How Long Did It Take To Build That?

Over the weekend, we took my son and my 16-year-old (almost 17 years old, now) to visit the Hall of Justice.

All right, all right, I’m kidding.  Slightly. That building up there (which really was the inspiration for the Hall of Justice) is the Cincinnati Museum Center. It’s not quite as impressive as usual, because there’s a whole lot of internal and external renovations going on, but it’s still pretty cool.

“How long did it take to build that?” my niece asked.

“Two years!” my son declared.

“I don’t know,” I confess.

“Maybe forty years,” my niece suggests.

How long did it take?

Well, according to the Museum Center web site, construction started in August 1929 and was completed on March 31, 1933. So, about 3 and 1/2 years.

Well. That was short.

The construction time? Or the article?

Both.

Yeah, well, the building was built in the 20th century. As I pointed out to my niece when she guessed – half tongue-in-cheek – that it took 40 years, the building was originally designed to be a rail hub. They had ways to haul supplies and materials in, and things like cranes and bulldozers and the like. It wasn’t all teams of oxen dragging granite blocks and the like.

Rail hub?

The building that is now the Cincinnati Museum Center started out as Cincinnati Union Terminal. See, as Ohio History Central explains, Cincinnati was linked to “a number of other major cities through its rail lines, but the original system had not been well-coordinated. Trains ran through several different railroad stations around the city. In the early 1900s, railroad companies began developing plans for a single railroad terminal that would provide service for all passenger and freight lines entering the city. It was not until the late 1920s that construction actually began on the project, which became known as Union Terminal.”

The Union Terminal complex, at its height, took up 287 square miles acres and had 94 miles of track – some of which you can still see if you visit today. It was designed to handle a lot of traffic. See the way that the building rises up in a hemisphere in the center? That facade covers a half-dome that, when it was built, was the largest half-dome in the world (and is still the largest in the western hemisphere). The terminal could handle 108 arriving and 108 departing trains a day, and was designed to accommodate as many as 17,000 people (although it hit over 20,000 during World War II, when soldiers passed through on the way to their posts).

Union Terminal operated from 1931 to 1972, when it finally closed for business. The city of Cincinnati purchased the site in 1974. In 1979, the Joseph Skilken Organization converted it into a mall, which opened with 40 tenants on August 4, 1980. The mall failed and closed officially in 1984, although a single store (Loehmann’s) continued in operation there until 1985 and a weekend flea market operated on the site for several years.

In 1986, a Hamilton County bond levy was passed to fund renovation of the site and to convert it into a museum. Four years later, in November 1990, the terminal reopened as the Cincinnati Musuem Center. The next year, it also began serving as Union Terminal once more. Amtrak began thrice-weekly passenger train runs on July 29, 1991.

So, how long did it take?

It depends, ultimately, on what you’re looking at. It took three and a half years to build the original Union Terminal facility. Turning it into a mall took 23 months, and turning it into the Cincinnati Museum Center took four and a half years.

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Are Emeralds Real?

“Dad?” my son said from the back seat of the car. “Are emeralds real?”

Mercifully, there is some context for that question. He’d been over at a friend’s house, and they’d been playing Minecraft. I don’t know much about the game, but apparently “emerald” is one of the construction materials in the game. Which led to the question.

“Yes,” I tell him. “They are.”

“Wow!” he says.

You knew this one, didn’t you?

Yes. Yes I did. But let’s have some fun with it anyway, because I don’t know as much about them as I’d like.

What is an emerald?

Every source I found (which includes mindat.org, minerals.net, and Wikipedia agree that emerald is a variety of beryl. Chemically it’s beryllium aluminum silicate (Be3Al2Si6O18), with a green color that derives from trace amounts of chromium (the mineral that gives us chrome) and (occasionally) vanadium (a silvery grey mineral). Both minerals oxidize in a variety of colors, which explains how a silvery mineral can turn the mineral green. It naturally forms into hexagonal crystals.

The full market value of an emerald is based on four factors: color, clarity, cut, and carat weight.

  • Color: To be an emerald, the mineral must have a medium to dark green color (light green stones are classified as “Green Beryl“, which is not considered as valuable), as measured on a scale from 0% (colorless) to 100% (opaque and black) – the finest emeralds rank about 75% on this scale.
  • Clarity: All crystals will have some level of flaws, mostly consisting of inclusions (other minerals trapped in the crystal) and cracks. Flawlessly emeralds are stones with no inclusions or fissures visible to the naked eye.
  • Cut: This is not a natural property of the stone, but the way it was cut after it was mined. Raw stones are less valuable for the same reason that a tree trunk sells for less per pound than a table of the same wood, but a bad cut can destroy the stone.
  • Carat weight. A carat is 0.2 grams (or 0.007055 oz). The value of stones of th same quality does not change in a linear fashion, because larger high-quality stones are rarer than smaller ones. Consulting Singhal Gems International, a good quality 1.0 carat emerald can range from $500 to $1,125, while a good quality 5.0 carat emerald can range from $7,500 to $15,000 in value.

Where are they found?

The largest emerald deposits can be found in Colombia, Brazil, and Zambia. They are mined elsewhere in the world, but those three nations produce most of them. Colombian emeralds are often considered to be the overall finest form of emerald, as they are primarily colored by chromium. Zambian and Brazilian emeralds are more frequently colored by vanadium, with Brazilian emeralds being darker and more heavily included and Zambian emeralds having a bluish-green or grayish-green color.

What is the biggest emerald ever found?

That’s… tricky. What, exactly, do you mean by that question?

The International Gem Society website breaks them down into three categories: named emeralds, unnamed emeralds, and “other large emeralds”. They state that the largest named emerald is the “Emerald Unguentarium”, a 2,860 carat emerald vase currently on display in the Imperial Treasury in Vienna.

The Daily Mail disagrees with this statement, as they report on a watermelon-sized emerald named Teodora, which came in at 57,500 carats. It should be noted, however, that gem experts were skeptical of this claim, and that the owner was arrested on multiple fraud charges. A gem expert who studied it found evidence that it was lower-quality emerald (possibly mixed with white beryl) that had been dyed to make it appear more valuable. Because of this, when it went up for auction, no bids were made.

The largest unnamed emerald is an uncut Colombian crystal in a private collection that weighs 7,052 carats.

“Other large emeralds” is dominated by the Bahia Emerald, which was an 840 pound stone from Bahia, Brazil. The stone “reportedly contains over 180,000 carats of emeralds”, one of which is a single stone that is apparently described as the size of a man’s thigh. There is an ongoing legal battle over ownership of this stone, which shouldn’t surprise anyone since it’s been valued at upwards of $400 million. This stone, unlike Teodora, appears to be genuine.

Genuine, and large.

How Long Would It Take To Get To The Moon?

“Dad?” my son asked while we were playing with his Legos. “How long would it take to get to the moon?”

“I think that depends on how fast you’re going,” I replied.

“No,” he says, sounding exasperated as only a 6-year-old can, “I mean, if you were going as fast as the Death Star!” Because that was entirely clear from the context, right?

“I don’t know,” I tell him. “I don’t know how fast the Death Star is.”

“It’s really fast,” he assures me.

Where to start?

There are a couple of things we need to know here, in order to answer the question. How far away is the moon? How fast do we have to go at minimum to make it? Oh, and how fast is the Death Star? So, let’s dig in.

How far is it to the moon?

The distance from the Earth to the Moon varies based on the time of the month, because the Moon orbits us in an ellipse – so it gets closer and then moves further away. At apogee (the farthest it gets from us), it’s 405,400 km away, while it gets as close as 362,600 km at perigee. So, clearly, how long it takes will really depend on how fast we’re going – just like any other trip we can take.

How fast do we need to go?

How fast you need to go to get to the moon will depend on the method you’re using to get there, and the amount of time you want to take. So, let’s start with the concept of escape velocity. This is the minimum speed required to “out-pull” gravity and leave an object behind. If you launch at that speed or greater, you fly away. If you don’t, you fall back to the surface. Eventually. Escape velocity varies with the gravity of the object and is approximately 11.2 km/s, or 40,320 kph on Earth. Assuming there is no friction, which is a popular physics assumption to keep equations simple. If you launch at that speed, you fly away from the earth – you slow down over time, as Earth’s gravity pulls on you, but you never actually stop moving. Ever.

There’s a down side to trying to get to the moon by launching at escape velocity (say, by using a variant of Project HARP’s big gun): Earth’s force of gravity is 9.807 m/s2, so you’re pulling around 1,142 gravities at the instant of launch. You would be a thin, wide smear on your pilot’s chair well before you reached the moon.

Clearly, we didn’t send a gelatinized melange of Neil Armstrong, Michael Collins and Edwin Aldrin to the moon on Apollo 11 – those three men made it to the moon and back with bones and organs intact, after all. So, how did they do it? Well, the important thing to remember is that escape velocity is only needed if you have an initial push and then add no additional thrust after that. This isn’t how the Saturn V – or any other rocket for that matter – works. They lift themselves at a slower pace, but apply a constant (or near-constant) thrust by carrying fuel. There’s a point of diminishing returns on this, because you have to lift your fuel as well as the ship (something described in the Tsiolkosky rocket equation, which I discussed when I tried to describe how to make a house fly).

The Saturn V was a multi-stage rocket, with the first stage burning for 2 minutes 41 seconds and pushing the rocket about 68 km into the air (hitting a velocity of 2,756 meters per second). Then it ditched the first stage and started the second stage burn. This pushed it another 107 km (for a total of 175 km) into the air over the course of 6 minutes, reaching a velocity of 6,995 meters per second). Stage 3 burned for about 2 minutes 30 seconds, reaching a velocity of 7,793 meters per second and putting it in orbit at an altitude of 191.1 km. Stage 4 burned for six minutes, pushing the ship to a velocity of 10,800 meters per second once it was time to head for the moon.

So, how long would it take?

How fast are you going?

Let’s say you just boosted off Earth with a canon, firing you straight up at escape velocity. Let’s also say you timed things so that you’d intersect with the moon at perigee. That’s 362,600 km, or 362,600,000 meters. At 11.2 meters per second, that’s 32,375,000 seconds to reach the moon. This translates into 8,993 days, or 24 years, 7 and one half months. Approximately. Your gelatanized corpse has a long trip ahead.

Apollo 11 was moving at 10.8 kilometers per second, which (mathematically) means you’d expect the trip to the moon to take 33,574.07 seconds. In theory, this means 9.326 hours. It actually took three days. Why? Well, there’s two reasons and they’re both gravity. See, the Apollo 11 wasn’t maintaining constant thrust. It had fuel that it used for course corrections and orbital insertions and the like, but it coasted most of the way. Earth’s gravity pulled on the ship the whole time, slowing it down. In addition, the ship didn’t fly in a straight line. It was in a long, figure-eight-shaped orbit with the Earth and the Moon – like so:

But what about the Death Star?

Ah, yes. That. Well, it still depends on the speed the ship can manage.

How fast is the Death star?

This is… questionable. According to the DS-1 Orbital Battle Station entry on Wookieepedia, the Death star had a speed of 10 megalight (MGLT).

So, what’s a megalight? Well, also according to Wookeepedia, a megalight “was a standard unit of distance in space”. Which is entirely unhelpful, although it does indicate that when it was used in the Star Wars: X-Wing Alliance instruction manual, it appeared to be a unit of distance and that when used as speed it should imply “megalights per hour”.

In all likelihood, “megalight” is a word that got made up because it sounded cool and had no actual meaning attached to it. But if we try to break it down, “mega” as a metric prefix means million. So, one megalight could be a million light seconds. However, this would mean that the Death star flies at 10 million light seconds per hour, or 2,777.7 times the speed of light – meaning that it could reach Alpha Centauri from earth in less than 14 hours of cruising on its “sublight” drives.  So I’m going to assume that this is not what was intended.

The Star Wars Technical Commentaries on TheForce.net speculate in “Standard Units” on what MGLT means in terms of real world [i]anything[/i]. The author of the article comes to the conclusion that 1 MGLT is “at least 400 m/s2” acceleration, which is roughly 40 gravities of acceleration.

One thing we also know about ships in Star Wars is that constant acceleration isn’t an issue – they have something close to the “massless, infinite fuel” I mentioned above. The Death Star isn’t fast, compared to the other ships in Star Wars, but it can accellerate at a constant 4 kilometers per second. Now Dummies.dom provides us with a simple formula for determining the distance (s) covered for a given time (t) at a particular acceleration (a), and that formula is s = 0.5at2. Which means we can reverse engineer, because all we need is the time. The equation looks like this:

362,600 = 0.5(4)t2
362,600 = 2t2
181,300 = t2
t = square root of 181,300 = 425.7933771208754 seconds

So, assuming that the Death Star didn’t engage it’s hyperdrive, it would take a little over 7 minutes to reach the Moon at a velocity of approximately 1,703.17 kilometers per second. And it would keep going, because it can only slow down at 4 kilometers per second. So, if the Death Star wanted to stop at the Moon, it would need to slow down about halfway there (yes, I know that orbital mechanics are a little more complex than this, but we’re talking about a 160 kilometer diameter ship that can accelerate at 4 kilometers per second. So cut me some slack, would you?). That it would have to accelerate to halfway to the moon, and then decelerate the rest of the way. So, that would look something like this:

2(181,300 = 0.5(4)t2)
2(181,300 = 2t2)
2(90,650 = t2)
2(t = square root of 90,650 = 301.0813843464919)
t = 602.1627686929838 seconds, or slightly over 10 minutes.

“All your tides are belong to us, now.”