Longitudinal Pacejka Model

[Boston]

The tire data provided by the TTC includes Pacejka96 model coefficients. I am trying to model longitudional forces. There are 12 coefficients listed for the longitudional model. I'm having a problem reading the equations themselves. Several parts of the equation call for dfz (derivative with respect to z?). I don't understand this part - other sources seem to replace this with normal force. When I do this, thrust becomes constant for all ranges of wheel slip. I don't understand why calculus would be involved!

[Boston]

I guess what im asking is: how did others interperate the equations given with the TTC tire data?

[Kerry]

I think dfz is "normalized load on the tire" or some such thing... Try to get ahold of Pacejka's "Tire and Vehicle Dynamics" or one of his SAE papers. He breaks it down an explains all the coefficients, inputs, etc.

We don't have a car simulation yet, so we haven't used either of the tire models that is provided with the data, but we do plot the raw data to look at slip angles, camber angles, and justify our tire choice.

[Jersey Tom]

Holy crap. They give you the Pacejka coefficients to go along with the data?? Friggin sweet I'm buyin it.

[Marc Jaxa-Rozen]

In this Pacejka version it's the normalized load increment, the coefficients provided include Fz0 (nominal vertical load) and dfz = (Fz-Fz0)/Fz0.

Marc Jaxa-Rozen
École Polytechnique de Montréal
http://www.fsae.polymtl.ca

[Gareth]

I noticed that this equation was omitted from Stackpole's overview of the Pacejka model. Without too much hassle I found the equations also listed in the ADAMS/Tire documentation at:

http://www.me.utexas.edu/~lotario/VSDC/adams/tire/tire_ug/tire_ug.pdf (http://www.me.utexas.edu/%7Elotario/VSDC/adams/tire/tire_ug/tire_ug.pdf)

[Boston]

Originally posted by Marc Jaxa-Rozen:
In this Pacejka version it's the normalized load increment, the coefficients provided include Fz0 (nominal vertical load) and dfz = (Fz-Fz0)/Fz0.

Marc Jaxa-Rozen
École Polytechnique de Montréal
http://www.fsae.polymtl.ca

I think this is what I need. Thanks!

[IsheeM]

Regarding the equations used to find the longitudinal force:

Is dfz^2 (in Eqn 1.6) the second derivative of fz or is it dfz squared? Either way it doesnt change the max force much but does slightly change the shape of the F vs SR plot.