Wednesday, November 14, 2012

For the Analy Retentive Cycist: Part II, Gears

In the previous post, we looked at what causes loss of energy between feet and road, and then suggested that ceramic bearings in hubs, bottom brackets, pulleys, and pedals, save energy--especially when lubricated optimally to reduce friction.

In this post, we'll look at the drive train--the crank, the chain and the cassette--and try to find ways to reduce friction loss.
Graeme Obree and his townie

I've always wondered if certain gears were more efficient than others, in the same manner as Nigel Tufnel wondered if Dmin was "the saddest of all keys."  Researchers at Rohloff, a maker of internal geared hubs found some interesting results when testing out gearing.  It turns out that some gears are more efficient than others.  Test were conducted at a constant power output of 314w at 60rpm.  They tested new, well-lubed equipment as well as old, worn, and dirty equipment that had been subjected to 1000k of riding.  That is why you don' t find a single data point at each ratio in the graph (below), but instead a swath--e.g., at a gear ratio of 26-28, the swath ranges from about 96-98% efficiency.

The first thing to notice is that it is not a horizontal, thin line.  A thin line would indicate that gearing and wear and tear do not effect efficiency, and a horizontal line would indicate that neither gearing nor wear and tear have any effect.

Takeaway #1: Drive train efficiency is variable--that is, things can change it.

(This also interesting because it suggest that there is even some variance in efficiency for fixed gear bikes! More on that later.)

Back to the graph--notice how it isn't a straight line, and it doesn't tilt either way as the gears change size.  This suggests that there isn't a constant relationship between bigger gears and efficiency, so we can't say "bigger/smaller gears are more efficient."  The gearing is most efficient at 46/14 and least efficient at 36/12.  This jump, as the chain is moved onto the big ring up front, does suggest some kind of relationship between throwing it in the big ring and efficiency.  But notice that the least and most efficient gears are right next to each other in terms of distance travelled per crank revolution.

This suggests two separate variables:
(1) The ratio of gears to each other, which gives us distance travel per pedal stroke (teeth on front / teeth on back);
(2) The size of both the gears (teeth on front + teeth on back).

But that's all fairly complicated.  Point is, we can't determine if the ratio of gears to each other is correlated with efficiency, but we can come away with a simple takeaway:

Takeaway #2: Gears effect efficiency.

So which gears are the fastest of all?

From our graph, we can see that simply throwing it on the big ring on the crank (and dropping from the 14 to the 12 on the back) resulted in about a 1% increase in efficiency (i.e., 94.9 - 97.8% at 36/12 jumped to 96.3 - 98.7% on the 46/14). This is the first takeaway from Rohloff's graph (above):  certain gear sizes are more efficient than others--as much as 6w at 314w output.

This suggests, ceteris paribus, that some gears are better than others.

Takeaway #3:  Some gears are more efficient than others, ceteris paribus.

So is the big ring always more efficient than the small ring?  Well, no.  Take a look at the lowest efficiency measured at 46/14--96.3%.  Now look at the highest efficiency measured at 36/12--97.8%).  Sometimes, being in the small ring is more efficient!

What's going on?

Well, you're seeing a range of different readings for the same gearing.  And for good reason--earlier I mentioned that Rohloff took two measurements:  one of clean and new equipment, and another of old and dirty equipment.  That's what you're seeing.    The high end of the scores--the most efficient equipment, no matter what gear--are measurements of new stuff; the low end of scores are old equipment.

This suggests that a worn, dirty 46/14 is less efficient than a new, clean 36/12.  This leads to a fourth takeaway:

Takeaway #4:  The condition of equipment can change efficiency.

I'll come back to condition of equipment, but for now I'll look at why the 42/14 might be the most efficient ratio of those tested.  One simple conclusion is that it is the largest.  42+14 = 56 total teeth on the sprockets.

Is it that ratio?  No, can't be the ratio, because the 46/11 is a larger ratio, but is less efficient.

Is it just size?

Some testers think size of sprockets matters for efficiency, and for good reason:  when the chain slips onto a larger sprocket, its links pivot less than they do on smaller sprockets, and this--and here is the important part--results in less friction.  Of course, larger sprockets weigh more, so there is a trade off, but it is a trade off worth making, according to Cozy Beehive, who estimates that Boardman would have travelled 100m further, during his hour record attempt, had he doubled his sprocket size--increasing efficiency from 98.8 to 99.4%.

Suppose Boardman ran a 53/11.  Cozy Beehive was suggesting that he'd have gone further had he run a--get ready for this--106/22.  Note, this does not alter the distance travelled per pedal stroke.  What it does, according to CB, is reduce the friction loss in the chain, so that the energy required to move that distance per stroke, is 0.6% less.  Of course, throwing a 106/22 on the bike would add a bit of weight, but, according to CB, the increased efficiency of the gigantic drive train would more than compensate.

Takeaway #5: Larger gears (at same ratio) are more efficient than smaller gears

There are a lot more possible ways to save energy with gear choice, but I'm not sure they're worth calling takeaways.  For instance, placement of gears may effect efficiency. Gears situated further from the center of the wheel are less efficient.  Here's an extreme example to illustrate the idea:  imagine if the bicycle had 300 gears and the caseete was 6 feet wide; the casette furthest from the wheel would have to twist a 6-foot long hub and axle, which would then twist the wheel.  The longer that hub, the more energy lost.

Thus, if you have a 11x23, your 23 will lose less energy by transmission through the hub because it is closer to the center of the wheel.

I'm not sure whether this is even a quantifiable loss of energy, but I thought I'd bring it up as an example.  Gearing seems fairly simple, but when it comes to energy loss, there are a whole lot of factors at even the basic level of ratio and size.  This leads to one more takeaway:

Takeaway #6:  Shit's complicated

And in the end, the gears you select should maximize the efficiency of your body, so we're limited in our choices here.  Yes, a 46/14 may be more efficient than a 46/11, but, dammit, I'll spin out in the sprint if I can't drop it down into the 11.

Back to the original question:  What's the fastest of all gears?  If you're Chris Boardman, probably the 106/22.  For the rest of us, it's a bit more complicated, although the big ring is probably better than the little ring, for reasons of chord action.

Up Next
A much more important and clear way to improve efficiency is to address the variance seen in the Rohloff graph above.  In the next post I'll look more closely at lubes for the drive train, and whether chainstretch and cassette wear really matters.

1 comment:

Anonymous said...

If chainring to cog is not in a straight line, you are loosing energy to the sideways force. Draw the triangle to visually see the loss ratio, you could do the math from it too.