Longest GH definition to produce a single line?

This is my first post, so greetings GH folk. What follows is pretty involved, so I’m not sure the chances that anyone will be interested enough to really get into it, but it presents a GH puzzle that I recommend if anyone is looking for a challenge (at least I found it challenging...). The attached definition is the solution I came up with; I’m sure – I’m hoping – there are others. It defines the profile geometry of a solar collector as expressed in the attached patent. Actually, the attachment only has the key pages, but there is enough info there that you can find the rest if interested. The reason the geometry described in the patent makes a great GH puzzle is that the foundation that the rest of the geometry depends on is variable. The patent doesn’t define a specific geometry so much as a set of (clever) geometric relationships.

I’ve attached three files: a pdf with the patent pages, a GH definition, and a rhino file (which only contains a single point and isn’t essential until the “analysis” portion of the definition (more on that later).

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Replies to This Discussion

Permalink Reply by Derek Kaplan on July 10, 2011 at 11:44pm

In brief summary, each reflector side has two parts: A) the lowest portion of the trough which is a section of a circle involute (en.wikipedia.org/wiki/Involute); and B) the upper portion which is defined by a “shadow line” of variable angle. This angle is a choice made by the maker, which determines the geometry of section B of the reflector. The curvature is defined such that using this angle as the angle of incidence, the angle of reflection is always a tangent of the circular collector. This defines the limiting angle of incoming light, so that any light arriving by a steeper angle either hits the body of the collector or is captured by the reflector and returned to the collector by some number of reflections, depending on the angle. The transition point between the two, depends on the angle of the shadow line.

I’d rather not try to type out a walk-through of the definition, things are mostly labeled by their function – but if anybody does go far enough into this to have a question, I’d love to chat about it. Re: the single point in the rhino file. The location of this point defines the angle of incoming light that the “analysis” portion of the definition models. If this point is located on the first (lowest) shadow line that is tangent to the collector, then the incoming light angle is set to the angle of the shadow line and should return a tangent to the collector as the angle of reflection. If the point is set above this line, then other angles of incoming light can be tested.

Permalink Reply by Derek Kaplan on July 11, 2011 at 11:11am

adding screen shot: