Tuesday, June 24, 2008

Is There an Optimum Bicycle Crank Length ?

Here is a strange fact: humans come in an enormous range of sizes, bicycle frames vary nearly as much, bike riders adjust their seat heights based on their leg lengths, but yet bicycle crank arms are all nearly identical in length, with perhaps 98% of them ranging in length by just half a centimeter. That's less than a quarter of an inch.

So, why is that?

Well, there are probably several reasons why, but unfortunately none of the reasons are based on logic, evidence, or on our understanding of human physiology. Perhaps some of the best ways to describe why bike cranks are all nearly the same length is, 'manufacturing expediency' and, of course, the always present, 'tradition'. Occasionally, even various people in cycling or in the bike business assert that either crank length has no effect at all, or that cranks sized over a very small size range in tiny increments (such as 2.5 mm) are adequate to fit nearly all riders. While others say that the mechanical advantage differences provided by different crank arm lengths are irrelevant because of bicycle gearing (changing gears does indeed change the force applied to the pedals, but it does not address range of motion).

Unfortunately, there is not a lot of evidence to support most of these assertions. So the intent of this essay is to use known physiological evidence and principles to support a more logic-based approach to examine a seeming "revolutionary" (no, not really revolutionary) idea: the theory that in general bicycle crank arms should be sized approximately in proportion to the rider's legs. In other words, the idea that short legs generally work best pedaling shorter cranks, and that long legs generally work best pedaling longer cranks. This essay will also try to show that there is evidence to support the idea that, for a given sized cyclist riding a specified cycling event (such as, say, a 40 km cycling time trial), there may exist an optimum (and proportional) crank length for a rider of that particular size in that type of event.

For now, we will ignore the way that crank length can affect hip and knee angle at top dead center when a rider is in a highly bent over TT position. Instead, we'll assume a moderate but fairly aero road or gravel riding position and then examine the arguments and basis (if any) for proportional crank length. But, even among those readers that accept the general idea of proportional crank length, the question comes up: aren't cranks already proportionally sized if you can easily get them in 170 mm, 172.5 mm, and 175 mm lengths?

Well, not exactly. Say you assume that someone with a 31-inch (78.7 cm) inseam should ride 170 mm cranks. Well, if you accept a proportional crank-to-leg relationship, then 175 mm cranks will fit a rider with just a 31.9-inch (81.1 cm) inseam.

So with most bicycle cranks, you actually end up with less than one inch (2.5 cm) of leg size range. And cranks longer or shorter than those like 165 mm and 180 mm lengths (which are more difficult to find and fewer riders use) will only increase the proportional inseam range a little more, from 30.1 inches (76.5 cm) to 32.8 inches (83.3 cm). So, if you consider the real human family and were to go out and measure the inseams of a few taller male riders and those of a few smaller female riders, you'll very quickly discover how ridiculously small that range actually is.

And just as bicycle seat height has been shown (in lab tests and research) to affect bike rider power output and efficiency, crank length also likely has an effect on power output. But, like seat height, if crank length changes by only 1 mm, it's unlikely that any performance difference will be large. Instead, the power difference may be so small as to be essentially undetectable. However, if crank length changes by larger increments such as 5 mm, 10 mm, or 50 mm, well, then the story changes entirely.

To support the idea that bicycle cranks in a size proportional to the rider make a difference in cycling power output, we will use a bit of logic, a little common sense, and some basic knowledge of human biomechanics and physiology. We will also make a few assumptions along the way, but they'll be assumptions that even a skeptical reader will be able to accept fairly easily. So, read on, look at the figures, follow the reasoning, and then decide for yourself.

While there have been a few research studies published that have tried to examine some aspects of human performance and bike crank length, little of the research to date has shed light on the relationship between submaximal cycling performance and crank length (submaximal means that the work occurs over an extended time and at less than 100% effort). Also, many of the crank length studies to date have had some significant limitations regarding the variables examined, the methodology used, the sample size, etc. Doing a truly thorough real-world study to adequately examine the relationship between bicycle crank length, rider leg length, and endurance cycling performance would not be an easy endeavor, as it would take quite a bit of time money.

But, interestingly, there might be an alternative.

Using just a few basic assumptions, the argument for proportional crank length can also be explored by conducting a dinner napkin "thought experiment." Using just known physiological principles and some basic logic, it is possible to examine whether or not bicycle crank length could have an effect on sustained cycling power output and rider efficiency and this can be done (to a degree of course) without actually doing a scientific study. While the results of such a "virtual" experiment like this will clearly not be the final word on this topic, the results may point the way to where the real answers might lie.

To begin this thought experiment, one can start with just a single virtual individual as a test subject, a person, say, about 5'8" (1.7 meters) in height. We can all safely assume that, if he or she is very fit, experience tells us that he or she will likely be able to generate decent levels of power with bicycle cranks that are 170 mm long.

So, for such a thought experiment, let's assume that our imaginary 5'8" (1.7 meter) tall test subject is a very fit endurance athlete (a runner would probably do fine), but one who has never trained on a bike (this last requirement may be important because, if the subject has already trained a lot on a bike, his legs have likely already begun adapting to the crank length he was using previously (most likely 170 mm cranks, because they are the most common).

One can start this case study by generating a baseline. This would be done by testing our virtual human subject and determining his maximum oxygen uptake (max VO2) on an ergometer (an indoor bike trainer) with standard 170 mm cranks just so that we can get a rough idea of his maximum ability to generate work (generate power).

Once the rider's max VO2 is quantified, the next step would be to test the rider with a few different length cranks and then see how many average watts (as measured at the bottom bracket or rear wheel) he can generate for a somewhat sustained effort at, say, 85% of his max VO2. The idea behind this is, if one crank length was indeed 'better' or more efficient than another length, then the subject would be able to generate more sustained average watts with the 'better' length crank while still pedaling at the same effort level.

So one could begin this experiment by testing the subject with just three different length cranks. On this and all the following protocols, it would be desirable to do each and every test when the rider is completely rested so that only accurate and repeatable results are generated. An initial protocol would be to test the subject at 85% of his VO2 max with cranks that are 170 mm long and then two totally 'crazy' crank lengths: a test with ultra-short 50 mm cranks, and a test with ultra-long 300 mm cranks. And in each test, ergometer's seat height will be adjusted so that it will remain constant relative to the pedal position at bottom dead center (as measured parallel and along the seat tube). The subject will be allowed to self-select his own pedaling cadence, but during the test protocol, the subject will have a chance to try a wide range of normal cadences. The cadences that result in the highest sustained wattages (at 85% of his VO2 max) will be identified and the test rider will be encouraged to use those higher wattage cadences.

So what kind of data will be collected? Well, since this experiment is imaginary, obviously absolute power numbers will not be provided, but it is reasonable to assume that (and most experienced riders and exercise physiologists would agree) if one were to take a physically fit 5'8" (1.7 meter) tall human subject through the test protocol described roughly above, the first 3 data points would very likely look a lot like this:

(click on any of the figures below to zoom in)


If there is agreement that this is indeed the kind of data that would be collected in the first part of the experiment, the next interesting question would be what would happen if one could take the same test subject and then test him with the same basic protocol as before, but this time test him on every single crank length (say, in 5 mm increments) in the entire range between 50 mm super short cranks and 300 mm super long cranks (e.g., crank lengths of 50 mm, 55 mm, 60 mm, 65 mm, 70 mm, and so on, all the way to crank lengths of 280 mm, 285 mm, 290 mm, 295 mm, and 300 mm) ?

So if one went ahead and did that as the next part of the experiment, what kind of data would be collected as the subject was tested through this wide range of cranks lengths? And then, if all of those data points were graphed similarly and approximated with a curve, what would this curve look like? Again, since this experiment is imaginary, absolute hard numbers cannot be provided, nor can an absolute data curve be generated. But, based on even fairly basic knowledge of human physiology and biomechanics and on the accepted understanding that the human body is essentially an analog and not a digital machine, it is pretty safe to assume that the curve though the data points collected in this part of the experiment would most definitely not look like this:

Fig. 2

But, of course, this then begs a more interesting question, if the data curve would not look like fig. 2, then what would the data curve look like? And what is that curve going to indicate?

Well, since the same basic test procedure was used in every test so far, basic logic would dictate that the curve would have to at least intersect the first three data points that were collected in the first part of the experiment (the theoretical data shown in fig. 1). This means that the curve is going to indicate that somewhere between 50 mm cranks and 300 mm cranks, for this test subject there is some optimal crank length range where this rider is able to generate more sustained watts (at 85% of his max VO2) than he could with the extremely short or with the extremely long crank lengths. So, based on this general line of reasoning, the curve through all these data points might very well look like this:

Fig. 3

But not necessarily. The data curve would look like fig. 3 only if it just so happened that a 170 mm crank length was exactly the optimal length for this test subject. Which might not be likely.

So, what would the curve look like if this was not the case? What would we see if perhaps there was some crank length longer or shorter than 170 mm where the subject was able to generate more watts? Would it be possible to have a viable curve that would still intersect the original three data points and not follow a highly unrealistic "digital" shape (like the digital curve shown in fig. 2) ?

Actually, yes, this would be possible. This is what the data curve might look like if cranks somewhat longer than 170 mm were better for this particular test subject:

Fig. 4

And this is what the data curve might look like if cranks somewhat shorter than 170 mm were better for this test subject:

Fig. 5

One could (and should) do this same series of tests with other human subjects, individuals much shorter or much taller than our initial 5'8" (1.7 meter) test subject. To do the same basic tests on different sized subjects, it would be smart to proportionally adjust the baseline test crank length and also the sizes of the "crazy length" test cranks (i.e., make the range of all the test cranks lengths longer for tall test riders, and make the cranks all shorter for small test riders). But logic would suggest that essentially similar data curves would be generated which would suggest the same general conclusions.

As an aside, in this test, the "crazy length" super long and super short cranks were not chosen because there is something magical about the 50 mm or 300 mm crank lengths. No, those dimensions might be chosen (if arbitrarily) because, for an average-sized bike rider, those two lengths are incredibly short (or incredibly long). Based on experience and common sense, those crank lengths are very likely to be less efficient for a 5'8" (1.7 meter) tall rider than standard 170 mm long cranks. (But if one were to do this test on a bike rider that is 7' (2.1 meters) tall, a 170 mm long crank would probably be an almost 'crazy short' length crank for him, and a 300 mm long crank might not be nearly so 'crazy long.')

It is important to point out that this thought experiment does not prove that any particular rider should be riding with "long" cranks or with "short" cranks. What it does try to show is that there is physiological, biomechanical, and logical support behind the conclusion that there likely exists an optimum crank length (or crank length range) for riders of every single size, and that it may be close in length to 170 mm, or it may not. (Actually, given the very wide range of leg lengths out there in the cycling world, it is likely that for most riders 170 mm cranks will not be optimal.)

Essentially, all other things being equal, this results of an experiment like this would suggest that, based on the reasoning above, one's optimal crank length is likely to be somewhat proportional to leg length. In reality, this theory is far from revolutionary but it seems to run against some accepted cycling "tradition."

If any of this makes logical sense to you, it might be interesting to look at the link at the very top right of this page (link to Kirby Palm's crank length formula page). On his page, Mr. Palm proposes a basic formula for determining crank length based, not on what's convenient for bike manufacturers, but on the rider's actual leg length. Read his supporting info, measure your own legs, put your measurement into the formula, and you might be surprised. Easily 9 out of 10 riders who do that will discover that the cranks they are using right now may not be the right size.

If you have ideas, comments, and/or questions about this topic, you can email me (the author) at bicyclecranklength at gmail dot com. In my experience, riders that are taller or shorter than average tend to be a little more interested and passionate about crank length questions, probably because taller or shorter cyclists find that riding on standard-length cranks is not always so comfortable or efficient for them. For a lot a riders, the shortcomings of standard-length cranks are not very problematic when riding at lower effort levels or on mostly flatter terrain. But when riding fast or when climbing big hills or mountains, having cranks that are not optimally sized can noticeably affect comfort, performance, or usually both.

If you want to continue the conversation, another way to do this might be to start a thread about this topic on an online cycling forum. If you post a link to this article, you might get some interesting responses. And, if you're in the academic world, and have some funds and some time, this might be a very interesting thesis project ...