# Theoretical Climb Limits

Is there a practical or theoretical limit to how steep a climb can be undertaken on a unicycle? Straight on, no weaving.

Or is it just a matter of how strongly the rider can pull on the seat and keep the rhythm going?

I have climbed most of the steep streets in Murwillumbah and I am now looking at what I suspect is the steepest. It is the only one I know of with a sign at the bottom and it says 26% (~15 degrees).

It increases gradient in three stages. Until the join in the road surface near the power pole it ramps up to what looks like about 11 degrees. This followed by a short section to just beyond the next driveway on the left that I measured at 13 degrees then presumably the full 15 degrees as indicated on the sign.

I used my gradient gauge on the kerb to measure the 13 degree section. (I realised it was pretty steep because the gauge started sliding down the concrete.)

I’m riding a 24 inch with 125 mm cranks. I can manage the first section comfortably and ride right across the second section but that is at my current limit.

Is the long 15 degree section remotely plausible with a bit more training?

Hill climb

Unigeezer did this climb

125’s might be a bit too short for such a climb, especially going straight up. Longer cranks will provide additional leverage and torque needed to maintain momentum.

Can’t get a much more authoritative opinion than from the master of climbs himself.

I have the original 150s that were on the uni when I bought it so I will give then a go some time.

The coefficient of static friction between the tire (which varies) and the road surface (which also varies) would determine a theoretical limit to the possible steepness of a climb. At some point the tire will just slide on the road surface.

Usually long before the tire starts to slide my maximum sustainable heart rate is reached. I usually decide to step off the pedals as my bpm assends much beyond 200. If I do manage to control my heart rate by decreasing assent speed the next limiting factor for me is when my lungs turn inside out.

Those standing around the finish line said I turned my lungs inside out when I collasped just after the finish line on the Issaquah, WA Cougar Mountain Hill Climb.

I sure Terry has faced both of these limits multiple times.

JM

What a great article! Congrats!

I agree, Joe, that there is a human endurance limit that comes into play well before the coefficient of static friction.

Unless the road’s wet!

Can’t help it, I’m an Engineer…

Doing a little free body diagram of a wheel on an incline, the theoretical limit comes out to:

(Wheel Radius) X sin(road angle) = min crank length

That is the absolute limit for the power part of the stroke when your pedals are at 3 and 9. This assumes the wheel isn’t slipping (probably not a problem on dry surfaces) and of course toque goes to nothing when the pedals are 12 and 6. So the practical limit is less since you need to generate some momentum to carry you through the low torque part of the rotation.

Not sure if this helps, thought I’d chip in.

So a 24" wheel with 125mm cranks would be at a stand still with the rider standing on one pedal at 3 o’clock on a hill of 24.1 degrees.

Not sure if your calculation above would apply to every rider though. Btw, 24.1 degrees is 44.6% grade.

Oh yeah, not suggesting the calculation is very useful. It doesn’t do any good to be at a stand still during your power stroke.

The practical experience is much more useful. I know I struggle with hills a lot in Muni. Especially lumpy ones! And no where near 44% grade.

I am not an engineer, but my understanding is that pinned pedals allow you to exert lateral force at the 12:00/6:00 position.

I’ve always reached the human endurance limit while climbing on wet pavement. We ride a lot of wet pavement in Bellingham and the Pacific Northwest. Never yet have I found the coefficient of static friction on wet pavement, only frosted pavement (went down on some of this a week ago), snow, ice, sand, gravel, and mud.

Greg, what about you?

aspenmike hasn’t commented yet either…

JM

Maybe they haven’t discovered any limits in climbing yet …

On dry pavement I peter out WELL before you ever would. The only tire slip I can get on a unicycle during a climb is on loose gravel or sloppy mud. On a bicycle I can get tire slip on wet pavement but bicycles, as we all know, are for sissies.

Thank you for the formula- I’d been thinking the ‘simple’ solution was something like this.

But then I got distracted by the following complicating observations of…

When the grade starts getting steep I’m grabbing the seat handle and pulling up to effectively increase the force on the pedals more than that generated by my mass alone.

Not that clipping in is common on a unicycle, but the counter force of pulling up on the back part of the pedal revolution could also effectively increases the theoretical limit beyond this formula. Doing this on my bike on steep grades is the only way to get a big gear up.

Which gets us back to Harper’s coefficient of friction.

Several have climbed the steepest road in the world (Baldwin St. in New Zealand) I think Ken Loi (sp?) did it streight.

Love to see the video! As they say, it didn’t happen otherwise! But I can believe it since it’s only 2% steeper than Fargo’s 33% grade, which I’ve also climbed straight up on a 29er.

from Wiki: Guinness officially recognizes Baldwin Street as the world’s steepest street at a 35% grade.