A geometry lesson

During the conservation commission meeting on Wednesday, October 3, there was a discussion and vote on an order of conditions for a cantilvered deck. This particular deck was denied by the commission a year ago because it would shade a coastal bank, potentially affecting the growth of the plants that grow on and stabilize that bank. That would have been a reasonable argument, except that basic geometry disproves it.

Let's examine this in more detail.

The latitude of Falmouth is about 41.6 degrees north. The summer solstice - June 21 - is both the longest day of the year and the day when the sun is at its highest point above the horizon because of the Earth's tilt of 23.5 degrees to the ecliptic. If a cantilevered deck is going to shade anything, it will be at noon on this day because the sun will be lower in the sky at all other times of the day and year.

The deck in question will be 9 feet above the ground and extend 4 feet from the building. On June 21, the sun is about 65.1 degrees above the horizon (41.6 degrees + 23.5 degrees). Knowing this, we can determine how far the deck can extend before shading the ground below:

a = 24.9
y = 9

tan(a) = x/y

tan(a) * y = x

tan(24.9) * 9 = 4.176

So a 4-foot deck will never shade the ground below.

I know what you're thinking: What about taller plants? Anything more than a few inches above the ground will be shaded.

True. However, there's a path around the building for maintenance access. This keeps the plants away from the building, allowing them to get full sun higher from the ground.

So...

a = 24.9
x = 2

tan(a) = x/y

x/tan(a) = y

2/tan(24.9) = 4.3

9 - 4.3 = 4.7

...any vegetation growing two feet from the building can grow to a height of more than 4-1/2 feet before getting shaded (at noon on June 21). Moreover, plants grow out as well as up, so anything growing under the deck will get nearly full sun all year round. The original argument about shading affecting the growth of the plants was false and the homeowner should have been allowed to build the deck.

However, our story is not over. This information is one year old.

This time, the homeowner came back with an offer to use decking that would allow 68 percent of the light to penetrate. In other words, there will be almost no shaded area under the deck at any time.

Yet this still wasn't enough to convince several of the commissioners who argued and voted against the deck. Were it not for the chair - who voted to break a 3-3 tie and approve the deck - this hapless homeowner would have been out of luck yet again.

And all for want of a bit of geometry.

P.S. - It's worth noting that one of the commissioners who argued and voted against the deck has a Ph.D. in the biological sciences. So much for education.