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I am trying to create a formula to get the right gearing on my two BMX bikes. On my 24" Cruiser I have a 40/16, 40 tooth front and 16 tooth rear cog. The chart says that is a 60, and 188.5 roll-out. On the 20" BMX I have a 45/16 which the chart gives as 54.9 and 172.3.

The tire diameters are 24 for the 24 and the 20" is just under 20". So the question is how do I account for the tire diameter in the equation so that I have the same "feel" on both bikes.

Trial and error is expensive and bothersome.

If anyone wants to explain why simply having the same roll-out is not the same, I would appreciate that as well.

Essentially I think that is had to do with the length of the lever, the tire radius, somehow.

3 Answers 3

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You don't need trial and error and you don't need a chart, you need math.

(Chainring teeth / sprocket teeth) × tire outside diameter = gear inches

Rollout is just gear inches multiplied by π.

Tire outside diameter can be approximated by adding double the tire width to the bead seat diameter of the rim, so if you've got a tire that's (for instance) 44 × 406 mm (you should see a number like "44-406" stamped on the side of the tire), that has a computed outside diameter of 494 mm, or 19.52".

You don't have the same rollout on the two bikes—the 20" bike has roughly 8% lower rollout. That's a noticeable difference. If you want to equalize the two, you'll want to make small changes to your gearing. Setting up your 24" bike as 36×16 or 40×18 should get it very close to the 20" bike.

Gear Calculator is a good tool for playing around with gearing.

Note that there will be unavoidable differences in the feel of the two bikes. The 24" wheels have more inertia, so they'll be a little slower to accelerate, but should coast a little better. You can't make that go away.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Gary.Ray
    Dec 30, 2021 at 20:22
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Using simple gearing comparison math to get the same or closest possible gear between a 20" and 24" BMX race bike only makes sense if you're assuming your target cadence will also be the same. The postures you're in between the two are very different, so there's not a lot of reason to make that assumption.

How to mathematically predict the effect of those postural changes is a fine question, but it's a complex one and the kind of thing that usually gets settled by feel in practice.

The effect of wheel size on inertia is relevant too, but it's not the only factor here.

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Poking numbers into https://www.sheldonbrown.com/gear-calc.html returns:

24" wheel with 40:16 gives 28.7 km/h at 100 RPM
20" wheel with 45:16 gives 25.2 km/h at 100 RPM

To get the same numbers you'd want to try

  • 35:16 on the 24" to get 25.1 km/h at 100 RPM
  • 40:18 on the 24" to get 25.5 km/h at 100 RPM or
  • 51:16 on the 20" to get 28.5 km/h at 100 RPM

However with most things in cycling, there's more to it. The larger wheel will be heavier as will the frame to hold it, and being larger will be slower to accelerate, feeling less snappy or more lethargic. This means the 24" will require more explosive power to accelerate.

The frames won't be identical either - the 24" will have the BB lower than the 20" frame, when compared to the wheel-axle height. If the BB was the same difference to the rear axle, then the 24" bike's BB would be an extra ~2 inches off the ground, which means the pedals are also that much higher.

The 24" bike is probably longer too, or the bigger front wheel is more likely to induce toe strike.

Upshot - two different frames can never feel identical unless they are of similar size and design.

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  • 1
    Nobody has mentioned crank length or Q factor ...
    – bertie
    Dec 31, 2021 at 22:26

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