Nate Holt's Blog

July 5, 2009

Sun rarely sets on AutoCAD Electrical development

Filed under: Musings — nateholt @ 8:51 am

(note: this was originally posted on the old blog site, April 2006)

If it does manage to set, it pops back up again pretty quickly. Conference calls and web-based meetings with development team members spread out across the globe have become an almost daily (and often nightly) occurrence. We have to keep track of time differences, what day it is, and when to greet with “Good (morning/afternoon/evening/all of the above)” from here in Novi, Michigan versus other development locations like Singapore which nearly straddle the earth’s equator on the opposite side of the globe.

We’ve now have had a couple flips between Daylight Savings Time and back again. Just this last weekend was the less-desirable flip… we (in the US) lost an hour of sleep Saturday night.

The previous time this happened, I asked my Singapore counterparts if this Daylight Savings Time concept made any sense on that side of the world. It didn’t really… with Singapore located on the equator, DST seemed to be an unknown like windshield ice scrapers, antifreeze, long johns, and chewing gum.

Question: Why? Are days and nights on the earth’s equator always the same length? Does the sun rise and sun set at the same time, every day, year round on the equator? Hmm… visualizing the spinning globe with an appropriately placed flashlight, it seems that the equator would always be illuminated for exactly half a rotation, no matter how the globe was tilted to mimic the four seasons. Better check this out for sure.

Answer: Sure enough. On the equator, day lengths are consist year-round. Sun rise and sun set tables for both Singapore and Novi for 2006 (http://aa.usno.navy.mil/data/docs/RS_OneYear.html) show the huge difference and why DST makes sense only for cities significantly removed from the equator. Here’s the data for the first day of each season:

Singapore (year 2006)
Date Sunrise Sunset Daylength
Mar 21 0604 1811 = 12:07
Jun 21 0558 1805 = 12:07
Sep 21 0550 1756 = 12:06
Dec 21 0554 1802 = 12:08

Novi, Michigan (year 2006)
Date Sunrise Sunset Daylength
Mar 21 0636 1847 = 12:11
Jun 21 0457 2015 = 15:18
Sep 21 0620 1833 = 12:13
Dec 21 0800 1704 = 9:04

Wow! Novi – 6 hour swing in day length throughout the year, Singapore, 2 minute swing.

But the Singapore day length number column uncovers a new mystery. How can the average day length throughout the year 2006 always be seven minutes greater than 12 hours. Shouldn’t it average out to exactly 12 hours of day and 12 hours of night? Hmm… better do some more thinking about this.

Clue – the table data definition for sunrise is the top of the disk just peeking above the horizon. That’s fine. But the definition for sunset is the top of the disk just disappearing below the horizon. Hmm… night-time is getting cheated out of one width of the sun’s disk. To be fair, sunset should be the bottom of the disk just touching the horizon. So, does this injustice account for the mystery 7 minutes in Singapore? Let’s figure it out. The sun is about 0.8 million miles across and is 93 million miles away. Enter this AutoLisp expression: (* (/ 180.0 pi) (atan (/ 0.8 93.0))) [Enter]*. This works out to the sun’s apparent disk width being one half degree of arc. This is about the same width as holding a quarter (US $0.25 coin) about 10 feet away from your eye (if you try this, use the moon, it’s safer – the moon is the same apparent size as the sun – convenient for total solar eclipses).

So, how long does the sun take to fully set in Singapore, from the time a 1/2 degree width disk touches the horizon until the time the last bit disappears. Let’s figure it out. 24 hours to go through 360 degrees works out to about two minutes to rotate through the 1/2 degree needed to hide the setting sun. Hmm… still have 5 minutes to account for.

Clue #2 – Okay, between sunrise in Singapore and sunset about 12 hours later, the earth has moved along its orbit, gently turning a corner toward the sun. The earth’s rotation direction is the same direction as its rotation around the sun (I think), counter-clockwise if viewed looking down from above the North pole. So, after 12 hours, wouldn’t the earth have to rotate just a tiny bit more to make up for this gradual 12 hour turn? If so, let’s figure it out. 365 days to go through 360 degrees, so about one degree per full day/night or a half degree during a 12 hour Singapore day. Another two minutes accounted for: now four of the mystery 7 minutes.

Clue #3 – Three mystery minutes of excessive daytime remain. The only thing I can think of at this point is that the earth’s atmosphere might bend the light a bit when viewing along the horizon. It would have to make the very top of the sun’s disk still visible (stretching it) even when the sun had actually fully sunk below the horizon at sunset (and the top of the sun appear a bit prematurely at sunrise). Anybody?

* Needed to get something AutoCAD-related into this posting!

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