There was a pretty interesting picture floating around the web today and you can see it here.
What caught my eye wasn’t the picture itself (which was pretty neat, no doubt) but the explanation in the text that it was thought to have been caused by a Prandtl-Glauert singularity. And I thought it might be worth talking for a bit about what this is.
The title of today’s blog - "What’s the plural?" – is meant to highlight the fact that the word singularity has nothing to do with single (as in only one). What it refers to is something that’s infinitely large, but only exists in an infinitesimally small place. The big deal in the universe that goes along with this are black holes. They’re called singularities because they have an infinitely strong gravitational field but, mathematically, only occupy a point in space. That’s pretty weird.
But such weirdness exists closer to home as well. When you bang a coffee cup against the table you’ll often see a drop of coffee shoot up from the middle of the cup. That’s because the surface is trying to produce a singularity – a circular "wave" of coffee at the center with an infinitely tall height. Real coffee won’t allow this, of course, so it breaks into a droplet.
Well, back to the Prandtl-Glauert singularity. Prandtl was a scientist specializing in fluid motion (like air, water, and so forth) and was particularly interested in the behavior of air at very high speeds – such as supersonic. Glauert was a British aerodynamicist who first published what Prandtl had been dealing with for a while. And what this was was the observation that the pressure coefficient (a standard aerodynamic measure) isn’t constant with speed. And, in fact, it increases as mach 1 is approached. So much so that, when one reaches mach 1, the pressure coefficient becomes infinite.That’s because it is (roughly) equal to a constant (like, say, 2.4) divided by 1-M, where M is the mach number. When M=1 we’re at mach 1 and we’re also dividing a finite number by zero. To infinity and beyond!
Now this would be "a bad thing" if it really worked like that. But, just as with the coffee cup, although the simplified mathematics says the pressure coefficient should go to infinity, real world effects conspire to keep this from happening. And if Prandtl’s model had been more accurate, it would have indicated this as well.
But the whole point of today’s discussion isn’t what actually happens near mach 1 but rather what’s really meant when someone says "there’s a singularity." And now you know. A singularity indicates something that’s getting infinitely large very, very quickly. Like when my computer shows the spinning "please wait" ball when I try to save a file. My temper goes off to infinity so fast …
- And that’s today’s word from the bird
