## Friday, February 25, 2011

### Let there be light!

Welcome to Excel Math's blog on using elementary math when you grow up.
A very long time ago, in Internet terms, I did a few blogs on changing the windows at my house. If you wish to refresh your memory, here are some links.  Measuring 101 and An Inch Here and Inch There. And here are pictures:

Version 1:

Version 2:

Version 3:

Yesterday we finished replacing the kitchen window for the second time, with the new, improved Version 3 that solved some technical difficulties experienced with Version 2. It's slightly larger than the one we took out, and still smaller than the original window.

My wife wondered if the difference in size would be "significant" to us. A perfect question for her Excel Math expert. Here's how we figure it out. The following drawings are done to scale using the actual dimensions I measured off the windows:

Version 1:
Version 2:
Version 3:

I calculated the square inches of the entire window, then subtracted the space occupied by the pillars. Each pillar was quite thin on Version 1 (1 inch x 36) with the original steel window framing, but quite fat (3x31 or 3x33) on Versions 2 and 3 with aluminum framing.

Because the newest windows have thinner frames around the perimeter, there's more glass area in Version 3. The gain is 227 square inches, or about 1.6 square feet. Is that significant?

Take a look at the small window below. It's 17.5 x 13.0 inches in size, or 227.5 square inches. That's how much extra glass area we gained in the Version 3 kitchen window.

Now that we can see there is more glass, does that mean more light comes in? Maybe. It depends on the Visible Transmittance (VT) factor of the window.

VT is an optical property that indicates the amount of visible light coming through the window; it is expressed as a number between 0 and 1. The higher the VT, the more light is transmitted. That sounds like a chance to use some more math. Next time.