However, they are not the same. I own both of these configurations and the 24 is faster on timed laps.
To help understand why the two unicycles described above are not the same, please consider exaggerated examples of unicycles with a 1.0 TGR. Imagine riding/walking on a little 2” radius wheel with 2” cranks. You would be taking tiny steps every time a crank hit the ground. However, on a 20” wheel with 10” inch cranks you could move at a much faster pace. The small wheel is the equivalent of walking with your shoelaces tied together. The larger wheel fit’s more with a natural human stride.
That’s the problem. Unicycles are easy to make mathematical models of, humans are not. How people “fit” with their unicycles is so hard to define, describe, calculate.
I believe an accurate model would be quadratic with the vertex being the ideal setup. If we had a way to collect the data, could we use a large number of riders timed riding a variety of unicycles and take a quadratic regression to find the best fitting equation.
It wouldn’t be as easy to remember or use as TGR, but it might be useful to some of us.
I enjoy the TGR concept, but I want to add a concern about cadence:
Cadence
One obvious problem with the TGR equivalence of different unicycles is that most riders are more comfortable (and probably more efficient) in a given cadence range. (The TGR assumes that a constant foot velocity is the key, but as others have pointed out, this assumption is obviously wrong with very small or very large cranks.) Apparently bike riders often use 60-80 RPM cadences for most comfortable riding. Maybe we can push it to 100+ RPM on an appropriate unicycle. These numbers directly give us the speed of the unicycle for any configuration (and completely ignore the crank size.) Presumably different crank sizes make faster and slower cadences more effective and extend the range normally quoted for bicycle riders.
Here is a formula for MPH:
MPH = RPM X WD X GR X 0.00297
Where MPH = miles per hour
RPM = cadence in revolutions per minute
WD = Wheel diameter in inches
GR = hub gear ratio (1.00 unless you spent a lot of money on your unicycle)
(Notice that the crank length does not show up in this equation—it is implicit in the RPM term.)
The TGR theory suggests that the preferred cadence should be inversely proportional to the crank length. Has anyone measured comfortable cadences with different cranks on a unicycle? If not, I would suggest having someone with a large selection of different cranks try this test. Mount the cranks on a 24" unicycle and try a fast but comfortable pace with each set. Record the comfortable maximum RPM with each crank set. (One could measure MPH and back calculate RPM if that is an easier measurement.) That might give us a sense of how a comfortable cadence varies with crank size. I am suggesting a relatively small unicycle (24") so that the resistance is not very high (the TGR is small). One could then compare these measured cadence with the prediction of TGR theory that cadence should increase linearly with decreasing crank length.
As I mentioned in my initial post, Mikefule did some good (hands-on, or rather feet-on) research on this subject. He reported the results in this forum, but I was too lazy at the time, and I am still, to search for it and provide a link. Mikefule used not only various crank lengths but also various wheel sizes. He concluded that while cadence is not exactly inversely proportional to crank length, for a single step in crank length, and then within certain reasonable limits, the Constant Foot Speed Hypothesis is useful.
But let me say again that the Total Gear Ratio is a gear ratio. It may be interpreted as a predictor for speed, or somewhat more safely as a predictor for speed potential, but entirely at your own risk. YMMV.
I’d just like to ping this thread to let everyone know that I’ve put an article about Total Gear Ratio on Adventure Unicyclist, kindly written by Klaas Bil.
I think it’s a great way to conceptualise unicycle gearing, and hopefully will be a good reference for all unicyclists in future.
I did up a spreadsheet and colored in the similar values for easier visualization of similar gain ratios. The comments at the bottom are just what I think the various ratios would be suited for. The chart also demonstrates the jump in wheel sizes between 29 and 36. I wonder if that gap will ever get filled?
I used nominal values for the wheel sizes and a gearing ratio of 1.5 for the geared numbers but it should be good enough to give people a good idea of what kind of gain ratio they have in various setups.
The other factor that needs to be included is the total weight of the rider and the unicycle. I believe this could affect the TGR dramitally but can be included in the calculation.
This is super. I was doing exactly the same thing the other day to figure out what crank length I should put my my ungeared 36 to get some practice for when I get my high-geared machine together. Good to know there’s a term for it, it’ll make talking about speedy machines much easier.
Of course weight does matter, but if you want to compare how would you feel on the various unis, then the weight is more or less constant.
If you want to compare various persons, then TGR, anyway, does not take into account the personal preferences eg in crank size, so it will not be a full comparison. Then also the raider height matters especially for bigger wheels. I think it is better to keep the parameter simple.
Unfortunately I don’t think that will help much. You can fit cranks which will give a similar level of torque, but the difference in length means you use very different parts of your leg muscles with a geared uni. Getting good at spinning tiny cranks is a specific skill, but guni riding is another kettle of fish. I definitely can’t go up hills in high gear on my g36/150mm which I can do with my ungeared/100mm.
The best practice/training to prepare your legs for guni riding is a bike. That will have more similar length cranks, and you can push harder in higher gears on them than on any short-cranked ungeared uni.
The coloured chart is great. Thanks Eric - it’s an easy way of browsing TGRs.
The general public supposedly associates unicyclists with clowns, whereas I have always associated unicyclists with nerds. this fantastic post amongst several others this week alone has vindicated my thinking. Wow. I love it!
What? Oh, you’re new here. Yup, it’s a nerd-o-rama! I especially like when people bring in physics equations that tell you something, but usually not in relation to the realities of the situation under discussion…
I think riding a GUni in high gear has more in common with riding a bike in terms of leg load than it has with single speed uni regardless of crank length.
I have a 26" Nimbus with square tapered 152mm cranks.
I noticed in my garage I have a beat up punk/runt bike like this one with 92mm cranks.
If I succeed in putting the 92mm cranks on my nimbus my TGR will change:
152mm TGR = 2.17
92mm TGR = 3.59
That would give me a TGR similar to a Coker with 130’s.
TGR is the “speed potential”. So I should have the potential to go as fast as this Coker.
I’m excited about trying this. Will it be a no brainer to just ride and be fast. Or is there some lack of technique that will keep my “potential” from becoming realized?
Gain ratio ( I am not a fan on the term TGR since most of us don’t have gears) is only one factor on how fast you will go.
When riding a 29 with 102s I can get top speeds about the same as my top speeds with a 36 and 127s (30-35km/h) but I feel like I have more control with the 36 and am able to keep a higher average speed with the larger wheel and longer cranks but similar gain ratio.
I crashed pretty hard a few years ago using 102mm cranks and no-loner feel comfortable on anything shorter than 114s. Probably just a mental block and I will have to put some short cranks on a 20 to get over it.
You can continue to use the term TGR and secretly think Total Gain Ratio.
I use “gear” also as reference to the “gear” resulting from the crank being shorter than the wheel radius. People on this forum have called this “gear” for years. Looking at it that way, every unicyclist rides geared
A 26" with 92 mm cranks is still a reasonable unicycle. You will need quite a bit of training to acquire the technique of spinning really fast (meaning it is not a no-brainer), but then I think you would be almost as fast as with the same amount of training on a Coker with the same TGR.
(BTW, how did you calculate 130? My calculator gives 92 * (36/26) = 127 mm.)
