Tag Archives: home school

The liquid crystal display explained!

Three inventions moved clocks and watches away from being mechanical/analogue so they could become digital: The quartz crystal, the circuit board and the liquid crystal display.

Okay, I sort of explained how a battery works. I kind of explained how a quartz crystal works. The circuit board was easy—even a shmo like me can explain printed metallic ink on a plastic card. But—liquid crystal display? I started this post about 17 times and kept getting lost in the weeds with carrot juice and double melting points and twisted nematics and polarization…

Let’s start here: analogue clocks and watches were inaccurate because they have physical, mechanical moving parts. So we replaced the wound-up mainspring with a battery. We replaced the balance wheel with a vibrating quartz crystal. Now we need to replace the moving mechanical gears, hour-hand and minute-hand with a digital (just the numbers) display of the correct time. How do we do that?

A digital wristwatch made by the Japanese company Casio.

Instead of mechanical gears and hands, we’re going to use electricity and light.

We want a watch-face that will light up and show us what time it is. We want most of the face to light up except the numbers, which should be black so we can read ‘em easily. We’ll block the light in the shape of each number so it shows up black. The numbers will change every minute, so we need a way to change the blocked areas every minute.

In order to block the light, we need a filter. The filter lets us control which rays of light pass through and which rays get blocked. A filter could be a wall of liquid filled with crystals that all face the same direction. The lined-up crystals let the light pass through. We’ll sandwich this wall between 2 plates of glass. The crystals still let light pass through—until we zap them with a little electricity. The electricity upsets the crystals so they don’t line up anymore and light can’t pass through.

We’re only going to zap in certain areas. We want those certain areas to be shaped like numbers. For instance, when we zap the glass in the shape of a ‘3,’ those crystals in the 3-shape get upset and don’t line up with the rest of the crystals in the wall. Light can’t pass through the 3-shape, so we see a black ‘3’ on a lighted watch-face.

Just like on a circuit board, we’ll print the numbers onto the glass in ink. This ink is transparent—and it conducts electricity. Each number is designed as a 7-segment figure, so we can zap only the segments that form a ‘3,’ or whichever number we want. Each segment is wired to the battery.

This is the principle behind LCDs. It’s a simplification. I left out a lot of stuff. But you get the idea, right?


Many thanks to a couple of the Western Civ Irregulars, Diana (Ms Physics) and engineering-wiz Don M—both pals of mine since childhood. They pointed me in the right direction when I couldn’t find a way to explain this one.

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Eratosthanes and longitude

Old-time tv newsrooms had clocks on the wall set to local times of the big cities.

How did Eratosthanes or Ptolemy determine where the longitude lines should go? I got this from the History Stack Exchange site:

Longitude is calculated by comparing the elevation of an astronomical object to the pre-calculated (or observed) elevation of the same object at a reference location at the precisely simultaneous moment in time. Everything in the sky rotates once around that vast celestial sphere every 24 hours, so the more precisely one can establish simultaneity the more precise one’s measurement of longitude will be.

Whew! In other words: 2 people standing in 2 different places can measure the height in the sky of the moon, or the Sun, or the North Star to figure out how far east or west they are from each other. BUT—the measurement must be taken at exactly the same moment. Eratosthanes figured a way to find longitude without the measuring. Eratosthanes (in Alexandria) and an assistant (in someplace to the west—maybe Benghazi?) watched a lunar eclipse. They agreed to mark the exact local time the eclipse began. The local times won’t be the same, right? When it’s midnight in Benghazi, it will be 12:36 am in Alexandria. The difference in their times told Eratosthanes how many degrees apart from each other they were.

I’ll tell you how in the next post.

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Like a pendulum do

One time while sitting in church, Galileo noticed a lamp suspended from the ceiling that was swinging back and forth. That motion is known as a pendulum. As it swung, he observed the lamp kept the same rate of speed. It occurred to Galileo that you could use a pendulum’s regular rate of speed to regulate a clock.

We learned that in Galileo’s time a clock was powered by a weight that slowly released its energy as it was pulled to Earth by gravity. The mechanism that slowed down—regulated—the weight’s energy is called an escapement. Galileo thought to replace the verge and foliot escapement with a pendulum escapement.

Just like the verge and foliot, as the pendulum swings back and forth it allows a gear to move forward a little bit just before a pawl stops it—until the pendulum swings to the other side. The pendulum escapement releases-stops-releases-stops the gears as they move the hands of the clock. Here is an excellent animation of Galileo’s escapement. Notice how when the gear turns it gives the pendulum a teensy little push.


Watch this guy make a wooden pendulum clock: https://www.youtube.com/watch?v=rvU37Aho4FA

Here’s some terrible music:

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Fixing Julius Caesar’s calendar

A couple of posts ago, we saw that by the late 1500s the Julian calendar was seriously off. How to fix it?

A doctor, Aloysius Lilius, thought there were too many leap years. The Julian calendar adds a day—February 29th—every 4 years, no exceptions. What if on some leap years we didn’t add the extra day? His idea was that any leap year that ends in 00—unless it can be divided by 400—gets no extra day.
That would solve the problem! Pope Gregory XIII liked the idea so much he made it official on February 24, 1582. Later that year, ten days disappeared! October 4th was followed by October 15th in order to reset the calendar. The new calendar is called the Gregorian calendar. We still use it today.

The last year that ended in 00 was 2000. Because it can be divided by 400, it was a leap year with February 29 added. The next one will be 2100—it will be a common year with no extra day. I’ve been cutting out the fatty snacks so maybe I’ll live to see that happen.

Here’s the inside-baseball, blow-by-blow account of how the new calendar was adopted by Pope Gregory: http://www.newadvent.org/cathen/09247c.htm


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Have a blessed Good Friday!

Julius Caesar’s calendar was getting out of whack.

Over the centuries, the first day of Spring—the vernal equinox—was happening earlier and earlier. By 1582 it was 10 days too early, on March 11th. It needs to occur every year on March 21st. An equinox is a day that has the exact same hours of both day and night. You’ve probably noticed we have lots more day in the Summer and lots more night in the Winter. The equinox occurs twice a year, in the Spring (vernal) and Fall (autumnal).

The problem was that the Julian year runs 11 minutes longer than the Earth’s trip around the Sun. After 15 centuries that adds up.

What to do?

How to slow down a clock

How did they do it?

Those medieval clock-designers came up with a system to slow down the unwinding. First, they attached a gear around the drive-shaft that meshed with a couple of other gears. As you saw with Archimedes’ odometer, the ratio of gear sizes and number of teeth-per-gear can control how fast one gear turns another gear.

That still wasn’t slow enough, though. You want a clock to operate for at least 24 hours before you have to wind it again. How can you make that unwinding even slower?

The answer: an invention called an escapement. An escapement is a mechanical device that interferes with the gear. It actually stops the gear’s movement for a second, then lets go for a second, stops it, lets go, stops it, lets go, stops it, lets go. The first escapement was called the verge and foliot. The verge is a second shaft (not the drive-shaft) with two paddles, or pallets, set at 90 degrees to each other. These pallets interact with a saw-toothed gear which is powered by the drive shaft. As the drive-shaft turns the saw-toothed gear, one pallet stops the gear for a moment until the other pallet is pushed aside.

This stop-and-let-go motion is controlled even further by a bar at the top of the verge shaft, called the foliot. The foliot has a weight hung on each end so that inertia (the weights’ unwillingness to move) slows down oscillation of the verge-shaft. You can control how fast the foliot swings back and forth by moving the weights closer or farther from the center.




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Archimedes and his odometer

Archimedes was a Greek mathematician who specialized in measuring space. He was certain that there must be a way to accurately measure how much space is in a circle—area—or how much space is in a sphere or a cylinder—volume (he figured out how to measure volume when he noticed that a certain amount of water spilled out when he got into a bath tub). Archimedes was influenced by other great mathematicians, like Pythagorus and Euclid.

Archimedes invented many wonderful machines, like a screw for drawing up water, or catapults that were used to fight off invading navies. Although we don’t have his plans for it, Archimedes is said to have invented a way to measure distance. This machine is called an odometer.

Archimedes’ odometer operated on the idea that every time a wheel goes around, it travels its own circumference. The odometer adds up those circumferences and marks when the wheel has traveled a mile. In our last post, we showed how a standard Roman chariot wheel goes around 42 times to travel a mile.

We know about Archimedes’ odometer because the Roman military engineer Marcus Vitruvius Pollio (80–70 bc – 15 bc), or Vitruvius for short, wrote about it in his 10-volume book De Architectura. Engineers build stuff. As the Roman Empire expanded, the army took along a corps of engineers to build fortifications; siege engines; bridges; tunnels; aqueducts to provide water; and roads. These engineers did such a good job that you can still find Roman bridges, aqueducts and roads today.

Emperor Caesar Augustus wanted to know exactly how big the empire was and decreed that mile markers should be put up along the newly-built roads. Vitruvius decided to build Archimedes’ odometer to accurately measure the miles.

We only know what Vitruvius’ odometer looked like from a fanciful drawing. We don’t know exactly how it worked. Some people, including Leonardo da Vinci, have come up with some pretty good guesses about how it worked. You can see Leonardo’s drawings here—plus, you can even download plans if you’d like to build one yourself! Now that’s cool.

We do know that every time the chariot wheel goes completely around, it moves other gears. The other gears are set up to mark a mile at the 42nd revolution of the chariot wheel. The trick is gear ratio—meaning some gears are bigger, some gears have more teeth. If the gear on the drive shaft has only one tooth and the gear holding the marbles has 42, the marble-gear moves 1/42 of a revolution every time the chariot wheel goes completely around. At the 42nd revolution, a hole with a marble lines up with a hole underneath the gear and the marble drops into a bucket. Each dropped marble represents one mile traveled.



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