Deriving a unicycle crank length formula?

There have been lots of threads on crank length with various suggestions on what you should use for various size unicycles in various riding situations resulting in information that is probably not all that helpful, particularly for new riders. Yet the data from all these experienced riders is helpful if only it could be collected and used in a more unified manner.

This got me thinking (a little bit dangerous but still) that if this empirical data could be collected some form of useful crank length formula may be able to be derived. My line of thinking is that the crank length a rider prefers (after experimentation) is dependant on the individuals height, leg length (maybe upper/lower proportion as well), wheel size and the terrain/style of riding. The awkward one is defining the terrain/style of riding to be understandable and relatively consistent.

It may be that with this data collected there is no defining correlation between them but knowing that would be better than the situation is now. If there was a correlation or the data pointed to further ideas a useful general formula might be derived that would help unicyclists, especially new ones, choose an approximately appropriate crank length. Whilst I was searching I came upon this site about a bike crank length formula that I found interesting.

So what do you think? How would it be best to collect this data? Is there any other data that would be useful like seat height above pedals?

BTW I’m not asking for the data to be posted here just a discussion on the merits of collecting data to derive a general crank length formula.

Re: Deriving a unicycle crank length formula?

Firstly, you’d need to survey everyone on the forum and find out all these measurements, for all their unicycles. The main thing is to do a good questionnaire, or the following analysis will be made harder and its conclusions weaker. Also, getting lots of respondents will be particularly important, as many people will ride with suboptimal crank lengths and you will need as large numbers as possible to “average out” this effect.

Then you’d have to analyse the data with regression analysis, keeping data from different terrain/style of riding separate (muni/freestyle/distance etc.) as this is discrete and cannot be quantified, which I think you were touching on. Right now, I can’t think of the best way for allowing for people who use a unicycle for two different sorts of riding. I think you might have to exclude them. Also, I think the data will be overwhelmed by “stock” unicycles with their default crank lengths, and you might need to exclude people who haven’t â€œthoughtâ€ about crank length or something like that.

During analysis of this number of pairs of variables, you’d be very likely to find several statistically significant correlations, a high proportion of which would be false positives.

You could certainly make a formula for crank length, but I doubt it would have any predictive value, although it could be a good starting point for beginners, as you suggested.

All this said, if you want to investigate it and you would like some help, I’d quite enjoy helping.

That would be a very interesting excercise, but possibly quite difficult to carry out usefully. It would be good to see how the theories people spend so long arguing about actually fit into reality. But, as has been suggested already, it would only really make any sense if the data came from people who have tried a few crank lengths and settled on a favourite, rather than people who have just got used to what they have. I’ve got reasonably quick on my 26x3 with the default 165 cranks, and my maximum speed (i.e. top speed in a short sprint, not very sustainable) is up to about 13mph, cruising at 9 or 10ish on easy trails. When I first had it, I could only manage about 9mph max, but I haven’t changed anything, just got used to it.

I’ve been thinking about trying some 150s to see what it’s like, but there are some hills on my usual route to work that I can only just climb (and only just descend without killing my knees) on 165s, so I’m a bit undecided. Lots of people rave about shorter cranks, but I don’t want to have to walk half way home just for the sake of a higher top speed on the flat bits. I’m quite tall and I’ve always ridden a relatively high cadence on a bike compared with some cyclists, so perhaps the 165s happen to be a good length for me. It would certainly be interesting to collect some hard data. I’ll probably try some 150s anyway though, just to see what happens. If Mike’s theory on the other thread applies (crank length change proportional to speed change for small differences) then I’ll only gain about 1mph in speed, and may have to walk up a few hills that I used to be able to ride. But then again, if the riding feels smoother with shorter cranks that may compensate slightly… hmmm… looks like I’ll have to get hold of some cranks and try it for myself.

:o Well that got a bit waffly - and half of it probably belongs in the other thread…

Rider weight or body mass index may also play a role. Probably more of a factor for muni than road riding.

I’ve been losing some weight and I’ve noticed that I’m having an easier time pedaling now and climbing. Could be because I’m also getting more fit at the same time. Slightly shorter cranks now may feel better to me. I should give them a try again and see.

If you’re riding to work on roads, you should try out 150s. I recently switched from 150mm to 125mm on my road uni, and I haven’t yet found a hill I could make it up on the 150mm that I couldn’t on the 125mm, on road. Off-road is a different story. It’s worth a try.

I think that personal preference has more of a role than any formula or application. For example, I like long cranks. For everything. I think the 6 inch (150s) on my 28 feel small.
I love the 175s on my Guni. I wouldn’t mind longer cranks, say, 175s on my 24" Muni.
I’d probably actually like 175s on everything, regardless of type of uni. So, I don’t think a forumula will really work–at least not for me.

Infidel! You must have faith in the unifying power of the scientific method!

Seriously though. Is it really worth that much effort? Isn’t it easier for newbies to just try some different lengths than to receive a mathematical explanation of which crank length best suits them? Since most newbies buy complete unicycles complete with cranks, isn’t the following enough?

If you want to go faster and give up control, get shorter cranks. If you want more control and don’t mind giving up speed, get longer cranks.

‘If you want more control but don’t want to sacrifice speed, just practice! You’ll become better in time and wonder why you were ever thinking about using longer cranks in the first place’

Often, barring certain things like limits of the equipment (splined vs. square taper hubs going off huge drops), it’s all in the mind and fine motor control of the rider. What I could do three months ago vs. what I can do now is quite a bit different, but I’m still on the same uni.

Get a bigger wheel.

tholub:
My route is mainly off-road (non-technical though) but with a couple of miles of road. The steep hills I mentioned are on tarmac.

phlegm:
I wasn’t hoping for an alternative to actually testing different cranks, just suggesting that it would be an interesting survey. People seem to have very strong views on crank lengths, but different people have quite different views, and similarly different arguments to back up their beliefs. It’s almost like arguing about religion - everybody strongly believes they are right but they can’t all be. I feel perfectly comfortable with my 165s, but reading all the crank length agruments has made me curious to try some different ones for myself. At the moment, and with my limited experience with unicycles (but considerable experience with bicycling) it seems to me that crank length is a very personal choice, based on leg length, strength, stamina, preferred riding style and, possibly, skill/technique.

Rob

This is absolutely right.

Unfortunately being right about this means that you are wrong when you say not everyone can be right, because it is possible to imagine a world with no crank zealots, where everybody realises that crank length is a matter of personal preference.

Also, it’s time to knock another silly belief on the head - that shortening your cranks will always make you go faster, at the expense of control and acceleration. (You do lose control and acceleration, but your maximum speed does not increase without limit.)

Most people appreciate the potential for an increase in speed due to the decrease in the circumference of the circles that your feet have to move through when you put on shorter cranks.

Relatively few people seem to appreciate that the maximum torque you can exert also decreases. The maximum torque dictates your maximum speed as you will reach* a speed at which the resistive forces (friction, rolling resistance and air resistance) match the torque and you can no longer accelerate past this speed.

I hope that the diagram is visible when I submit my reply, because it’s nowhere to be seen in the preview and that it clarifies what I’ve said above.

(* You won’t actually reach this speed, but get asymptotically close to it in my idealised, mathematical world.)

Please excuse that hideous spelling mistake in the diagram.

I think you are wrong. If speed does not increase without limit (which nobody claims it does) then you do not lose control or acceleration. How long does it take to reach max speed on short muni cranks (short in this discussion means 140-150mm)? Only a few pedal revolutions at most. Control? Losing control? Yeah right. Go back and practise against a fence until you figure out how to balance. Maximum torque means maximum energy spent keeping your top speed, so unless your mountains only have downhill and no up- then short rules!

This is why your post is so full of rubbish! You’re failing to engage with the limits that I’m talking about. When I’m talking about short cranks, I’m talking about arbitrarily short cranks - possibly as long as 89mm on a 28" uni but probably not. Seeing as this is this is your first foray into this discussion you have no business telling me what short in this discussion means!

The particular steepness of the gradients involved in muni means that everybody rides with longer cranks than they would do otherwise.

For the time being, just forget about gradients and consider two 24" munis racing on the flat. One has 89mm cranks on, the other has 140s. You say that the 140s accelerate quickly. Well, they do! That’s because 140mm cranks are actually fairly long when you’re on the flat. I wouldn’t put 140s on a 28" wheel for a hilly route, never mind a 24" on the flat. In the end though, the 89s will cream the 140s as their maximum speed is so much higher.

Don’t patronise me. My balance is sufficient for riding a unicycle, thank you very much. If you go and ride down a long, steep slope on a unicycle with short cranks, such that the slope is steep enough and the cranks are short enough that the maximum reverse torque you can apply is less than the torque due to the weight of the wheel, you will lose control as you get faster and faster. No matter how good your balance is, unless you can glide, you will reach a point where you fall off because you won’t be able to pedal fast enough. You can practise against a fence all you want, but that’s not going to help you in this case.

I don’t understand what you mean here.

Tough

You are wrong, cos not everyone can be right regardless of the crank zealots and coming to terms with it being personal preference.

Lol! Did it take you 35 minutes to think of that?

For someone who doesn’t like to be patronised, you are pretty dumb in assuming that the time a message was posted determines how long that person has been pondering their reply. It may be some indication, especially in fast replies (an indication that they didn’t think long) but it is not an accurate measure. I can tell by your reply that you didn’t think for 56 minutes before coming up with that lame reply. Unless you really are stupid!

Ok, that’s a fair point.

Ok, you’re not stupid if you got that so quick. Back to the topic eh? (Sorry I am guilty of thread jacking for my selfish argumentative purposes). Crank length-
Determining a formula is an interesting idea, but the number of variables would make it a very complex formula. Someone mentioned cadence. It’s a concept I vaguely understand, but I looked it up in the dictionary and couldn’t find a cycling definition for it- something about rythym was about the best description for it. Q-factor is another thing to consider too- cos the length of the cranks does not include any distance it sticks out- wide Q-factor can cause more wobbling and slower top speeds. As for determining your own preference- I think one of the best ways to find out is to go to a Unicycle weekend gathering and try everyone elses unicycles out- and hopefully they will have variations on crank lengths. Otherwise it could be an expensive business trying out the different lengths- especially if the ones you like get bent!