A baseline telescopic heliostat array and its fill and blocking factors

In this baseline design, heliostats at 0.707 r_o operate at their designed beaming angle. The distance (shown out of scale in the diagram) between the field center and the target point is 0.84 r_o.

Previous posts suggested aiming heliostats at a point 0.84 r_o behind the center of the array, and arranging the heliostats with constant spacing along a phyllotaxis spiral, and operating the heliostats at 0.707 r_o at their design beaming angle. We will fix these values as the baseline design.

For a heliostat at a distance r from the center, the distance, d, to the target point is d = r + 0.84 r_o. For the heliostats operating at the designed beaming angle d = (0.707 + 0.84) * r_o = 1.55 r_o. Since all angles are small, the extra elongation of the ellipse for a heliostat at distance r from the center is

(r + 0.84 r_o)/(1.55 r_o) = 0.65 * (r/r_o) + 0.54

Using a processing sketch to apply this elongation factor to each ellipse yields this image:

Secondary ellipses for the baseline telescopic heliostat array. The variable elongation of the ellipses corresponds to a target point at 0.84 ro behind the field center.

Histogram analysis shows:

BASELINE TELESCOPIC HELIOSTAT FIELD PROPERTIES

Land fill factor = 70%
View fill factor = 61%
Secondary blocking factor = 1.4%