Passive solar greenhouse, angle of south facing "front" at my long-lat

Hey Permies Peeps.

I'm meeting with a builder to see if they will (help) build my passive solar greenhouse. I'm trying for a 26x54-ish footprint, more-or-less lean-to, north portion half underground, and tall enough to let a banana bear fruit whenever it wants to. I'm math challenged (being a wordsmith more than a numbers gal), and am NOT confident that my guesstimate at a "30-degree slope aught to work just fine" is correct here on my little chunk of NC. I plan to us double wall polycarb for all glazing, plus windows that open on the south vertical wall, and one or two each on the E and W walls, where they are above grade (yeah, duh). Plus at least one thermostatically activated vent fan (at peak on the N wall? W wall? E wall?), or more if the FarmTek guys can convince me I need more. Do I need an evaporative cooler? My 14x50 caterpillar tunnel is a sauna 8 months of the year, and kept my in-ground turmeric safe all winter, even through the big freeze in February (one end of the tunnel is still wide open, btw). So ... I'm running a half-way farm. Everything is halfway finished or halfway fixed. I just don't want it to be half correct on something this big that I'm investing a lot of time and money in.

Location specs: zone 7b, long-lat is 35° 51' 43" N, 80° 32' 40" W (35.862110, -80.544574) according to https://www.mappr.co/latitude-longitude-finder/.

I gleaned the images in the attached file from a sun path site, calculated at the solstices (should I have looked at equinoxes?) to see the variance ... and from that guessed my S-facing sloped roof glazing should be around 30-degrees. Is this close? How should I have calculated it?  Should my non-glazed area at the top of the roof be more than 6'? Less? I don't want to be dragging shade cloth around the structure's roof during the July-Aug heat wave next year ...

Sorry to seem to naive on this. I know I have a lot to learn, so I'm hoping someone out there can help me with some shortcuts so I don't spend money I don't need to, or do a poor job with planning and negate the great benefits that passive solar allows! And I'm sure there are questions I should be asking that I just don't know I need to ask. Please help!

Looking forward to hearing back ...
Felicia

Welcome to the forum!

You are a step ahead of me so go for it.

Update: Was referred to another part of the company I want to deal with. The other part makes custom carports and such using metal tubing. One of the specs I gave the builder is that none of this passive solar greenhouse can be made from wood. Yes, it will cost more up front, but will eliminate almost 100% of the pest pressure: molds, fungi, insects all find ready homes in wood structures, and once embedded, are hard to eliminate. The greenhouse at school (I just finished doing a associates program in sustainable ag at the local community college) periodically clears out every plant from the greenhouse during a hot spell, pressure washes everything, then turns off all ventilation to heat the greenhouse up over 120-degrees. Kills a lot of the embedded pests, but ...
My greenhouse is for production - food, herb plants for my farm and for sale, and a few permanent residents (previously mentioned bananas, and probably a couple of lemons and a mango or two). So larger, harder to clean out, thus preventive up-front measures as I'm aware and able.
All hints and tips and wisdom welcome here! Let me know if you spot something you think I need to know. I'm here to learn!
Felicia

Plus at least one thermostatically activated vent fan (at peak on the N wall? W wall? E wall?)

if you are venting, don't forget air intake. Put it the coolest place you can, as low as you can.   Output fan at the highest peak in the building, wherever that is. If you have a lot of high peak, do both ends.

If you actually freeze (not sure of your climate) insulating the ground a couple of feet down keeps the frozen outside ground temp out.

Sun angle: 30 is probably fine. You want as much as you can get in spring and fall, summer will be a LOT of excess gain at best.

If you are doing metal and planning it to go underground, waterproof it. Those carports WILL rust out. Takes them a while, but dirt contact will accelerate it.

Something to take into account is water flow across the land, both above and below ground, above ground will flood your greenhouse out, below will possibly affect your plants and moisture issues.

MAKE SURE IT'S ANCHORED DOWN HARD!!!

Swamp cooler adds moisture, take that into account. If you want fans for air flow, input as close to ground as you can get for coolness, output as high as you can. If you run forced air at the bottom you don't need the top to have fans, unless you want them to run separate too.

Should my non-glazed area at the top of the roof be more than 6'? Less? I don't want to be dragging shade cloth around the structure's roof during the July-Aug heat wave next year ...

 Do you really WANT much glazed area on the roof? Lets in more heat in summer, lets out more heat in winter. And you definitely WILL end up doing shade cloth if you do that.  You might think on that hard.

Without a sketch it's hard to guess what your building angles are, so on the unglazed part of the roof I'd worry most about making sure the peak, wherever it is, is DEFINITELY waterproofed WELL. And waterproofed where it hits the glazing.

Double wall polycarb rocks, BUT be sure it's installed horizontally, it works like a solar chimney making air flow up it's tubes if you don't. Great in the summer, problematic in winter, depending on where it manages to find an air gap to pull in air as it moves heat up.

You also might consider thermal mass in there, as well as reflective surfaces, depending on how you are doing things.

I assume the North wall is totally unglazed? Depending on your climate heavy insulation on that wall may be wise.

:D