss = 9.535 (3.288%)
50/25 w/ 12T pulleys: Ploss = 9.486 (3.271%)
52/26 w/ 12T pulleys: Ploss = 9.452 (3.259%)
54/27 w/ 12T pulleys: Ploss = 9.432 (3.252%)
56/28 w/ 12T pulleys: Ploss = 9.423 (3.249%)

50 watts @ 90 rpm
28/14 w/ 12T pulleys: Ploss = 5.128 (10.256%)
30/15 w/ 12T pulleys: Ploss = 5.195 (10.390%)
32/16 w/ 12T pulleys: Ploss = 5.274 (10.547%)
34/17 w/ 12T pulleys: Ploss = 5.362 (10.724%)
36/18 w/ 12T pulleys: Ploss = 5.458 (10.917%)
39/19.5 w/ 12T pulleys: Ploss = 5.616 (11.232%)
42/21 w/ 12T pulleys: Ploss = 5.785 (11.570%)
44/22 w/ 12T pulleys: Ploss = 5.904 (11.807%)
46/23 w/ 12T pulleys: Ploss = 6.026 (12.052%)
48/24 w/ 12T pulleys: Ploss = 6.151 (12.303%)
50/25 w/ 12T pulleys: Ploss = 6.280 (12.559%)
52/26 w/ 12T pulleys: Ploss = 6.411 (12.821%)
54/27 w/ 12T pulleys: Ploss = 6.544 (13.087%)
56/28 w/ 12T pulleys: Ploss = 6.679 (13.358%)

3 comments:

specialist said...

Can you show the calculations you did on WW comparing jockey wheel cog sizes? I was surprised by the size of the gains you found.

djconnel said...

I have a bit of that in my previous post in this series. It's tucked in near the end, hard to find, like so much in this rambling blog :).

Actually, the size of the pulley had very little importance.

I've been using 12 teeth as a reference. Most pulleys are actually 11, although you can find 12 tooth pulleys, as well. The key point is the pulley size isn't terribly important: bearing losses in good pulleys are small (ceramic isn't a big issue: my Rival pulleys spin as well as the worse of my two Red pulleys, for example, although my better Red pulley spins longer; all spin "long enough") and the chain is under low tension when it threads through the pulleys so chain loss shouldn't be a big deal.

Of course it's possibly my parameters are off. I did the best I could with these. The pulleys become more important, for example, if my coefficient of friction for chain bending under load is too large.

specialist said...

Not sure how I missed that. If you are right then it might just be a marginal gain worth aggregating for the right price though especially for something like a 100mile TT or 12hr event.