## Bicycle Crank Length: Read This Before Flaming Me

As mentioned in the derivation of this formula, it is based on three assumptions and one piece of empirical data. Getting from these four inputs to the formula itself is simple mathematics; there's no error there. If there is something -- anything -- wrong with this formula, it lies in either the three assumptions or the empirical data.

Suggesting that the empirical data -- that a 170mm crank is the correct length for a cyclist with a 31-inch inseam -- must be flawed is an easy attack. An incorrect correlation here would mean that the 5.48 constant is off; presuming that a 170mm crank were a perfect fit for a cyclist with a 30-inch inseam, for example, would result in a constant of 5.67.  This could, in fact, be the case; in the discussion, I point out that it may actually be between 5.48 and 5.6, and I'm sure there could even be arguments for it being somewhere beyond that range. But arguing about this value -- or the empirical data it is based on -- won't address the objections most cyclists have to this formula. Even if this value is increased to 6 or decreased to 5, we are still talking about crank lengths that change by 5mm or more for every inch of inseam change! And that is what people find objectionable.

The third assumption, that the formula can be based on inseam length, also comes under attack often. People have suggested all sorts of body measurements that they feel would be more accurate or more representative than inseam length. There's actually no arguing this point; basing the formula on the length of the upper leg alone would be better -- if it were possible to conveniently and consistently obtain accurate measurements of the upper leg.  Unfortunately, it is not, and even if it were, the difference in the results would be minor.  The resulting formula would still call for crank lengths varying from 150mm to 200mm and beyond for adult human beings of different sizes, which would still appear extreme and unreasonable to those whose minds are bound by current tradition.

The second assumption, that crank length should be proportional to some bodily measurement, is also often a source of doubts.  Some have suggested that crank length should perhaps have some non-proportional relation to leg length; a formula of the form

L = A + (B x I)

for example, where A is some fixed base crank length and B is multiplied by the inseam measurement to provide some "adjustment" to the base length to correct for differing leg lengths.  This general formula is actually nearly universally agreed to; only the values of A and B are in question.  In the formula I have proposed, A is zero and B is 5.48, while the status quo is that A is 170 and B is zero.  Could the true answer lie somewhere in between?  Perhaps.  People with long legs don't move exactly the same way as people with short legs, so simply scaling up crank lengths may not be perfectly valid.  This would mean the true answer would involve some non-zero values for both A and B.

But when applying such a formula to extremes such as small children, one quickly realizes that the fixed basic length A must be quite small while the (B x I) component must be the dominating part of this formula -- which will still result in crank lengths that vary by several mm for each inch of inseam length.  Those who insist that 170mm must be pretty close to correct for everyone are thinking the other way around, that A is large (nearly 170mm) and B must be tiny and insignificant, resulting in only a couple of mm variation from the shortest cyclist to the tallest.

In other words, their objection isn't really with the second assumption; it's with the first assumption.

The first assumption -- that crank length should vary with the leg length of the cyclist -- is the real cause of consternation among cyclists objecting to my formula. If you steadfastly believe that the current practices of crank length selection are correct or nearly correct, what you are saying is that you disagree with this first assumption, and feel that all cyclists should be using the same size crank. Pointing out that there are 170mm, 172.5mm, and 175mm cranks available says nothing, since these variations are less than 2% - less than an eighth of an inch each. This is simply insignificant; if you put a 170mm crank on one side of your bike and a 172.5mm on the other, you'd be hard pressed to tell which side was longer when riding.

The concept that all riders should be using the same length crank has the strength of being the status quo, but I fail to see any logic whatsoever behind it. Some have suggested that all cranks should be the same length because of something to do with the nature of the sport, the same way that baseball players all use the same length bat and tennis players all use the same length racket.  But those are artificial limitations intended to force all players to compete on equal terms, not personal fit issues.  Golfers use different length clubs depending on how tall they are, and runners use shoes that fit their feet -- and take whatever length stride suits them, with taller runners generally taking longer strides than shorter runners.  Cyclists choose shoes, frames, and clothing that fits their bodies -- why not cranks as well?

If anyone can provide rational arguments that all cyclists should be using the same length cranks, I'd love to hear them.

There is the inevitable argument that if this formula was correct and crank lengths should vary with leg length, surely that would have been discovered long ago.  Such arguments must necessarily be based on the idea that the cycling community was more open to new ideas at some time in the past than they are today, since the vast majority of cyclists today are totally unwilling to even consider this formula much less buy a crank and try it out.  I find the entire concept of an enlightened era of cycling questionable; I've been involved with cycling since the 1970's, and during that time there has never been more willingness to try new ideas than there is today.  In fact, in the 70's it was all but impossible to convince a competitive cyclist to use a component that didn't have "Campagnolo" written on it, regardless of the technical advances being offered by other companies.  It would not surprise me at all to learn that the cycling community has always been resistant to new ideas such as crank length variations based on leg length, and that they simply have never been seriously tested.  The few times they have been tried -- such as tall Miguel Indurain's use of longer cranks, revealed only after his retirement -- the results seem to have been encouraging.  After all, Indurain did win the Tour de France five times, and didn't seem to suffer any adverse effects from his use of long cranks for competition.

The only real problem with the formula is that it results in crank length numbers that just don't sound right.  So, allow me to suggest this: instead of talking about crank lengths in mm, start talking about them in cm.  The standard crank length is 17cm, and if you shop around you can find cranks with 17-1/4 or 17-1/2 cm lengths.  These are silly variations; it would make more sense if cranks were commonly available in lengths from 15 to 19 cm in 1/2 cm increments, with custom cranks available even longer for unusually tall riders and shorter versions available for children.  There, does that sound better?