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Derivation of Tail Swing large vehicle

  1. Apr 27, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to derive a formula for figuring out the distance the rear of a large truck swings outward when turning a corner. Picture one of thos large moving trucks that you can rent, the back end over hangs the tires by a lot. Now picture it turning a corner and the rear end crossing the center line. That is what I am trying to figure out.



    2. Relevant equations

    Hypotenuse = sqr (opposite ² + adjacent ²)
    Sin = opposite / hypotenuse
    Opposite = (.5144) hypotenuse
    deg = 180 / (( 2 ) ( pi ) ( rad ))
    R [ABC] = A’B’C’
    Ts = ((sqr ( A ² + C ² )) – ( E – D )) ( 0.15)




    3. The attempt at a solution

    Where:
    A = adjacent = 500 cm – distance to rear of vehicle
    B = hypotenuse = 583.0951895
    C = opposite = 300 cm – track width
    E = lane width = 600 cm
    D = distance from curb = 100 cm
    a = 55.7 degrees

    Calculate Hypotenuse

    Hypotenuse = sqr (opposite ² + adjacent ²)
    Hypotenuse = 583.0951859

    Verify Hypotenuse

    Sin = opposite / hypotenuse
    .5144 = 300 / 583.0951895

    Opposite = (.5144) hypotenuse
    300.00 = (.5144) (583.0951895)


    deg = 180 / (( 2 ) ( pi ) ( rad ))
    Angle of hypotenuse = 55.7 deg.


    Calculate Tail Swing Over Line

    R [ABC] = A’B’C’

    Ts = ((sqr ( A ² + C ² )) – ( E – D )) ( 0.15)
    12.46 = (sqr (300² + 500²)) – ( 600 – 100)
    Ts = 12.46 cm

    If Ts is negative then Tail Swing will not enter other lane.
     
    Last edited: Apr 27, 2012
  2. jcsd
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