Grand Prix Racing - | The Science of Fast Pinewood Cars |

A ramp is one type of track that some clubs use to race Grand Prix cars. But most clubs use a track with a flat run out at the end of the ramp. Some clubs have a track that is "S"-shaped. Others use tracks with "waves" in them. The easiest type of track to model is one with a ramp followed by a straight, flat part. The transition between the ramp and flat part can be handled in at least two ways. It is "ignored" here, to obtain a closed set of equations.

To make a track model that is useful for predicting car behavior, a set of model parameters is introduced. In this manual, the Official AWANA Grand Prix Track is used in all model applications, unless stated otherwise. Read the discussion on using your own track parameters.

Each different track geometry affects car behavior in some way. But there are only three categories of track shapes that are commonly used and that call for different car design strategies.

The Official AWANA Grand Prix Track can be simply modeled by a ramp followed by a long flat. The ramp is modeled by measuring and extending the ramp part of the Official AWANA Grand Prix Track. This gives us a measurement for the height, H, of the starting line of the ramp (from the surface of the flat part), the ramp angle, O, from horizontal and the length of the surface of the ramp, Lr, from the starting line to the flat.

The flat part of the ramp is what is left over to make the total length of the racing surface. Note, this is only an approximation of the shape of the Official AWANA Grand Prix Track since the real one has a gentle transition between the ramp and the flat. The point where the simplified ramp and flat come together is estimated by extending (mathematically or on graph paper) the ramp part and the flat part until they meet. The resulting measurements follow.

**Official AWANA Grand Prix Track Geometric
Parameters**

SYMBOL | MEASURE | UNITS | DESCRIPTION |

O | -21.1781 | degrees | Ramp angle, measured from the base |

H | 39.9 | inches | Ramp height at starting line |

Lr | 110.5 | inches | Length of ramp surface |

Lf | 249.5 | inches | Length of flat surface |

A model is not measurements. It also includes useful relationships among the measurements. These relationships are written as mathematical expressions. One relationship that will be very useful in developing the full race model is an expression for the height of the track at any distance from the starting line, hr(y). Others merely note the allowed values of the track variables, y and x. Note that the value of x starts at zero on the flat and is not defined on the ramp.

Model Of Official AWANA Grand Prix Track Geometry

EXPRESSION | UNITS | DESCRIPTION |

0 <= y <= Lr | inches | Range of distance from the starting line on the ramp |

hr(y) = ysinO + H | inches | Height of ramp in terms of distance along the ramp |

hf(x) = 0 | inches | Height of flat part of track |

0 <= x <= Lf | inches | Range of distance along the flat |

y = Lr + x | inches | Distance from the starting line on the flat |

These modeled relations form the basis for the models of track/car behavior found throughout this manual.

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Grand Prix Racing - | The Science of Fast Pinewood Cars |

Copyright © 1997, 2004 by Michael Lastufka, All rights reserved worldwide. |