Grand Prix Racing - The Science of Fast Pinewood Cars

Measure Your Car's Crosssection

Your car's frontal crosssection is used to model the aerodynamic drag of your car. This simple method is possible because the air flow around Grand Prix cars is smooth and not turbulent. Frontal crosssection is more like a shadow than a cross-cut. It is the area of your car you see when looking directly at its nose.

This area usually includes two wheel rectangles, the widest vertical section of your car and the forward "shadows" of any assessories or other parts of the car. Since Grand Prix cars come in every imaginable shape I suggest drawing the front view of your car on graph paper and counting squares. As an alternative, a few other measurements work for most cars. To manage your numbers, print this page out, copy it to a text editor or write the results on your drawing.

Draw and count squares

The easiest and most acurate way to find the area of your car's crosssection is to start with a good drawing. Of course the measurement will only be as good as the drawing and size of the squares on the graph paper. The smaller the squares, the more accurate the measure. Here's how to do it.

  1. Get a sheet of graph paper with at least quarter inch squares marked on it. The smaller the squares are the better.
  2. Measure the size of your squares if you don't already know it, call it S and write its value here: _________ inches.
  3. From the front, wheels mostly look like rectangles. Draw the rectangles made by the tread "shadows" first to act as a reference drawing. Tires may bulge out a bit beyond the tread and probably have a bit of the inside part of the hub and axle showing. Draw these parts of the wheels in proportion to the tread rectangles.
  4. The bottom of most Grand Prix cars is flat. Draw the bottom line of your car between the wheels taking care to notice how far below the axles it is.
  5. Draw a limit line for the top of your car. You may want to measure the highest point on your car instead just "eyeing" it.
  6. Once the top limit line is set, it should be fairly easy to sketch in the contours of your car body as they appear from the front. If your car is symmetrical, all you have to do is draw one side. Just copy it to the other side by counting squares to points that "stick out". You can also copy it by tracing it to another paper and cutting out the copy to use as a template.
  7. Erase any lines that are inside the drawing so you only have the shadow left.
  8. Count all the squares inside the shadow that are at least half way in the shadow. Call your count "C". Write the value of C here: ________ squares. This can get tricky. For example, if a line of squares crosses the wheel outline so they are almost half way in, you should count every other one to get a better count. If a line of squares is a quarter of the way in, every fourth square should be counted. The idea is to "make" as many full squares from parts of squares inside the shadow as you can. Us older people usually estimate the percent of area of a square in the shadow and add them up as we consider more squares (this is the idea behind "integration").
  9. Once you have a total square count, square the size of the squares, S, to get S2. Write the value of S2 here: ________ in2.
  10. Multiply S2 by C to get the area of the shadow, A. Write the value of CS2 = A here: _______ in2.

An alternative estimate

If you don't have time for the above, make the following measurements.

SYMBOL VALUE UNITS How to measure
Ww (Wheel width) ________ inches Measure the widest part of a wheel
Wh (Wheel height) ________ inches Measure the tallest part of a wheel
Bw (Body width) ________ inches Measure the separation between the front wheels
Bh (Body height) ________ inches Measure the tallest part of your car body from its base
Fo (form factor) ________ scalar If your car body looks rectangular from the front, use the value 1.
If it is a rounded rectangle, use 0.9.
If it's round, use 0.8.
If it's triangular, use 0.5.
If it's half of one or the other, use a value in between.
A ________ in2 Compute by evaluating A = 2WwWh + FoBwBh
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Grand Prix Racing - The Science of Fast Pinewood Cars
Copyright © 1997, 2004 by Michael Lastufka, All rights reserved worldwide.