# Thread: Annual day-night swings by latitude

1. ## Annual day-night swings by latitude

Are there any maps or charts showing how wide these swings are for different latitude ranges? (For example, at one latitude it gets as drastic as 15+9, at another latitude it gets as drastic as 18+6, at another it gets as drastic as 20+4...)

I'm sure there's also a mathematical formula for it, but, having never studied 3-dimensional geometry or used & maintained the calculus I did study years ago, I can easily see that formula getting out-of-control for me...

2. Daylight hours per day, by day, by latitude, charts? That's a large, 3-dimensional set of data.

US Naval Observatory: Duration of Daylight/Darkness Table for One Year

With multiple requests, you could build a set of tables, for 90 North, to 90 South, by steps of, say, 5 degrees. Each page would give you a two-dimensional table of daylight hours for each day of the year.

Then reduce it all to the two-dimensional maximums-vs-latitude you are really after.

3. Established Member
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Feb 2009
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Sunrise and sunset times, from
https://en.wikipedia.org/wiki/Solar_zenith_angle
must satisfy equation

cos ⁡ h0 = − tan ⁡ Φ tan ⁡ δ
where
h0 is hour angle
δ is the current declination of the Sun
Φ is the local latitude.
Last edited by chornedsnorkack; 2017-Apr-14 at 06:55 AM.

4. Originally Posted by Delvo
Are there any maps or charts showing how wide these swings are for different latitude ranges? (For example, at one latitude it gets as drastic as 15+9, at another latitude it gets as drastic as 18+6, at another it gets as drastic as 20+4...)

I'm sure there's also a mathematical formula for it, but, having never studied 3-dimensional geometry or used & maintained the calculus I did study years ago, I can easily see that formula getting out-of-control for me...
Here you go (click on the thumbnail to see the graph properly):

daylight.jpg

If you ignore refraction and the ellipticity of the Earth's orbit, it's a fairly simple trigonometrical ratio to calculate the maximum length of daylight, in hours, for a given latitude. It of course plateaus at 24 hours when you get to the polar circles.

For latitudes less than the polar circles, divide tan(latitude) by tan(latitude of the polar circle). Take the arccos of that. Divide by 180 degrees or pi radians, according to taste. The result is the smallest fraction of the day occupied by night (summer) or day (winter).

The derivation is left as an exercise for the interested student.

Grant Hutchison

5. I didn't really expect the thread to just die at that point. Oh well.

Grant Hutchison

6. It's a useful topic. Sunrise sunset tables are easily available. That analemma keeps things from being simple.

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