Welcome to Winter (Solstice)

Just a stab in the “dark”: dibs on the two 23.5 degrees off the equator.

 

Felt somewhat of the trendsetter with panels still being quite expensive in the 2000s . Our system was commissioned january 2008. Rated at 8kW AC.



(always thought DC ratings were a marketing gimmick as that's not what your system ultimately needs to output). Charging 2 Cars + home electricity - it paid for itself in just over 6 years (as feds picked up ⅓ of the cost). Our electric bill was usually a couple hundred dollars a month average (So Cal) prior to 2008 - having some of the highest rates in the nation. The utility rates just kept going up & up, & PV kept zeroing out.
Now, we're living up north and are considering bifacial panels - which run 15%-30% more efficient:



Ideally aligned from North to south, they convert sunlight on both sides, & in snowy conditions especially - light capturing can include reflection off snow. Our roof in the NW is horrible for locating PV on any south facing directions - but we have a good amount of land - which will make this weird verticle install more practical. Plus, way way easier to keep Montana snow off - compared to flat / relatively flat roof mounts.

 

Now that others have had some time to chime in, here is the solution I'm leaning towards, at least so far. It uses astronomical equations very similar to what I located and put on my old unix workstation back before they migrated us to WinDoze:

https://oikofuge.com/which-place-gets-the-most-daylight/


Shortest total daylight at the South Pole with 4388 hours, longest on Arctic Circle with 4649 hours, a difference of 261 hours. Go mountain climbing, and get 5052 hours atop Mount Forel in Greenland. Denali and a few other peaks in Alaska and Siberia exceed 5000 hours, but still fall more than a day short of Forel.

Other charts show the work path towards this final chart. He also mentions some additional complications not factored in.

I've long accounted for the solar disc not being a point, and for atmospheric refraction, but for some reason had never considered the north-south difference caused by Earth's elliptical orbit. This non-circular orbit effectively lengthens the North's summer a bit when Earth is farther away from the Sun and moving slower, while shortening the South's summer when closer and moving faster. Perihelion (closest point to Sun) is in early January, aphelion (farthest point) in early July.

= = = =

This has a significant discrepancy between its Arctic Circle and your 80 degrees latitude. The discrepancy deserves some exploration.

 

Geesh, I wasn't even close...

Article Circle equals the points beyond which you'll experience at least one day per year where the sun will never set, and a reciprical day where it'll never get above the horizon.

 

My understanding is that this is an economic thing: when considering where to spend your last incremental system dollars, do you get greater production $$ return by adding more DC capacity (larger or more PV panels), or more AC (larger inverters), or both in balance?

When DC capacity exceeds AC capacity, the peak PV output under the best conditions gets clipped and some is lost. But the system spends very little total time in this peak condition, the great majority of operating time is on the 'shoulders' of the daily output curve, and all the extra PV output can be processed by the inverters. In non-ideal weather, hazy conditions, and non-ideal orientations (both directional and seasonal), the PV simply won't reach its rated output capacity, so there is even less clipping, if any at all.

IOW, extra DC will be contributing most of the time, while extra AC will be used only rarely.

The ideal economic balance ratio between DC and AC capacity is a function of the relative prices of the available PV panels vs inverters, which are continually moving, so there is no fixed answer. And available equipment choices at any given moment greatly constrain the practical solutions.

This orientation also produces a very different daily power/energy schedule than the more common south facing orientation, which doesn't fit any utility's demand or load pattern.

Absent batteries, a mixture of orientations can better fit the load patterns. But no mix of solar orientations can fit the 24 hour demand pattern, so batteries or other sources are needed. Figuring the best fit is a very complex problem.

For those of us on simple flat rate net metering, the goal is to maximize annual production, regardless of timing. For most, facing due south works best for that. When home solar producers get put on Time Of Use/Production metering, everything changes.

 

The picture of our PV above shows 2 gables, each array with 4kWs (ideal conditions) max output. The system had two 4kw inverters (micro inverters hadn't reached their potential/reliability/pricepoint back then). Cold days late spring with light cloudy conditions - the panels could cool down to maybe low 60s°f then the sun would come out from behind the clouds. The Gable facing the sun would over produce as much as 20% for a few brief moments until the panels heated back up. The inverter cooling fans would really rev! Apparently the inverters are underrated - in order to accommodate such conditions because they never let the smoke out.

 

It is enough to say that:

My guess going in was also within tropical latitudes.
Reality is daylight peaks at very high latitudes where few plants are able to drink it in. Ergo
Light ain't heat.

 

From the chart at #43, why the cusps as the Arctic/Antarctic Circles? Let's see if I can explain ...

Everywhere on Earth, the speed of the sun's daily apparent motion -- high across the sky or far below the horizon, think in terms of the entire celestial sphere -- is the same at any moment. (It varies slightly across seasons, but by less than 10%.) From any vantage point, this speed can be broken up separate vertical and horizontal components, which strongly depend are both your location on Earth and the sun's direction.

At the equator, the sun rises and sets almost exactly vertically, with almost no sideways motion. So it goes down fast. (Or up at sunrise, but I'll focus on just sunset here.) Excluding refraction, sunset from bottom edge to top edge would be barely over 2 minutes, though refraction stretches it out longer. The hang time or dwell time while it is on the horizon, is short. Twilight is also short for similar reasons.

As you move farther away from the equator, the apparent motion angle of sunset changes, becoming shallow at higher latitudes. The vertical speed gets smaller and sunset takes longer, while the horizontal speed increases and the sun visibly moves sideways during the process. The hang time or dwell time while it is on the horizon, just partially set, increases.

At the Arctic Circle, at the solstices, the apparent vertical speed goes to zero and the sun appears to skim almost perfectly horizontally across the horizon. The hang time becomes huge. And thanks to the sun's diameter and atmospheric refraction and how slowly the sun's celestial declination changes around the solstices, this huge hang time last many days. All the hang time that happens when the true un-refracted solar center is below the horizon, is added daylight. This effect is maximized at the Arctic and Antarctic circles.

At the poles, disc diameter and refraction cause sunset to happen a bit after the fall equinox, with partial sunset lasting several days as is travels full circles around the horizon. But solar declination is changing at its most rapid rate, so the added hang time is less than the total of those many days of long hang time at the Circles. The Circles win this most-daylight contest.

Does this make sense?

 

Have I missed some elements of your earlier findings that we should still consider and explore? Or have those been obsoleted?

 

Finding some refreshers, I'm reminded that the sun's apparent radius averages 16 arc-minutes, varying only a couple percent across the seasons.

... and most almanac calculations fix the atmospheric refraction as 34 arc-minutes. They are computed much too far in advance to forecast the real refraction on any given day, so just settle on this as a standard.

Together, these mean that sunrise and sunset are computed as the moment when the true (un-refracted) solar center is 50 arc-minutes, or 50/60ths of a degree, below the horizon.

= = = =

Bonus question: when cruising in an airliner at full altitude, how much lower is the visible horizon than a 'level' horizon?

I enjoy watching sunrise/set patterns (and very many other things) from the window seats, and have witnessed a lot, include my only sighting of the "green flash". That is, when the 'window nazis' (flight attendants) don't demand the shades be drawn. Or now in B787s and A350s, forcibly dim them electrically and disable the individual controls.

 

I picked arbitrary locations from the map on timeanddate.com at approximately my longitude, at 10 degree latitude steps, to get a general idea of this phenom. Your graph with cusps is a better treatment. All that refraction stuff is why daylength at equatorial (sea level) sites is 7 ish minutes too long.

Super great on green flash! Never had that pleasure. How about the Brocken spectre?

I hold higher opinions than you do about cabin attendants.

We are to believe that sun and moon arc-minutes being the same (and causing eclipses) is pure coincidence. Well, I guess so...

Bonus question: as moon recedes and looks smaller, there will only be annular eclipses, when will the last 'total' one be seen on Earth?

 

At least your names of things will stay the same. We down south used to have that. I wouldn’t be surprised if our man didn’t proclaim the solstices in his name, in gold capital letters of course.

 

“Let there be light” as the Good Book says, and still applies imo. Not really an opinion, but we and everything are made of light. We just see the bonding results, with our eyes and brain made of the same bonds.
Lets see if they can figure THIS out says the creator. Who apparently is not made of bonds, but something we have no grasp of what it is.
My guess going in was tropical latitudes, because every traveler knows it’s sunny there about the same all year. But that’s one of those easy things to believe.