Insulating the foundation

Here's a picture of my lovely wife and assistant cutting 2'' Styrofoam SM boards for the foundation. She's very crafty with a knife. We are installing 4'' on the outside and 2'' on the inside. Today we nailed it to the sill on the outside. We'll need to nail into the concrete on the inside. Hello power drill.

This gives us R-30 insulation value. Overkill? Not with a radiant slab. The temperature of the slab will be maintained at 75 C (22 C) whereas the temperature of the air will be closer to 65 F ( 18 C) (for very toasty toes). If you want to keep the heat in, you need to insulate the slab. Moreover, with a solar system you want to store solar heat from the day and summer through the night and winter. You need to insulate below the slab as well.