How to calculate the frontal area of a convex closed surface?
Example application is the frontal area of a car, which is required to calculate the aerodynamic coefficients.


The frontal area can be calculated with the following CEL:

IntegrationVariable = Normal X/abs(Normal X + 1e-8)
FrontalArea = 0.5 * areaInt_x( IntegrationVariable )@Body

This example CEL is for the frontal area in x-direction.

With areaInt_x the integral of the area components in x-direction multiplied with an integration variable Phi is obtained. To obtain the area in x-direction, the integration variable must have a value of 1. However, as the x-component of the areas has a sign, the expression areaInt_x(1)@body will result in a value of zero for a closed surface.
So use the integration variable Phi = Normal X/abs(Normal X) to obtain a +1 or -1 depending on the local area, and hence to obtain the integral of the absolute values of the area x-component. The small number is just required to avoid division by zero for area that have no x-component. The result is the double of the frontal area, so include the 0.5 to get the correct frontal area.

Note that this approach works only for convex surfaces.





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