I'd like to plant some shade trees to help keep our place cooler in the summer. We have lot's of SW facing windows. I've tried searching online for specifics, but everything I've found is very basic ("plant trees to the SW of the house"...).
Can anyone suggest a location where I could find specific calculations? How tall of a tree will shade what height of window from which direction at whatever latitude... The math can't be hard, all I need is some formulas or rules of thumb.
When I see an adult on a bicycle, I do not despair for the future of the human race. ~H.G. Wells
Specifically, what time of year? Our hottest month is June. By the first of August, it's monsoon season and the clouds help. I've lived in other places where June is still cool. If you plant a tree to give shade on August 1, you will also have shade on May 15 (unless it;s a really late leafing out tree). Your angle will change a lot because you are so far north, so knowing the targeted times will make a huge diff.
If you have a smart phone, you can download an app for photographers that shows the altitude and angle of sun on any given day/time at your location. We use these apps to plan angles on photoshoots, so there are quite a few. I think TPE, The Photographers' Ephemeris does this, but you may have to search around). Alternately, about where the full moon sets now is where it the sun will set in high summer (don't ask me why). You will likely fine\d, as far north as you are, that putting a tree where the sun is at 3 pm on June 21 is not optimal for 6 weeks later, so you may need more than one, or to make some compromises if space is short. Or even a hedge if it's the late afternoon sun that is the problem.
Likely you will never find anything more specific. The reason is that tree placement has a whole host of other things playing into it. For example what are your goals for the tree? how long are you willing to wait for that to be reached?, are you trying to maintain solar gain for either year round or winter time?(which one too?)(this time of year you are at the ideal time for checking sun path if your goal is to maintain winter solar gain), local wind direction?(this one is both in terms of risk to the house and possible energy gains to the house from maybe blocking the wind, are there views you want to maintain at ground level, what shape is your house? What species tree do you want to plant leads you to other information like What is its mature height in your area and what is its typical shape. Others that might come into consideration are things like under ground line locations, driving paths, cistern or well locations, how it affects your neighbors, future building plans etc.
I will share the thinking that went into planting trees here and the lack of shade trees for the house. I don't have shade trees for this house because the answers to those other questions sort of preclude it. This house is passive solar so nothing that blocks winter sun other than very slightly is acceptable. So that basically eliminates anything south of the house. The house is long and narrow with the long side facing south so I would probably need trees at both ends. to get any coverage of the house. Having grown up around neighbors with mature trees close to their homes I would never plant a big tree closer than about 40 feet to the home for protection from limbs falling or trees being blown over.(ideally if it was a cottonwood I would like to keep it 60 feet from the home) Already my possible summer shade is getting limited. Going east of the house out 40 feet puts you over the intersection of both the household water line and the non potable water line plus south of the house on that corner is an old cistern that still sort of works that we should stay at least the mature height of the tree away from. Also the good mountain views are north-northeast of the home and future expansion plans call for windows facing that way and tree there would put the trunk right in the middle of those views. So an eastern tree isn't looking so good. How about west. Same location west puts it in the middle of the road that accesses the rest of the property and directly over the sewer line and close to the septic tank. Also not a good idea. Plus a tree there would create a snow fence affect that given our prevailing wind direction and would bury the main part of the area in front of the house in a snow drift. So it would be putting a drift on where the cars park and on the road in. There is a strong wind break north of the house but its distance is such the snow should drop before it gets to parking and the road in.
Location: Torrey, UT; 6,840'/2085m; 7.5" precip; 125 frost-free days