At the time I first derived this formula, I was a small-time bicycle racer and aspiring engineering student. The logic of the formula -- all three assumptions and the empirical data -- all seemed obvious to me from very early on. However, the conclusions -- that I myself, with a 34-inch inseam, needed a 186mm crankset -- struck me as preposterous, same as it strikes most people. What's more, I was a poor student riding $150 bicycles and the opportunity to test a crank of such length was not likely to come around any time soon.
While I did have some small success as a racer, I proved more adept at bikebuilding. Although I never did it for a living, I did end up assembling a lot of bikes for friends, relatives, co-workers, etc. over the years. Building so many bikes for friends kept me keeping an eye out for parts, used bikes, etc. A bicycle parts wholesaler near where I lived in North Palm Beach went bankrupt and auctioned off the works, so I went down there and stocked up. Among the stuff loaded into my attic was a good supply of cranksets of various lengths up to 180mm.
Of course, I then started trying the longer lengths on my own bike. The result of these tests was an immediate confirmation of the formula I had derived years before! I knew I needed a 185mm crankset, and set about finding one. It was tough, but I did locate a TA crankset of that length. TA cranksets were popular for touring use at the time, due to an excellent selection of chainring sizes. Didn't matter which size I used, the chainrings were garbage, I broke every one I ever installed. I eventually had an adapter made up to fit generic chainrings, and haven't had any trouble since.
I'm old and fat now, and don't ride much anymore. But I
had this
crank long enough ago to put many thousands of miles on it, including
some trips through the mountains of New England and New York State. I
stand convinced that this formula is accurate; this crankset seems the
perfect length
for me.
Meanwhile, while building bikes for others there were several other instances of large or small riders where the formula was applied. One notable case was a young lady who was extremely athletic and wanted to do some serious riding, but was only 5'-0" with a 27-inch inseam and was having difficulty finding a decent bike for her uses. The mixte she had been riding simply didn't meet her needs. After some consultation and shopping, she purchased a Cannondale bike with a polished aluminum frame and 650C wheels. This was a truly excellent bike and was fitted with special small handlebars, special small brake levers, special small seat, etc. However, for all this attention to the needs of the smaller rider, the bike came with a 165mm crank. It also came with some obscenely tall gearing, but that was easily corrected.
For this young lady, I took one of the 170mm cranks I had
laying
around and shortened it to a 151mm; I explain how this is done on my
page of tips. She thanked me many
times over the ensuing
years, always reiterating how excellently this crankset fits her.
She regularly
used this bike to climb the mountain passes in the Rocky Mountain
National
Park.
I occasionally get feedback from people who have visited
this site
and acted on what they've read. It's always positive, although I
tend to
put less stock in it because I don't really know what these people are
doing
and cannot verify their results in person. One guy in New Zealand
claimed
to be something like 6'10" tall and riding a 215mm crank, and swears
this
formula is the best thing that's ever happened to his cycling.
Andrew
Bradley got involved to the point where he has set up his own web site
on
the subject, http://www.thankstomycranks.com
-- well worth a visit.
John A. Sinibaldi is 6'6"
with
a 34" inseam and installed 190mm cranks. He sent the following
report:
"They have definitely helped my riding; I am stronger and more consistent than when I had the 175's.
"They've added probably 3 mph on my sprint - and more importantly, my jump (the initial move from the peloton into full sprint mode) has also improved dramatically. This is all the more amazing because I weigh about 260 lbs (and most people my height and weight have absolutely no jump). I've got to say, it gives me a great deal of pleasure to "stand on it" and go from 25 mph to 35 mph in perhaps two dozen pedal strokes (and it never ceases to catch the little guys off guard).
"Finally, my spin has, indeed, changed because of the longer crank length. I still spin at a very high RPM when sprinting, and also when on the front during a fast ride (usually 92-94 rpms). However, when I'm in the back in a recovery mode (between pulls, or between sprints), I find myself kicking back to as low as 72 rpms. With the longer cranks, I can "loaf" in the back - which allows me to recover between extreme efforts much faster. Plus, if I am on an easy day, I can sit in the middle of the pack and turn over the cranks at 78-86 rpms all day long without getting winded.
"Finally, sometimes even when I'm on the front, if the ride is a medium effort, I find myself doing more mashing (lower cadence) simply because I can, with no pain, and less effort.
"Incidentally, I went to the hills today for the first time with the longer cranks - no problem. On the smaller rolling hills, the longer cranks made it easy to push over the top at a good pace - and on the longer, steeper hills, the extra leverage afforded by the longer cranks also was welcomed."
Lennard Zinn, former U.S. National Cycling Team member, 6'6" tall, and purveyor of custom bicycles with long cranks designed especially for tall people (http://www.zinncycles.com), says: "I have not found a single person who was not happy with the proportional crank I set them up with. I just wish these things had been available 25 years ago when I was racing, because I certainly would have used them, and I do think I would have done better with them."
Dave Hallock, founder of the Disciples of Dirt Mtn Bike Club of Eugene, Oregon, writes: "I'm a 50 year old avid cyclist who's been riding since I was in high school. I have about a dozen bikes, including a couple of custom frames designed around extra-length cranks. I'm 6'3" tall with a 36" inseam. Two of my bikes have 202mm cranks and two others are outfitted with 195mm cranks. I've been riding extra-length cranks (or should I say properly sized cranks) since '92 and have been singing their praises ever since that time. Glad I stumbled onto your site. Now I can provide a link to your well thought out crank length formula and well written arguments instead of trying to explain it all personally.
"In 2001 (at age 47) I entered the Cascade Cream Puff 100 Mile mountain bike race (regarded as the "toughest 100 mile mountain bike race in America") which features over 17,000 vertical feet of climbing. I rode a 7-speed mountain bike outfitted with 195mm cranks. I won my division (Masters, 45+), setting a new CCP100 course record by an hour and a half in the process.
"Do I owe my success strictly to properly sized cranks? No. But nobody can convince me that long cranks (oops -- properly sized cranks) are slower, harder on a rider's knees, cannot be ridden for epic distances, etc. Heck, I'm just an everyday guy. Prior to 2001, I'd never entered a bicycle race in my life. I'm still riding a lot, enjoying it a lot and my knees have never felt better. Too bad frame manufacturers are unwilling to factor another variable (namely bottom bracket height) into the frame building equation."
Michael Greif, who rides a fixed gear bike, wrote in April 2004: "Whelp, fer what its wurth, my anecdotal evidence. I have been riding the 185s on a 52/20 drivetrain since early March. Knee pain is reduced to simple muscle stiffness.
I ride 3-5 days per week and currently average 96 r.p.m.; at the end of my usual ride [a 40 minute ride around (and around and around) a lake] I am turning 102 r.p.m. and I expect that will increase over the next few months.
"If I get another bike I would seriously consider even
longer
cranks. I calculated using your formula that I should use 186.75s
but I don't see a limitation on using something even bigger (I don't
think the archimedian advantage has been topped out). I do not
percieve a limitation other than bouncing my knees of my stomach.
"I do note that riding correctly with least harm to my
knees
requires I keep them as close in to the frame as I can. This
seems sensible as it ensures that the lateral pressures on the knee are
minimized."
Kieran Cox wrote in August 2006: "I've been perusing your site off an on for a few months now. In particular the crank length part. I'm a bicycle racer (nothing big, Cat 4 in the Bay Area), and I have to admit your formula struck me as absurd when I first saw it. However, I am also an engineer (Computer Engineer is, EE,CS) so I couldn't turn away from the obvious facts you supplied and the simple logic of it.
"I'm 6'4" and have the legs that should probably be on a man 6'6". My inseam is 93cm which suggests I should be riding a 200.88mm crank. Well, that was hard to come by so I grabbed the lowest hanging fruit and bought a set of 180's. I could feel the slight power increase and I never looked back at the 175's.
"After some more calculation I figured the 180's
represented about
3% mechanical increase over the 175's and the 200s are about 11% over
the 180's. So after some more thought I figured, screw it, I'll
buy a custom bike. I ordered a custom from Lennard Zinn's custom
shop in April and it just arrived last week.
"...As expected the math is correct, the circle feels completely
natural, and my cadence is now almost the same as shorter riders.
Granted I'm still not used to turning the 200mm radius circle and it is
recruiting a larger muscle group, some of which are not as well-trained
as the others in the 180mm radius. I can tell you this, though: I
am at least as fast on the
flats even with some weaker muscles, and I'm already 10% faster uphill.
I just wanted to say thank you, Kirby. All of your
assumptions
are correct, and your formula is right on for me. I already could
outsprint most people on the 180's; I can't wait to put the sprint down
with the new cranks!"
Cox also sent a report on a 30 mile ride: "1: The
shorter
cranks provided a physical reminder to keep your cadence up because it
stings so much when my cadence drops below 100 while riding fast on
flats. Not so with the proportional cranks. The torque curve has
been broadened, and because I'm used to listening to my body tell me to
spin faster so it doesn't hurt, I found myself plodding along at 80 to
90 rpm at times, and not shifting much. I have to be vigilant about
keeping that cadence at or over 100 even if it feels ridiculously easy.
"2: The course suddenly felt a lot flatter than before. I steam rolled
over most grades that other riders would come out of saddle on.
"3: There is more power, but it is not for free. I'm able to draw
more watts from my body, and I definitely feel like more are coming
out. In essence it doesn't feel like I'm going faster until I
check my
speedometer. For instance on the last 2 miles of the ride I
pulled out to the front and started riding hard in the drops. I
felt like **** and wasn't motivated to sprint near the end. I was
surprised no one really tried to come around me. Then I looked at
my speedometer....I had been driving the pace at 33.5mph for the past
flat mile or so while splitting my own wind, and I wasn't sprinting
yet...."
Occasionally, I have allowed other riders who were over 6 feet tall to try out my own bike. I've never yet loaned it long enough for anyone to become accustomed to it, but even a ride around the block usually instills a great deal of respect for the crank length formula. When tall people try out a crankset that's somewhere near the right length for them, they know immediately what is wrong with using a 170mm.
Return to Kirby Palm's home page.
Of course, if you have questions or comments, you are welcome to send e-mail to me at palmk@nettally.com.