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Thread: RPM vs MPH (calculation question)

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    Junior Member mmarlatt's Avatar
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    Question RPM vs MPH (calculation question)

    I was trying to calculate my RPMs at 60 miles per hour and I can't do it. So I did a google search and found an equation: MPH=RPMx(Tire diameter)/((Gear Ratio)*336)

    Where does the 336 come from?

    My gear ratio should be 4.08*0.705 [rear ratio*overdrive ratio].

    Can anyone help?
    2003 Stratosphere Mica SR5 Access Cab
    Shocks: Bilstein 5100 coilovers and 5100s in the rear.
    Wheels: Toyo Open Country A/T 275/70/16s on MB Blitz rims

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    Lifetime Member HotRod8's Avatar
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    I think the formula is sort of correct the brackets need to be in the right places. Its MPH = RPM x (Tire Dia/(Gear Ratio x 336)).

    The 336 is the constant which takes into account pi (3.14159), 60 minutes in an hour and 63 360 inches in a mile.

    You see the tire diameter x pi x rpm(of the wheel, not the driveshaft) will give the inches per minute that you will travel to get MPH you need to multiply by 60 minutes/hour and divide by 63,360 inches/mile.

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    Junior Member mmarlatt's Avatar
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    Quote Originally Posted by HotRod8
    I think the formula is sort of correct the brackets need to be in the right places. Its MPH = RPM x (Tire Dia/(Gear Ratio x 336)).
    Both equations would give the same answer, you just reduced the number of parentheses. .

    Quote Originally Posted by HotRod8
    The 336 is the constant which takes into account pi (3.14159), 60 minutes in an hour and 63 360 inches in a mile.

    You see the tire diameter x pi x rpm(of the wheel, not the driveshaft) will give the inches per minute that you will travel to get MPH you need to multiply by 60 minutes/hour and divide by 63,360 inches/mile.
    Thanks for the input on the constant, it is now clear. I think I still have to better define my gear ratio since when I use 4.08*0.705, which is my fourth gear and 4.08 rear end ratio, and my 30.6" tires (267/70/16) the equation yields less than 2000 RPMs. I cruise at a higher RPM than 2000 at 60 mph.
    2003 Stratosphere Mica SR5 Access Cab
    Shocks: Bilstein 5100 coilovers and 5100s in the rear.
    Wheels: Toyo Open Country A/T 275/70/16s on MB Blitz rims

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    Junior Member MrBeanley's Avatar
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    Quote Originally Posted by mmarlatt
    Both equations would give the same answer, you just reduced the number of parentheses. .



    Thanks for the input on the constant, it is now clear. I think I still have to better define my gear ratio since when I use 4.08*0.705, which is my fourth gear and 4.08 rear end ratio, and my 30.6" tires (267/70/16) the equation yields less than 2000 RPMs. I cruise at a higher RPM than 2000 at 60 mph.

    When I "do the math", I get:
    RPM = ( Speed * gear ratio * 336 ) / Tire Diameter
    RPM = ( 70 * 4.08*0.705 * 336 ) / 30.84
    RPM = ( 67652.928 ) / 30.84
    RPM = 2193.6747081712062256809338521401

    ...which seems about right.

    BTW, I took the original equation and just solved it for RPM instead of MPH to come up with this bit. So:

    MPH = RPM x (Tire Dia/(Gear Ratio x 336))becomes

    MPH * Gear Ratio * 336 = RPM * Tire Dia
    which then becomes...

    RPM = ( MPH * Gear Ratio * 336 ) / Tire Dia

    PS: Notice that I used 30.84" for the tire diameter instead of 30.6". I figured that a 265/70r16 "should have" 30.84" of diameter. Remember that the p-metric tire sizing is width of tread (in mm)/ % of that number in height of sidewall. So, your 265/70r16's have a 265 mm tread width, 185.5 mm sidewall height and, of course, the 16" rim.

    Gosh, I love math!
    MrBeanley
    Glenville, New York
    2004 Tundra Double Cab 4x4


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    Junior Member mmarlatt's Avatar
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    Quote Originally Posted by MrBeanley
    When I "do the math", I get:
    RPM = ( Speed * gear ratio * 336 ) / Tire Diameter
    RPM = ( 70 * 4.08*0.705 * 336 ) / 30.84
    RPM = ( 67652.928 ) / 30.84
    RPM = 2193.6747081712062256809338521401

    ...which seems about right.

    BTW, I took the original equation and just solved it for RPM instead of MPH to come up with this bit. So:

    MPH = RPM x (Tire Dia/(Gear Ratio x 336))becomes

    MPH * Gear Ratio * 336 = RPM * Tire Dia
    which then becomes...

    RPM = ( MPH * Gear Ratio * 336 ) / Tire Dia

    PS: Notice that I used 30.84" for the tire diameter instead of 30.6". I figured that a 265/70r16 "should have" 30.84" of diameter. Remember that the p-metric tire sizing is width of tread (in mm)/ % of that number in height of sidewall. So, your 265/70r16's have a 265 mm tread width, 185.5 mm sidewall height and, of course, the 16" rim.

    Gosh, I love math!

    Ok, driving home from work I was cruising at 60 MPH and I was at 2050 RPMs.

    Ok, where did you get your tire size? I have bridgestone HTs and www.bridgestone.com list them with a 30.4" diameter. 265*.70 = 185.5 mm sidewall, but 185.5*2= 371mm.

    371mm / (25.4mm / cm) + 16" rims = 30.606"... anyway using a smaller diameter gives me a higher RPM, which is where I need to be.

    You did your solving for RPM correct:

    Quote Originally Posted by MrBeanley
    MPH = RPM x (Tire Dia/(Gear Ratio x 336))becomes
    But you used 70 MPH, not 60 MPH. Use 60 mph and you will find that yor answer is less than 2000 RPM at 60 MPH.

    I must be getting the wrong answer because of the final gear ratio, something to do with overdrive... If you have any thoughts let me know. I appreciate the help.
    2003 Stratosphere Mica SR5 Access Cab
    Shocks: Bilstein 5100 coilovers and 5100s in the rear.
    Wheels: Toyo Open Country A/T 275/70/16s on MB Blitz rims

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    Junior Member MrBeanley's Avatar
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    Sorry 'bout the 70mph vs 60 mph thing. I missed that one.

    I think the difference in our tire sizes is that I used 25 mm per inch as my conversion factor - not the 25.4 that you used. When I do it that way, I get the same TD you had.

    Just for quacks, try holding a tape measure up to the tire and measuring the diameter. I'm curious how close to the 30.6" it really measures. I had a set of 31x10.5's on my old '94 that measured only 29" in diameter, when fully aired. I never did figure that one out!!

    Good luck...
    MrBeanley
    Glenville, New York
    2004 Tundra Double Cab 4x4


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