Explain how 10 sprockets are used to provide 21 speeds?

Question

Explain how 10 sprockets are used to provide 21 speeds?

Answer 1

The shifters let you move the chain to select any gear in the front or the back. The total  number of combinations ("speeds") is the number of front gears multiplied by the number of back gears.

For road bikes, common front configurations are 2 or 3 gears. Common back configurations are 7, 9, or 10 gears. For a road bike you'd buy now, you'd see 18, 20, 27, or 30 gears.

2 front x 9 back = 18

2 front x 10 back = 20

3 front x 9 back = 27

3 front x 10 back = 30

There is a lot of overlap, so not all possible combinations represent truly different gear ratios. On my bike, changing a front gear is about equivalent to changing 3 back gears. Also, some combinations are not really useable. On a 30 speed bike, about 6 ratios are impractical because of bad chain angles.

HTH

HTH

Answer 2

They don't.  10 speed sprockets (freewheel or cassette) are in the rear, and the total number of theoretical gear ratios you can achieve is determined by multiplying the rear number by the number of chainrings in the front.

So, with a 10 speed sprocket you can have 10 speeds (single in the front), 20 speeds (double in the front), or 30 speeds (triple in the front).

To get 21 "speeds" you would need a 7 speed rear sprocket and a triple front chainring.  7 x 3 = 21.

However, this is a total of theoretical ratios.  Some may be identical final ratios (measured by gear inches per revolution) and some are not usable.  That is, many systems won't permit largest chainring to largest rear sprocket and smallest chainring to smallest rear sproket.  Both of these combinations create an extreme chain angle and result in rubbing and premature drivetrain wear even if you can shift to them.

I've put a couple of gear chart calculators in the links below that may help illustrate the arithmetic involved.

Hope this helps.

Ben

Answer 3

'Cause you Multiply.

Multiplication is more complicated than adding.

7 x 3 = 21

what you did was add instead of multiply (7+3=10)