Tag Archives: engineering

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.

https://discoveringancienthistory.wordpress.com/2017/01/01/engineering-an-empire-roman-units-of-measurement-part-1-of-3/
http://www.leonardo-da-vinci-models.com/odometer.html
https://www.ancient.eu/Roman_Engineering/


http://www.archimedespalimpsest.org/about/history/archimedes.php

Back to the beginning of The Western Civ User’s Guide to Time & Space

How to build a better water clock

Ctesibius of Alexandria. Believe it or not, this guy’s dad was a barber.

If you’ve been following this blog, you’ll remember that a couple of posts ago I ranted about how Egyptian water-clocks seemed impractical and I didn’t see how they could even function as clocks at all.

Well, apparently back around 270 bc, an inventor named Ctesibius (Teh-SEE-bee-us) of Alexandria thought the same thing. He identified two problems:

One) The water-clock wasn’t a clock, but rather a timer. It only worked while there was water in it.

Two) The water came out of the bung-hole at the bottom at different rates of speed: quickly when the jar was full, slowly as it grew empty. That’s because the weight of the water on top pushed down on the water that was escaping—less water, less pressure, slower dripping of water. That made it unreliable for keeping time.

So how did Ctesibius fix these problems? Well, he figured in order to keep constant pressure on the hole at the bottom, the water clock should always be full. So he set up a second jar of water to keep the first one filled. The second jar had a hole at the bottom that leaked water into the first jar.

THEN, a third, empty jar was placed under the first jar. Instead of telling the time by how much water had leaked out, this empty jar told time by how much water had leaked into it.

Ctesibius even made a float to put into the empty jar. As the water level rose, an arrow—attached to the float—pointed to the hour.

A tip of the hat to Heidi K. for sending me a link to this video!