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Help needed for Vehicle Systems problem

  1. Oct 11, 2016 #1

    eqm

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    1. The problem statement, all variables and given/known data

    Determine the maximum velocity attainable by a vehicle with the following conditions:
    • RWD
    • 6% grade
    • Weight = 20 kN
    • CG is 1.25 m behind front axle and 0.5 m above ground level.
    • Wheel base is 2.8 m.
    • Effective rolling radius of wheel = 30 cm
    • Coefficient of aerodynamic drag = 0.45 with frontal area 2.3m2
    • ρ = 1.25 kg/m3
    • Engine develops peak torque at 45 kW and 4000 rpm
    • The rotating inertia of the gearbox is and engine is 0.454 kgm2
    • The rotating inertia of each wheel with driveline is 1.76 kgm2
    • coefficient of friction between road and tire μ = 0.8

    2. Relevant equations

    Wr = (W l1cosθ + Rah + W h sinθ)/L

    Max Tractive Effort = μ Wr

    Ra = 1/2 ρ V2 A CD

    3. The attempt at a solution

    To solve this problem, I was going to first determine if the wheel torque is limited by the vehicle motor or by road adhesion, then find the maximum velocity using the limiting torque. I can get motor torque but am stuck at this point as I am not given a gear ratio to be able to convert motor torque to wheel torque.

    TM = 30 P nrpm / π = 107.43 N/m

    I know how to solve for everything else, its really just the the conversion to wheel torque that I'm stuck at (unless I'm approaching this problem entirely wrong).

     
  2. jcsd
  3. Oct 14, 2016 #2

    jack action

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    Science Advisor
    Gold Member

    Instead of converting engine power to engine torque, convert all resistances ##R## to power by multiplying them by the car velocity. So instead of:

    ##F_{wheels} - \sum{R} = ma##

    Since wheel power is equal to engine power ##P_{eng}##, you can use:

    ##P_{eng} - \left(\sum{R}\right)v = mav##
     
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