Targeting and spacing of telescopic heliostats

Summarizing the results of a previous post: in an optimized heliostat field, the farther out heliostats (i.e., beyond 0.707 r_o) should be spaced extra distance apart to accommodate lower aiming angles and the correspondingly increased area of their more elongated ellipses; nearer in, the heliostats should be placed as close as mechanically possible because higher beaming angles will produce less elongated ellipses having less area. (Note that all of the ellipses have the same minor axis dimension—the width of the secondary.)

In the design proposed in that earlier post, the elongation at the last row is 1.50x when the projection is taken for the lowest rays (1.19x when the projection is taken for the central rays.) Even if the heliostat spacing is kept constant, secondary blocking is not too severe. Here are histogram results for 12,000 heliostats arrayed on a phyllotaxis spiral, Baumgardner factor = 0.86, without any extra heliostat spacing.

SECONDARY BLOCKING WITH LOW AIMING

Elongation factor              View fill factor            Blocking factor
1.5                                     85.8%                         10.2%
1.25                                   76.6%                           3.9%
1.0                                     63.9%                           0.8%
0.75                                   48.7%                           0.1%

It seems extra spacing of the outer heliostats is a matter for a more fine-grained optimization to consider. A reasonable baseline design can use target point aiming with constant heliostat spacing.