A Certain Ratio

AArrgghh!!  That, perhaps, is thew worst, most predictable and derivative of all the puns I have employed over the years to entitle my articles.  I’m sorry.  Unless, of course, you’re from Manchester.  Actually, this article isn’t about 1980s funk bands from the rainy north-west.  It’s about gear ratios.

I have been increasingly interested in this subject since I obtained my lovely new bike with its Rohloff Speedhub, encasing as it does 14 wonderful gears in a sealed metal casing that is as impervious to the outside world as John Prescott.  So in my casual browsing of the encyclopaedia of bike maters that is Sheldonbrown.com, I happened upon the gear ratio calculator.  This is a really useful tool if you want to lean more about your gears – either derailleur or hub.  Not possessing a slide rule (I recall having one as a teenager, but as with many things, had no idea how to use it….), I decided to investigate further, in a quest to try and make sense of what happens when you push on the pedals.

I recently changed my chainring, the bike originally having been specced by a ride who lived in Yorkshire, within reach of the Pennines.  I suspect that this geographic area was the reason why a 42 tooth chainring was fitted – great for hilly roads, but almost unusable when ridden in flat East Anglia.  I was aware that gearing of this kind was not suitable as soon as I rode the bike – my gear 11 was causing a cadence similar to that of Lance Armstrong, while anything below gear 10 was basically unusable, so I was almost permanently in gears 12-14, and felt like I had a very expensive fixed wheel bike!

The definition of ‘Gear Inches’ – the UK method of calculating your ratios – is succinct:

“The simplest system in common use is the “gear inch” system. This dates back to before the invention of the chain-drive bicycle. It originally was the diameter of the drive wheel of a high-wheel bicycle. When chain-drive “safety” bikes came in, the same system was used, multiplying the drive wheel diameter by the sprocket ratio. It is very easy to calculate: the diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear sprocket. This gives a convenient two- or three-digit number.”

Changing the ring to a new Thorn 46 tooth one has made a huge difference – the ratios are shown below – and though I rarely go below about gear 9, it is immensely rideable.  With the wind behind you, and on a nice flat, open road, you are pushing a 109 inch top gear; considerably higher than the top gear on my road bike, which I typically rode in the 68-100 inch range, whereas the Rohloff lets me go down to 20 inches if I really need it!!!

Now, as Sheldon states, the problem with inches as a gearing measurement is that it lacks the subtlety of the length of the bike’s crank – which, if you have ever used a long spanner as opposed to a short spanner to move a stubborn bolt, you will know is a highly significant factor!  You might like to read his theory on this, as the proposed method, ‘gain ratios’, does in fact take into account crank length and thus provides a much more multidimensional way of understanding what is happening under your feet.

Quite simply, and you won’t need me to tell you this, but hey; ‘gain’ as a physical concept is the distance traveled forward by the bike during one complete orbital revolution of the pedals.  It is a constant; every inch, metre or KM the pedal travels around its orbit, the bike moves forward a proportional distance.

It’s actually, when you think about it, one of those beautifully simple and consistent rules.  Because it takes the length of the crank into account as a factor (and basically then compares this against wheel diameter), it is unique to a certain size model of the same bike, but it also applies to any gear on that bike!

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