# how much faster?

This is a boring question but is a 24" tyre much faster than a 20" tyre? Cuz im sick of pedaling so fast and going nowhere!

well, what kind of riding do you do? If its for sheer distance purposes, you should probably look into a coker.

e39m5

yeah, it’s faster, but they’re both slow as hell. Get a bike if you are actually thinking about practicality.

Musketman wrote:
“This is a boring question but is a 24” tyre much faster than a 20" tyre? Cuz im sick of pedaling so fast and going nowhere"

Yes, a 24" is noticeably faster than a 20".

But, whenever I’m pedaling a 24" it feels like the thing is going nowhere. Consider a 26" or even better, a 29" Unicycle.

Multiply the diameter times pi to find out the circumference. Subtract the smaller number (small tire) from the big one. Whatever’s left over is how much farther you’ll go with each turn of the pedals.

This of course rules out pedaling faster

say after me “Constant Footspeed Hypothesis

say it again and again

If I did my math right (I got up 45 minutes ago, which isn’t long for me) if you pedal at the same rpm, a 24 inch goes 1.2 times as fast as a 20 inch.

If you want speed but still want to unicycle, why not just learn to glide down hills which would make it faster and less tiring, or you could just get a geared unicycle.

Re: how much faster?

Bigger wheels go faster. To optimize for speed, find
the shortest cranks you can efficiently control.

[Long analysis]]

“GILD” <GILD@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> say after me "‘Constant Footspeed Hypothesis’

Do you mean to imply that the “constant footspeed hypothesis” is a
good model for describing the speed we obtain on different unicycles?

The idea is appealing simple: Maintaining a constant crank length to
wheel diameter ratio yields the same foot speed for different
unicycles traveling at the same rate. Fortuitously, maintaining equal
crank rations gives approximately equal control of the unicycle as
well.

Unfortunately, this theory ignores the energy required of the rider.
If reduce wheel size and crank size proportionally with that, you’ll
quickly find you can’t spin fast enough to keep up with the original
wheel. The reason is that your foot has to accelerate faster on the
smaller wheel, and that takes more energy.

As an alternative, I suggest considering a “constant foot acceleration
hypothesis”, where pedalling energy, rather than foot speed, is
maintained as a constant. If you do this, you find that the cranks on
smaller unicycles need to be proportionally smaller than those on
larger wheels to maintain the same forward speed. This means you have
proportionally less torque on the smaller wheel, which is consequently
harder to control. If you keep cranks within a reasonable range
(which depends on rider skill), you’ll find that bigger wheels go
faster.

Let’s put the “constant footspeed hypothesis” to rest. It is an
inaccurate model with little predictive power.

Ken

…in that case, get a motorcycle.

Re: Re: how much faster?

no, but it’s a hell of a fun read

the posts i linked to make it quite clear that it’s more of a bit of fun and a very broad ‘rule of thumb’ than serious scientific stuff
i’ve allways enjoyed the discussions around that topic and i didn’t want a new person to the forum to never know the same joy

Re: Re: how much faster?

It is a rule of thumb, no-one’s suggesting it’s anything more than that. However, lots of experienced riders of short cranks / big wheels seem to think it’s a pretty good one. In my experience over thousands of miles on each, it works okay between a 29" and a 36" wheel until you get to very silly short cranks (<100mm) on the 29er where you’re just so lacking in control that the bumps take you off.

It’s nice to calculate some super clever answer, but that’s never going to be much use as a rule of thumb that you can just work out in your head. It still going to be inaccurate due to the many variables ignored by both methods, such as the different weight of the wheel relative to the foot / the moving parts of the body / the rider, the differing accelerations of various body parts and how that relates to the acceleration of the foot, ie. what percentage of the body weight you’re accelerating is just going round in circles etc.

Joe

Re: how much faster?

“joemarshall” <joemarshall@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> It is a rule of thumb, no-one’s suggesting it’s anything more than that.
> However, lots of experienced riders of short cranks / big wheels seem to
> think it’s a pretty good one.

As a rule of thumb it is great. Changing crank length proportionally
with wheel size makes sense since it yields equal force on thewheel
when making control corrections.

What doesn’t make sense is pretending that pedal velocity is a primary
factor in determining riding speed. It is not. The term “constant
footspeed hypothesis” is misleading. Come up with a different name
and I’ll stop complaining.

Ken

Re: Re: how much faster?

Have you run any sample calculations for constant foot acceleration compared to constant foot speed? I’m too lazy to run the numbers right now and it has also been a long time since I’ve done any dynamics so I’m all rusty with the equations.

I can see how acceleration is a better measurement than speed since your feet are moving in a fast circle. Anything moving around in a circle is accelerating even if it is moving at a constant speed.

Re: how much faster?

Let’s make it interesting, then. A 20" tire dropped from a tall building is much faster than a 24" tire that is on the floor. They are the same speed when they are duct-taped together. Putting a person on a unicycle with one of these tires attached in a conventional manner adds complications which make it not as fun or interesting.

A 20" tire fired from a canon is much faster than a 24" tire thrown from a mule. A 24" tire being carried by a camel, however, is faster than a 20" tire at the bottom of a still pond.

…with a 1000cc engine. Anything smaller than that is just too slow!

Thanks GILD. These are great posts.

Re: how much faster?

“john_childs” <john_childs@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> Have you run any sample calculations for constant foot acceleration
> compared to constant foot speed? I’m too lazy to run the numbers right
> now and it has also been a long time since I’ve done any dynamics so I’m
> all rusty with the equations.

Yes, but before I go on, I’m not claiming this is very useful. The
problem being that as cranks get really short, you lose mechanical
advantage for controlling the unicycle and watse energy trying to
maintain stability.

That said, the equations are pretty simple. The magnitude of
acceleration, a, needed to keep your foot spinning on the pedal is

a = l*v^2/r^2

where l is crank length,
v is the unicycle’s speed, and

Keeping forward speed and pedal speed constant yields the equation

l1 / r1^2 = l2 / r2^2

In words, crank length grows with the square of wheel size.

Concretely, taking a coker with 175mm cranks as the largest likely
combination and scaling down yields the following table of
iso-accelerated unicycles:

36" with 175mm cranks
29" with 113mm
26" with 91mm
24" with 78mm
20" with 54mm

To compare a different combination, you can multiply all the crank
lengths by the constant of your choice.

Ken

To be meaningful, I think you’d have to take into account leg mass, which is different for the different sections of the leg. Shorter cranks use much more movement of the lower, less massy sections of the leg than longer cranks.

And mules are even massier! So the mire gets deeper…