Uncategorized

Supersonic Submarine

I seem to be obsessed with submarines, which isn’t something I realized until now. There’s nothing worse than a stealth obsession.

Anyway: sound has a speed. That speed depends on the properties of the medium. The speed of sound in air is about 330 meters per second. The speed of sound in olive oil is 1430 meters per second (Yes, somebody measured that, and here’s the proof, along with some other handy tables of speeds of sound in other materials). The speed of sound in aluminum is 6320 m/s. The speed of sound in beryllium is an amazing 12,900 m/s, which is not only faster than the International Space Station’s orbital velocity, it’s actually faster than Earth escape velocity.

The speed of sound in seawater is a much tamer 1500 m/s (the exact speed depends on depth (meaning pressure), temperature, and salinity). That got me thinking that, since I’ve abandoned the submarine car in favor of an actual submarine, why not make it a supersonic submarine?

There’s nothing in the laws of physics to stop me. There’s no physical reason that makes it impossible to move through water faster than the speed of sound in water. There are plenty of engineering reasons, but we’ll get to those in a second.

The interesting thing about moving supersonically in water is that water isn’t a gas. Air isn’t very dense, it’s compressible, and it doesn’t have many phase transitions readily available. It can liquefy if you compress it while keeping it cool, and it can turn to plasma if you compress it and let it heat up. But when you’re talking about supersonic vehicles, the air heats up rather than cooling down. It heats up a lot. The air around re-entering spacecraft turns into plasma.

Water, on the other hand, is much denser (pure water is about 1,000 kilograms per cubic meter), and compared to air, is almost incompressible. Water is about five orders of magnitude less compressible than air. This means that a whole slew of new phenomena happen in supersonic submarines that don’t happen in supersonic aircraft. The coolest one is cavitation.

Cavitation is what happens when, for one reason or another, the pressure on a volume of water drops below that water’s vapor pressure, or when something moves through the water so fast that the cavity in the water doesn’t have time to close around the object. There are all sorts of cool videos of cavitation on the Internet, but I think this is my favorite:

Ain’t that beautiful? Many thanks to The Slow Mo Guys and Smarter Every Day for filming that, and for doing exactly what I would have done if I had access to one of those slow-motion cameras.

Notice the large cavity that opens behind the bullet as it travels. The spherical cavity around the gun’s muzzle is from the blast of hot, escaping gas, but the sort of sausage-shaped bubble attached to the bullet is pure cavitation. The bullet slams the water aside so hard that, even though water is usually very good at closing voids within itself, it has no choice but to stand aside for a fraction of a second. For the brief period that it exists, that cavity is full of a little water vapor that evaporated from the surface and not much else, and as soon as the moving water has deposited its inertia in the stationary water around it, pressure wins out and makes the bubble collapse again.

But a cavitation bubble isn’t the same thing as a sonic boom. The bullet in that video was fired from a revolver. Since I don’t know the make of the revolver or what kind of ammunition it was using, I don’t know the muzzle velocity, but if we assume it was in the same class as a Ruger firing .357 Magnums, then the muzzle velocity would have been around 450 meters per second. Not faster than the speed of sound in water. Barely faster than the speed of sound in air.

Either way, we know that our supersonic submarine would cut quite a large hole in the water as it flew. (Flew? That doesn’t sound right. What is the right verb for a submarine’s movement? Somebody let me know. That’s gonna bother me now). It would also, true to acoustics, generate a sonic boom. I would guess that this sonic boom would be more than enough to rupture the eardrums of unlucky divers who happened to get in its way, and that the drop in pressure after the shock would probably create a whole swarm of smaller cavitation bubbles in its wake. And because the water that evaporated from the surface of the cavity would be moving roughly in the same direction as the cavity (relative to the submarine), the submarine would likely create a second, much slower-moving sonic boom in the water vapor. After the submarine passed, the cavity would expand to a maximum size, then slam closed, possibly heating the gases inside enough to glow. This is called sonoluminescence, and is very impressive:

After the collapse, you’d have a soup of very hot bubbles and very hot water vibrating and rising to the surface. The water would be hot from the collapse of the cavity. Here’s about what our supersonic sub would look like:

Supersonic Submarine

And, from a practical perspective, it would be hot for another reason. To break the speed of sound in water, you’d need the engine power of 4 Saturn V moon-rockets.

Yes, really. This comes from the basic drag formula I’ve been using all along:

drag force = (1/2) * (density of medium) * (velocity of object)^2 * (drag coefficient (depends on shape and texture of object)) * (projected or cross-sectional area of the object)

I have no idea where we’re going to get a rocket four times as powerful as a Saturn V. I guess we could just make the end of the submarine a parabolic reflector and drop antimatter out the back and ride the blast of steam, but I hear people get pretty upset if you go dumping antimatter in the ocean. Especially if they happen to be swimming behind you.

But that’s the least of our worries. At 1500 meters per second, the front of the submarine would be experiencing pressures ten times greater than at the bottom of the Mariana Trench. Not unsurvivable, but between the pressure of the water against the front of the hull and the cavitation going on around the back of the hull, the whole thing’s going to need to be a pressure vessel. That’s going to be one heavy submarine. While we’re pretending that a submarine-sized craft could produce 141 million Newtons of thrust for an extended period, why not just turn the bastard into a rocket? Besides, I’m afraid that if I tooled around underwater making watery sonic booms, I might upset an octopus, and I have a deep and inexplicable affection for octopuses.

But before we stop doing weird things underwater, there’s a question that demands to be answered: if our supersonic submarine would need four times the thrust of a Saturn V to travel through the water, how fast would the Saturn V itself be able to go underwater. Well, input some reasonable values into the drag equation, set the drag equation equal to 35 million newtons (the Saturn V’s first-stage thrust), and we have:

41.2 meters per second

or

92 miles per hour

or

148 kilometers per hour

The Saturn V is one of the most powerful rockets ever built. And, under ideal conditions, it could manage 92 miles an hour underwater. I have driven my car faster than that. A good baseball pitcher or cricket bowler can throw faster than that. I guess the people at NASA weren’t planning for the possibility that the space between the Earth and Moon might inexplicably be filled with seawater. The fools.

But, although 92 miles an hour is not a very impressive speed, especially by rocket standards, you have to admit, it’d be one hell of a sight to behold:

SaturnV

Now that‘s a fucking torpedo!

Standard
Uncategorized

Decibels of DEATH!

Ear Protection

When I see the word “decibel,” I think two things. First, I think “Noise.” Then, I think “Oh god, decibels confuse the hell out of me…”

Well, I think I finally understand the decibel. It’s kind of a weird unit, but it’s also nifty, and it showcases one of the coolest things in mathematics: the logarithm.

Here’s how you compute the decibel-level of a sound. First, you figure out the acoustic power of that sound, probably using a microphone (or using a sound engineer who has a microphone and understands better than I do the difference between “acoustic power” and “sound amplitude.”) The acoustic power tells you the maximum pressure the sound wave exerts on things (say, your eardrums). Most of the time, you measure that sound pressure in pascals. Take that sound pressure and divide it by 20 micro-pascals. 20 micro-pascals is a semi-arbitrary reference point. It’s about the sound pressure where a 1000-Hertz sine wave first becomes audible to a human ear. It’s not a lot of pressure. The pressure 10 meters underwater is about twice what it is at sea level, which means the overpressure is about 1 atmosphere (1000 hectopascals. I’d like to note that Hectopascal would be a good name for a movie villain.) Well, the depth of water it would take to get an overpressure of 20 micropascals is 2 nanometers, which is about the diameter of a strand of DNA. Did you know human ears were that sensitive? I didn’t.

Anyway, you can use decibels to express a wide range of noise levels without using too many digits (Because, let’s face it, we all start zoning out after you get beyond about six digits, give or take.) To get the decibel number, you divide your sound pressure by 20 micropascals, take the base-10 logarithm of that, and multiply the result by 20. For example: a sound pressure of 20 micropascals gives you 20 * log10(20/20) = 20 * log10(1) = 20 * 0 = 0 dB.

With a title like Decibels of Death, you knew this article was going to be all about extremes. The quietest officially-measured place in the world is the anechoic chamber at Orfield Laboratories. It’s a room encased in a foot-thick concrete vault. The room itself sits on I-beams which are on springs to isolate external vibration. The inside of the room is full of wedge-shaped foam blocks which prevent echoes and dampen the sound from outside even further. The Guinness Book of World Records measured the sound level in the Orfield anechoic chamber at -9.4 decibels. That works out to a sound pressure level of 6.8 micropascals. To produce an overpressure that small, you’d only need a layer of water 0.612 nanometers thick. At that point, it’s less a puddle and more a molecular stack. That’s pretty damn quiet.

It’s actually intolerably quiet, apparently. The longest anybody’s ever spent in the chamber is 45 minutes, according to that Daily Mail article I linked above. I’ve heard stories about people who freaked out in the chamber because, all of a sudden, they can hear their heartbeats. And some people have auditory hallucinations when deprived of sound long enough, which probably makes the Orfield chamber even scarier.

So -9.4 dB is quiet enough to make you crazy. 0 dB is the threshold of hearing. 10 dB is about the quietest environment you or I will ever experience, and that’s only if we don’t breathe too loud. 25 dB is a very quiet room. According to a funky app I’ve got on my smartphone, the noise level at this desk is 51 dB. The EPA (the US environmental agency) recommends your everyday environment not exceed 70 dB. 85 dB can cause hearing damage over the long-term. 130 dB is painful. 150 dB can rupture your eardrums. This is what I was talking about earlier: logarithmic scales allow you to convert numbers orders of magnitude apart into nice numbers with low digit counts, which makes it easier to compare them side-by-side. When we started out, back at -9.4 decibels, the pressures were so low they were almost impossible to measure. Now, they’re so high they’re doing organ damage.

And speaking of organ damage… The strength of a blast wave is measured by its overpressure, just like the strength of a sound wave. In this fascinating and unnerving paper, some doctors report the effects of 62,000-pascal blast waves on rats. They speak of “minimal to mild alveolar hemorrhages,” as though there were such a thing as a mild case of bleeding fucking lungs. The upshot of all this is that, although 150 dB may burst your eardrums, 189.9 decibels (which is the decibel equivalent of 62,000 pascals overpressure) can actually damage your guts.

But if you’re catching a 190-decibel blast, you’ve got more serious things to worry about than bleeding lungs. Yes, really. There are a lot of reports of soldiers who have been hit by blasts from roadside bombs and car bombs and other such nasty things. Some of these soldiers, although they didn’t hit their heads on anything and nothing hit them in the head, developed serious cognitive problems: difficulty concentrating and short-term memory loss, enough to pretty much spoil their day-to-day lives. In another experiment, rats exposed to a blast overpressure of 20 kilopascals (180 decibels) experienced similar symptoms, and when they were dissected, had lots of dying brain cells. Which is all really pretty damn sad.

As it turns out, there’s actually technically a maximum sound pressure, at least if you want an undistorted sound wave. A pure tone has the shape of a sine wave: the pressure rises a certain amount above atmospheric, drops in a graceful sinusoidal curve, falls that same amount below atmospheric pressure, returns to atmospheric pressure, rinse and repeat. The thing about these kinds of sine waves is that, after their maximum overpressure, they have to drop that far below atmospheric pressure. And if the sound pressure of your sine wave happens to be greater than atmospheric pressure, that can’t happen: pressure is a number that doesn’t go any lower than zero, which is a vacuum. So a sine wave with a sound pressure larger than 1013 hectopascals (1 atmosphere) will sound all right when the pressure goes up, but will get cut off (“clipped,” the sound-engineer people call it) when it goes down. (And when I say “Will sound all right” I mean “Will rupture your aorta, destroy your lungs, tear your limbs off, and knock your house down,” as we learned from nuclear tests.) The maximum for unclipped sound, therefore, is 194.1 decibels.

But since we’re already blowing everything up, why worry about a little distortion? You know the Barrett M82? The big-ass .50-caliber sniper rifle? That one from that movie The Hurt Locker? The big scary one? Well, when that thing fires, its cartridge sees a blast wave of 265.5 decibels, which is just one more reason not to live in a rifle barrel.

You would experience 270 decibels if you were standing about 100 meters (350 feet) from a 1-megaton nuclear bomb when it went off. I use “experience” loosely here, since you wouldn’t have long to enjoy the racket before you were spread over an alarmingly large area.

Now, let’s say you were standing on the surface of a star just as it went supernova. Well, you’d be exposed to a blast pressure of something in the (very rough) neighborhood of 476 decibels, which I’m pretty sure the EPA would classify as “potentially hazardous.”

As it turns out, there’s a maximum pressure that is still physically meaningful, at least according to our current understanding of physics. It’s called the Planck Pressure, and it’s very large. It’s the kind of pressure you get inside black holes. It’s the kind of pressure the universe experienced (we think) right after the Big Bang. The Big Bang had a noise rating of 2,367.3 decibels. The explosion that set the current universe in motion had a pressure which can be quantified in five significant digits.

That’s what I mean about logarithmic scales being awesome. They turn unimaginable cosmic numbers into nice, manageable, comprehensible numbers. You’d better believe I’m going to be playing with logarithmic scales again soon. Which sounds way dirtier than I intended.

Standard