Well, I asked this in my “what will the angle of the sun” thread, but it had 1) fallen off the front page, and 2) was really another question. So I’ll ask again, hoping dearly that Mrs. Murphy is not a Doper.
I need to put my raised beds on the north side of my house where the house will not shade them. I need to know where the shade will (or won’t) be starting, say, April 1. If the angle of the sun is 34 degrees now and will be around 60 in April, and the eaves of the house are 13 feet up, and the length of the shadow now is 14 feet, how long will the shadow be when the angle is at 60?
All those stupid flagpole problems in high school, and now that I need it I can’t remember! I think it uses the sine of the angle, right? Help!
The noontime azimuth of the Sun in Charleston, SC is currently 45 degrees. On April 1 it will be 62 degrees.
The tangent of this angle, or “Opposite/Adjacent”, equals the ratio of the height of the wall (13 feet) to the length of the shadow.
The tangent of 45 degrees, of course, is 1, so your shadow should currently be 13 feet long at high noon. The tangent of 62 degrees is 1.88, so at high noon on April 1 the shadow will be 13/1.88, or about 7 feet long.
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
So, what do we have here?
The height of the eaves is the opposite side from the angle we are looking at. The length of the shadow, assuming the ground is flat, is the side adjacent to the angle we are looking at. The hypotenuse would be a line going from the edge of the eaves to the end of the shadow, which we don’t really care much about. Since we have the angle and the length of the opposite side, we can use tan to figure out the length of the adjacent side.
If the angle is 34 deg, then we know tan(34)=13/x where x is the length of the shadow. According to this, the shadow should be about 19 feet right now, which doesn’t quite match what you measured. Either the angle is off, or the measurements aren’t quite right, or the ground isn’t flat.
If the angle is 60 deg, tan(60)=13/x, and x = approx 7 1/2 feet.
Well, 34 is the angle somebody else found for me in my first thread. Also, of course the ground isn’t flat. I’m in Columbia, if that would make a significant difference from Charleston.
So, however, roughly, since my nearest bed is six feet long, and right now the sun just barely touches its far end, it should be okay in April. Right? Theoretically? I was planning on putting the earliest crops in where there’s already plenty of sun, I just want to be sure that when it comes time to plant tomatoes and cucumbers that I’ll be sunny.
I just don’t want to have to move anything once I get the dirt in!
Columbia is about a degree north of Charleston–and I should have said altitude, not azimuth! :smack: Here are the relevant figures for April 1 for Columbia, SC:
Astronomical Applications Dept.
U.S. Naval Observatory
Washington, DC 20392-5420
COLUMBIA, South Carolina
Altitude and Azimuth of the Sun
Apr 1, 2006
Eastern Standard Time