On Bicycles, and.... what else is there?

There's been an almost religious response to SRAM releasing 1×11 for the road. I find this puzzling, as to me it represents a valid choice for riding where super-wide range gearing isn't needed. And in the vast majority of the United States, the idea regularly riding extended steep climbs is at best a fantasy. It's restricted to European bike tours, etc. 1×11 provides basically the same gear spacing as 2×8, which honestly back in the day was fine, although also not for everyone, and those who wanted more went to triple chainrings. Today a lot of those who used triples back then are fine with wide-range 2×10 and 2×11 options. But if you want to avoid dealing with a front shifter, and maybe save a bit of weight, 1×11 can be an attractive choice. I was riding with an old colleague from Stanford Cycling, Mark, who's been riding SRAM 1×11 on hilly San Francisco Bay area rides and he loves it. But then he started racing with 2×6, and so learned to ride at a somewhat w...

After I commented on the cleverness of the Da Vinci tandem drivetrain, the guy manning the booth told me "we've been here 17 years in a row". I responded, "but this is my first time here." So this may not be new, and I've likely seen it before @ NAHBS, but in any case I considered it cool. The goal is to allow the stoker to pedal independently of the captain, independently coasting, although still constrained to the same cadence. A side effect of this is the pedals can come out of synchronization, although the stoker could time reinitiation of pedaling to synchronize as desired. Despite their longevity they don't seem to have caught on, as most tandem riders seem content to remain locked together with a fixed timing chain. Da Vinci tandem drivetrain Da Vinci drivetrain, stoker close-up Another curious drivetrain was the " string bike ". This was quite remarkable, converting a circular motion on the pedals to a piston-like motion of ...

A lot of fuss was made in the Tour about the Berner SRAM derailleur upgrades used by Alberto Contador and Andy Schleck. By going from 11 teeth to 15 teeth on the lower rear pulley, the chain bends less upon entry and exit to the pulley while the pulley additionally turns more slowly. Each of these effects reduces drivetrain losses, and that means more of the power to the pedals goes to the road instead of to heating up the bike and air. Berner mod to a Red rear derailleur on a Team Saxo Bank SL/3 ( BikeRadar ) SRAM has evaluated this and claims the results are inconclusive. So much for experimental data: what's a model show? I spent several posts looking at a drivetrain model. I ended up with the following: P loss = (K / L) P (1 / N f + 1 / N r ) + C T 0 K (1 + N f /N r + N f [ 1 / N dt + 1 / N db ] ) + K d C N f [ 1 / N dt + 1 / N db ] / 2 where I define: P loss = power lost to drivetrain, N f = chainring teeth, N r = cog teeth, N db = bottom pu...

Last two times I looked at the results on drivetrain efficiency from having the same gear ratio, riding at the same power. This went to the question of whether it was better to ride a chainring with more or less teeth, choosing a rear cog to match cadence at the same power and speed. The answer was for low power/high cadence, you're better off in a low chainring, while at high power/low cadence you're better off with a bigger ring. A lot of issues go into gear choice, obviously. Ted Huang told me he put a 27-tooth cog on so he could ride the Cat's Hill Criterium , which has a climb of around 15% ( video from 2009 here ) so he wouldn't need to front-shift at the top. The model suggests he may have been better off doing so anyway, although it fails to penalize cross-chaining in any way (consistent with the experimental evidence, which isn't very sensitive to the matter). Hmmm, Ted, that doesn't look like the big ring to me... Anyway, another option is I'm...

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...

After reviewing data from Spicer, from Kyle and Berto, from d'Herripon and Verhoeven, all I get is a headache. So to heck with experimental data. It's always a mistake to let experimental data get in the way of a good theory. So I'm going to forge ahead, and pull the numbers I like from the experiments, and resort to a simple theoretical model for the effect of chain tension on drivetrain loss. I'll start by trusting the pulley friction measurement data I used before , based on experimental data, sure, but experiments on a simpler system (a pulley on bearings) than on a more complex system (a full drivetrain): Kd = 94 mJ/rev for Shimano Dura-Ace Kd = 2.4 mJ/rev for CeramicSpeed pulleys Data measured by Mark Kelly : Kd = 37 mJ/rev (standard bearings) Kd = 6.4 mJ/rev (high quality steel bearings) Then based on a pin diameter of 5/32 inches = 3.97 mm, and using a coefficient of friction for steel-on-steel with a smooth oxide coating = 0.27 , with a tooth pi...

In Human Power 48 (1999) , Dave Wilson does a nice review of posts to the now defunct Bicycling Science mailing list (previously called "Hardcore Bicycle Science", presumably named to discourage the usual idle chatter which had diluted the rec.bicycles.tech USENET group). The most relevant data to my purpose was credited to Jan Verhoeven, although details were not available. Searching the list archives, I found similar data from Bas d'Herripon . Both tests were on a Shimano Deore LX drivetrain. Here's the results from d'Herripon: N f N r efficiency 22 28 98.2 22 24 97.3 22 21 97.9 22 18 96.5 32 21 95.3 32 18 94.4 32 16 93.8 32 14 93.3 42 16 92.8 42 14 91.5 42 12 91.6 42 11 91.6 For d'Herripon, crank cadence was at 70 rpm. I assume the same for Verhoeven. Both data sets were for drive power of 200 watts. My model has three unknowns: K, T 0 , and K d . But as before, I can set K d based on specific measurements, using a value of 94 mJ/revolution measured o...

Last time I discussed Spicer's measurements published in Human Power 50 (2000) . The key issue there is that drivetrain efficiency consisted of a component associated with infinite chain tension, plus an additional contribution proportional to the recprocal of chain tension. Each of these terms, the slope and intercept versus 1/tension, depends on some combination of the reciprocals of chainring teeth, cog teeth, and pulley teeth. The problem is for infinite tension, or worst with infinite tension and infinite-sized chainrings and cogs, the extrapolated efficiency exceeded 100%. For example my regressions had a maximum efficiency of 106.6%. Bonanza! The energy crisis is solved! But onward to other measurements. In Human Power 52, summer 2001 , Chester Kyle and Frank Berto published some really nice experiments measuring drivetrain efficiency, of primary interest being those of an Ultegra 3×9 system. They did their measurements with the crank driving the hub, and the hub d...

Recall Spicer did some nice drivetrain efficiency measurements, which he published in Human Power 50, 2000. His argument is that chain tension is an important parameter, that higher tension tends to yield higher efficiency. Here's his result again: Spicer 's efficiency measurements as a function of reciprocal chain tension for each of three rear cogs My model described dissipated power rather than drivetrain efficiency. To get efficiency (ν), I take the power dissipation as a function of T and divide it by power P, where T / P = chain speed = R L = C N f L. ν ≡ 1 ‒ P dt / P = 1 ‒ (K / L) [1/N f + 1/N r + 2 (T 0 / T) (1/N f + 1/N r + 2/N d )] ‒ K d / (N d T L). Spicer says efficiency depends on T but is independent of chain speed. However, since Spicer uses a conatant N f , for him constant chain speed simply means constant C. the above equation is indeed independent of C. Furthermore, Spicer says ν is well fit by a formula ν = ν ∞ ‒ α / T for some constant ν ...

My model for drivetrain losses, which I'm sure is unoriginal as it's so obvious, is to model the power loss as each chain link completes a circuit: Bicycle drivetrain from Wikipedia . Start at the bottom of the crank. The chain link is at a fixed tension determined by the derailleur spring. It moves backward, not bending, until it reaches the bottom derailleur pulley. This motion dissipates negligible energy. Note there is some bending here due to a nonideal chain line. But I'll believe Spicer 's assertion, which I found surprising, that chainline is relatively unimportant. The chain link bends as it contacts the bottom deraileur pulley. It does so under low tension. The amount of bending is independent of the gear selection. This dissipates some energy. The chain link moves along with the pulley. This dissipates negligible energy. The chain link unbends after losing contact with the bottom pulley. This dissipates energy. Still the tension is low, set by the...

Drivetrain losses are an important factor in cycling. A sort of canonical number is they are responsible for 3% of total power during high-intensity riding. Wilson's Bicycling Science 3rd edition (2004, MIT Press) page 343 shows data indicating at 200 watts, losses vary from 2.4% to 3.1% among three gear choices with a clean chain:   6-speed derailleur Power (W) 24T cog 19T cog 13T cog 50 94.2% 94.1% 92.1% 100 96.2% 96.4% 94.9% 200 97.4% 97.6% 96.9% 400 98.1% 98.4% 97.8% A comparison of a "no rust, lubricated" chain to a "rusty, dry" chain yields a difference of 4-5% (absolute) at 200 watts, which is huge. Anyway, from these data it's clear a fixed "drivetrain efficiency" is a poor model. Even if you allow the efficiency to vary from one gear to another, there's a clear power dependence. And allowing an "efficiency" to vary with power is obviously obfuscated: you're applying a model that drivetrain losses are propo...