Maximizing Energy Efficiency: Calculating Tabeshband Width and Window Height

[trina1990]

Homework Statement

In a typical Persian architecture, on top of south side windows there is a
structure called "Tabeshband" (shader), which controls sunlight in summer and winter. In
summer when the Sun is high, Tabeshband prevents sunlight to enter rooms and keeps
inside cooler. In the modern architecture it is verified that the Tabeshband saves about 20%
of energy cost. Figure (1) shows a vertical section of this design at latitude of 36°. 0 N with
window and Tabeshband.

calculate the maximum width of the Tabeshband,
X, and maximum height of the window , H in such a way that:
i) No direct sunlight can enter to the room in the summer solstice at noon.
ii) The direct sunlight reaches the end of the room on the opposite lower corner side of the window(indicated by the point A in the
figure) in the winter solstice at noon.

provided that the height of the room is 3m & width is 4.50m?

Homework Equations

to solve it out i run the stellarium to determine the altitude of sun at summer solstice for that latitude & found it to be approximately 70 degree..then i applied
tan 20=X/3 & answered the X=1.637m

for height of the window i found out the altitude at window solstice to be 20 degree & i applied tan20=H1/4.5=1.63 then H=1.36

my question is if the process's to solve it was right & if there any other convenient process to solve it out?

The Attempt at a Solution

ere's a link for the original thread
Attached Files
ioaa2009theoreticalshortproblems.pdf (146.4 KB, 2 views)

 

[gneill]

Your link to the image file doesn't seem to work, so I can't comment on your solution other than to say that you might have worked out the Sun's altitude on the solstices using basic geometry, knowing that the Earth's axial tilt is about 23.4 degrees.