The Pitch of Speed

I’ve come up with an idea: Rational Speed.

It is equal to real speed divided by length of object (along axis of motion). The unit, perhaps a little surprisingly, is Hertz. This is because the two lengths (distance covered in a second and length of moving object) have the same units, and because one is divided by the other they cancel out – and the remaining units are 1/seconds, which is equivalent to “things per second”.

First example: human locomotion

If my body is 30cm from front to back (hopefully not too optimistic) and I am jogging at 4 m/s, my rational speed is just over 13Hz.

Jumbo Jet

Here’s another example. The Boeing 747-8, which I believe is the longest Jumbo Jet, is 76.25m long. Let’s assume it’s flying at Mach 0.8 at an altitude of 30,000 feet (9,144m). At that altitude, Mach 1 is 678.1mph, or 303m/s. Therefore the speed is 303 x 0.8 = 242m/s – and the rational speed is 242/76.25 = 3.17Hz.

What we can deduce from the above is that, in rational speed terms, I can jog about four times as fast as – or maybe I could say two octaves higher than – a Jumbo Jet can fly.

Let’s do some more!

My car (a Hyundai Kona EV)

Length: 4.165m.
At 70mph (31.29m/s) the rational speed is 7.5Hz.

My jogging speed is faster than my car, and both of them are faster than a 747. This new perspective is kind of odd!

Common Swift

Maximum speed in level flight is 69.3mph = 31.0m/s.
Length is about 16cm = 0.16m.
Rational speed = 194Hz (that’s the G below Middle C).

Peregrine falcon

Maximum speed in level flight is 68mph = 30.4m/s.
Maximum speed in a dive is… wait, let me check again, surely that’s wrong. Nope, it’s right – 242mph (HOLY CRAP!). That’s 108.2m/s.
Length: about 18 inches = 0.46m.
Rational speed (level flight) = 66Hz.
Rational speed (dive) = 235Hz (even closer to Middle C – it’s Bb).

What about a space rocket? Do we count the orbital speed? Once that’s been attained, the power has ceased. However, even if we are counting orbital speed, the rocket is much shorter by the time it reaches it. Strictly speaking, we’d have to examine it just before stage separation for each stage as well, and compare notes!

Escaping Earth

Saturn V, for example, is 101.6m when launched. How long is it at each stage? And how fast was it travelling as it reached the end of that stage? Those are the numbers we want, and I found them, after some effort, on Wikipedia. It’s important to remember to include the Launch Escape System, that little rocket on top of the nose, during the first stage. This is jettisoned after the first engine cutoff and stage separation. The page gives speeds at the end of each stage as well, so I was able to work out the maximum rational speed during each stage. It turns out that the later ones are far higher than the first one, but surprisingly low, due to the rocket’s length (even in the third stage burn).

Just before main engine cutoff the rational speed is a mere 22.64Hz, which is almost below audio frequency, but by the time the third stage engine cuts off after reaching Earth orbit it’s moving at a hefty 7,793m/s (17,432mph), but the rational speed is still just 244.29Hz, which is pleasingly close to that of a stooping falcon. Nature and Technology meet to sing this near-unison duet just below Middle C.

I’ve included a chart below, for information. I really like the idea that moving objects have an associated frequency, and perhaps I can somehow work this into my music. Let’s wait and see.