Which Windows will win?

Windows for the green house
Windows for the ARC
Windows for Dug's place
The choices aren't stark!

Introduction
Windows are an key part of any building. Especially so if you want to heat your building with the help of the sun. I have been trying to understand the basic performance issues involving glass, u value, local climate and solar gain.

Insolation
We began by looking at the amount of heat a window can gain. We looked up the solar incidence (insolation) for our location. NASA has big tables full of information for all over the country. So we got a table of information listing the number of btus/ft^2 per day on a south facing vertical surface for each month of the year here in Pine River.

Insolation for south facing, vertical surface

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Solar btus/Ft^2/day	922	1123	1056	995	912	871	931	960	922	954	858	807

The heat gained from a window is the Solar Heat Gain Coefficient (SHGC) times the insolation. The SHGC is a function of the glass and every window manufacturer publishes it.

Heat Gained (btus/month) = Insolation (per day) X 30(Days/month) X SHGC

Heat Loss
Then we got information on our average temperatures to determine how many btus a window will lose. This document from Noaa has MN climatic data. http://cdo.ncdc.noaa.gov/climatenormals/clim81/MNnorm.pdf
So we got the degree days for Pine River. The degree days in this document are based on 65F, but in a super insulated house it is generally more useful to go with degree days based on 50F.

Heating Degree Days (HDD) for Pine River, MN

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
HDD (50F)	1489	1112	785	275	43	1.8	0	0	45	319	918	1516

We multiply the degree hours per month by the windows U value to come to the btu's lost. The U value for a window is also published. Many web sites list the center of glass U value, but the frame around the glass makes a big difference, so you need to get the total unit U value for that window.

Heat Loss (btus/month) = HDD(per month) X (24 hours/day) X U value

Putting it Together

So the overall rating we are looking for is the ratio of heat gain to heat loss. Ideally we are looking for a window that gains more heat than it loses, on average for every month of the year. If we represent that as a ratio we get:

Heat Gained (btus/month) = Insolation (per day) X 30(Days/month) X SHGC

Heat Loss (btus/month) = HDD(per month) X (24 hours/day) X U value

The ratio on the left is the relative performance. The middle term is the location specific numbers that will change from place to place and with different solar panel orientation. And the third term is the window performance numbers.

In a break even, the Heat Gained over Heat Loss must be 1.

If we divide both sides by the location term, we get:

So, to get break even performance our window specs must be proportionate to the location specific term. If we revisit our tables from up above and format them to be per month, we get the following.

Lat 46.5	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Lon -94.5
HDH (50F)	35,726	26,698	18,835	6,610	1,037	43	0	0	1,080	7,646	22,032	36,374
Insolation (btus/month/ft^2)	27,649	33,676	31,667	29,849	27,362	26,118	27,936	28,797	27,649	28,605	25,735	24,205
Degree Hours / Insolation	1.29	0.79	0.59	0.22	0.04	0	0	0	0.04	0.27	0.86	1.5

The most important thing to note is that in our location, December is the worst month. To break even in December, we need a window with SHGC or 1.5 that of the U Value.

More later on which windows we find that meets these.