Technical FAQ: Calculating drivetrain friction losses
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This week’s column references a question from Lennard’s December 3 column about drivetrain friction caused by cross-chaining.
You loved Brad’s calculations— can you help me understand why? Perhaps I haven’t followed what he meant to say.
“The way I recall it, drivetrain gurus have pointed out that during each pass over the chainring, **every link in the chain bends precisely once per pedal revolution.**”
I’m lost right away: Certainly the whole length of a chain doesn’t usually pass, in one revolution of a chainring smaller than about 110 teeth. He doesn’t mean that the ones that do bend just once — he uses “whole chain” again below.
So, “Then if one is on a bike with a given chain length and one selects a given gear ratio using larger rather than smaller cogs using the existing chain, larger gears have less total articulation because the articulation angle per link is reduced, but the number of links stayed the same.”
For the same ratio, using smaller chainring and cogs obviously passes less chain per pedal revolution: the number of links is precisely the number of teeth in the chainring, on each revolution. The number of links that articulate, per pedal revolution, is actually greater for larger chainrings. For fixed ratio and cadence, chain speed is higher, with large chainrings, that’s how driving power can be the same, despite reduced chain tension.
Of course, it’s more complicated, since friction depends on local chain tension, and that tension drops over the first few teeth engaged at the top of the chainring — it’s not spread over the engaged teeth. Easy to see: bike held, pedal forward, press down on the pedal and try lifting links on the chainring, starting at the top.
So, did you leave this letter in, just to make discussion? 😉
Indeed I did. What I loved about it was that Brad was that interested and passionate about it to think about it so much that he made that calculation and wrote in about it, even if it was based on a flawed assumption.
I have found over the years that the best way to catch my own errors is to make them very public; the urge to correct them is almost irresistible once I have posted them, and I begin cringing about what readers must be thinking. And that is exactly what happened in this case. When I replied to Brad’s email, he replied two days later with this (too late to be included in that particular post):
“Regarding Chain Articulation comments: D’oh! I decided it was wrong 30 minutes after I sent it! It must have given you a good chuckle. How embarrassing! I now believe that the other fellow was absolutely right!
The most convenient basis of a fair comparison of the loss rate in two drivetrains would be loss per pedal revolution, in which case a 52 ring bends 52 links by a 360/52 degree angle for a total of 360 degrees of link bending, while a 46-tooth ring would bend 46 links by a 360/46 degree angle for a total of 360 degrees of link bending. Indeed, the number of teeth is “a wash” and the chain tension makes all the difference, just as Louis had said. The smaller gears magnify the chain tension which must directly magnify the link bearing friction and thus the losses. This idea bravely fought its way through my thick, sloping forehead!
A more careful accounting of a comparison between two drivetrains with the same gear ratio but different sized gears is shown in the handwritten graph above.
The main premise of the calculation is to compare the estimated chain friction losses for a 20 mph velocity on two gear setups: a big one (52 X 26) and a small one (26 X 13). My guiding assumption is that the friction loss in the chain per pedal revolution is to consider each point where the chain bends and calculate the product of number-of-bent-links X link-bend-angle X chain-tension-force. Then I am supposing this total would correlate with the relative magnitude of friction losses in the chain. By this estimate, the smaller gear case has higher losses by about 30 percent.
I was able to calculate an estimate for the chain tension on the upper run between cog and chainring due to time-averaged pedal force, but I do not know the chain tension due to the derailleur return spring — so I estimated it to be 10 lbF.
After feeling ashamed of my earlier submission, it is a wonder that I am daring to send additional evidence of my feebleness now. Hope springs eternal!
I of course am very pleased when any reader takes this much initiative and is this tenacious in adding to the discussion here. The table Brad made is particularly illustrative of what is going on. It never occurred to me to make such a table in the original magazine article . And unlike when I make errors in this column, I keep your last names anonymous, so the cringing when you make an error that is posted here is hopefully not as intense as mine sometimes is!
I’m thinking of putting drop bars on my Niner hard tail and using SRAM brake/shift levers to actuate the XO 2X10 drivetrain.
My questions: Will the SRAM drop bar shifters pull enough cable to work with mountain bike derailleurs?
Will hydraulic brake levers work with my Magura MT5 two piston calipers and rotors?
SRAM road shifters do work with SRAM MTB derailleurs. However, you cannot use Magura brake calipers with SRAM levers. SRAM hydraulic brakes use DOT brake fluid, whereas Magura brakes use mineral oil. Those two fluids are incompatible. If you were to put mineral oil in it, you would destroy the seals in the SRAM lever, and if you were to put DOT fluid in, you would destroy the seals in the Magura caliper. In either case, your brakes would not work.
Lennard Zinn, our longtime technical writer, joined VeloNews in 1987. He is also a custom frame builder (www.zinncycles.com) and purveyor of non-custom huge bikes (bikeclydesdale.com), a former U.S. national team rider, co-author of “The Haywire Heart,” and author of many bicycle books including “Zinn and the Art of Road Bike Maintenance,” “DVD, as well as “Zinn and the Art of Triathlon Bikes” and “Zinn’s Cycling Primer: Maintenance Tips and Skill Building for Cyclists.”
He holds a bachelor’s in physics from Colorado College.