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Lets do hot-rod math--tire diameter, rearend ratio, engine RPM

Discussion in 'The Hokey Ass Message Board' started by brianangus, Nov 21, 2005.

  1. Our project car is running 31" tall rear tires with a 3.55:1 rearend ratio, and a non-overdrive (1:1) ratio transmission.

    Lets do math. A 31 " diameter tire is 31 x 3.1416=97.3896" circumferance. A mile is 5,280 feet. or x 12=63360 inches. So. in order to travel one mile. the tire has to turn 63360/97.3896=650.6 times.
    At 60 miles per hour, your car is travelling 1 mile per minute.
    That means that your tire has to rotate 650.6 times in one minute to reach the speed of 60 miles an hour.
    If you are using a 3.55:1 rearend ratio, then you multiply the ratio times the number of tire rotations in one minute, so 3.55 x 650.6=2309.6---that is the speed at which your rearend input pinion and driveshaft would be turning.
    If your car does not have an overdrive transmission, then we can assume that the transmission ratio in high gear is 1:1---this is hard and true for manual transmissions, with a very small percentage of slippage for "non lock-up" transmissions like a powerglide.
    This means that at 60 miles an hour, your engine will be turning 2309.6 RPM. with 31" diameter tires and a 3.55:1 rearend ratio.
    If you were to use a 4.11:1 rearend ratio, then the engine would be turning at 4.11 x 650.6=2674 RPM.
  2. farna
    Joined: Jul 8, 2005
    Posts: 1,122


    And for those who don't want to do all the math, go to! Just put in 1 for the transfer case ratio. "Gear Ratio" does the tire size/rpm/mph calculations. he formulas used are on the same page as the calculations just in case you ant to double check things.
  3. Smokin Joe
    Joined: Mar 19, 2002
    Posts: 3,769

    Smokin Joe

    I remember in high school having a whole book of formulas for figuring that stuff, CID, HP needed to reach top end speed with tire size and weight of car, etc. We got this stuff from magazines, race teams, those little "is/was" wheels from the speed shops, etc. And we always checked it out with the math teacher who encouraged us all the way. Did all this because we thought it was fun and we could see a real world use for it. Once he sold us on this, it was easier for him to feed us square roots in out pi.

    Today I get calls from my neighbor down the street because the high school grad pizza kid couldn't read the house number correctly. So I go stand outside waving with the exact change so I don't have to wait while this future pre-med student figures how make change from a $20.
  4. CruZer
    Joined: Jan 24, 2003
    Posts: 1,895


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  5. squirrel
    Joined: Sep 23, 2004
    Posts: 37,019


    how do you measure the tires to get an accurate number? the overall diameter? the radius at the bottom of the tire when it's sitting on the car with weight on it? or something in between?

    I never get a real accurate result with the math because of this problem....
  6. How accurate do you have to be??? I would just measure the maximum tire diameter at rest. At 60 miles per hour, centrigugal force will make the tire marginally larger in diameter anyways, and the tire won't be squabbed out on the underside anyways, partially because of aerodynamic lift on the car body.
  7. squirrel
    Joined: Sep 23, 2004
    Posts: 37,019


    well, since you are running the rpm calcuation out to a couple decimal places I figured you must have got it pretty accurate. I usually get within 5% or so,but sometimes it's off enough that I have to change the speedo gear after I calculate it out with the math, because it's off too far by the mileposts.

    So usually I end up measuring the tire "short"
  8. Bluto
    Joined: Feb 15, 2005
    Posts: 4,838


    Isky sells little round gizmos that have been in my tool boxes for too many years

    No thinking just put in what data you have :eek: :eek:
  9. Here's an easy to remember formula:

    MPH = RPM x Tire Diameter divided by Axle Ratio x 336

    You could measure the radius of the tire, center to bottom and double that to get an exact figure . . . except :eek: . . . tires grow at speed so simply measuring the diameter ground to top of tire works well.

    Used to hit the RPM figure right on the money when I went through the last ET light at San Fernando dragstrip.
    I got the speed from the timing ticket.
  10. I am just rounding things off at 3 or 4 decimal places, because the numbers go on to infinity on a pocket calculator. I carry "all those formulas" around in my head. When you have designed machinery for 40 years as I have, the math just sticks in your head from repeated use. I know a lot of that stuff is available from the computer now, however in the first 20 years of my career, there weren't computers so readily available. You came across as not to bright if you had to carry a book of formulas around in your pocket to refer to on job sights. I started out with slide rules and logarithmic tables, and you had to know the relationships of sine, cosine, and tangent functions in your head. Then in the early 70's we moved up to hand held calculators. Now its all computers---but just because there is new stuff to use, it doesn't make all the old stuff dissapear out of your head.
  11. I never use tire diameter. I stretch a 1/4" X 10' tape around the tire and measure the circumference. That way I eliminate brianangus' first step, multiplying dia. by pi (3.14159), and it's a tad more accurate.
  12. Rand Man
    Joined: Aug 23, 2004
    Posts: 3,284

    Rand Man

    This graphic could be helpful.

    Attached Files:

    • 123.jpg
      File size:
      73.3 KB
  13. Here ya go

    Attached Files:

  14. Glen
    Joined: Mar 21, 2001
    Posts: 1,789


  15. Chrome Shop Mafia
    Joined: Jul 14, 2005
    Posts: 555

    Chrome Shop Mafia

    Thanks for the math tech, guys!!!

    I have one question... In terms of speed, won't you have to factor in the final weight of the car to figure out accuratley how many rpm's are required to reach a desired mile per hour??? Or am I just thinking to critically???

    God Bless...

    Take care...

  16. troy- weight has nothing to do with the gear ratios- they are all non adjustable measurements. the engine will always turn the same speed at a given mph, no matter how much the car weighs, or how much power the engine makes (discounting any slippage of course)
  17. Bluto
    Joined: Feb 15, 2005
    Posts: 4,838


    I see it's simple like'' 30 days has Sept. April,June......... and'' ........I forgot

    The Isky gizmo!!? Where did I put it???? :D :D :D

  18. The Dream Wheel is buried in the drawer with your bent degree wheel....:)

    Anyhoo . . . not to get too far off, easy way to remember the months is:

    Count em on your knuckles and between your knuckles starting at the index finger knuckle.
    When you get to July on your little finger knuckle start over.

    Months named on top of your knucks have 31 days.
    Months named in between have 30 days or less.

    From C9's list of weird and useful information....:D
  19. porknbeaner
    Joined: Sep 12, 2003
    Posts: 38,751


    Actually you're only going to ball park it anyway.

    You tire is going to grow, but the numbers never take into account parisitical loss (slippage etc) in the drive train or wind resistance that adds to the parisitical loss, etc.

    For the most part close is cool. I have a Java script and the formula that C9 put out both here. I only use them to figure somewhere in the neighborhood.

    For instance if I have a 6,000 RPM motor and I wanna try and hit 130 I figure my gear ratio and tire height for 140 at said RPM then work toward getting my ride hit the target speed.

    The you always have to take into account if your mill will actually make enough torque to pull to said RPM at speed. Its a nasty demon that we battle with.

    The downside to all this is that if or when I hit the target speed its only really cool for a few minutes then here is another rainbow to catch. :eek:

    good discussion though, there is never enough attention paid to gear ratios/tire sizes. Too many times we just grab whatever gear we happen to have or do what everyone else is doing at the time.

    I'm a firm believer in makeing your ride do what you want it to do instead of trying to make it do one of everything which is another rainbow altogether.

    For isntance my old push truck gets down the road real well, fair milage, good RPM at cruising speed, but it doesn't do worth a flip on the strip. It could but then it wouldn't make the trip on the HWY.
  20. Great tech post. I'm going to bookmark this one.
  21. ian
    Joined: Aug 6, 2005
    Posts: 743


    nice explination. too bad there isn't a "math-tech week"

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