Comments on: Shocking Good Fun

By: ajm

ajm — Thu, 04 Mar 2010 07:26:52 +0000

One perhaps minor point – I don’t think the waves in the video are gravity waves. In the atmosphere these have phase speeds that are much too slow. These would really be internal gravity waves, and the relevant frequency would be the buoyancy frequency (the American Meteorological Society Glossary here has some good definitions.)
The wave period for an internal gravity wave is more on the order of minutes, not fractions of seconds as we see in the video.

So, anything in the video is a shockwave or acoustic wave, I’d think. I’m not sure there is a clear, sharp distinction between the two. It makes the most sense to me to think of the initial, fastest waves as shockwaves, and the later waves as acoustic waves. In between is some gray area.

By: Mark Gubrud

Mark Gubrud — Tue, 02 Mar 2010 21:35:34 +0000

Okay, I see why it’s sin(alpha)=v_sound/v_rocket; this follows from the shock/sonic boom propagating at v_sound perpendicular to the surface of the cone. So I had that wrong.

However, I still think all the circular waves that we see are gravity waves at one boundary which the rocket passes through, and they are excited by the shocks as well as by the exhaust after the rocket has passed the boundary. And even if some of what we see is the direct effect of the wake field of the rocket, I don’t believe you can correlate the rings with features on the rocket.

If you watch the video, the rings appear more or less simultaneously over a large field, first long wavelengths, then the strong short wavelength rings that you highlighted, then more long-wavelength ripples well after the rocket has passed. All through, the rings are expanding, dissipating and dispersing. Dispersion or disorder comparable to a wavelength is enough to destroy any correlation between the waves and identifiable features of the rocket. I think there is at least that much disorder in the wake field of the rocket at the distance where the rings become visible. I think if you were to examine the entire video frame-by-frame and identify and follow each visible ripple from when it appears to when it disappears, you would find many more of them than can be accounted for in terms of features on the rocket.

By: Geoff Forden

Geoff Forden — Tue, 02 Mar 2010 03:05:36 +0000

Mark, I'm sorry, but I have no idea what you are talking about. Oh well, I guess we will simply not agree about this. Here, by the way, is the Wikipedia reference for cone angles for shock waves.

By: Mark Gubrud

Mark Gubrud — Tue, 02 Mar 2010 02:54:56 +0000

Geoff, your formula for the half angle of the shock cone may be true in the near field for a blunt nose. In the far field the formula for the half angle of the “sonic boom” cone is tan(alpha)=speed of sound/speed of vehicle. There is no shock cone in the far field, because the shocks dissipate into linear waves. Tell me this is not the case in any of the images you posted above, where the rings appear to fill an interval of radius an order of magnitude larger than the length of the rocket, which is also a comparable distance above the altitude of the rings. The rings are in the far field of the shock cones. Don’t you see how incoherent and dynamic the wave field is? How can you pick out one frame and suggest a correspondence with features on the rocket? My thinking is that the wave field appears after the rocket has passed through the boundary layer that supports these gravity waves. After the rocket has traveled a certain distance beyond the boundary, the shock/sonic boom cone has spread out and interacts with the boundary layer over a large area, transferring some of its momentum to gravity waves in the boundary. Later, the rocket exhaust mixing with the atmosphere continues to excite weaker ripples in the boundary layer.

By: Geoff Forden

Geoff Forden — Mon, 01 Mar 2010 21:11:40 +0000

Mark, I feel your pain about soft arguments. After all, many of the comments I receive start off with things like “I feel that you are wrong…” But that, of course, is no reason why I should be so cavalier about my responses. Hopefully, this will set things right.

I’m not sure why you keep suggesting that the shock waves come off at 45 degrees to the rocket airframe. (I hope it’s not my “cartoon,” which I used just to illustrate the motion of the shocks and the clouds.) After all, the shadow graph of shocks from the aircraft model clearly come off at a much shallower angle (nearly 60 degrees by my crude measurement.) The formula for the half angle of the shock cone is sin(alpha)=speed of sound/speed of the vehicle. Thus, as the rocket just crosses the speed of sound the cone is nearly a plain but does become “sharper and sharper.” That is enough to ruin the 1-to-1 length correspondence between the missile features and the clouds you seem to be looking for.

Here are three images that show the origin of what I call shockwave induced rings. They are frames 4428, 4432, and 4435 of the original video. Thus, they cover a time span of nearly a quarter of a second; assuming a frame rate of 30 frames per second. They show that the rings first appear well separated from the missile’s trajectory. This is consistent with the shockwaves having been formed at that moment.

Frame 4428 shows the Sun Dog is still there and there is little evidence of the rings being formed yet.

Frame 4432 shows what might be the formation of the rings far from the trajectory of the rocket.

Frame 4435 shows “clear” rings appearing far from the rocket trajectory. (Well, you do have to look very closely to the see the rings but they are there.)

By: Mark Gubrud

Mark Gubrud — Mon, 01 Mar 2010 04:55:43 +0000

Geoff, other than italicizing not, I don’t know why you think the “shockwave induced” rings are not gravity waves, even if they are pumped by the shockwave (and also by the exhaust). I also don’t know how you could watch that chaotic sequence of rings appearing simultaneously over the whole field, then spreading out, all while shifting and dissipating, and imagine that some slice of some snapshot of part of the ring field displayed a correspondence with features on the rocket. Or how you explain the scale mismatch between the rings and the rocket, in view of the nearly 45 degree (Mach 1) projection angle between vertical and horizontal, under your hypothesis.

By: Geoff Forden

Geoff Forden — Sat, 27 Feb 2010 02:09:02 +0000

Mark, I still disagree with you. As I pointed out above, the gravity waves occur considerably after the shockwave induced rings, which are not gravity waves.

By: Mark Gubrud

Mark Gubrud — Sat, 27 Feb 2010 02:02:01 +0000

The slow-motion videos, such as this one: http://www.youtube.com/watch?v=Qvc6c7E-UF4&NR=1
make it much easier to see what is going on. The waves we see are probably gravity waves at a boundary, and their visibility is either due to condensation or refraction. The waves are excited by 1. the rocket, 2. its sonic shocks, and 3. the supersonic exhaust plume, at the center of the ring pattern where all three pass through the boundary that supports the gravity waves. No way does the gravity wave pattern correspond with features on the rocket. This is very clear just from watching the slow-mo video.

By: PinkyLeft

PinkyLeft — Fri, 26 Feb 2010 20:57:57 +0000

So the idea is that those were pressure waves from the rocket? Wouldn’t they actually lag it at that speed rather than proceed it so far?

By: Mark Gubrud

Mark Gubrud — Thu, 25 Feb 2010 15:42:20 +0000

Geoff, the shadowgraph image you show only shows us the near field close to the airframe. If you look, you see that three major shocks corresponding to features on the airframe (nose tip, front of wing, end of engine) are indeed coming off parallel. One just behind the wing is coming off at a different angle, but again, this is just the near field. In the far field, these shocks will all have dissipated into linear waves which will be spreading out with a centroid propagating along a cone determined by the speed of sound.

I think these far-field waves are what we see in the video, and they are visualized due to condensation at a boundary layer, not somehow oriented ice crystals.

When I watch the video, I see the entire wave field sort of appear at once rather than propagating out from first appearance at a center.

I think any correlation between the spacing of rings and the spacing of features on the rocket is accidental.