Friday, January 3, 2014

Phi plus an integer (φ + n) heliostat arrangements


Since the center of the heliostat field will be occupied by the central optics anyway, it may be advantageous to arrange the heliostats in a higher frequency phyllotaxis spiral, i.e., φ + n dots per turn rather than φ dots per turn.

 The problem presented by a low frequency (for example, frequency = φ = 1.61803398… dots per turn) is that the genetic spiral—the spiral that connects each dot to the next in order of radial distance—becomes so tightly wrapped upon itself that it will be useless as a structural element or indexing principle. Since we don't need to pack primaries closely in the center field, we may be better off with higher frequency spiral.

Again, these packings still work if the the dots are radially oriented ellipses.


Such ellipses explore possible mutual blocking between secondaries. The video shows that secondaries of telescopic heliostats can be centered directly over primaries that arranged along a phyllotaxis spiral, and still reasonably fill the field of view from the central optics with little overlap (which would indicate one secondary blocking the beam of another.)

Processing sketch here.

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