> The sun does rise and set in the east and west at the equinoxes, but
> *not* at other times of the year. In June, it rises and sets well to
> the north of east and west, and in December it rises and sets to the
> south of due east and west. (This is true for observers in both
> hemispheres.) Therefore, at times well removed from noon, and at dates
> that are not the equinoxes, the trough *cannot* properly focus sunlight
> onto its collector tube.
In theory it may not "properly focus sunlight" but it seems that it works
fairly well in practice. A quick search of the internet will give you
several hits on people who have made just such collectors and are using
them.
> Okay. Here's an argument that I think proves that the east-west
> "trough" collector cannot focus sunlight accurately onto its tube
> throughout the day, except at the equinoxes.
> The trough essentially defines a plane in which the sun must be in
> order for its light to be properly focussed. The plane includes the
> focal line, in which the collector tube is located, and projects into
> the sky in the direction in which the parabolic trough is aimed. If the
> aim of the trough is not exactly horizontal - which would never happen
> in practice at temperate latitudes - the plane intersects the horizon
> exactly in the east and west directions. Therefore, in order for
> sunlight to be properly focussed when the sun is close to the horizon,
> at sunrise and sunset, the sun must be due east or west.
> The sun does rise and set in the east and west at the equinoxes, but
> *not* at other times of the year. In June, it rises and sets well to
> the north of east and west, and in December it rises and sets to the
> south of due east and west. (This is true for observers in both
> hemispheres.) Therefore, at times well removed from noon, and at dates
> that are not the equinoxes, the trough *cannot* properly focus sunlight
> onto its collector tube.
> Which is exactly what my calculations showed.
I have to agree with you. For example, here in NY the summer solstice puts
the noon day sun about 70 degrees above the horizon. If I were to orient a
trough collector for this it would be east-west with a tilt of 20 degrees
from the vertical. But I can easily see the sun rising and setting in the
northeast and northwest. For a month or so, the *north* side of my house
actually gets some morning sun!!!
The line of the trough and the 'directerix' through the parabola of the
trough form a plane in three dimensional space as you state. If the trough
were aimed straight up, the plane would intersect with the 'center' of the
earth (okay, not quite since the earth isn't a perfect sphere). But with it
tiled to the south slightly, the plane just sort of 'slices off the top' a
section and would come out the other side at a lower (closer to the equator)
latitude.
If you picture the earth in space during the equinox with the sun directly
to the 'right' of your viewpoint, the plane formed by the east-west-up
orientation of the collector would be 'horizontal' to your point of view and
interest the day-night perimeter at right angles. Since the day-night
perimeter is parallel to the polar axis, the 'plane' of the collecter would
remain 'horizontal' and intersect the sun as the planet turned throughout
the day (i.e. the trough would always be 'aimed' correctly).
But in the summer solstice, because the pole is tilted toward the sun, when
you have the sun again to the right you would see that the trough is
perpendicular to the pole axis and thus would *not* be perpendicular to the
day-night perimeter. As the planet rotated on this day, the plane of the
trough would sweep out a conic shape and only at noon would it intersect the
sun.
For the proper theoretical aim of the trough, it would need a tracker
mechanism that 1) aimed the end of the trough to the point on the horizon
where the sun would rise, 2) slowly turn throughout the morning so it was
oriented exactly east-west at local solar noon and 3)continue turning as the
sun traces across the sky such that the opposite end of the trough ends up
pointing exactly where the sun sets everyday.
On the equinoxes this would be zero amount of rotation throughout the day.
In the summer it would start 'facing' southeast with the east end pointing
in the northeast and twist 'clockwise' throughout the day and end up
'facing' southwest with the west end pointing to the northwest. Curiously,
in the winter it would start 'facing' southwest with the east end pointing
to the southeast and twist 'counter-clockwise' throughout the day and end up
'facing' southeast with the west end pointing southwest. Quite a tracker
(unless you just use a computer to figure out the motion every day).
Tracking a long narrow trough is probably harder than a square-ish flat
plate collector too.
daestrom
P.S. That's not to say a simple east-west orientation is useless, far from
it. But it isn't 'optimal'.
>-> > hemispheres.) Therefore, at times well removed from noon, and at dates
> -> > that are not the equinoxes, the trough *cannot* properly focus
> sunlight
> -> > onto its collector tube.
> -> In theory it may not "properly focus sunlight" but it seems that it
> works
> -> fairly well in practice. A quick search of the internet will give you
> -> several hits on people who have made just such collectors and are using
> -> them.
> Oh, sure. That's true. For about six hours per day, they do perform
> well. But the myth is that they focus sunlight properly throughout the
> day, and that is not true. The question is, why have few, if any,
> people noticed the drop-off of performance in mid-afternoon? Maybe they
> mistakenly ascribe it to the "cosine law", which also causes a drop in
> performance, but much less abrupt. Or maybe they just think their
> collector is poorly adjusted. Who knows?
My point is for most of the things you want a trough for they work 'well
enough' and their simplicity makes them very attractive. I'm looking into
solar cooling and plan on doing some experiments with a trough reflector and
NH3. Use the heat to evaporate the NH3 during the day and let the system
run backwards at night. Hopefully I'll have ice in the mornings. I could
go through all the trouble to make any of several types of tracking
reflectors and get more energy but why bother? The small scale and the KISS
principle say that a trough is the way to go, for now at least.
>-> My point is for most of the things you want a trough for they work 'well
> -> enough' and their simplicity makes them very attractive. I'm looking
> into
> -> solar cooling and plan on doing some experiments with a trough
> reflector and
> -> NH3. Use the heat to evaporate the NH3 during the day and let the
> system
> -> run backwards at night. Hopefully I'll have ice in the mornings. I
> could
> -> go through all the trouble to make any of several types of tracking
> -> reflectors and get more energy but why bother? The small scale and the
> KISS
> -> principle say that a trough is the way to go, for now at least.
> Absolutely! I have *not* been trying to say that troughs are useless.
> Far from it. All I have been saying is that, under certain
> circumstances - early or late in the day, and not near an equinox -
> they do not perform properly.
I would suggest that praps what you meant was 'optimally' in place of
properly.... Am I correct?
> dow
>-> > Absolutely! I have *not* been trying to say that troughs are useless.
> -> > Far from it. All I have been saying is that, under certain
> -> > circumstances - early or late in the day, and not near an equinox -
> -> > they do not perform properly.
> -> I would suggest that praps what you meant was 'optimally' in place
> of
> -> properly.... Am I correct?
> -> >
> -> > dow
> No. Properly. In the early morning and late afternoon, sunlight that
> is reflected from the parabola
Sorry, forgot this bit. Why should it be a parabola and not just a
simple arc?
Jim, temporarily brain-dead (hopefully temp.!)
misses any reasonable-sized collector
> tube altogether. The reflector is completely useless. I think that
> qualifies as not performing properly!
> dow
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> *not* at other times of the year. In June, it rises and sets well to
> the north of east and west, and in December it rises and sets to the
> south of due east and west. (This is true for observers in both
> hemispheres.) Therefore, at times well removed from noon, and at dates
> that are not the equinoxes, the trough *cannot* properly focus sunlight
> onto its collector tube.