# steepest grade climbable on unicycle

After watching numerous 30% and even steeper grade hill climbing videos (thx unigeezer!) I began to wonder what is possible.

Here’s my main question:

1. what is the steepest angle a unicycle can climb?
Here are some assumptions to better explain my question - 1)Imagine you have a 25ft long ramp that is a fresh paved road surface, where you could vary the steepness/angle of the ramp from 0deg to 90deg. 2) you enter ramp/slope at <5mph so you don’t accomplish the climb with prior momentum 3) unicyclist has impeccable technique (not sure how to define this) and elite cyclist power/strength 4)non-geared unicycle

Here’s a couple other questions:
2) Based on the geometry of a unicycle and bicycle, which contraption (uni or bike) can climb a steeper angle?

3) What do you think the ultimate climbing technique is on a constant slope? pedaling, hopping facing the slope, hopping sideways up the slope, wheel walking, something else?

FYI A Physicist discusses a similar question for road bicycles here:

There are several things he identifies that will limit the steepest possible climbing angle. One of them we should certainly consider is friction - if your tire slips then the angle is not possible to climb! The author estimated a tire will not slip until 38.7 deg (80% grade) based on a coefficient of static friction table found here (http://hypertextbook.com/facts/2006/…Michaels.shtml). He’s assuming dry conditions with clean road and tire.

Anyone up for an 80% grade climbing experiment? While roads for cars seem to top out at 40% grade (World's Steepest Streets), I’m sure there are other features (skate parks, culverts, overpasses) that would push the “what is possible” barrier for steepness.

Let me clarify something that initially confused me during my research, which is the difference in angle and grade. We’ve all seen both: e.g. road signs that say “next 2 miles, 6% grade”. And from math class we know a 0 degree angle is flat ground and 90degree angle is a vertical wall. There are many sites such as this one (http://theclimbingcyclist.com/articles/gradient-the-basics/ ) that explain the calculation- here’s my take away notes.

-Road grade is a percentage measured by (100* rise/run). It’s a ratio of how much “rise” you get over a certain distance of “run”. So if for example you are climbing a 10% grade hill, for every 10ft of horizontal distance (run) you will be climbing 1ft (run).

To convert a road grade (RG) to angle: (arcTan [RG/100]). Here’s a table i made to help me and perhaps others see how grade and angle compare and relate:

1% 0.57 deg
3% 1.71 deg
5% 2.86 deg
10% 5.71 deg
15% 8.53 deg
20% 11.3 deg
25% 14.0 deg
30% 16.6 deg
35% 19.2 deg
40% 21.8 deg
45% 24.2 deg
50% 26.5 deg
60% 30.9 deg
70% 34.9 deg
80% 38.6 deg
90% 41.9 deg
100% 45 deg
125% 51.3 deg
150% 56.3 deg
175% 60.2 deg
200% 63.4 deg
225% 66.0 deg
250% 68.1 deg
275% 70.0 deg
300% 71.5 deg
400% 75.9 deg
500% 78.6 deg
600% 80.5 deg
1000% 84.2 deg
2000% 87.1 deg
10000% 89.4 deg

I always wondered how rise was defined (never thought to Google it.) Thanks for the info. Interesting question. I’m trying to work on hill climbing now. I’ve watched Terry’s video. Can’t see how you could climb anything much steeper than that!

Terry seemed to mostly be traversing on that video, not sure how much straight up the 30% grade happened.

I used to routinely ride measured 40% grades on my mountain bike (on concrete) without even coming close to running out of traction, gearing, or stability, and I’m guessing a bike would win any real world contest.

If you have the kind of super low gearing a bike can get, hopping loses out, because you need better traction (to accelerate from a standstill to flying-through-the-air speeds) than a continuously rolling climb would need. For an ungeared unicycle I imagine hopping would beat pedaling, though.

edit - oh, I did use to be able to sort of “walk” my way up hills one wheel at a time with the bike mostly sideways, similar to the way you can walk the bike up stairs diagonally. That might let you bypass the friction issue. Doesn’t seem like there’s a unicycle equivalent, though.

I would love to see that “40%” grade [concrete] hill. Nothing “routine” about a hill that steep, lol! And of course bikes with ultra low gearing make climbing MUCH easier than on a 1:1 unicycle! But I’ve ridden up 30% and steeper grades straight up, but even if traversed, you are still climbing it, and making Fargo to the top any way you can is what it’s all about. I can ride it straight up for a pretty good distance, but at a certain point you simply run out of forward momentum, and you either start to tack or stall out.

Most choose the former. But tacking on a uni up a 33% grade can be just as hard in its own way. You have to hop twist at each side, have to often do corrective hops, and gravity throws you down a good foot each time! So in addition to stamina, leg strength and being able to stay in anaerobic threshold, it takes a lot of added technique.

Here’s the straight up 30+% I did recently. several times in a row.

Leedaclimber,
You and I discussed this the other day, but just to clue everyone else in to the rest of our conversation. When looking at a bicycle, if you had to go straight up a hill, eventually the frame would get in the way and cause your center of gravity to be outside your balance envelope. A unicycle does not have this issue, thus giving the unicycle a possible advantage in climbing straight up the hill. Of course, this is ignoring gear ratios, but no theory is ever perfect when comparing apples to oranges

It sounds like, based on your research, that friction would become a problem long before you would fall outside of your balance envelope.

We need to do some experimenting. I wonder how steep Houston Street is between MLK and 8th?

I honestly thought 30% was steep until I read that table. Quite shallow really.

We have a couple of hills here (measured in the old British fashion) that are “1 in 3” - which means they rise one foot for every 3 feet horizontally travelled. I thought that was 33%, but it seems it’s actually 60% from that table above?

Looks steeper than 1 in 6 on Terry’s videos though, you sure these measurements are right?

Sorry - that table’s maths is making my brain hurt. We use an old British system here and a steep hill is a “1 in 3”.

I think, wrapping my head round things, that a ‘1 in 1’ would be 45 degrees, so a ‘1 in 3’ is a 15 degree hill or around 27%??

I guess I’m just an old dinosaur. I do remember that cars used to break down on 1 in 3 hills, with overheated engines, when I was a kid

1 in 1 would be 45 degrees, which is 100%; 1 in 3 would be 33%. 33% is a very steep hill, but climbable on uni.

I don’t think there are any paved roads on the planet which are unclimbable on uni or bike. I would guess that the theoretical limits of traction and leverage would start to take hold around 50% (1 in 2), but we don’t make roads that steep.

i agree any public roads are probably <50% grade and well within reach for bike or uni. but there are plenty of paved features much steeper (eg. the underside of overpasses, skate parks, private driveways?, culverts etc…) that would allow the unicyclist to push steepness boundaries and experiment. If someone is willing to accept this challenge, I would love to hear how it goes- or even better watch some footage of the attempts.