Bicycling
Chain crossing
2025-07-24 16:08
Chain crossing
In this video, can you spot something that could be improved?
https://www.facebook.com/reel/24195587820047478
After seeing these illustrations, can you spot it?
When the chain is crossed between the front chainring and the rear sprocket, it adds lateral stress on the chain and increases the friction on the gear teeth.
How to avoid chain crossing
Suppose f represents the number of teeth on the front chainring and r represents the number of teeth on the rear cog.
Example. Suppose we have a gear selection of f1 = 40T and r1 = 11T, and suppose we want to change the front chainring from f1 = 40T to f2 = 54T. We then want to find the equivalent rear cog r2 that would give us the same number of wheel revolutions per pedal stroke.
Looking at the formula above, the problem of finding r2 becomes:
r2 = r1 ÷ f1 × f2 = 11T ÷ 40T × 54T = 14.85T
Since 14.85T is not a standard sprocket size, we choose the closest available cog, e.g., 15T.
It is not an exact match, but the error is minimal.
54T/15T: Gear Ratio = 54 ÷ 15 = 3.6 40T/11T: Gear Ratio = 40 ÷ 11 ≈ 3.64 (~1% error, almost equal)
Thus, 54T/15T is an equivalent non-crossed combination to 40T/11T.
In this video, can you spot something that could be improved?
https://www.facebook.com/reel/24195587820047478
After seeing these illustrations, can you spot it?
When the chain is crossed between the front chainring and the rear sprocket, it adds lateral stress on the chain and increases the friction on the gear teeth.
How to avoid chain crossing
Suppose f represents the number of teeth on the front chainring and r represents the number of teeth on the rear cog.
- The formula f ÷ r gives the gear ratio produced by a certain selection of front and rear gears.
- For two gear selections to produce the same number of wheel revolutions per pedal stroke, the ratios of f ÷ t must be equal; that is to say f1 ÷ r1 = f2 ÷ r2
Example. Suppose we have a gear selection of f1 = 40T and r1 = 11T, and suppose we want to change the front chainring from f1 = 40T to f2 = 54T. We then want to find the equivalent rear cog r2 that would give us the same number of wheel revolutions per pedal stroke.
Looking at the formula above, the problem of finding r2 becomes:
r2 = r1 ÷ f1 × f2 = 11T ÷ 40T × 54T = 14.85T
Since 14.85T is not a standard sprocket size, we choose the closest available cog, e.g., 15T.
It is not an exact match, but the error is minimal.
54T/15T: Gear Ratio = 54 ÷ 15 = 3.6 40T/11T: Gear Ratio = 40 ÷ 11 ≈ 3.64 (~1% error, almost equal)
Thus, 54T/15T is an equivalent non-crossed combination to 40T/11T.