Nice... 12' high x 40' long? With some windows near the top for shop light, with reflective lightshelves below and a reflective ceiling?
If the shop roof's thermal conductance is 34x54/R20 = 41 Btu/h-F and the 136' of non-collector wall has 12x136/R20 = 82, the total is 123.
And the shop is detatched from the home and the water heats the home and maybe water for showers, after an efficient greywater heat exchanger?
NREL says 460 Btu/ft^2 of solar energy falls on the ground and 810 falls on a south wall on an average 21.7 F December day with a 29.8 daily max and ground reflectance Rho = 0.2 in Madison, so the average daytime temp is about 26.
With Rho = 0.6, eg snow or white pebbles, the south wall would receive
810+0.5(0.6-0.2)460 = 902 Btu/ft^2. With a 70 F shop air temp, R1 Dynaglas ($1/ft^2 corrugated greenhouse roofing in 4'x12' corrugated sheets with a 10 year guarantee) with 90% solar transmission might collect 0.9x902 = 812 Btu/ft^2 and lose 6h(70-26)1ft^2/R1 = 264, for a net gain of 548, ie 12x40x548 = 263K Btu/day.If the shop is used 6h/day and it doesn't store much heat, it needs about
6h(70-26)123 = 32.5K Btu/day, which leaves 230.6K for the house, collected at 230.6K/6h = 38.4K Btu/h. A 2'-4' deep heater with shop air in the space between black fiberglass window screen with the top of the screen attached to the south edge of the heater ceiling and the bottom attached near the shop wall and 150 F air in the space under the heater ceiling might heat 150-38.4K/1600 = 126 F water with 320' of f>The alternative here would be to build somethng similar to a greenhouse allHave you been listening to crooked masonry salesmen? :-) The wall gets most of the low-angle winter sun, and thermal mass raises the cost and makes the "greenhouse" cool all the time, vs hot during the day and cold at night. If 12x40x812 = 389.8K Btu = 24h(T-21.7)x12x40/R1+6h(T-26)123, T = 54 F. Yuck! A cool shop, with no useful heat storage and no heat left for the house.
Nick