# New concept: Total Gear Ratio

Yup, that is what it is. If people want a really accurate number they should probably use this method.

Most people just want a general idea of what their ratio is and I think the chart does a pretty good approximation.

The formula I used in the chart is

Gain ratio=(diameter in inches)*12.7/(crank size in mm)

more accurate ratio would be found with the formula

Gain ratio=(loaded axle height)/(crank length)

For schlumpf gearing I just multiplied the wheel diameter by 1.5 but for a more accurate number you should use 11/7. Mostly I used 1.5 so i could use the 36" column twice.

The chart is simplified for simplicity

Really I think people just want to use this to see what would be similar and don’t need to calculate to 5 decimal places.

You are right that the result depends on rider weight and tyre pressure. It also depends on tyre wear, uni weight (in addition to the rider) and some less significant factors.

However, the rollout of a wheel is not the axle height times 2 pi. That would only be true if the tyre deforms to its loaded shape everywhere it is in contact with the road. The contact patch however is flat (as opposed to constant radius), and so outside the middle of the contact patch the tyre has deformed less. The tyre undergoes deformation from hitting the road to leaving the road: it goes from unloaded to maximum deformation and back to unloaded (and this is only 2D, in reality the deformations are still different outside the centre plane of the wheel). Therefore the rollout is 2 times pi times an “effective radius” that is between the axle height and the unloaded radius. I’ve published some thoughts on this in 2003 on my otherwise somewhat outdated Coker rollout page.

Yes that is MORE accurate. For a FULLY accurate number use 17/11.

The more I think about it the more I think Doug would be fine with the 92s. I was using 102s on a 29 equivalent (27x1-1/4) and my crash was due to many factors including a weighted wheel with road tire at 120psi, poor roads, large backpack filled with text books and binders but not properly strapped on, and excessive speed due to the fact I was going to be almost late for my Native Law final. If he takes it easy and just has fun he should be fine. I guess I am just a bigger wheel instead of smaller cranks kind of guy.

Thanks, I pulled 11/7 out of my head and even as I was posting it it felt a bit course. I was close, all 1s and 7s and all Would have looked it up but last minute post before going to work.

It does seem to make sense like that, if you want to see the results of swapping cranks from one uni to another. And your point is especially clear, if those cranks are fairly extreme (165) for a particular uni (20).

But if I am looking to get different cranks for my uni to match the TGR of another ride, I might find there isn’t anything prohibiting me like pedal strikes. For example, if I want a 26 to have a TGR of a G26 on flat roads (green), I look it up and see I’d want a TGR between 4.13 and 4.50. Looking back to the 26, I see I can get 4.40 with 75’s. But wouldn’t that be significantly less comfortable to ride?
(I really don’t have the experience to say, I just gather from these forums that that would be a bit extreme.)

Not exactly clear to me which two setups you are comparing. One is a 26" with 75 mm cranks, I think. The other a geared-up 26"? With what cranks?
Anyway, for most people a 26" wheel with 75 mm cranks will be less comfortable to ride, especially when one wants to ride fast, than a bigger wheel (say, 36" - or a geared-up 26" for that matter) with the same TGR. OTOH, ride comfort is also a matter of getting used to a particular setup.

TGR is a mathematical number referring to the total gear ratio resulting from crank size, wheel size and gearing. It can be construed as an approximate indicator for speed potential, but “at your own risk”. In any case, it is not an exact predictor for maximum or cruising speed. Even less so (I think), it is a predictor for ride comfort.

OOOOooooo colours…

For those of you who prefer graphs to charts

matched the colours as well as I could to the original chart.

I love this whole concept and the chart is amazing. I think it would be really interesting to disect the 29" format where these numbers would end up being vastly different from set-up to set-up. I have 2 29" tires that measure almost 2.5" inches in diameter different. By these calculations my Kenda Kwest with 125mm cranks only comes out to 2.69(measures marginally better than 26.5"), which only makes it slightly better than a 26" with the same lenght cranks, whereas my Schwalbe Big Apple 29 (actually 29") gives me a much better TGR for cruising at 2.95 with 125mm cranks.

Wow…this is great.

Comparing my limited experience of several different crank lenghs on my 24" & 29" uni’s I agree completely with what the chart says for my effort/comfort etc.
It also supports my thinking that 150’s on my yet-to-be-delivered 26" Guni may be just a bit too long after I’ve got the hang of it.

This chart should be a ‘sticky’ somewhere so newbie’s can find it easily.

So get the 150/125s and have the best of both worlds

billnye
John M

I’ve got a set on my 29" and change the position depending on what I’m riding (3 times yesterday for Muni, then fire road then back to Muni in a 12 mile ride) - hoping to get away from this messing about with theb geared hub as I’m going to use the 150’s I’ve got spare…although I can feel an ‘upgrade’ coming on!!

How would you differentiate ‘cruising around town’-type-riding from ‘commuting’?

When I read that chart, I take it that ‘cruising’ is more of a leisure ride, while ‘commuting’ is about covering a distance.

Science of Unicycling & TGR

Here’s a video we made inspired by the TGR

Ha, I like it. You guys did a great job explaining the effect of wheel size. I think though that you should have included more about crank length, and probably also about gearing (hub). At least if your goal is to explain Total Gear Ratio, which really depends on all three.

Of course you are right Klaas, perhaps a trilogy!
I. Wheel Size - why so many.
II. Crank Length, it matters
III. Geared Hubs, Schlumpf’s revenge

Awesome idea. And then somehow weave the overarching concept of Total Gear Ratio in there, or maybe as part IV of a quadrology

A thorough discussion of the overall ratio should consider the geometry of the rider’s legs. As part of the complete drive mechanisms we consider the main forces are applied in two different places and the articulations of the knee and ankle.

Most riders who have experienced a range of unis will know how much faster one can pedal by having the seat high enough to minimise the bend in the knees and strongly articulating the ankles on a uni with short cranks.

Despite the decreased leverage of the shorter cranks, hill climbing ability is not severely sacrificed because the efficiency of the transfer of the energy improves in the leg itself.

I’m actually working on a model that includes leg motion, ankling, seat height etc. But the Total Gear Ratio is aimed at being similar/comparable to the gear ratio of a bike. In other words: it is a property of the cycle, not the total drive mechanism. For that reason, leg geometry and motion are not included in TGR.

Yes I suppose the leg is more like the engine than the transmission.