Chicagoist: Ask Chicagoist: How Do the Hours of Sunlight in a Day Change?

lwitucki

Mon, 13 Oct 2008 08:17:48 -0600

I'm teaching sinusoidal curves in precalculus this week... First of all, complications caused by nature aside, the curve described is sinusoidal, because its shape is a transformation of the sine curve. Sinusoidal curves do not have to be balanced across the x-axis - a vertical shift (or translation or glide) can eliminate that sine-graph feature completely. This is necessary in many applications of the sine function to real life occurences. In the basic sinusoidal equation, y = A*sin(Bx-C) + D, the D takes care of that shift. Secondly, the curve in question cannot be a parabola, since both tails of a parabolic function either extend downward or upward infinitely. There is a day with the longest sunlight and one with the shortest, so there are no tails extending infinitely upward or downward in the hours of sunlight graph.

artdude75

Fri, 26 Sep 2008 14:22:38 -0600

i kinda like it getting darker earlier. I'm a fan of shooting night photography, and i'll be able to shoot s'more. :-)

bjh2000

Fri, 26 Sep 2008 13:30:26 -0600

The graph shape (which comes from the function) is not more or less a parabola. The up-down graph shape repeats every year - I.E it's really up-down-up-down-up-down... No parabola can do that. To call the graph shape a parabola is like arguing that the earth is flat because from 6 feet up it looks flat.

YoknapatawphaTourismBoard

Thu, 25 Sep 2008 15:32:37 -0600

The graph shape is more or less a parabola, not the function. Sheesh.

tinder

Thu, 25 Sep 2008 15:21:22 -0600

not much for the math at chicagoist it seems... that function is not a parabola or even parabolic. the functional form of daylight length is only sinusoidal if you stay away from the poles, ie it depends greatly on latitude, and is in reality a bit more complicated. that chart taken from the math tutorial is for Nashville. would have been nice to plot it for Chicago so we can see exactly how many hours of darkness we have to look forward to this winter.

YoknapatawphaTourismBoard

Thu, 25 Sep 2008 15:07:52 -0600

That's not a sine wave. A sine wave is symmetrical about the x-axis and has an equal part of its periodicity in the negative. That, sir, is a parabola.