I’ve done maybe 650 miles on my N36 since I got it in November '07. (Usually in spurts… 60 miles here, 40 miles there, 30 miles here, and they add up slowly because I don’t ride enough :-P). I hope I can give you a bit of a comparison as to how hillclimbing on the 36 compares to climbing on the bike. (I have maybe 13,000 miles on my bikes since 2006)
Anyway, I’ve recently begun doing hillclimbing on my Coker, as I’ve been climbing with my road bike for a good couple years now; these are methoughts. There’s a hill around where I school that is about a mile long and does a good 500-550 feet of gain, which makes for a ~10/11% grade… steep for a bike. I can get into a tough pace on my bike on that hill and hold 8-8.5, and I average 7.5 up it on my Nimbus 36". I’m very confident that I could beat many road riders (with racing bikes, yes) up that hill, assuming that they can sustain perhaps 85% or less of my max power on that hill. Obviously, if I raced myself on a bike, the bike-me would win, but there are plenty of people weaker and way more who are stronger. If you get in super good shape and find a hill that really, really bites (one where you’re NOT able to sit and spin, because the bikes will win hands down), then you just might be able to compete, and, if you’re a stronger rider than they are, win.
I think it’s about aerobic threshold and the assumption of a long (i.e. 10-minute to an hour) hill that gets the cyclists in the same gear ratio as you. If your aerobic threshold pace on a bike is 15-20% faster than theirs is when you’re both on bikes, you could probably hold pace with them on a unicycle maxed out going up that hill. If you’re stronger than that, then you got 'em!
For reference, my road bike gearing is 39 teeth front, 23 rear (in first gear, which is required on that hill) on a 700c wheel, which makes for a 45.7" equivalent wheel size in cadence-to-ground-distance ratio. However, my bike cranks are 175mm (vs. 125mm on my coker), so, if you cancel that out and normalize to 125mm, it’s like a 45.7*125/175 = 32.7-inch wheel with 125 cranks when you look at it from the perspective of “how far your foot moves, in centimeters” versus “how far the bike moves, in centimeters”.
With my 36" wheel with 125 cranks, I end up in a slightly higher “gear”, but it’s close enough that I can come very close to matching the speed that the same rider (me) would be capable of on my racing bike, and exceeding the sustainable speed of another slightly less fit rider. It would also allow someone more fit than me to leave me in the dust with me on my bike and him/her on my unicycle.
Assume that riders are of equal fitness.
In a sprint, a bike will ALWAYS beat a unicycle, due to the aforementioned instantaneous power advantage (bars)
In long, un-sprintable hill climbs, a unicycle will never actually have the advantage, but can get “close.” The 30-50% more power from clipless pedals on the bike, as with the pulling up on the bars to get sprintmadness, vanish when you the bottleneck in your ability to sustain power is your cardio rather than your sheer muscle. If you’re at your aerobic threshold, you’re not going to go any faster, if at all, if you can pull up with your arms and hamstrings; being able to distribute the load across different muscle groups will take the burn off and allow you to keep it up longer before fatigue, but as far as the instantaneous wattage goes, it won’t help much. So, if you can get a longer hill, you can remove the sprinty advantages a bike offers. Longer, as in, probably a mile or longer, 3/4 at minimum. Once you’re doing that, all you need to do is make sure that you’ve got a grade that is optimum for your wheel size… one where they’ll have to shift into a gear such that their equivalent wheel size from their gear ratio (compensated with crank length) is the same as your wheel. Then you’ll be able to at least hold your ground, but because bikes are more efficient, if you assume that they’re in identical shape, they’ll probably get you after a time.