It's The Great Space Coaster... Ummm... Elevator

May 14, 2008 – 12:15 am

Recently in my travels, I was alerted to the upcoming Space Elevator Conference happening in Redmond, Washington in July with Microsoft as a major sponsor. Of course, the moment I read "space elevator," being a proud member of generation X, the theme for "The Great Space Coaster" started going through my head.

And before we get to all the fun math the space elevator inspired me to do, I want to give you the opportunity to have that magical tune run through your head, so I've embedded a YouTube video of the opening sequence below. Click "play" to get on board.

Are we all good now? Anyone need a hit of the "New Zoo Revue" theme or maybe "Villa Alegre" before we move on? Okay.

So, anyhoo, the mention of the Space Elevator Conference eventually led me to spaceelevator.com which, in the header for most pages, says "Climbers ascend a ribbon, 100,000 km long, strung between an anchor on Earth and a counterweight in space." I thought of that ribbon and then thought of all the potential fun math in it.

See, the first thought was how much 100,000 kilometers of bologna slices would weigh. But I held off, because the second thought was: "that counterweight's going to be moving awfully fast." See, if that counterweight is in geosynchronous orbit (i.e. stays above the same point on the earth), then...

The earth is roughly 25,000 miles around at the equator. So a point on the equator is going to move around a 25,000 mile circle every 24 hours. That point is basically moving at a little over 1,043 miles per hour. But what about that counterweight? It's going around its circle every 24 hours too so it can stay right above the same point on the equator, but that circle is 200,000 kilometers wider than the earth.

Now, the formula to get the circumference of a circle is simply π (or 3.14159) times the diameter (width) of the circle. If we take the radius of the earth (half its width), which is 3,963 miles, add 62,137 miles for the 100,000 kilometer tether, and then double that, we have a diameter of 132,200 miles. Multiply that by 3.14159 and you have a circle that's 415,318 miles around. Divide that by 24 and that counterweight is moving at roughly 17,305 miles per hour.

But another thing that got me was how long it might take to get to the top. Let's say that you averaged 500 miles per hour up that ribbon. You'd be going significantly faster than the fastest maglev train... straight up. Yet you'd still be looking at trip that would take a little over 5 days. If they made climbers with the amenities of cruise ships, it could be a nice trip, but it's orders of magnitude longer than the trip would take in a rocket.

Of course, I still come back to 100,000 kilometers of bologna slices, laid end to end. Bologna has nowhere near the tensile strength to be used as a construction material for the space elevator ribbon, but that much of it (985,434,353 slices) would weigh 61,589,647 pounds, contain 88,689,091,770 Calories and 17,375,178 pounds of fat... or for a Rough Equivalent... just the fat in 100,000 kilometers of Oscar Mayer bologna slices laid end to end would weigh as much as 2,465,897 babies.

Perhaps we need a lighter, stronger material... what about U.S. dollar bills? Instead of 1 ounce per 4.25 inches like the bologna, they offer 1 gram per 6.14 inches (or roughly 15.6 centimeters), meaning we'd only need to stitch together 641,025,641 dollar bills at a weight of 1,412,820 pounds with no fat.

I'm sort of inclined to suggest making it out of a sort of papier-mâché using Krazy Glue instead of paste. I mean, if that stuff can glue a construction worker to a girder, or your little brother to the dog, it would molecularly bond the paper together strongly enough to create the space elevator ribbon. The only problem would be terrorists with bottles of nail polish remover.

So, what Rough Equivalents can you come up with for 100,000 kilometers? Post them in the comments section below.