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    Discussion in 'Calculations' started by Koko, Feb 2, 2012.

    1. Koko

      Koko New Member

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      Hi,


      I have these equations which represent the car steering angles and velocity. These equations were obtained from a car simulation model. They are used for continuous turning motion. However, I could not understand how do they operate or what model do they represent. I would like some hints if any body is familiar with them or have any other similar equations or references:


      PSI=arcsin( (v/d)*sin(Tyre Angle) );
      course=Beta+PSI;
      Gamma=Tyre Angle+course;


      B=L*cos(Beta)+v*cos(Gamma)-L*cos(course);
      C=cos(course);


      rear velocity=B/C;


      where
      L : length between tyres.
      Beta: is the slip angle( car angle)
      PSI:is the angle below of Beta
       
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    3. Virgule

      Virgule Active Member

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      Could you provide a drawing of what the angles, velocities and lenghts represent ?

      I could provide you with basic rack and pinion theory.
       
    4. Steve6br

      Steve6br Member

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      Does this help?

      These equations are about calculating the so called slip angle that occurs when a vehicle negotiates a corner. i.e they elate to the dynamics of the car on the road rather than the internal mechanism of the steering.

      Suppose the driver of the vehicle turns the steering wheel to negotiate a corner and the wheels turn by, say, 5 degrees. Variables such as the road surface friction and tyre deformation result in the vehicle actually cornering as if the tyre is only turned by a smaller angle. The difference between the actual turning angle and the resulting vehicle direction is called the slip angle. This is the equation that states that the course = Beta + PSI. The "angle below beta" seems to refer to the turn angle of the tyre.

      Beyond that I am unsure what the other variables refer to but have a book I will take a look at to see if I can recognise anything that looks similar.
       

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