Landscaping Math Question

12 years ago

Hi all,

The west side of my house and backyard(south) are more or less a blank canvas right now.

Prioritizing what I'd like to have done first, I think getting a couple of shade trees that would block direct sunlight on my west-side windows (or south) would be a good idea. This would help keep things a little cooler in my living room and kitchen during the summer.

My problem is, how does one figure out tree placement based on the following variables: 1) angle of sun in the sky during a particular time of year (i.e. height of summer) 2)how that angle affects the casting of the shadow that would block the sunlight 3)the height and width of the tree versus my windows and how the shadow will cast based on that 4) the distance and 'angle' of the tree in relation to the window

Is there (hopefully) some sort of easy do-it-yourself equation that can be used to figure out the best placement of a tree for shade purposes? (ps. I did not major in Math, but I can follow directions!)

I've heard there are some nifty software programs that might be able to similate this type of thing, but I am on a budget so not sure the less expensive programs would have what I want. If someone could recommend one that's user-friendly and cheap that would also be appreciated.

Comments (7)

quotetheraven
12 years ago
Hi, didn't major in math either, lol..but the summer sun is the killer, so on the south and west I lined up decidious trees, warm sun can come thru in the winter and blocks the deadly rays in the summer..it's nice to never have to turn on heat in the winter, since what I pay aps in the summer is enough for the whole year!! passive solar I think they call it...don't know if this helps..we just lined those trees up..lol..steph
waterbug_guy
12 years ago
1. There are free online calculators to find the sun angle for a given location and time of year.

2. Use the Pythagorean Theorem.

3. Width of the tree will be the width of the shade. Well, within a millionth of an inch.

4. The angle of the tree should be 90 degrees. Measuring from the house to the trunk would be a good estimate of the distance of the tree's crown since it should be directly above the trunk.

So using the letters from the free online calculator

A = 77 degrees. That's the altitude angle of the sun for Phoenix on June 1 at 12 noon.

a = height of tree minus the height of whatever you wanted shaded. So say a 40' (50' - 10' wall).

Hit "Calculate" and you get b, the distance to plant the tree from the house, 9.23 feet.

I'm not sure what you're asking in #3, but the azimuth angle will tell you how the shadow moves throughout the day. You use the right triangle calculator again, but this time a = distance of tree to house.
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xica_da_silva
Original Author
12 years ago
You are awesome, waterbug guy! Thanks so much!!! Can't wait to play with the online tool.

Quotetheraven, thanks as well, because if I can't handle the math as waterbug guy has suggested here, then lining up a row of shrubs/trees might be the Plan B! :)
xoxos
12 years ago
things to consider - the angle of the sun of course changes throughout the year. in my opinion, you want southern exposure to your house.

in winter in arizona, the sun is low on the southern horizon. you want it to pass through your windows and into your house.

in the summer, the sun not only passes overhead but is actually slightly to the north in the middle of summer.

if i were putting a shade tree to the west/south, i'd put it as northerly as possible, so that it wouldn't block the sun in the afternoon in the winter, but would in the summer.

here's the ceramics apse at arcosanti, nicely illustrating this -

http://www.arcosanti.org/project/activities/ceramics/main.html

the mouth of the apse faces south, providing shade in the summer and passive solar heating in the winter :)
waterbug_guy
12 years ago
Slightly to the north in the middle of summer??? Are you in AZ? We'd have to be less than 23.5 latitude for that and all of AZ is north of 30 degrees.
xoxos
12 years ago
:) every place i've lived with a north facing wall has had the shade creep past the eaves in midsummer, eg. ~2' eaves and plants at the bottom of the wall get toasted.
waterbug_guy
12 years ago
I would check for wormholes, they can bend light. ;)

Beyond that the wall couldn't have being facing true north. We are pretty close, just 20 degrees or so short of the sun being directly overhead. So it wouldn't take much out of true north to have sun hit it.