Derekm, you definitely have some interesting ideas. I can’t disagree with your physics. I also agree that your approach is probably more thermally efficient than mine. I view my foam hives as a work in progress. They’re not perfect. I go through the typical development process with these things. Design based on what I know, build units, hive some bees and monitor the results. Make changes based on what worked and didn’t work and repeat the process. I try not to have too many iterations of the development process, but when dealing with bees, unexpected problems can arise.
We have weeks and weeks of temperatures that never get above 0C for highs here mid winter. A cold spell would be lows down to about -30C. The great lakes moderate our winter lows by keeping a lot of cloud cover (insulation) over head most of the winter.
My goal last winter was to keep my bees warm enough so they didn’t’ have to cluster (60 to 70F; 15C to 21C). My reasoning was, if they don’t have to cluster, they can’t starve to death in the middle of winter from being frozen in one spot in the hive. After a development cycle of such a design, I discovered an un-expected problem in my bee yard. The bees loved the warm temps, but so did the wax moths.
This year, I’m relaxing my thermal goals a little. My goal this winter is more modest, I just want to keep them from experiencing the full brunt of a Michigan winter. My current design goal is to not overheat them. If I loose some thermal efficiency due to the chimney effect; that’s acceptable to me. I won’t really know for sure how wise, or un-wise, this strategy is until spring.
BTW, last year I used a top only entrance/vent. There were NO bottom holes. I was more concerned about the heat loss due to the chimney effect last winter.