m Ransley errs again:

Nick you are an idiot, there is to little sunshine in winter to give a
net gain, the days are to short, the suns angle to low at Chicago
latitudes... You also Assume its always sunny in chicago.

You are wrong on all counts. Try numbers :-)

One more time: 460 Btu/ft^2 of sun falls on the ground on an average 26.7 F
December day in Chicago. Unlike insulation, any skylight with more than 2
layers of glazing will gain more solar heat than it loses... 6 is optimal:

20 FOR N=1 TO 8'layers of glazing
30 GAIN=460*.9^N-24*(65-26.7)/N'Btu-ft^2-day
40 PRINT 100+N;"'";GAIN
50 NEXT

layers net gain

1 -505.2 Btu/ft^2-day
2 -87
3 28.93997
4 72.00598
5 87.78537
6 91.26282
7 88.70224
8 83.11487

A skylight with a south tilt or a shutter or a reflector can gain more.

Insulation can only LOSE heat.

Nick