Approximate dimensions of the beam-down optics

Dimensions of the beam-down optics for a field of 6x telescopic heliostats. The radius of the heliostat field is taken as 1.

Based on the heliostat targeting described in an earlier post, here is a rough approximation of the dimensions of the beam-down optics, the optics in the center of the heliostat field that redirect concentrated sunlight toward the furnace opening or oculus. Taking the radius of the heliostat field to be 1, then, as found in the earlier post, the height of the optics is 0.071. Assuming the beam-down optics, when viewed from the furnace opening (oculus,) fill all but a 30°-zenith distance of the sky, and approximating the beam-down optics as a cylinder, the cylinder diameter is 0.082. If sunlight filled the entire sky at the oculus, geometric concentration would be 40,000x. The 30°-zenith distance hole in the sky reduces this to 30,000x, giving an oculus radius of 1/√30,000 = 0.0058, or a diameter of 0.012. The heliostat field radius is 173x the oculus radius.

The cylinder diameter is about 6.8x the oculus diameter, and the cylinder height is about 5.9x the occults diameter. The cylinder has an area of pi * 0.082 * 0.071, while the heliostat field has an area of pi, giving a geometric concentration on the beam-down optics of 172.

In summary, geometric concentration factors are approximately:

telescopic heliostat primary: 1x

telescopic heliostat secondary: 36x

beam-down optics: 172x

oculus: 30,000x

From the earlier post, the aiming target is 0.84 behind the center of the field, and at a height of 0.084.