Help! Unicycling Math Project

I need some help, as the title suggests.

This year I’m in IB Math 2, which means that I have to write an essay which involves the application of math. I can do the math, but first I need some data. That’s where you all come in.

I need data on the max speed a unicycle can achieve based on its wheel diameter (in mph) peddling at an average cadence of 60 rotations per minute.

I want to look at as many different wheel diameters as possible. If anyone happens to have data or knows where I can find that information online that would be incredibly helpful! A point in the right direction would be appreciated if no one has the data on hand.

If you do have data please post a link or source to where you found it. I have to cite all of my sources, and an online forum is not considered reliable.

Thank you!

You are not asking for data. You are describing an equation relating wheel diameter to speed at a fixed rotation speed.

D: diameter in inches
S: speed in mph

S = 0.178*D

60 rotations a minute is fairly slow pedaling, but in any case it is a constant, so the only data you can get from us are wheel diameters in inches: 20, 24, 26, 29, 36. Some people on this forum have built unicycles with a 32" wheel as well, but you won’t see those advertised on just yet. Some have also experimented with 48" or larger wheels, but those are fairly rare. Oh- and wheel diameters are somewhat approximate, often influenced by marketing concerns and by how fat a tire you have. Unicycles with a 19" rim use such a fat tire overall wheel diameter is the same as a 20, or larger. The 29 rim is actually the same diameter as a 27," but built to fit a much fatter tire so that the overall diameter is more like 28 or 29 inches… Hope this helps.

EDIT: Oops! Harper beat me to it.

Just work with Yetis calculation chart and the concept of total gear ratio:

I don’t understand this question. I mean, you said you can do the math so … just do it. You have the cadence, you have the diameter, so you have the circumference which is the distance covered with one rotation. What else could be missing?

My maths is a bit rusty but this is how I would do the calculation:-

Multiply the radius by 3.14 to get the circumference

Then multiply the circumference by 60 to get the distance covered at 60 rpm. This will give you the distance travelled per minute since you’re travelling at 60rpm.

There are 60 minutes in one hour so…Multiply the above by 60 and you have the distance covered per hour.

Hope this helps:)


Thanks Eric:)

ooops! I should have said multiply the DIAMETER by 3.14:)

@unibokk (1/2)a+ :wink:
@Nimajk you can also use some data out of this thread Fastest speed on a unicycle to get some more interesting calculations than based on constant rpm.

Yeah, I made a big blooper there. lol!

Hmm. But on my 29er I do 7.9mph at 60rpm when your formula suggests 5.2mph.

mirevdiameter(in)*pi1 ft.````1 mi.60 min
----- = ---- * ------------------- * ------ * --------- * --------
hrmin``````revolution12 in.``5280 ft.```1 hr

if you are writing for IB math, maybe you want to look at something with more math and application, so that you can write about it and give examples/explain (word count / page count)

Dealing with only speed on unicycles(fixed gear) is just a bit too limited.

ie, torque/power to go up an incline. Someone’s already done it before for bikes, but as long as you write it out and explain it yourself…and your teacher likes the math you are using… you can get a good enough grade.

Thanks everyone! I have enough data to do my project now!

This isn’t the only math I’m doing, but it’s a part of the data I need in order to get started and begin analysis.

It would appear, then, that you have a geared hub.

That’s what I get too
291.5Pi*3600/12/5280=7.7647 mph

You need a factor of 1.5625, not 1.5 :wink: