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• # Simple gear reduction formula?

Discussion in 'Calculations' started by jawnn, Feb 17, 2012.

1. ### jawnnWell-Known Member

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I donâ€™t think this is right, but I used up so much B vitamins that I could not figure it out. And it is probably back words for a mathematician. So how do I figure out a tow or three stage gear reduction for a bicycle that will bring the peak efficiency rpm down to a legal speed?
I write math visually, and canâ€™t understand it, unless it produces a logical number.
3000rpm x (3â€pulley/12â€) x (3â€/12â€) = rpm x 1036.828milimeters, circumference of 26â€ tire /80467.2 millimeters per mile= mph?

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3. ### Ramana RaoWell-Known Member

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Tire circumference = Pi x 26 x 25.4 = 2074.71mm ( tire diameter 26")
Distance covered in 1 minute = 187.5 x 2074.71 = 389,008 mm
Distance covered in 1 hour = 389,008 x 60 = 23,340,487 mm = 23.34Kmph
equivalent mph = 14.5mph ( 1Km = 0.621504 mile)

4. ### Ramana RaoWell-Known Member

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Sorry I missed the first few lines. here is the complete one.
Input rpm = 3000
output rpm = 3000 x (3”pulley/12”) x (3”/12”) = 187.5
Tire circumference = Pi x 26 x 25.4 = 2074.71mm ( tire diameter 26")
Distance covered in 1 minute = 187.5 x 2074.71 = 389,008 mm
Distance covered in 1 hour = 389,008 x 60 = 23,340,487 mm = 23.34Kmph
equivalent mph = 14.5mph ( 1Km = 0.621504 mile)

5. ### jawnnWell-Known Member

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2 stage reduction

So 3000rpm x (3"/9") x (3"/12") x 2074.71 circumference x 60minutes x .621504 mi/km= 19.3mph

But how do you account for the decimal being in the wrong place?​

6. ### Ramana RaoWell-Known Member

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In your last post the ratio was 3"/12" x 3"/12", with the result as shown. Now you have changed it to 3"/9" x 3"/12" which will give you a higher speed.

7. ### Ramana RaoWell-Known Member

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You have omitted to convert mm to KM. (1,000,000mm = 1Km)

8. ### amrshoofNew Member

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This is the same thing as Ramana's answer but just in a compact form

where S is the total reduction ratio (reduction ratio 1 * reduction ratio 2 * reduction ratio whatever)
just solve for S to find out the required reduction ratio and change the ratios for the individual stages as you like.

9. ### subhassarkar56New Member

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Please clarify your q.For eg what speed you req to travel at ?

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