The Pacejka "Magic Formula" Tire Models
Pacejka has developed a series of tire design models over the last 20 years. They were named the 'magic formula' because there is no particular physical basis for the structure of the equations chosen, but they fit a wide variety of tire constructions and operating conditions. Each tire is characterized by 10-20 coefficients for each important force that it can produce at the contact patch, typically lateral and longitudinal force, and self-aligning torque, as a best fit between experimental data and the model. These coefficients are then used to generate equations showing how much force is generated for a given vertical load on the tire, camber angle and slip angle.
The Pacejka tire models are widely used in professional vehicle dynamics simulations, and racing car games, as they are reasonably accurate, easy to program, and solve quickly. A problem with Pacejka's model is that when implemented into computer code, it doesn't work for low speeds (from around the pit-entry speed), because a velocity term in the denominator makes the formula diverge. An alternative to Pacejka tire models are brush tire models, which can be analytically derived, although empirical curve fitting is still required for good correlation, and they tend to be less accurate than the MF models.
The general form of the magic formula is: where b, c, d and e represent fitting constants and R is a force or moment resulting from a slip parameter k.
Read more about this topic: Hans B. Pacejka
Famous quotes containing the words magic, formula, tire and/or models:
“The middle years of parenthood are characterized by ambiguity. Our kids are no longer helpless, but neither are they independent. We are still active parents but we have more time now to concentrate on our personal needs. Our children’s world has expanded. It is not enclosed within a kind of magic dotted line drawn by us. Although we are still the most important adults in their lives, we are no longer the only significant adults.”
—Ruth Davidson Bell. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)
“I cannot give you the formula for success, but I can give you the formula for failure—which is: Try to please everybody.”
—Herbert B. Swope (1882–1958)
“Thou wilt be like a lover presently
And tire the hearer with a book of words.”
—William Shakespeare (1564–1616)
“The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
—Samuel Butler (1835–1902)