surface medium level calculation
Application (any shape grid)
The medium level of the surface shown in the following figure has to be calculated. The grid is 20 x 20 m, formed by different planes, but with one only plane for each square of the grid. The altimetric levels, expressed in meters, are shown in the figure.
The altimetric levels of the grid station vertex show in the formula calculation only once, the levels of the perimeter twice, the levels of the internal station three times and the central levels four times. Therefore the coefficients 1, 2, 3, 4 show in the formula at the numerator and at the denominator and this is the general mathematical formula.
This formula is useful to calculate any volume of geometric figure, such as the volume of a mountain, the water volume in a lake or any other hollow. Simply it is sufficient to find the medium height of the surface and multiply it by the area of the surface itself.
(Published March/April 1978 on “Noi Geometri”)