Simple gear reduction formula?

[jawnn]

I don’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 can’t understand it, unless it produces a logical number.
3000rpm x (3”pulley/12”) x (3”/12”) = rpm x 1036.828milimeters, circumference of 26” tire /80467.2 millimeters per mile= mph?

[Ramana Rao]

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)

[Ramana Rao]

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)

[jawnn]

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?

[Ramana Rao]

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.

[Ramana Rao]

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

[amrshoof]

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

LegalSpeed (km/h) = S*InputRPM*RadiusOfTyre(in mm)*0.0003768

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.

[subhassarkar56]

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

[jawnn]

The wheel the speed I am trying to calculate is under 20mph.....it all depend on the power needed to climb the hills. most people with cargo bikes on average hills will not need more that a two thirds hp motor if they pedal hard.

If I build this it will be with a one hp motor on trike velomobile.

If you looked at my blog you could see that it took me years of asking questions just find out how simple it was. Because most people can't understand that motors do not get the full HP until they spin at peak efficiency rpm.

And because they all want to go as fast as they can despite any laws.