Formulas for finding maxs speed

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Jul 24, 2003
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#1
I’m trying to create a table that will show different top speeds, given wheel size, and front and rear sprocket selection. I’m missing some key data. First would be the maximum revolutions the CDI allows the engine to revolve. Second is the meaning of the ratio number given for the gears. For instants, first gears having a ratio of 1.800. Is this the reduction of my crank rpm? So it would make the front sprocket turn .556 per revolution of the motor. If I’m doing my math properly this cant be right... saying that I have my bike in first gear revving at 10,000 rpm and my front tooth sprocket is 14 and rear is 50 and my rear wheel being 21 inches top to bottom. What would my Mph be? I would take .556 times 10,000, which is 5560. That would be the number of turns the front sprocket would be moving at that rpm. Then the ratio of 14/50, which would be 3.571. So for every 3.6 turns of the front it would turn my rear wheel once. Now I take 5560 / 3.571. To give me the number of revolutions the rear tire is making. So 1561.798 times the rear wheel diameter being near 80 inches. 124943.820 then convert that to feet so 10411.985 feet, and then divided by feet in a mile which is 5280 I think... that’s 1.972 miles per hour
That is not how slow I’m going in first gear. I think I would be doing at least 25 mph. Can someone help me with what I’m doing wrong. I don’t have a real good idea of what they are describing the ratio to be for the gears.
1st is 1.8
2nd is 1.47
3rd 1.210
4th 1.00
5th .869
any help is much appreciated.. Thanks
 

dirt bike dave

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#2
Two things I see you are missing.

First, there is a primary drive reduction which reduces the crankshaft rpm before it reaches the tranny.  I don't have my CR250 shop manual handy, but it is probably approx. 3:1.

Secondly, you are measuring crank and wheel rpm in revs per minute, but you are trying to measure speed in miles per HOUR. 

If you stick with your current model and divide the speed you got by the primary drive ratio, then multiplied by 60, you should have an approx speed at 10,000 rpm in first gear given the wheel size, gear ration and sprockets you gave.

FWIW, I would guess your CR250 makes peak power at more like 9000 rpm, and most have 13 teeth front sprockets. 
 
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#3
okay so the final reduction willgive me the correct miles per min. then timesing that by 60 gives me mph.

thanks a bunch.
 

James

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#4
Formula is:

RPM/(Primary*Gear Ratio*Rear Sprocket/Front Sprocket)*3.14*Wheel diameter incl tire*60/12/5280

For my CR in 5th gear at 9000 RPM with 13/50 sprockets:

9000/(3.85*.89*50/13)*3.14*28*60/12/5280 = 56.9 MPH
 

dirt bike dave

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#5
Thanks for the forumla, James.

Just checked my shop manual and the primary drive reduction for the '97-'99 CR250 is in fact 3.0  (the actual primary gears are 63/21).  And as James showed in his example, your estimate of 21" rear wheel diameter is too low for a dirt bike tire.  My bike has an 18" rear rim and the tire is approx. 27" in diameter.
 
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