Bicycle Crank Length: Some References

I am including some references for those who wish to read further. Most of these were sent to me; I haven't read them all myself. Reportedly, this study did not allow that different length cranks might produce optimal power at different cadences. If so, it's totally invalid. Reportedly, this mathematical model assumed a rigid ankle joint. If so, it's totally invalid. These studies reportedly used a mathematical model to evaluate cadence, crank length, seat tube angle, seat height, and foot position on the "cost" of pedalling at 200 watts. This essentially means the "efficiency" -- how to produce that much power with the least wasted effort. Unfortunately, the "cost" or "efficiency" is of no importance whatsoever in the design of a crankset; the only things of importance are maximum power (at several different conditions, of course) and comfort. The study concluded that the optimum crank length (least cost at 200W) for an average size rider is 140mm. It did conclude that the optimum length varies with rider size. This test apparently evaluated crank lengths from 150mm to 185mm, all at the same cadence. In other words, totally invalid. However, Zinn recognized that the test was invalid -- because he questioned the conclusion that the shorter the crank, the better -- so he performed a second study. Since I have a copy of this report, I can address its shortcomings in more detail:

For this second test, a different cadence was used for each crank length; but rather than actually determining experimentally what the ideal cadence would be -- or, better yet, allowing the rider to set his own cadence for each -- Zinn came up with a formula for constant pedal speed and forced all tests to be at the same constant pedal speed. In the course of testing, this pedal speed proved inefficient or even unattainable on short cranks -- an indication that this methodology is as flawed as the constant cadence idea was, only in the opposite direction.

Among his conclusions: "Long cranks excel in steady-state cycling, which our test mimics, but acceleration is slower at their lower cadences". One wonders how he arrived at this conclusion since his tests involved an ergometer rather than a bicycle.

"Also, a higher likelihood of joint and connective tissue injuries exists with longer cranks, due to the large range of motion they require."  Since no one was reported to have suffered any joint or connective tissue injuries during these tests, apparently this assertion was made without any basis.  Obviously a longer crank results in a larger range of motion, but if a large range of motion was somehow risky or damaging, no one would ever stretch before exercising.

"Our results do nothing to take away from short cranks for low-power, high-cadence pedalling..." Obviously this is invaluable information for all those interested in low-power pedalling.  Of course, if one is truly interested in low-power pedalling, one should try a long crank in a tall gear for a very low cadence -- but this test didn't allow for such variations in cadence.

"Our results suggest that if a rider does opt for longer cranks, the transition should be gradual -- perhaps in 2.5mm increments."   Again, one wonders just which part of this test actually suggests a need for gradual changes in crank length.  It is obvious that switching to a significantly longer crank will take some getting used to, but the guy who needs to move from a 170mm up to a 185mm needs to pay for six cranksets like he needs a hole in the head.

"I wish we were able to offer a definitive formula to apply to riders -- something like fitting a frame. But, if our results suggest anything, it is that such a formula is not really possible, since there are so many factors to consider when choosing an appropriate crank length."  Interestingly, this author was contacted by Lennard Zinn in 2003, and he said: "It is interesting the .216 factor you have. I have been using .21 for some time now."  In other words, he had derived on his own almost exactly the same formula as presented on this site.  Apparently there weren't that many factors after all.

Of course, I had to ask about his 1996 tests.  His response:  "Well, I have made many attempts since then to come up with a decent, publishable test.  As you so eloquently point out, my first two tests never should have been published in the first place.  Also, I wrote that 1996 article largely out of surprise, because I had just assumed that it would be obvious to people that crank length should be proportional to leg length. Assuming that, I figured nobody would be able to do anything on a 130mm or shorter.  I was amazed at how well I could keep up on group rides, no matter what length I used from 100mm to 220mm, with little adaptation.  I did want to write about that, since I had expected a very big effect that would make riding very fast with a crank 10% of one's leg length impossible.  Assuming that the average rider would expect that they should get a proportional crank was a mistake, and the wording should have been way different, had I understood the listening I was writing into among the readers. Anyway, I was unable to see the trend I had hoped for of a length standing out for each size rider.  I wanted to write something after all of the time and effort I had spent on that (I even built that ergometer that allowed realistic positioning of very small and very tall riders over a huge range).  Unfortunately, the results did not warrant publishing it, and there is no way to undo something like that, once it is out there. Oh well."

I just have to include one more quote from Zinn:  "When I was on the national cycling team, I was harassed endlessly for my 180mm cranks.  Now I use 203mm and love them!"

Today Zinn specializes in bicycles for very tall people -- including long cranks.  You can see what he's up to at http://www.zinncycles.com.

Thanks to Enrico Pastori for pointing out this article.  The article can be reviewed online by following the link to the Journal site and then to the appropriate volume, issue, and title.

The intention of these researchers was to investigate a hypothesis regarding cyclic muscle activity and only happens to use a bicycle-like setup for testing.  Their conclusion is that they "demonstrated that impulse–cyclic velocity relationships were independent of strain or crank length above some threshold length."  Basically, that's saying that the muscles behave similarly regardless of what size crank is used, but that's not the same thing as saying the length of the crank doesn't matter to the cyclist.  In fact, they apparently made no effort whatsoever to draw conclusions about optimal crank length; they only wanted to know how the muscles behaved when subjected to different amounts of stretch in cyclical applications.

Considering all of the misguided scientific analysis referenced above, it should be clear that just because somebody has an ergometer in his lab and has written an article in a magazine doesn't mean he knows what he's talking about.  However, that doesn't mean everybody working with ergometers or writing magazine articles should be ignored; it merely means one needs to be selective and make judgements about which studies are valid.  There have been a few studies done by people on the right track:

This is an excellent article written by a very tall person who is a cyclist, engineer, and researcher for Schwinn. The article includes nomograms for determining correct crank length based on type of riding (road, track, etc.) and "leg length", which is the measurement from the top of the thigh bone to the floor. The ideal was found to be a constant "length ratio"; in other words, crank length should be proportional to leg length. Since inseam is essentially proportional to leg length, this conclusion is basically the same as that presented here. The nomogram has an advantage over the formula presented on this WWW site in that it includes built-in variations for the different riding styles.

The article also includes a discussion on determining the proper gearing to use with different length cranks, and another nomogram for that. Unfortunately, this latter argument concludes that the objective is a constant pedal speed -- the same erroneous conclusion as Zinn's above.  Oh, well, you can't win them all.

Buttars also mentions two other studies on crank length, concluding that they were both invalid for using a constant cadence for different lengths.

This article reportedly claims that the optimal length is 0.2 x leg length, and they define leg length as the height of symphysis pubis which is a little taller than inseam.  For all intents and purposes, this formula is exactly the same as the one proposed here -- and therefore obviously correct!  It also predates any claims I may have to originating the formula myself, even though I was working on mine as early as 1975 and never saw this reference.

Michael Wolf reports on a couple of other sources:  "In his book, Touring Bikes, Tony Oliver suggests some crank sizes proportional to leg length, based on experience.  He also tunes his frames to accept bigger cranks, but there a 2-year wait for one.

"Chris Juden of the Cyclists Touring Club is another advocate of proportional crank sizing.  He has a particular rant against childrens bikes with unfeasably long cranks."

Perhaps the most interesting feature of the Martin/Brown/Anderson/Spirduso article mentioned above is a reference to another work:

Apparently this research showed that the amount of work generated by muscles in cyclic activity decreases with increasing frequency of the cycle because the relaxation kinetics between muscle contractions hampers full excitation of the muscle.  In other words, a higher cadence results in a lower force on the pedal, regardless of crank length.  Sorta makes sense, doesn't it?  You know how hard you can push on a pedal at a standstill; imagine how difficult it would be to apply that same amount of force at 100 strokes/minute.  This is a powerful argument that a cyclist should be using the longest crank that he can comfortably ride, since this will permit the lowest possible cadence at a given pedal force and power output and hence permit the highest excitation state in the muscles.

Andrew Bradley has set up a www site with an analysis of crank length and pedalling dynamics at http://www.cranklength.info.

OK, Kirby, you're so smart, how would you conduct a test on crank lengths? A fair question, for which I will offer two answers.

For my first answer, the ideal crank length study would involve a large group of active cyclists of all sorts (perhaps a local club) being given the opportunity to exchange their cranksets for whatever length they wanna try, free of charge, as many times as they like and for as long as they wanna experiment. After they have all tried whatever they wanted and established their favorite lengths, discuss with each one the reasons behind their decision and discard the data from anyone whose decision was based on unacceptable criteria -- such as they wanted to use what the "experts" were using, or were too lazy to try different cranks, or some such. From the remaining subjects, the selected crank lengths then can be plotted against various body measurements, riding styles, etc., and a suitable basis for a formula can be derived.

As long as we're talking ideals here, the cyclists should also have access to free exchange of chainrings so they can optimize their ratios along with the crank length changes, and they should have access to alternative framesets with differing bottom bracket heights. Chainring swaps shouldn't be too difficult; however, to be practical, exchanges of framesets could be avoided by simply discounting data from any rider whose concern for ground clearance affected their selection of crank length. The exchange of framesets would likely introduce far too many variables into the study, compromising the results more than the deletion of the tallest riders with ground clearance problems.

My second answer addresses the fact that most researchers don't seem to like any study that doesn't involve some fancy equipment; if they can't use some machinery in the lab, they aren't interested. So, for those determined to use an ergometer or some such to get data, I can offer the following tips to avoid going too far astray:

First and foremost, abandon the idea of telling the subjects what cadence to use. When a test subject mounts the ergometer with some crank length fitted, allow him to establish his own seat position and cadence in the course of warming up at low load. After the test it will be a simple matter to determine the power generated based on the load and the cadence.

Encourage subjects to use riding positions that are unlikely to cause their knees to hit their chests when using long cranks. The use of shorter-than-optimum cranks to allow a lower riding position is a perfectly valid consideration, but introduces several additional variables into the test -- and is of only minor importance to most riders. This consideration should be kept out of this test so that the optimum crank length can be determined independently of riding position or aerodynamic considerations. Riders will then know what the optimum length actually is, and can then judge for themselves how much shorter they should go in a tradeoff between power output and aerodynamics.

Note that pedalling uphill in low gear doesn't feel the same as pedalling on level ground in a middle gear or motorpacing in high gear. The same type of difference will occur between different cadences while riding an ergometer with a fixed gear but different crank lengths, and can affect the findings if not compensated for. Once the proper cadence is established, the gearing between the crankset and the flywheel should be adjusted so that the flywheel is turning at nearly the same speed for all tests.

Test the rider for maximum continuous power output. Testing for any lesser condition is unimportant; testing for anaerobic performance is not likely to produce consistent results.

And finally, ask the subjects if they were comfortable pedalling the length crank being tested. If they aren't comfortable and aren't likely to get comfortable when they get accustomed to it, the crank length is unacceptable for that size person. Hopefully, the discomfort will be reflected in the ergometer results and the deletion of these cases won't affect the conclusions, but if they do it is a necessary result.


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Of course, if you have questions or comments, you are welcome to send e-mail to me at  palmk@nettally.com.