Finding the right glass angle for a south-facing sunroom/attached greenhouse

Hi, permies! I come seeking guidance and/or directions to the best resources once again.

We're planning to attach a sunroom/greenhouse to the southern wall of our house, and I want to make sure we plan for the right angle of the glass windows for our latitude, which is 31.748081 N. I know I've seen charts or a formula for figuring this out in some book(s) somewhere, but I can't remember where, so I'm trying to recreate this.

Sciencing says (https://sciencing.com/calculate-winter-solstice-sun-angle-8744966.html) to add 23.5 to our latitude to account for the direct rays of the sun falling at the tropic lines -- this would be 55.248081 for us -- and then subtract that from 90 degrees to get the angle of elevation from the horizon of the sun during midday on the winter solstice. The final number for us would be 34.751919 degrees.

What do I do next to figure out that ideal angle for the glass? Is the ideal angle of incidence 90 degrees, which would mean the glass should be at 124.75 degrees on the obtuse side, in other words 55.248081 degrees on the acute side (facing/towards the house)?

Also, if I understand correctly, the east and west vertical walls of the sunroom should be opaque (except when the doors at either end are open to screens for cross-ventilation). Is that right?

Since it gets so sunny and hot here in the summer and we really don't want to heat our house then anymore than it already is, we're thinking of making the top part of the angled wall opaque as well (maybe two or three feet), with glass below that, just to be absolutely sure of enough shade in the summer. Are we thinking along the right lines here, or is that unnecessary (and maybe would block some of the sun we need for plants in the winter)? Would a seasonally movable shade like a roll-down shutter be a better solution?

Confirmation or correction of these thoughts and calculations would be much appreciated, as well as any other suggestions or recommended resources. Thank you very much, everyone!

I angled my greenhouse roof to the north rather than the south. Greenhouses were designed to hold heat for areas with cool summers and frigid winters, areas where additional heat is needed pretty much year-round. My entirely passive greenhouse stays about 5-10 degrees warmer than the outside in the summer with both side doors open. Summer sun never hits the roof, and the angle is wrong during the summer for it to hit the front wall directly. However, it does hit the front wall directly during the winter, when we need the extra heat.

Making the roof opaque might have the same effect, or it might cause problems depending on how deep your greenhouse is.

If I were to build my greenhouse again, I would angle the whole south side SLIGHTLY, maybe 5-10 degrees, to allow for better heating and light during the winter, but the angle wouldn't be steep enough for the summer sun to hit it. i.e., calculate based on the winter sun angle rather than the summer sun angle, and still try to minimize summer heat collection.

Hey, Lauren, thanks so much for your response! It looks like you actually get an inch less of rainfall per year than us on average. I'm impressed. Does monsoon get up your way? It seems ours is just starting, pulling in from the Sea of Cortez toward the Four Corners.

What you say makes sense. It seems to me, though, that it wouldn't work to have an attached greenhouse on the north side of our house because it wouldn't get enough sun in winter. Is that right? What we're trying to do is create a space in which we can keep less frost-hardy perennials alive through the winter, start seeds, etc., while also hopefully creating a little passive heating for the house in winter without adding any heat in summer. It seems like a tricky balance. ;)

Do I understand right from what you say that, if we angle that south-facing glass at something like 80 or 85 degrees rather than the 55 that my calculations said would be "ideal," we'd still get enough light and warmth in winter but overheat the space less in summer? Thanks!

You are correct that an attached greenhouse on the north would be pointless. My greenhouse faces south--it's the roof that is angled north (see attached). Maybe consider doing your proposed angle with clear plastic for a season, and see how it works? That way you're not laying out a lot of money for the addition, only to find that you need to make changes.

My greenhouse is 9 feet deep. During the deepest part of winter the light hits the back wall. During the summer it's lightly shadowed with just a strip at the front in full sun. With a door on either side in the direction of the prevailing winds (open all summer) the temperature remains relatively steady. If the front wall was tilted just slightly it would collect more sun during the winter. I can't say how that would affect the summer, but I suspect it wouldn't be enough to make a difference in the temperature. The hottest part of the year in this greenhouse is fall, when the sun is hitting the front wall and the outside temperatures are also still high.

I'm at apx 40 degrees latitude, which means a 26 degree angle to the sun in mid-winter. You're at about 31, which means a 35 degree angle. Just rough (90 degrees - 23.5 - your latitude). So your sun angle would be higher summer and winter, and nearly overhead during the summer. Roughly, a 35 degree angle in my greenhouse would have the winter sun hitting the bottom of the back wall. Depending on how deep your space is, a perpendicular or slightly angled wall SHOULD give you the heat you need in winter without turning your house into an oven in the summer.

Thanks, Lauren, especially for the picture! I doubt we'll spend any money on this project, actually. We've got used windows and wood framing and roofing metal and hardware in our "resource pile." Most plastic doesn't even make it through one summer in our conditions out here.

A large part of why I've been assuming the south-facing glass would be slanted is because I've spent a lot of time in such a sunroom whose angle was very carefully calculated by the engineer who built it from mostly recycled materials, and it's quite nice. That's at about lat. 35 N in northern AZ, where the summer sun can definitely be intense but where the summer high temp's are significantly lower than here. It contributes significant heating to the house in winter. I think the owner mostly just turns on the radiant floor heat to low at night. There's some thermal mass against the house wall that radiates a little of the sunroom's heat for part of the night as well. It's maybe 6-8 ft. deep and grows lots of herbs, tomatoes, greens, etc. year-round as well as being a great place to start plants in spring. There's a door at each end, with screens, so a cross-breeze keeps it from overheating in summer. I'm jealous and want one more or less just like it for ourselves!

There is at least one example of a sunroom closer to us, actually, but it's more of an atrium and I don't believe it has any slanted walls. I think the copious vegetation in it contributes to it being cooler in summer than it might otherwise be, plus I believe it has some shade cloths. Those are both things I'll keep in mind. Thanks for keeping me thinking, Lauren!