D
David Williams
- Jan 1, 1970
- 0
A lot of people use simple solar concentrators that are shaped like long
troughs, with a parabolic cross-section. A pipe containing the fluid to
be heated runs along the focal line of the trough, which is aligned
east-west and tilted to point at the noon-day sun. The general idea is
that, as the sun moves across the sky from east to west, its light will
continue to be focussed onto the pipe throughout the day. The only
adjustment needed is a change to the angle of tilt. This has to be done
every few days to compensate for the sun's north-south seasonal
movements.
But it is *not* (usually) true that the sun's motion across the sky
will keep its light focussed on the tube throughout the day. This
happens only on two days of the year, the equinoxes, when the sun
rises exactly in the east and sets exactly in the west. On all other
dates, the sun moves away from the plane defined by the axis of the
parabola.
Since I've recently been writing programs concerned with the location
of the sun, I have a bunch of relevant routines that I could easily
patch together to calculate the size of this effect. I projected the
direction of sunlight onto a north-south vertical plane, and calculated
the angle it made with the parabolic axis. Ideally, this angle should
be zero throughout the day. Here are my results, calculated on the 21st
days of March, April, May, and June, and for each hour up to 5 hours on
either side of solar noon.
Month (21st day) Hour (difference from noon) Angle (degrees)
March 0 0
1 0
2 0
3 0
4 0
5 0
April 0 0
1 0
2 2
3 5
4 11
5 27
May 0 0
1 1
2 3
3 7
4 16
5 35
June 0 0
1 1
2 3
3 8
4 17
5 36
Of course, on March 21, an equinox, the angle is always zero. And at
noon on all dates the angle is zero since it is assumed that the trough
is alighned to point to the noon-day sun. But at times in the early
morning or late afternoon on the 21st days of the other months, the
angle is far from zero. The exact designs of collectors very, but it
is reasonable to guess that if the angle is more than about 10 degrees,
the trough will not focus sunlight onto the pipe, so the collector will
be essentially useless. Interestingly, for all the months except March,
this means that the tough will work adequately well at times up to 3
hours from noon, i.e. from 9 a.m. to 3 p.m., but will be unsatisfactory
at times 4 or more hours from noon. At or before 8 a.m., or at or after
4 p.m., the trough collector will not work.
Of course, although I have calculated the angles only for the months
March through June, similar results would be obtained during the other
quarters of the year, by symmetry.
My calculations suggest that trough collectors should work better in
the equinoctial months, March and September, than in the other months.
Have people found this to be true, from experience?
Interesting...
dow
troughs, with a parabolic cross-section. A pipe containing the fluid to
be heated runs along the focal line of the trough, which is aligned
east-west and tilted to point at the noon-day sun. The general idea is
that, as the sun moves across the sky from east to west, its light will
continue to be focussed onto the pipe throughout the day. The only
adjustment needed is a change to the angle of tilt. This has to be done
every few days to compensate for the sun's north-south seasonal
movements.
But it is *not* (usually) true that the sun's motion across the sky
will keep its light focussed on the tube throughout the day. This
happens only on two days of the year, the equinoxes, when the sun
rises exactly in the east and sets exactly in the west. On all other
dates, the sun moves away from the plane defined by the axis of the
parabola.
Since I've recently been writing programs concerned with the location
of the sun, I have a bunch of relevant routines that I could easily
patch together to calculate the size of this effect. I projected the
direction of sunlight onto a north-south vertical plane, and calculated
the angle it made with the parabolic axis. Ideally, this angle should
be zero throughout the day. Here are my results, calculated on the 21st
days of March, April, May, and June, and for each hour up to 5 hours on
either side of solar noon.
Month (21st day) Hour (difference from noon) Angle (degrees)
March 0 0
1 0
2 0
3 0
4 0
5 0
April 0 0
1 0
2 2
3 5
4 11
5 27
May 0 0
1 1
2 3
3 7
4 16
5 35
June 0 0
1 1
2 3
3 8
4 17
5 36
Of course, on March 21, an equinox, the angle is always zero. And at
noon on all dates the angle is zero since it is assumed that the trough
is alighned to point to the noon-day sun. But at times in the early
morning or late afternoon on the 21st days of the other months, the
angle is far from zero. The exact designs of collectors very, but it
is reasonable to guess that if the angle is more than about 10 degrees,
the trough will not focus sunlight onto the pipe, so the collector will
be essentially useless. Interestingly, for all the months except March,
this means that the tough will work adequately well at times up to 3
hours from noon, i.e. from 9 a.m. to 3 p.m., but will be unsatisfactory
at times 4 or more hours from noon. At or before 8 a.m., or at or after
4 p.m., the trough collector will not work.
Of course, although I have calculated the angles only for the months
March through June, similar results would be obtained during the other
quarters of the year, by symmetry.
My calculations suggest that trough collectors should work better in
the equinoctial months, March and September, than in the other months.
Have people found this to be true, from experience?
Interesting...
dow
