Ok Ran the idea of turning the new back deck into a GH by my wife this morning and she loves the idea.
So we are Offically Starting the Planning stage However Thoughts and Inputs will be appreciated as a lot of thought is still going to need to go into this Project. We want it done right
Here is our initial thought looking out the back door you are facing South SouthEast. The GH will be about 7' 8" from the mobile home out and 8 to 12 ft from side to side. (the 7' 8" might seem strange but the guide wire from our utility pole prevents us from going further out

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We Plan on using 4 x4's in the corners for support Underpining and insulating the lower portion then decking it with marine grade plywood Then Covering the Marine grade plywood with a indoor out door carpet to help insulate. I am currently hunting down to windows I had out back one for the south wall and one for the west wall so we can open for ventelation. I am also trying to hunt down an old storm door with glass windows that open for the east side. The north side will be the exterior mobile home wall. The thing my wife likes about this idea is January getting to step from the mobile home directly into the green house with no need to face the elements at all since the back door will be inside the green house.
Well that is where we are at for right now. Any Thoughts or ideas at this point?
Oh we will be using pressure treated wood to help prevent rot.
Last thought around August first we will be budgeting 400 to get this project jump started till then Planning and cleaning and leveling the back area it has been used for remodling in the past and needs a bit of thourough clean up.
Jon