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# Fun with logarithms 2: A race between a snail and a beam of light.

In my last post, I mentioned how cool logarithmic scales were. A logarithmic scale, for instance, takes two numbers that differ by a factor of one trillion (say 0.001 and 1,000,000,000, which differ by 999,999,999.999) and reduce their difference to a much more manageable number: 12.

Logarithmic scales are handy in the universe we happen to live in, because, as you might have noticed, this universe contains a lot of very tiny things and a lot of ridiculously large things. It contains both bacteria and galaxies, which differ in scale by a factor of 950,000,000,000,000,000,000,000,000. But today, we’re not talking about distances. Today, we’re talking about speeds. Some things in the universe move very quickly. Others move very slowly. Continents drift together (and apart) at speeds of around 1.585×10^-9 meters per second, which is less than the diameter of a DNA helix every second. Light, on the other hand (which, as far as we know, moves as fast as it is physically possible to move) travels at 299,792,458 m/s. This is the perfect place for a logarithmic scale.

Therefore, I present to you, the Bolt, a logarithmic scale named in honor of Usain Bolt, who is the fastest Jamaican in the world. He’s also the fastest human in the world. To get a measurement of an object’s speed in Bolts, divide that speed by our reference speed (1 meter per second, which is about walking speed), and take the base-10 logarithm of the result.

But actually, the Bolt is kind of a large unit. Ironically, we’ve gone from too large a scale (0.0000000015 m/s to 299,792,458 m/s) to too narrow a scale. So let’s take inspiration from the decibel, and multiply the result of our logarithmic calculation by 100, which gives us a measurement in centiBolts (cBo).

Let’s work an example before I get to the list, which is the fun part. The land speed record for a garden snail (which record, apparently, you can only challenge at the World Snail Racing Championships in Congham, England) is 0.002752 meters per second. To get the speed in centiBolts, we calculate 100 * log10((0.002752 m/s) / (1 m/s)), which works out to -256.035 centiBolts. Now that you know how the math is done, let’s compute the centiBolt rating for some ridiculously low and ridiculously high speeds!

With a helium-neon laser and a Michelson interferometer, you could (probably) measure a change in distance of 300 nanometers over the course of an hour, which is 0.00000000009 m/s or -1005.61 centiBolts.

Continents drift apart (or together) at a speed of about 3 centimeters per year, or -902.2 cBo.

Because it loses orbital energy by stretching the Earth (making tides) and slowing Earth’s rotation, the Moon’s orbit is very gradually getting larger. The moon, therefore is receding at about 3.8 cm/year, or -891.9 cBo.

Human hair grows at about 15 cm/year, or -832.3 cBo.

Bamboo grows at a rate of about 14 microns per second (meaning it can grow several feet in a day), giving it a speed of -485.4 cBo.

Jakobshavn Isbræ glacier, in Greenland, reaches a maximum speed of 12,600 meters per year, which comes out to -339.8 cBo.

As I mentioned before, the land speed record for a garden snail is 0.00275 m/s or -256.07 cBo.

A wind speed of 1 mile per hour (MPH) would just barely be detectable by the drift of smoke. It wouldn’t even move weather vanes. It gets a speed rating of -34.97 cBo.

1 m/s, being our reference point, gets a rating of 0 cBo.

Usain Bolt, for whom we named this unit, ran at an average speed of 10.438 m/s when he broke the 100 m world record. He was running at 101.9 cBo…

…but his maximum speed was 12.42 m/s, or 109.41 cBo.

In the United Sates, most non-residential roads have a speed limit of 45 MPH. In my experience, no matter the speed limit, people usually drive around 50 MPH, which is 134.9 cBo.

I once drove my car at 105 MPH (don’t tell anybody). I was moving at 167.2 cBo.

The Bugatti Veyron, the world’s fastest street-legal production car, can get up to 267.856 MPH (431.072 km/h), or 207.825 cBo.

The fastest wheel-driven car on record (as of May 2014) got up to 403.10 MPH (648.73 km/h), which is a terrifying 225.58 cBo.

The land speed record (again, as of May 2014, set by the ThrustSSC, the first land vehicle to break the sound barrier) is 760.343 MPH (1223.657 km/h), or 253.1356 cBo.

The F-22 raptor can supposedly reach Mach 2 (the actual top speed is probably classified), which is 277.093 cBo.

The awesome-looking (and sadly retired) SR-71 Blackbird could manage 2,193.2 MPH, or 299.1 cBo.

The even more awesome rocket-powered X-15 could do 4,160 MPH (6,695 km/h), or 326.9 cBo.

At this point, we’re moving from the realm of really fast aircraft to the realm of really slow spacecraft.

The International Space Station orbits at 7.656 km/s, which is 388.4 cBo. It moves so fast, that it only takes 14 milliseconds to travel its own length. Curious about what 14 milliseconds sounds like? So was I. It sounds like this: https://soundcloud.com/hobo-sullivan/the-iss-passes. Which is just barely long enough for my ears to recognize as an actual sound.

The human speed record (relative to the Earth) was set by the crew of Apollo 10, who reached 24,791 mph, or 404.5 cBo. At these speeds, which are frankly quite ridiculous, the spacecraft was covering 1 kilometer every 90 milliseconds. To give you an idea how fast that is, here’s a 90-millisecond tone: https://soundcloud.com/hobo-sullivan/apollo-10-travels-1-kilometer.

The light gas gun at Sandia Labs (which, it has been noted, is essentially a high-tech BB gun) can fire projectiles at a silly 36,000 MPH, or 420.7 cBo. At these speeds, a small plastic projectile can make a hand-sized crater in a block of aluminum.

The Helios 2 solar probe holds the record for the fastest human-made object. When it swung by the sun (getting slightly closer to the Sun than Mercury), it hit 157,100 MPH, or 484.7 cBo.

But, as all physics geeks know, 157,100 MPH isn’t all that fast. It’s only 0.00023 times the speed of light, or 0.00023 c (as science-fiction authors put it). There are much faster things in this crazy-ass universe.

Like, for instance, the brightest component of a lightning bolt, the return stroke, which, according to some measurements, reaches 220,000,000 MPH, or 0.3281 c, or 799.3 cBo.

The Large Hadron Collider can accelerate protons much faster. It can get them up to 670,615,282 MPH, 0.999999991 c, or 847.7 cBo.

Which is not far from the maximum speed any object can attain, the speed of light itself: 670,616,629 MPH, 299,792,458 meters per second, or 847.7 cBo.

Sorry, Mr. Bolt. You’re going to have to train harder. You’re still running 29,979,246 times slower than you could be. Are you even trying? Come on!

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