Quantifying the effect of unicycle gearing and crank length on speed.

(yes I am a nerd)

The physics behind different sized unicycles and cranks are well known, with larger wheels and smaller cranks allowing faster riding. However, at some point the uni becomes too hard to ride, depending on the terrain and wind of the course, and the strength of the rider. I have heard lots of personal anecdotes about what works best for different people but have never seen these relationships quantified.

My objective here was to check my performance around a standard course using 4 different setups, with a GPS watch to track my speed and heart rate. The course has only moderate hills so I predicted my speed would increase linearly with the Total Gear Ratio (TGR) of the wheel.

I rode a 2.3mile lap on paved roads with little traffic. There was about 100ft of vertical change (see figure). Nothing too steep, but there was a stiff headwind in one of the climbs.

I took advantage of a geared KH36 with 2-hole cranks to ride 4 different setups:

  • Low gear 167mm cranks, TGR = 2.77
  • Low gear 135mm cranks, TGR = 3.34
  • High gear 167mm cranks, TGR = 4.28
  • High gear 135mm cranks, TGR = 5.16

After a warm-up I rode one setup for one lap, took a little break, rode another, switched cranks, rode a third, took a break, rode the fourth. I started each lap from a standstill. I wore a GPS watch to track my speed as well as my heart rate.

I’ve been riding uni’s for 3 years, a guni for 10 month, and a geared 36er for 1 month. Most of my riding in the last month has been with 167cranks so my legs are still not as strong as they need to be to make the most of this wheel.

My average and max speed over the 2.3mi course increased roughly linearly with increasing TGR (see graph).

When geared down my speed was relatively steady over the course, compared with the faster, but more variable, geared-up laps. Gearing had a bigger effect on speed than crank size, increasing average speed 27% and 21% for the 165’s and 135’s respectively, compared with 7% and 3% increases in speed when shortening cranks in the ungeared, and geared, respectively.

My heart rate was relatively low when geared down (averages 151, 155 bpm) compared with geared up (average 169,168 bpm). Geared-up heart rates were also very consistent over the ride compared with the ungeared laps.

This experiment confirmed well-known relationships between gear ratios and speed showing that gearing can increase speed by roughly 25%, while crank size changes more in the 5-10% range.

The low-geared 165’s felt pretty silly out there on the road, certainly not an ideal setup, but it gives a good reference. Going faster on ungeared unis is less a cardio issue then a question of how fast can you spin your legs, at least for the 2.3 mile laps I rode. Truth is, it’s not the most efficient exercise.

However, once geared-up I was able to push myself to the limit, quickly getting my heart rate to the 90-95% range and holding in there for the rest of the ride. Variations in my speed, therefore, are due to changes in the elevation and wind more than changes in my effort. The wind was rather strong tonight, and I expect the speed/TGR relationship would be more linear without the wind. Indeed, a few nights ago I was averaging 17mph on the same course, in no wind, geared up with the 137’s.

I’m a little surprised my max speed wasn’t higher on the 137high, I’ve gone faster. Generally I think this is my setup for road riding, although I like having the 165’s for trail riding. If I keep riding maybe my legs will grow into a 125/150 setup.

While none of the hills were large, my legs were challenged to muscle the big gear up the hill into the wind with the shorter cranks. There is no doubt that gunis put a new emphasis on strong legs, compared with the egg-beater motion needed to spin ungeared wheels around. I’ve still got a ways to go in this department.

Of course in the real world I could just downshift up these hills, but tonight I suffered, in the name of science.

Wow, nice report Ro. You’re a maniac, and I’m glad I wasn’t with you. I got tired just reading your report.

Next week we should do the same experiment, but with two riders and 8 setups. Since we can switch unis without seat adjustments we could do:

29er, 1:1, 150s
29er, 1:1, 125s
29er, 1:1.5, 150s
29er, 1:1.5, 125s
36er, 1:1, 165s
36er, 1:1, 137s
36er, 1:1.5, 165s
36er, 1:1.5, 137s

I’ll bring my GPS, too, and we could make a total of sixteen(!) graphs.

Sounds good, maybe Monday? I’m off the rest of the week. We should do the shorter, inner-loop, if we’re going to do 8 laps, including 2 with the 1:1 29’er.



It would be interesting too if you (or someone) could compare a 24 in guni in high with a 36 in uni to see if the power loss in the gearing is discernible.

wow, cool idea, I wish I had a 24guni at my disposal to test this. Are there other pairs of different uni setups that have the game TGR?


Monday, the day after the 2hr muni race?!? Maybe science can wait until the following week.

Nice writeup Ro! The consistency of your heart-rate in high gear is really interesting. It looks a lot like the heart rate of a cyclist getting a good workout (i.e. no sprints or major hills), just pushing a good sized gear over time.

I’m curious about how the 29er guni will look. Do you expect both a lower heart rate and lower speed? Or just lower speed?

Very interesting article. For what it might be worth, I was pondering over which wheel size would best suit different applications, and wrote a couple of scripts to calculate speed and maximum slope. They are rather simplistic, but I think the assumptions are reasonable and they probably give a fair result. I’ve put them online: maximum slope and velocity. They are in Spanish and km/h; if there’s interest, it would be easy to do an English version.

Juan Reyero

This is consistent with my own data tracking; that higher gearing allows for faster speed, at a cost of greater energy output. Basically, being geared makes it possible to push harder.

Maybe I’ll graph my data points; I only have total times, though, not full ride data.

Nice write-up. The findings sound right to me. When I ride a lot in high gear, the extra work my legs do is just extra training, a plus rather than a minus!

It will be interesting to see your next 16 graphs. Man you guys are nerds but then so are we all.

Have fun!


Super cool data. I should do the geared 24" test vs ungeared (or low gear) coker. I need to get a set of 125/150’s for my coker to really do a comparison (or ride my geared 24 with the 150 holes, which is what my KH 36 has).


Meshing Losses

I look forward to reading about this test, I hope you do it. It won’t be that easy to decide if the gear losses are significant because they might amount to something around 1 to 2%. The loss appearing as a reduction in torque. Instead of getting 3/2 times the input speed and 2/3 of the input torque at the wheel, the speed multiple is 3/2 of course, but the torque is reduced by the amount of the losses. The rider has to work slightly harder to compensate.

The attachment shows the Variable Sheet from a TK Solver model for a planetary gear system to produce a 1.5 overdrive speed ratio. I am guessing at the Schlumpf numbers of teeth and center distance. The input speed and torque are nominal values.

http://www.uts.us.com/ <+++ Link for TK Solver

Are you using the Garmin forerunner 305 for these graphs? My speeds on trainingcenter never come out that smooth. I find most of the graphs to be rather worthless as they are never accurate and all over the place.

yep, there’s a smoothing button that cleans them up a bit. You can also change the settings to have it record data at different rates (I think mine is set to ‘adaptive’ or something like that). Or maybe you just ride more herky-jerky? :wink:


Here are my plots from RTL training. Tunnel Road in Oakland is a relatively steady 4% grade for 3.1km; we used it as an uphill and downhill training ride and speed test. The first three data points are from a ride we did relatively early in our training, trying out different uni setups on the same climb. The last data point is from my last training ride, a week before RTL, when I was in peak shape.

As you can see, for the three rides I did on the same day, there is a more or less linear linear relationship between TGR and average speed, although there is also some evidence of diminishing returns in the 4.52 TGR case (geared 29er). That makes sense; I couldn’t push the geared Coker up this hill in the 54" gear (I rode in the low gear), so the 44" gear ratio was nearing the envelop of doability.

I include the final training ride to illustrate one of the other things we learned through this process; the rider is more important than the cycle. The speed difference between a 36" with 150mm cranks and a geared 29er with 125mm cranks is small compared to difference between the same rider on the same unicycle with more training.

I don’t have heart rate data, but my subjective experience agrees with Roland’s data; I was working a lot harder in the higher gear.

The data aren’t as clean on the curvy downhill (same road):

Here, I rode the geared Coker in high gear, so it had a higher TGR than the geared 29er, yet I was still faster on the geared 29er. I think this reflected the fact that on downhills, people were faster on equipment they were accustomed to; I had very little geared 36 downhill training. Given equal training, I think we’d see a linear plot here as well. Again we see that the training difference is more significant than the cycle difference, though the effect is less pronounced on downhills (as I’d expect).

Subjectively, I felt I was working harder on the ungeared setup on the downhill; slower foot speed with the geared unicycles probably kept my heart rate lower than spinning madly on the ungeared Coker.

This will certainly be the interesting test. Roland’s was already a good start. I have always believed that lots of energy goes into maintaining stability with the narrow balance envelope of a geared unicycle. Heart rate plots for riding the 1.5 times 24" wheel compared to the 36" wheel with the same crank length will tell at least a part of the energy story. Fluid consumption for a long ride (weight of rider and fluid supply before and after the ride) tells another part but is much more objective. Both are tedious to do.

This might be an effect for new GUni riders, but I don’t think it’s an effect for experienced GUni riders. Almost all my energy goes into propelling the thing forward, unless I’m on an uneven surface.

Harper is the most experienced GUin-cyclist there is. He was GUni before it was called GUni.


and I would be a close second.