Ductwork suggestions

I am in the process of converting my 3-season porch to become a 4-season porch. I am located in Wisconsin and I need both both the heater and air conditioner to run on the same day. Just kidding about that but I do need both heat and cooling. Right now we cannot use the 3-season porch in the heat of summer because it is much to hot. In the winter it is not heated and we cannot use it because it is much to cold.

The sun porch was built on a deck. Therefore I would like to tap into a takeoff from my basement and cut a hole through a beam to allow the ductwork to the underside of the deck. The room is 16x14 with cathedral ceilings. How big should my ductwork be and how many run do you think I should have? I am planning on insulating all the ductwork that is outside.

Need more info...how many, size, orientation and U-factor for the windows, R-factor of ceiling insulation, and walls, and floor if it isn't enclosed. You need a heat load calculation - you can find calculators on the web that are fairly accurate. Then, you can figure out how many BTU/hour you need for both cooling and heating. Anything done before that calc is a WAG, and basically a waste.

Before you start cutting beams, you may want to consult with a structural engineer. Also, your existing a/c and heating plant may not have enough reserve to support the room addition. You may wish to consider one just for that room, or take this opportunity to upgrade the system you have to a more efficient system that can handle the new conditioned space.