For this study, I was asked to design a skyscraper who accommodates a system of panelization in which each panel is to be normal to the sun. One could think of these as either solar shades or PV panels. This condition allows for a level of sustainability about tall, topological projects, while still allowing the architect to control form while keeping the surfaces developable.
A number of steps went into solving the problem:
- Planar surfaces where created from the NURBS surface using LIFT Architects Grasshopper Primer.
- I then divided each panel into a 2x2 grid using U & V values, which yielded 9 points. I then extracted the corner points (1, 3, 7, and 9) and the middle points (5) into two distinct lists, or arrays.
- To create surfaces normal to the sun, I used trigonometry based on the vectors between the sun and the center/corner points of the original diagrid pieces. Because the magnitude (length) of the pre-existing vectors are known (both to the corners and to the center) as well as the angle between those vectors, a cosine function can be used to determine planar points along the corner vectors. Basically, as long as all end points of all lines draw a perpendicular vector to the existing central point vector, the surface, by definition, will be planar (see diagram).
GIVEN
SOLUTION
- Once I had the four new corner points, I used a ‘surface from four points’ component and baked the geometry into Rhino.
Because of the parametrics of grasshopper, one can view all possibilities of each panel, the number of panels, change the solar path relative to the building, etc.
To find the solar data I used an excellent excel spreadsheet put out by Greg Pelletier through the Washington State Department of Ecology (titled solrad.xls v1.2). It can be found on the web here.
Images
(panels fixed in July position except in the video)
Interior Perspectives (January vs. July)
