Monday, January 16, 2012

Factors Affecting Bicycle Transmission Efficiency

Recently I had been thinking about what kind of gear ratios I would need to climb Mount Washington on my derailleur equipped bike. Being an engineer, efficiency is a staple word in my daily mingling with other engineers.

So I started to think about gear to gear effect on a multi speed road bike, such as one with 30 speeds (3 gears up front, 10 in the back). If one could save a bit of power by choosing the most mechanically efficient gearing, that'd be a relief on a long climb (lesser energy expenditure) and could translate into quicker times.

Most people you talk to about this subject would snap that the well oiled bicycle chain is 98% efficient and the discussion would end there. However, missing from that discussion is several factors that could skew it one way or the other.

One factor may be obvious - chain tension. If the chain is too long for the job, the slack side tension is now more, which will subtract from the tight side tension in the power equation. You wont be riding for a long time this way because there is higher tendency for the chain to 'jump' or skip gears. Efficiency for a given cadence will be lower.

The second factor is the selected gear. When you move away from a single speed setup and loop your chain through a derailleur and a cog containing several sprockets, efficiency is not really constant per se from gear to gear. Some gears happen to be more efficient than others, perhaps because of what you can call lesser system 'restrictions'.  

If you picture yourself as a link on the chain and think about the challenge of having to maintain chain tension while bending around big and small gears alike, you'd carry power more easily the lesser you'd have to twist and bend. Atleast that's my theory. I'd like to think that a 11T small cog presents a bigger restriction to chain-link movement than a 17T cog.

Other things are less obvious. What could the effect on drivetrain wear be? I've written about an effect called chordal action when using high gears.

To measure gear to gear efficiency loss with any degree of high accuracy takes a dyno setup, load cells, a data acquisition system and lots of time. Fortunately, Chester Kyle, a mechanical engineering professor at Cal State Long Beach and founding father of IHPVA, did some very relevant work on this stuff back in the day. In Vol 52-2001 of the Human Power magazine, he describes using a single setup, with varying loads to measure efficiency in multiple drivetrain systems including hub gears.

Some of the findings were -

1) Efficiency generally increased with load : As you drive the crank to higher power inputs, the frictional factors eating away at that input becomes a lesser percentage as the input goes up. So frictional effects go up less rapidly. (Ofcourse, we're talking about mechanical efficiency here. If the human body is less efficient at oxygen intake and clearing away lactate at higher loads, there's really no point in trying to hammer away with higher gears. But that's a subject for another day)

2) There is generally a 1-3% difference in efficiency between adjacent gears. Prof. Kyle wrote that "an average of 2% difference in efficiency is thus easily possible if the wrong gears are chosen".

3) The efficiency (for all loads tested) tends to fall with higher gear ratios for all transmission systems tested.

Since I was thinking about my own road bike setup, I was particularly interested in the test he performed on the 27 speed Shimano system. The efficiency curve for this setup looked like this from the study :

A Shimano Ultegra 27-speed mountain- bike transmission with three front chainrings (44/32/22 teeth) and a 9-speed rear cluster (12, 14, 16, 18, 20, 23, 26, 30, and 34 teeth). Input cadence is constant at 75 rpm. Driven load power selected were 80 W, 150 W and 200 W. Dotted trend line shows average efficiency of setup tested at all loads decreasing with gear number.

Since Prof. Kyle ran out of time, only 15 of the 27 gears were tested.

I constructed the legend of the data points below. Gear ratio, calculated as driven teeth divided by driving teeth, decreases from top to bottom. Smaller gear ratio means "high gear" while the opposite is "low gear". Generally, the former is important if you wanted top speed and the latter would be if you cared for acceleration.

The graph show interesting things and I'd like to highlight a couple that caught my eye:

1) I'm seeing that higher gears and hence lower gear ratios mean you can lose efficiency but some perspective is important here. Between the lowest gear and the highest gears tested in this setup, there's a 1 point drop in average efficiency.

2) The 44/34T gear, which is a  big front-big rear cross chained scenario, shows the worst efficiency. Generally, cross chaining is not a good thing so this might be the proof of that.

3) The 44/12T gear, which is a big front-small rear cross chained scenario interestingly shows about the same efficiency at 75 rpm as a 44/26T. Why is this so, given that I said driving a chain around a smaller cog is probably worse for transmission efficiency? No idea. Perhaps its more straight chained than the latter. Moreover, this type of cross chaining shows higher efficiency than a big-front-big rear cross chain.  

4) 44/20T shows the highest efficiency of 95%, and if you included the 1-2% in friction loses in Prof. Kyle's study, that translates to 96-97% efficiency.. It must be straight chained as well. Could anyone verify this?

This study is truly interesting and has implications for performance improvement. I wonder if anyone else from another part of the world had a chance to investigate this more. It paves way for some interesting discussion.


52/12T vs 52/11T Gearing : A Look At Chordal Action

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