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Simple Calculations for Information on a Car

  1. Jul 13, 2011 #1
    I just bought a new car, nothing incredibly special. And being a nerd, I love creating theoretical calculations based on given data. So, I've been trying to predict the effects on my car under certain scenarios.

    I am doing my best to figure out the effects based of equations alone, and not taking my car in for a dyno test. Sadly, I am having difficulty with some equations

    I really hope someone out there can help me.

    These are the things I would like to determine:
    1) If my car is traveling on a flat road at a certain speed, what is the force of the car?

    2) If my car is traveling on a flat road at a certain speed, what is the torque that is being generated by the axle shaft?

    3) If my car is traveling on an uphill road at a specific angle at a certain speed, what is the force of the car?

    4) If my car is traveling on an uphill road at a specific angle at a certain speed, what is the torque that is being generated by the axle shaft?

    5) How much torque is being generated by the transmission at a certain engine RPM value?

    So far, this is what I have come up with, assuming the engine speed is 3000 RPM and I am only in 1st gear:

    Vehicle Speed (MPH) =
    (Engine Speed (RPM) x Tire Radius (in)) / (168 x Axle Ratio x Trans Ratio)
    Vehicle Speed (MPH) = 21 MPH

    Transmission Speed into Axle (RPM) = Engine Speed (RPM) / Trans Ratio
    Transmission Speed into Axle (RPM) = 669 RPM

    Wheel Speed (RPM) = (Vehicle Speed (MPH) x 5280 x 12) / (60 x PI x Wheel Diameter (in))
    Wheel Speed (RPM) = 242 RPM

    Axle Shaft Torque to Wheels (lb-ft) =
    Trans Torque into Axle (lb-ft) x Axle Ratio
    Axle Shaft Torque to Wheels (lb-ft) = ?????????????????????

    Trans Torque into Axle (lb-ft) = Engine Torque into Trans (lb-ft) x Trans Ratio
    Trans Torque into Axle (lb-ft) = ?????????????????????
    (I know the Max Torque at a given RPM value, but I want to find the torque at any RPM value)

    Torque of Axle Shaft (lb-ft) = radias of shaft (ft) x Force (lb)
    Torque of Axle Shaft (lb-ft) = 0.125 (ft) x ????????????????

    Torque of Wheel (lb-ft) = radias of wheel (ft) x Force (lb)
    Torque of Wheel (lb-ft) = 1.209 (ft) x ????????????????

    From a free body diagram, I have determined the summation of forces in the X and Y direction:
    FY = N - mgcos([itex]\vartheta[/itex]) = 0
    Fx = F(car) - F(friction) - mgsign([itex]\vartheta[/itex]) = ma

    N = mgcos([itex]\vartheta[/itex])
    F(friction) = [itex]\mu[/itex]N
    F(car) = ?????????????
    m = weight of car

    These are a few calculations I have determined and a few I am having a problem determining theoretically. I would like to find out these values for any engine RPM value and any given speed.

    Here are some specs of my car:

    Max Torque: 250 lb-ft @ 4500 RPM
    Max Horsepower: 265 HP @ 6250 RPM
    Weight: 4078 lb
    Axle Ratio: 2.77
    Trans Ratio:
    1st: 4.484
    2nd: 2.872
    3rd: 1.842
    4th: 1.414
    5th: 1.000
    6th: 0.742
    Rev: 2.882
    Wheel Diameter: 29.02 in
    Vehicle Performace: 0-60 mph in 7.4 seconds

    I'd really appreciate any help anyone can offer.


  2. jcsd
  3. Jul 13, 2011 #2


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    Staff: Mentor

    The question isn't worded correctly so doesn't have any meaning as written. Do you mean the force between the car and the ground? ....which is also equal to the force of wind resistance? Not easy to calculate from scratch. You at least need to measure your fuel consumption rate.
    Same as above.
    Same as above, but at least the potential energy part is equal. The power due to the "rise" of the hill is mgh/t. Power is fd/t. You should be able to take it from there, using geometry.
    Same as above.
    Torque does not depend on RPM alone.
  4. Jul 13, 2011 #3
    Maybe I can ask another question then:
    How would you calculate the force between the tire and the ground? I know T = r x F, so if I know the radius of the tire, how do I calculate the torque and/or force between the tires and the ground?

    Could I then use the torque generated by the tire and determine the torque of the axle shaft?
  5. Jul 14, 2011 #4


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    Science Advisor
    Homework Helper

    You can measure the wind resistance, if you can find a level road with a lack of other traffic, and calm weather so any "real" wind doesn't mess up the experiment.

    Put the car out of gear and measure the rate of deceleration (which will depend on the speed of course). All you need is the speedometer and a watch. The handbook will give the mass of the car, so you can calculate the force = mass x acceleration.
  6. Jul 14, 2011 #5

    jack action

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    Science Advisor
    Gold Member

    I think http://www.hpwizard.com/car-performance.html" [Broken] might answer a lot of your questions. Look for the theory at the bottom of the page.
    Last edited by a moderator: May 5, 2017
  7. Jul 15, 2011 #6


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    Staff: Mentor

    By knowing the wind resistance or the output of the engine.
    Absolutely. But finding the torque at the tire isn't any easier! You still have the same problem!
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