Calculation of the inclination of the single mirrors.

In order to calculate the inclination of the single mirrors we make reference to a panel of more reduced dimensions, as an example of 1 m x 1 m:

The single mirrors can be identified by means of their position of line and column; given the simmetria it is respect  x axis that respect y axis, we will consider only the mirrors of a generic quadrant; therefore on 32 mirrors only 8 types of different inclinations will be had, that is will be necessary only 8 groups of 4 supports among equal  for the 32 mirrors, also rotated in polar way.

This facilitates the realization of such supports.

 "raggio incidente" is the incident ray;

 "raggio riflesso" is the reflected ray; fila1, fila 2 fila3 are the corresponding mirrors' rows.

fixed:

 l = length of the side of square mirror (in the example  l = 15 cm)

 b = edge or space between two adjacent mirrors (in the example b = 1 cm)

 Zr = quote of the point of intersection of the normal to the mirror passing for its medium point with vertical

  axis  Z normal to the panel passing for the center Or

it results:  Zf = Zr/2

that is the distance of the focalization plan from the panel is the half of the distance from the point R of convergence of all the normals to the medium point of all the single mirrors.

 The abscissa Xmi of the medium point of a mirror place on the i-esima row is (in absolute value, since it is worth the simmetria is respect all.asse X that respect all.asse Y):

 Xmi = (i - 1) * (l + b) + l/2

 Adopting small approximations and knowing  that  α = β  turn out:

 tg α  = (Z1 -  Z0) / l ;     tg  β  = Xmi / Zr

Equalizing  the two expressions the height  Z1 of the chine  n° 1 turn out:

 Z1 = Z0 + (i - 1) * [ l * (l + b)/(2 * Zf) ] + l² / (4 * Zf)

Calling with n° 2 the diametrically opposite chine to n° 1, it will have to be raised regarding chine n° 0 in proportion to the position of the mirror on the column j, that is to the absolute value of the ordinate of the medium point of the mirror Ymj

Ymj = (j - 1) * (l + b) + l/2

for which the Z2 height of chine n° 2 it turns out:

Z2 = Z0 + (j - 1) * [ l * (l + b)/(2 * Zf) ] + l² / (4 * Zf)

Finally chine n° 3 of the mirror, diametrically opposite to chine n° 0, will be found at the more elevated height and will be expressed from the sum:

Z3 = (Z1- Z0) + (Z2 - Z0) + Z0

After the opportune passages turns out:

Z3 = Z0 + (i + j - 2) * (2 * l² + l * b) / (2 * Zf)

 return to the constructive characteristics