Solar
Envelope A construction method using AutoCAD 2000 by Thanos N. Stasinopoulos 
A
solar envelope is an imaginary surface covering a site like a
roof based on the perimeter of the plot. The slope of its facets is
adjusted so to avoid shading of the surroundings during a certain
period. 
Step 1: Data  

The
example illustrated here refers to a plot with a concave perimeter on
sloping ground, where the maximum permitted building height is H. Having established the two end moments of
insolation, each direction of solar rays is set according to solar azimuth
& altitude for the given latitude, day of the year and hour. That data
can be obtained through the Distant Light / Sun
Angle Calculator section of AutoCAD or from a sun path diagram.
[The dotted lines show the horizontal
projections of the plot and the solar rays at the selected moments.] 
Step
2: Height solid 


A
vertical Line of length H is
drawn from the topmost vertex of the perimeter. That line is used as Path
in order to Extrude the perimeter
into a solid volume. 
Step 3: Cropping  

The
top of the solid is not parallel to the ground but horizontal. The extra
part is cut off by Copying the solid
vertically at distance H, then Subtracting
the copy from the original. The final solid defines the maximum height H
at any point of the plot. 
Step 4: Solar direction  

Two
additional Lines
are drawn from the same topmost vertex as in Step 2, parallel to the set
solar directions. The top ends of
these lines should be substantially higher than the solid volume. 
Step 5: Solar volumes  

The
two lines from Step 4 are used as Paths
in order to Extrude the perimeter
into two new solids. All points within these two solid volumes
cast shadows inside the plot during the two end moments. 
Step 6: Solar envelope  

The
solar envelope is the Intersection
of the three solids constructed in Steps 3 & 5. The shadows of all points within the solar
envelope move inside the plot during the selected time period. This is due
to the fact that, during that time, the sun moves at higher altitude than
on the end moments, therefore shadows approach the southern side.
Furthermore, the sun is closer to NorthSouth axis, bringing shadows
towards the middle of the plot. 

Remarks The
same method is applied if the solar envelope base is set higher
from the ground in order to increase building density. If the vertices of the perimeter are not
coplanar, then the plot is divided into coplanar sections. Steps 25
are followed on each section as for separate plots, then the intersection
of Step 6 is applied to all solids. 