read on | A more detailed discussion of solar geometry can be found in norbert M. lechner’s book,
Heating, Cooling, Lighting: Sustainable Design Methods for Architects, 3rd edition, ©2009.
30 May 2012 SOLAR TODAY solartoday.org
heating on June 21, it is hottest in July/August.
Because of the Earth’s mass, it takes time for the
Earth to heat up after the previous winter. Similarly, the Earth receives the least solar heating
on Dec. 21, but the coldest months are January and February, because it takes time for the
Earth to cool down after the previous summer’s
heating. Thus, it is important to understand that
although sun angles and the solar heating effect
of the solar year are symmetrical about the insolation peak and low points of June 21 and Dec.
21 respectively, the resultant heating and cooling
requirements of the thermal year do not correspond with these dates — and, of course, buildings must be designed to respond to the thermal
year, not the solar year.
The sun path diagram shown in figure 3
is the horizontal projection of the sky dome
shown for 32 degrees north latitude. By again
using shades of red and blue to represent the
typical temperatures throughout the year, we can
superimpose the thermal year on top of the solar
year, as shown in figure 4 (at right). However,
since the thermal year and solar year are out of
phase, we will use two copies of the same sun
path diagram — one for June 21−Dec. 21 (left)
and the other for Dec. 21−June 21 (right). Note
how the hottest and coldest times are about one-and-a-half months after the days we get the most
and least solar heating. For this example, we are
using the climate in which the end of the overheated period is about Sept. 21 and the end of
the underheated period is about March 21.
Although the climate we’ve chosen for our
example seems like a special case, it is not. For
instance, a somewhat colder climate would have
the end of the overheated period (summer)
around Aug. 21 and the end of the underheated
period (winter) around April 21. Note that the
sun makes the same path across the sky on both
Aug. 21 and April 21. As with the climate where
we want full shade until Sept. 21 and full sun exposure until March 21, overhangs need to be able to
change from full shading to full sun exposure in
one day. Fixed overhangs, unfortunately, cannot
come even close to meeting this goal. Since the
daily changes in sun angles are small, it takes many
months for a fixed overhang to go from full shading to full solar exposure. Consequently, there are
many hot months when a fixed overhang does not
shade sufficiently and many cold months when
much of the valuable sunshine is blocked. See
my shading article in the March/April 2012 issue
(“Shading for Energy Savings,” solartoday.org/
digital) for a full explanation of this phenomenon.
Figure 3. A sun path dia- gram is a horizontal pro- jection of a sky dome. Besides the daily symme- try at about noon, there is also an annual symmetry around the June 21 and Dec. 21 curves. All the other curves represent two symmetrical months (e.g., March 21 and Sept. 21). The altitude and azimuth com- ponents of any sun ray can be measured from the par- allel circle and radial lines respectively.
Figure 4. Because the thermal year is out of phase with the solar year, two sun path diagrams are
necessary to show the relationship between the solar and thermal year. The left diagram shows the
overheated period ending on Sept. 21, and the right diagram shows the underheated period ending
