rpm math question

J

Jim in S.C.

Member
OK mathematicians, Can anyone tell me how many rpms a engine would be turning if you have a manual three speed transmission (no over drive)and you have a 4.44 differential and tires that are twenty eight inches in diameter and you are traveling forty miles per hour. Once again whats my rpms?
Wow, I have a headache trying to figure this out, HELP!
 
I added a small tach below my dash and use a gps to check my speedometer accuracy and get true speed.
 
There are three kinds of people in the world: those who are good with numbers and those who are not.
 
It's just steps, not hard if you pay attention:

(tire dia. in inches X 3.1416)/ 12" per foot = 28 X 3.1416/12 = 7.33' traveled per revolution

5280' per mile/feet traveled per revolution = 5280/7.33 = 720 revolutions per mile

revs of the tire per mile X gear ratio = 720 x 7.33 = 3197 engine revs per mile so at 60mph you would be wrapped out.

correct for 40mph which is less than a mile per minute by multiplying engine revs per mile X actual mph/60 = 3197 x 40/60 = 2132 engine rpms at 40 mph.

With your tires and gears you can apply this correction to any speed by putting your "actual mph" in the equation above.
 
A minor correction if you want is to use the rolling circumference of the tire. Because the weight of the car flattens the tire at the road the car travels slightly less distance than the tire diameter would indicate. Lower air pressure or more weight equals less distance per revolution. Mark the tire and the road and measure one revolution.
 
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