Based on a discussion in the German unicycling forum we want to shed light on the question what uphill gradients someone can ride with a unicycle. That of course depends on the rider's physical condition, as well as on wheel size, crank length, and gear ratio of the used unicycle. Additional influencing factors like wind, air drag, ground conditions, and friction loss shall be neglected.
Assuming the rider does not pull upward the seat, the maximum power a rider can use on the pedals results from his weight. In the sequel we will take that scenario as given and assume the rider only using his own body weight for pedaling.
Let's name the rider's body weight wr, the weight of the unicycle wu, crank length l, wheel circumference u, and gear ratio rt. Then we assume the rider pushing the pedals downward vertically when riding. Per crank rotation the advance vt is
vt = 4 wr g l / (u rt),
where g = 9.80665m/s2 means gravitation. The factor 4 results from performing 2 strokes of length 2 * l per crank rotation. The overall weight that needs to be moved is the sum of bodyweight wr and the weight of the unicycle wu. So to gain a rise of 1 meter you must move forward distance s where
s = (wr + wu) / vt.
As elevation refers to horizontal distance, not to ridden distance, the maximum ridable gradient a is
a = 1 / (s2 - 1m2)1/2.
This table displays the theoretical maximum ridable grandients for a set of unicycles and a rider weighing 90kg. Changes in the rider's weight only have minor effect on the resulting gradient.
| Crank length | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Unicycle |
Wheel diameter |
Rider's weight |
Gear ratio | 90mm | 100mm | 110mm | 125mm | 135mm | 145mm | 150mm | 165mm |
| 20" trial unicycle | 515mm | 5.4kg | 1 | 21% | 24% | 27% | 30% | 33% | 36% | 37% | 42% |
| 20" freestyle unicycle | 518mm | 5.0kg | 1 | 21% | 24% | 26% | 30% | 33% | 36% | 37% | 42% |
| 24" Muni | 655mm | 7.8kg | 1 | 16% | 18% | 20% | 23% | 25% | 27% | 28% | 31% |
| 26" muni | 720mm | 8.1kg | 1 | 15% | 16% | 18% | 21% | 22% | 24% | 25% | 28% |
| 29" XC unicycle | 725mm | 6.3kg | 1 | 15% | 17% | 18% | 21% | 23% | 25% | 25% | 28% |
| 29" XC unicycle | 725mm | 8.2kg | 17/11 | 9% | 10% | 12% | 13% | 14% | 15% | 16% | 17% |
| 36" unicycle | 918mm | 8.0kg | 1 | 12% | 13% | 14% | 16% | 17% | 19% | 19% | 21% |
| 36" unicycle | 918mm | 9.9kg | 17/11 | 7% | 8% | 9% | 10% | 11% | 12% | 12% | 13% |