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Car/motorcycle speed formula?

Discussion in 'Motorcycles & Boats' started by Air_Cooled_Nut, Apr 12, 2007.

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  1. Air_Cooled_Nut

    Air_Cooled_Nut Formula Junior

    Nov 25, 2004
    952
    Portland, Oregon
    Full Name:
    Toby Erkson
    #1 Air_Cooled_Nut, Apr 12, 2007
    Ok, I need a mathmatician's help here.

    I'm using Microsoft Excel so my variables -- tire circumference, R&P, and gears -- are each in their own cell and applied to a RPM table which updates automatically whenever a variable changes. I'd like to come up with a single value for motorcycles that could be dropped into the R&P variable. I have a separate area that I use for formulating the various ratios (tooth counts for front, clutch, tranny, & rear sprockets) and Primary, Final, and Overall drive ratios.

    I have found the following two formulas for figuring out speed (in MPH).
    Car (R&P = Ring & Pinion):
    Speed = (RPM x rear tire circumference) / (R&P x selected gear x 336)

    Motorcycle:
    Speed = (RPM x rear tire circumference x front sprocket) / (primary gear ratio x selected gear ratio x rear sprocket x 1056)

    I want to condense it down to one formula (if possible) and I can substitute one variable (R&P would be ideal). For example, substitute front sprocket/(primary gear x rear sprocket) for the R&P in the Car formula. Trouble is, there's those two different numbers in the denominator (336 and 1056). I was told the 1056 is a conversion number: 12 (inches per foot) * 5280 (ft per mile) / 60 (min per hour) = 1056. I don't know what the conversion unit is, though.

    Help? Suggestions? Alternate formulas/methods? TIA :)
     
  2. bretm

    bretm F1 Rookie

    Feb 1, 2001
    4,577
    Northern NJ
    Full Name:
    Bret
    #2 bretm, Apr 12, 2007
    Your basic formula is:
    [(rpm)/(overall ratio)][((rear tire diameter)(3.14))/12][60/5280]

    A simple example:
    On my single speed kart which revs to 17000rpms and has a 10 tooth front, 82 tooth rear sprocket, and 11" tall rear tire,would be:
    [(17000)/(8.2)][((11)(3.14))/12][60/5280] = 67.8mph

    On my shifter kart which revs to 14000rpms, has a 17/71 primary gear, 27/10 6th gear, 15 tooth front sprocket and 26 tooth rear sprocket, with an 11" rear tire, it would be the same formula, but you would have to calculate the overal ratio.
    (20/27)(71/17)(26/15) = 5.362
    sub this (and the rpms) into the formula above and it = 85.4mph

    You can then set it up in excel with the final ratio (primary times the gear ratio) for each of the 6 speeds; then put a column next to that for the overall ratio (ie, the final ratio times the sprockets' ratio) that can pull off a single cell, so all you have to do is change that cell when checking potential sprocket choices and the mph will change for all 6 gears.

    Keep in mind that the tire expands at speed, so you'll be going faster than calculated (unless you know how much it expands and factor that in).

    Don't get too hung up on formulas from books. Just think what you're doing. The engine spins a certain rpm, you want to see what that corresponds to on the axle, and then how much distance that factors into in relation to time.
     
  3. 208 GT4

    208 GT4 Formula 3

    Dec 27, 2003
    1,769
    Brighton (UK)
    Full Name:
    Dan
    #3 208 GT4, Apr 12, 2007
    It sounds like you are looking for a conversion from rear diff ratio in a car to front/rear sprocket ratio on a bike?

    The rear diff ratio is normally in a range of 2-4 for most cars I have seen. This would seem to suggest that you need to be getting a number > 1 so using the rear sprocket/front sprocket will do this for a bike. But I'm not sure if it's comparable?
     
  4. Air_Cooled_Nut

    Air_Cooled_Nut Formula Junior

    Nov 25, 2004
    952
    Portland, Oregon
    Full Name:
    Toby Erkson
    #4 Air_Cooled_Nut, Apr 12, 2007
    bretm, thanks, I'll chew on that.

    208GT4, love your taste in cars! I want a GT4 (with sunroof).
     

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