My Chicago Garden

[warning...math makes my brain bleed so I take no responsibility if the information below is completely wrong or calculates the shadows in effect on the moon instead of my house. Use at your own risk]

So I got to thinking of how to use the southern side of my house for growing plants.  I had thought about putting a couple rows of corn down that side or maybe a greenhouse.  But the 6 foot privacy fence on the property line casts a shadow, but I don’t know how far. I need to know how far to know if I can grow sun loving plants there.

Using a SunAngle calculator I was able to figure out that on the winter solstice the sun will be at it’s lowest angle at the highest point in the sky which is 24.67 degrees at high noon. (roughly)

So knowing the fence creates a right angle with the ground we can use geometry to figure out the distance of the noon shadow on December 21st.

a = 6 feet  high fence
A = 24.67 degrees
b = ?

The math:
Since we only know one side and one angle we can use a tangent to calculate the distance the shadow will cast.
a/tan(A*(2*PI/360)) = 6/tan(24.67*(2*3.1415/360)) = 13.06 foot shadow

Of course it took me 30 minutes of googling to get the math for this or I could have just used this calculator:
http://www.analyzemath.com/Geometry_calculators/right_triangle_calculator.html

Well stink! I don’t have 13 feet.  I only have 12 feet from fence to house. So I actually I have even less then that if I want to plant something sun loving (or a greenhouse perhaps?).  I’ll need at least 3 feet probably 4 feet of distance for planting. Which means now I need to calculate two things:

1. If I install a greenhouse, how high up the exterior wall of the greenhouse will the shadow cast at the lowest point of sun in winter
2. How many days of shade the floor area will be in during the lowest  angle of the sun in the winter.

Answers to both questions will help me determine if I can get optimal growing value for this location.

To answer #1 we need to calculate the height of ‘a’ when b is 4 feet and A is 24.67 degrees. It turns out a = 1.8 feet.   So if I install a greenhouse that is 4 feet wide, the bottom 2 feet of the structure will be in shade at noon on December 21st.  That’s actually not too bad.

To answer #2 we need to calculate what angle ‘A’ needs to be to cast an 8 foot shadow (12 feet of space - 4 feet of planting = 8 foot shadow). It turns out that 36.85 is the angle that will cast only 8 feet of shadow on a 6 foot fence.  So now I go back to the SunAngle calculator and find out how many days are below the 36.85 angle.  It calculates that from roughly Oct 28th to Feb 17th I would be fighting with shade.  Which is deep within the first frost and last frost danger times in our area!!!  So the area is perfectly fine for open air planting and even better for a greenhouse where plants can be raised up on platforms as needed.

Whoo hoo!! So I think 4 rows of corn will be going in next year and hopefully a greenhouse after that!

note: My calculations above assume perfect conditions of course. Also, calculating only a single point in time (eg: noon) only looks at the suns location at a single point in time. Plants need more than a split second of sun light to grow.  To be detailed about this I would have needed to calculate the shadow for every hour from sunrise to sunset to make sure I would get at least 6-8 hours of sun per day. But who has that kind of time!  We’re talking a about a hobby garden for crying out loud!  I probably shouldn’t even have done this much work.