Ride UK Tech Columns

#67 Super Small Gearing

(This article first appeared in Ride UK issue No. 67 and is reproduced here by kind permission of Ride UK.)

Gearing (again).

Well it's been nearly a year since the first article I wrote on gearing and a lot has happened since then.
Everything that the previous article covered still holds true and I wont be going over the same ground again. "Thank fuck." I hear you cry, "That previous gearing article was dull as ditch water that a tramp has pissed in".
Well don’t get too excited because this one will probably push the tedium to new levels. It's hard to say till I write it so lets wait and see what happens eh?

If you took any of the previous article in, hopefully you came away with an understanding of the basics. You are now quite comfortable comparing gear ratios by simply dividing the number of teeth on the front sprocket by the number on the back. Doing this simple sum gives you a number something like 2.75 and the ratio will perform much the same if you get the 2.75 by looking at a 36/13 or a 44/16.
Whilst the gear ratio will feel and perform much the same, the 36/13 is likely to save you nearly 3 links of chain and knock 30% or so off the weight of the sprocket. PLUS you will be less likely to bend the sprocket.

So taking this argument a step further we should look at getting the teeth down as low as possible. If we could fit a 10 tooth on there then we could manage with a 27 front sprocket; this would save another 3 links of chain and another 30% off the weight of the front sprocket.
Even better if we could make a 5 tooth rear sprocket we could have a 14 tooth front sprocket!

Well this is an idea that hasn’t escaped the notice of a few companies out there.

Cassette hubs were originally devised to allow easy changes of gear ratios on mountain and road bikes, when the cassette hubs came to BMX we ended up with a modified design of the same technology. Sprockets were easily interchangeable and available in sizes from 13 upwards. The 13 soon became the most popular size because of its ability to run the smaller gears mentioned above.

A few companies managed to bring out a 12 tooth sprocket to fit and the gears could get even smaller. Getting smaller than 12 wasn’t looking likely because there just wasn't room on the splines.

But BMX'ers really don’t need to be able to interchange sprockets, and we certainly don’t need them coming loose on us, so the logical next step was to make the "driver" (the part of the cassette that carries the sprockets) and the sprocket in one piece. Suddenly you have the ability to go much smaller and there is now no chance of the sprocket coming loose. Brilliant.
Odyssey now makes an 11 tooth driver for their cassette hubs and a 10 tooth is coming soon. Meanwhile Profile has gone right down to 9 teeth and even makes a cheeky little 9 toother to fit the Odyssey hub!

Okay. So we are all well aware of the advantages of going smaller but is there a downside?
Some people say that "there is no such thing as a free lunch", but I prefer "you never get owt for nowt"

The obvious problem is with brake clearance. If you have chainstay mounted brakes then you can pretty much forget running a 9 or 10 tooth driver. With a 25 tooth front sprocket the chain will be almost an inch closer to the brake than a 36! A 36 is damn close on most bikes as it is so an inch closer than this will be out of the question on most frames.

But the obvious problem is NOT the biggie. To explain the big problem with these ultra small set-ups we need to think about the forces involved and to make this clear please bear with me while I wonder off on a little explanatory example…

Imagine an elephant, African or Asian, its up to you (I would go with the Asian personally they tend to be a bit easier to manage and smaller which will be important later on) and imagine that this elephant likes swimming, specifically he likes diving. Now I realise that you might have been thinking of a female elephant but for the purposes of keeping this short please switch to a male.

Now rather bizarrely you have a big elephant specific swimming pool round the back of your house, (of course if you lived in Sheffield you would have at least one world class elephant highdiving training centre which you have to pay an enormous amount of council tax towards and never gets used, and the council would be planning a second) but for some reason your diving board is broken and just hangs limply over the pool. Just a hunch but it might be something to do with the frigging great elephant that keeps using it!

So whenever your elephant wants to go diving you have to hang upside-down from a helicopter and support the diving board. Now this wouldn’t be so bad if you could hold it at the end but obviously you would be completely in the way of the elephant diving off, so instead you have to hold it down near the attachment pivot.

Now it doesn’t take a genius to realise that the nearer the elephant you can hold it the easier its going to be and that the nearer the pivot you go the harder you will find it.

I am really regretting the way this example went and I am sorry, re-reading it I realise that it sucks, but I am not going to re-do it, so tough.

So (you wont have seen this coming, honest) the diving board is your crank arm, the elephant is your foot pressing down on the pedal and the poor bugger hanging from the helicopter is your chain wrapped round the front sprocket.
The chain already works at a mechanical disadvantage. If you press down on the pedal with a force of 1 elephant and the chain is exactly half way between the pivot and the pedal then the tension in the chain has to be 2 elephant. If the chain is a third of the way from the pivot to the pedal then the tension in the chain is 3 elephants!

So let's compare a 44 tooth sprocket a 36 tooth sprocket and a 25 tooth sprocket.

A 44 has a working radius of about 89mm so on a 180mm crank that’s almost bang on 1/2 way out. Therefore if you can press down with a force of 1000 Newtons (which you might well be capable of) the chain will have to take a load of around 2000 N.

A 36 has a radius of about 72mm so on a 180mm crank the chain tension will be 180/72 x 1000 which is about 2500 Newtons.

A 25 has a radius of only 50mm. With our 180mm crank we get a chain load of 3600 Newtons!

So on a 25-9 gear set up the chain has to take nearly twice the tension of an old school 44-16.

But there's more.
On any sprocket the chain wraps round approximately half the teeth, so on a 44 tooth sprocket that 2000 Newtons is spread over 22 teeth. Theoretically each tooth only has to take a load of just over 90N.
With the 25 we have to spread 3600 Newtons between just 12.5 teeth so each tooth has to take nearly 290 Newtons over three times the load!
Infact the chain can't share the load out evenly over all the teeth so it isn't quite this bad but it is a massive increase in contact force.

Similarly the rear sprocket is massively loaded. At the back end that same 3600 Newtons has to be shared between just 4 teeth! Nearly 900 Newtons per tooth (compared to 400 for a 13 tooth rear sprocket).
This load also has to be carried by the individual rollers of the chain.

So the forces involved are much much higher than in a normal drive train but the question is are they TOO high?

Well industrial chains of this size are typically quoted as having a tensile strength of just over 8000 Newtons, but this is not a working load this is a failure load! And this is a failure load under normal industrial operating conditions well lubed and looked after and new. The chains we use are cheap foreign ones that we treat like shit….

It’s a fair bet that running the new super small gear set-ups will lead to some new problems, expect chain stretch and tooth wear to be much faster than normal. If you are a big guy and like to crank hard at stuff then watch out for snapped chains and the associated slams. Stick to the quality chains and keep an eye out for signs of trouble.

Obviously if you NEED the small front sprocket to make certain crooked grinds possible then the trade off might well be worth it.
But if you are just in it for the weight savings then beware, you never get owt for nowt.

(Cheesy ending or what? Working back to that "owt for nowt" bit was forced as hell, wasn’t too bad in the end if you ignore the stuff about the elephant. This bracket kind of spoils it mind…)


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