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Do you plan on sidewall venting this (vent terminates outside the wall) or do you plan to go out then up above the roof?
The code requirement is that the vent must terminate at least 1' above the average expected snowfall for your area. This level is predetermined by local code enforcement. You can snorkel (2 90 elbow offset) to raise it higher if necessary.
It also can't terminate within 4' of any opening in the building.
You assessment is not correct. Snorkeling doesn't add to the horizontal run and you don't count the 2nd 90. You have to follow the manufacturer's installation guidelines. Some manufacturers want a 3' rise outdoors to create some natural draft. There may be similarities but the instructions are the last word on how to install it. Until you decide on a stove there's no way to pin this down. What I gave you is standard practice and is code compliant. You need to check with your local code authority about the snow depth number they use. At a minimum you vent termination must be 1' above the ground.
I don't need a picture of the instructions. If you have specific questions in relation to your installation then let me know.