I am building in Western NY. My zip is 14487. I would like to ensure I position my 2nd story windows so that the roof overhand allows sunlight in during the winter but not during the summer. What complicates this is that the South side of my house is the gabled end and with cathedral ceilings. This will be a log home with a large, 6-8 foot roof overhang to protect the logs from rain. Can someone help me with the math on where to position these windows? Very much appreciated.

In Livonia you're in US climate zone 5, and an IRC 2015 code-min unvented roof would need a minimum R49, at least R20 of which needs to be above the roof deck, which can be somewhat expensive. (In zone 6 that would have to be at least R25 above the roof deck). If you go higher-R, you need to keep the same ratio of exterior-R/total-R for dew point control at the roof deck to reduce the mold & rot risk.

With 6-8' overhangs you don't have to do the math- put the south facing windows as low on the wall as you can, but don't go hog-wild on window area, since you don't want mid-winter overheating. But if you want to play around with it, this shareware widget looks reasonable:

http://www.susdesign.com/overhang/

Or you can play around with online widgets:

http://www.ecowho.com/tools/passive_solar_eaves_calculator.php

Thank you very much for that top link, what a wonderful tool

The Sustainable by Design tools are wonderful for visualizing the light and shadow effect created by a passive solar roof overhang and Chris is also a great guy to work with too. However, if you don’t want to have an overheated building, you really do need to do the math and calculate the actual maximum daily clear sky solar heat gain BTUs that you could generate accounting for the roof overhang geometry, building orientation relative to true south, glass area, glass location on wall, glass SHGC, terrain obstacles, and the effect of any thermal mass used to buffer the daily irradiance heat gain.

When designing the roof overhang geometry, glass area, and glass location on wall, you should also consider and account for your climatic monthly high/low temperatures in addition to the latitude.

You should also do the math and calculate the average daily climatic heat gain BTUs you will likely generate so you can estimate what percentage of your total heating load will be provided by passive solar heating and take credit for this when sizing your supplemental heating system.

We have a fair amount of passive solar information and free DIY passive solar design tools on our website:

Borst Passive Solar Altitude Angle Software

Borst Passive Solar Roof Overhang Design Software

Borst Passive Solar Fenestration Exposure Software

Borst Passive Solar Heat Gain Software

Borst Passive Solar Thermal Mass Performance Software

WE used Google sketchup (free) and designed the building in 3D. It has a shadow feature that when used will tell you exactly what the sun/shadows look like any hour of any day.

We found it to be spot on. The shade lines proved to be exactly as sketchup predicted.