Deriving a unicycle crank length formula?

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...

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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.

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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.

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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.

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rob.northcott said:

*It would be good to see how the theories people spend so long arguing
about actually fit into reality.*

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.

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you forgot to add-

'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'

:P

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.

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phlegm said:

*

If you want to go faster *

Get a bigger wheel.

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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

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rob.northcott said:

*crank length is a very personal choice, based on leg length,
strength, stamina, preferred riding style and, possibly,
skill/technique*

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.)

+----------------------------------------------------------------+
| Attachment filename: crank length.png |
|Download attachment: http://www.unicyclist.com/attachment/365475|
+----------------------------------------------------------------+

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Please excuse that hideous spelling mistake in the diagram.

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Rowan said:

*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.*

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.

Quoted message said:

*Losing control? Yeah right. Go back and practise against a fence
until you figure out how to balance.*

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.

Quoted message said:

*Maximum torque means maximum energy spent keeping your top speed, so
unless your mountains only have downhill and no up- then short rules!*

I don't understand what you mean here.

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Rowan said:

*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?

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Rowan said:

*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.

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rupert said:

Rowan said:

*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.*

[snip]

Quoted message said:

Seeing as this is this is your first foray into this discussion you
have no business telling me what short in this discussion means!

And you have no business being so condescending. Relax a little and
remember that it is perfectly possible to read the entire discussion
many times without actually saying anything and so understanding what is
being discussed.

I think if you go back and have a look at the previous posts, you'll
find that with the exception of tholub mentioning 125mm cranks,
everybody else has mentioned 150mm as "short".

Either way, there is no call for rudeness.

Roger

Rowan said:

*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! *

Yeah, I know when I'm beaten.

If I had to guess, I'd think cadence is the wiggle from side to side.

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Roger Light said:

*rupert said:

Rowan said:

*How long does it take to reach max speed on short muni cranks

(short

Quoted message said:

Quoted message said:

in this discussion means 140-150mm)? Only a few pedal revolutions

at

Quoted message said:

Quoted message said:

most.*

[snip]

Quoted message said:

Seeing as this is this is your first foray into this discussion

you

Quoted message said:

have no business telling me what short in this discussion means!

And you have no business being so condescending. Relax a little and
remember that it is perfectly possible to read the entire discussion
many times without actually saying anything and so understanding what
is
being discussed.

I think if you go back and have a look at the previous posts, you'll
find that with the exception of tholub mentioning 125mm cranks,
everybody else has mentioned 150mm as "short".

Either way, there is no call for rudeness.

Roger *

Those posts are on a different thread, and hence a different discussion!
In my post, as I have tried to explain, it didn't matter how short it
actually was, just that it was very short, not in absolute terms but
relative to its previous value.

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Some interesting input even if there was a short side step, but hey it's
a discussion 😉

John mentioned BMI which is something I hadn't thought of but ought to
have as I've lost quite a bit just lately 😄. Whether it'd affect crank
choice I don't know but I'd just be interested what BMI's unicyclist
have :eek:

Q-factor I'd not thought of and could make quite a difference though
you'd probably have to take hip width into consideration.

Short? Long? Whatever size you consider as short or long doesn't matter
with regards to a formula.

Speed? Cadence? These may be determining factors for crank length choice
but I believe one size does not fit all people in a particular
situation, which is what the formula idea is about. Rider 1 may be as
fast as rider 2 with the same wheel size and the same situation but have
different crank sizes and different body sizes. So have their body sizes
contributed to their preferred crank size? Thus does it work the other
way, know the body size choose the cranks?

Preferred crank size after experimentation is the key for the data. As
has been pointed out it wouldn't be very informative if someone had
ridden with nothing but what came with their unicycle (even if it turned
out to be the ideal length). Which leads to - wouldn't it be better if
you had an idea what crank length would suit you when you first bought a
particular unicycle? One seat tube length doesn't fit all, and although
more complex, why should crank length?

Muni terrain could well be very difficult to quantify and categorise,
any ideas?

Oh and am I thinking too much 😕

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Having been bred an engineer, I spent some time thinking about this and
I offer the following. What we want to know is how will a given crank
on a given wheel feel in terms of power and control. Where feel means
many things as mentioned in the strings referenced--control, speed,
torque, rotational diameter, power, knee pain...etc.

Work equals force times distance. For different wheel sizes on
different rims to feel the same, will essentially require that the rider
be accomplishing the same amount of work.

Each wheel size has a different diameter, when circumference is
calculated...Pi times diameter, you can obtain a number for each wheel
size. Then by multiplying by 2.54 you can determine the circumference
in centimeter.

20� diameter times Pi equals 62.80 in or 159.51 cm
24� diameter times Pi equals 75.36 in or 191.41 cm
26� diameter times Pi equals 81.64 in or 207.37 cm
29� diameter times Pi equals 91.06 in or 231.29 cm
36� diameter times Pi equals 113.04 in or 287.12 cm

By accomplishing a ratio of circumference divided by crank length in
centimeters, you can determine a ratio for comparison. Using this
approach each crank length and wheel diameter can be compared in a grid.
I hope the chart works on the internet...

Wheel -- 20 24 26 29 36

Crank

85 -- 188 225 244 272 338

110 -- 145 174 189 210 261

114 -- 140 167 182 203 252

125 -- 127 153 166 185 230

140 -- 114 137 148 165 205

150 -- 106 127 138 154 191

165 -- 97 116 126 140 174

170 -- 94 113 122 136 169

175 -- 91 109 118 132 164

These numbers provide a referenced baseline for the work of a given
crank/wheel combination for the same distance output. Similar numbers
between columns will represent similar feel in terms of unicycle
performance--given that each of us has a different comfort level and
range of comfortable skill. Note that a 20 inch with a 125 crank gives a
rating of 127...which compares in terms of work and feel to a 24 inch
with a 150 (similarly a 127 work rating). Likewise a 26 inch with a 165
crank should feel about the same in terms of work but recognizing that
the larger rotation of the longer cranks has a subjective impact.

As I look at it, the ratio of around 125 to about 175 covers the range
of most riders comfort zones. The higher number being harder to pedal
with a smaller pedal arc and the opportunity for greater speed. The
lower number makes it easier to pedal a give distance due to increases
lever arm resulting in probably lower speeds due to larger pedal arcs.
As the crank to wheel size ratio goes down to about 100, the torque
skyrockets and traction probably becomes the limiter...although large
pedal arcs may be less comfortable. In the opposite direction, as the
ratio goes up...the opportunity for speed due to shorter pedal arcs
increases with a penalty in power and hill climbing ability.

Note that AspenMike, who as I recall, rides 175s on his 36 inch Coker,
carries a tougher pedal stroke than someone who rides a 20 inch unicycle
with 110s--making his performance on the Iron Horse all the more
remarkable. This chart should give riders the chance to decide how
cranks compare on different wheel sizes--recognizing that every one of
us will have a comfort zone on this chart of varying width based on
skill and strength.

I bought a 24 inch Torker LX with 150 cranks (work ratio 127) and
quickly went to 114s (work ratio 140) which are more comfortable in my
riding situation. On the KH29XC I bought with 29 inch wheel and 150
cranks (work ratio 154), I also want to optimize for speed so I bought a
set of 125 cranks (work ratio 185). By comparison, the 29 inch with
150s starts me at a higher work ratio than my previous riding situation
(harder cranking, less control, less power) and my decision to learn to
ride the same unicycle with only 125s is a commitment train to even
less control and power but this is offset by the ability for a better
spin and higher speed.

Hope this helps. Any subjective opinions on the field application of
this rough science is welcome.

Carey

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Having been bred an engineer, I spent some time thinking about this and
I offer the following. What we want to know is how will a given crank
on a given wheel feel in terms of power and control. Where feel means
many things as mentioned in the strings referenced--control, speed,
torque, rotational diameter, power, knee pain...etc.

Work equals force times distance. For different wheel sizes on
different rims to feel the same, will essentially require that the rider
be accomplishing the same amount of work.

Each wheel size has a different diameter, when circumference is
calculated...Pi times diameter, you can obtain a number for each wheel
size. Then by multiplying by 2.54 you can determine the circumference
in centimeter.

20 in diameter times Pi equals 62.80 in or 159.51 cm
24 in diameter times Pi equals 75.36 in or 191.41 cm
26 in diameter times Pi equals 81.64 in or 207.37 cm
29 in diameter times Pi equals 91.06 in or 231.29 cm
36 in diameter times Pi equals 113.04 in or 287.12 cm

By accomplishing a ratio of circumference divided by crank length in
centimeters, you can determine a ratio for comparison. Using this
approach each crank length and wheel diameter can be compared in a grid.
I hope the chart works on the internet...

Wheel -- 20 24 26 29 36

Crank

85 -- 188 225 244 272 338

110 -- 145 174 189 210 261

114 -- 140 167 182 203 252

125 -- 127 153 166 185 230

140 -- 114 137 148 165 205

150 -- 106 127 138 154 191

165 -- 97 116 126 140 174

170 -- 94 113 122 136 169

175 -- 91 109 118 132 164

These numbers provide a referenced baseline for the work of a given
crank/wheel combination for the same distance output. Similar numbers
between columns will represent similar feel in terms of unicycle
performance--given that each of us has a different comfort level and
range of comfortable skill. Note that a 20 inch with a 125 crank gives a
rating of 127...which compares in terms of work and feel to a 24 inch
with a 150 (similarly a 127 work rating). Likewise a 26 inch with a 165
crank should feel about the same in terms of work but recognizing that
the larger rotation of the longer cranks has a subjective impact.

As I look at it, the ratio of around 125 to about 175 covers the range
of most riders comfort zones. The higher number being harder to pedal
with a smaller pedal arc and the opportunity for greater speed. The
lower number makes it easier to pedal a give distance due to increases
lever arm resulting in probably lower speeds due to larger pedal arcs.
As the crank to wheel size ratio goes down to about 100, the torque
skyrockets and traction probably becomes the limiter...although large
pedal arcs may be less comfortable. In the opposite direction, as the
ratio goes up...the opportunity for speed due to shorter pedal arcs
increases with a penalty in power and hill climbing ability.

Note that AspenMike, who as I recall, rides 175s on his 36 inch Coker,
carries a tougher pedal stroke than someone who rides a 20 inch unicycle
with 110s--making his performance on the Iron Horse all the more
remarkable. This chart should give riders the chance to decide how
cranks compare on different wheel sizes--recognizing that every one of
us will have a comfort zone on this chart of varying width based on
skill and strength.

I bought a 24 inch Torker LX with 150 cranks (work ratio 127) and
quickly went to 114s (work ratio 140) which are more comfortable in my
riding situation. On the KH29XC I bought with 29 inch wheel and 150
cranks (work ratio 154), I also want to optimize for speed so I bought a
set of 125 cranks (work ratio 185). By comparison, the 29 inch with
150s starts me at a higher work ratio than my previous riding situation
(harder cranking, less control, less power) and my decision to learn to
ride the same unicycle with only 125s is a commitment train to even
less control and power but this is offset by the ability for a better
spin and higher speed.

Hope this helps. Any subjective opinions on the field application of
this rough science is welcome.

Carey

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