Geoff FordenShocking Good Fun

click on the image for a larger version

The Atlas V that carried the Solar Dynamics Observatory into orbit on 11 Feb. 2010 created shockwaves that rippled through a cloud layer. I’ve counted 11 distinct shockwaves, marked by arrows in this image.

Ok, this has little if anything to do with security or arms control (well, perhaps a little) but it is such fun that I couldn’t resist writing about it. And it is certainly very educational. There is a very fun video of the Solar Dynamics Observatory launched on February 11, 2010. In that video (and in the image above) you see the SDO’s Atlas V launch vehicle passing through a cloud layer, with shockwaves radiating out. Of course, the shockwaves are generated by the missile and the cloud layer is only providing a way of seeing them. In fact, what is visible is not a single shockwave radiating through the cloud layer but rather multiple shockwaves passing through the layer. As these shockwaves “follow” the missile, each point of intersection with the cloud layer moves outward. I’ve tried to indicate this with the cartoon below:

Shockwaves are formed at “discontinuities” along a rocket’s airframe. They radiate energy away from the point on the missile where they are created. As the missile moves along, this constant creation of shocks form what appears to be a continuous “cone” that trails along the rocket. The angle the cone makes with the rocket is therefore related to the rocket’s speed. Of course, the more discontinuities there are on the airframe, the more shockwaves are formed and the more energy is radiated away. That, by the way, explains why the “baby-bottle nose cone” of the Ghadr (also sometimes know as Shahab-3B and various other names, I wish we could all agree on names) has a higher drag coefficient than the simple cone on a Nodong or Shahab-3. Of course, as my friend and fellow former UNMOVIC inspector, Mike Elleman points out, the baby bottle shape allows the weight to cross sectional area of the detached warhead to be increased. This ratio is also know as the ballistic coefficient or Beta of the warhead and allows both a faster reentry and a more stable trajectory.

I’ve been able to make a rough correspondence between the number of discontinuities on the Atlas V and the number of shockwaves visible in the cloud layer. (See the image at the top of this post as well as the images to the left.) Of course, not all discontinuities make shockwaves that are visible around the entire vehicle. For instance, the vehicle’s airframe shields a whole hemisphere from a shockwave caused by a pipe sticking out on one side. But this correspondence is close enough to really illustrate this physical process.






  1. Scott K.


    What a great post! Very interesting!

    I wonder how the Prandtl-Meyer fan appears. Does it look like a simple bow shock or is it more complicated?


  2. Geoff Forden (History)

    Thanks Scott! My guess is that these are Prandtl-Meyer expansion fans. It seems to me that whenever you have an infinite number of anythings very close together, they will appear as a single thing (or simply cancel out). Any other number, ie any number other than 0 or 1, would be strange. At least, thats my guess. But I await your and other’s thoughts on that.

  3. Captain Ned (History)

    From Space Weather

    You can also see the shockwave as it destroys a sundog as seen from the ground.

  4. Paul Lutus

    The “cloud layer” is actually a thermal layer or boundary with warm, moist air below, cold air above, and a layer of ice crystals at the boundary. Such thermal barriers create optical refraction effects similar to those between glass and air, and critical angles beyond which they begin to reflect instead of refract. It’s the latter effect that’s responsible for the visible waves.

    It happened to be a very calm day with no wind or turbulence, which made the thermal layer abnormally flat and abrupt — pertect for the observed effect.

  5. Geoff Forden (History)

    Scott, I should clarify that I was talking about the “far-field” approximation.

  6. Logan Ford

    Captain Ned, it is a circumhorizontal arc, not a sundog.

  7. MK (History)

    I have no idea what you are talking about, but I am enjoying the conversation.

  8. Captain Ned (History)

    @Logan Ford:

    I’m just using the term as reported on both Space Weather and NASA. I wasn’t there, so I’ve no idea if the image was 22 degrees or 46 degrees from the Sun.

  9. Jim (History)

    Actually, it isn’t from shockwaves from the airframe. The vehicle hadn’t reached Max q yet. Those effects are from the acoustics of the engine.

  10. Geoff Forden (History)


    I think not. They announced the rocket was supersonic just after it passed through the cloud layer, which means it had reached Mach 1 sometime before, ie before it passed through the cloud layer. The engine does cause acoustic waves in the layer, but only after the rocket is considerably farther away. You see them later but there is a considerable gap between the shock induced waves and acoustic induces waves. If they were all caused by acoustic noise, why would there be that gap? Furthermore, the clearly acoustic waves do not propagate very far, while these indicators of shockwaves travel for sustained distances. You also see the acoustic waves being created at a single point; you do not see that for the shock induced waves.

  11. Mark Gubrud

    Geoff, I have watched the video, and where you see a definite number of bands which you can correlate to features on the rocket, I see broad wave fields of less coherence than your model suggests. The problem I have with your interpretation of the rings is that at Mach 1 the cones should open at 45 degree angles, which will project any structure in the vertical direction to horizontal rings if, say, a boundary zone cuts a section. The radial spacing of the rings should be the same as the vertical spacing on the rocket. How do you get these large, wide rings, instead of one narrow disorderly band? Is there a dispersion mechanism that effectively pushes nested shock cones apart? Or could the correlation you show between some of the rings at one point in the sequence and some features of the rocket be accidental?

    At other points in the video, I see as many as 20-30 rings, where you count 10. It seems to me that these rings represent a broad field of acoustic waves contained within an expanding (Mach 1) cone, where the shock has dissipated into linear waves by the time it is interacting with the atmospheric boundary layer to create these visual displays.

    The second set of ripples is probably due to supersonic exhaust at the point where it slows down and mixes with the atmosphere, creating much turbulence which shows as radially expanding disturbances of the boundary.

  12. Murray Anderson (History)

    According to the United Launch Alliance website, the rocket was supposed to go supersonic at 81 seconds into the flight. Based on the video above the shocks showed up at 77 seconds into the flight. Max Q was supposed to be at 92 seconds.
    When the rocket got in low earth orbit, the Centaur cut off about 5 seconds early, so the early events may have played out a little earlier than expected (according to some discussion at, the rocket had a “hot” RD-180).

  13. Geoff Forden (History)

    I think that those people who believe these clouds (the fast, long lasting ones) are do to acoustic effects—as opposed to shockwaves—need to explain why they are so long lasting and why they appear to be so “flat” as well as why there is a gap between them and the next phenomena: a “second” generation of waves which do not propagate very far. They also need to explain how an acoustic wave generates clouds. The second set of waves are clearly “gravity waves,” with a very low frequency acoustic (perhaps infrasound) wave from the rocket engine creating a vertical displacement to the interface which forms the cloud layer. That creates clouds because it is forcing some part of the upper layer down into the warmer, high moisture part with a follow on upwelling of the warmer layer into the cooler layer with a subsequent formation of a cloud. How does a sound wave create the long lasting, flat clouds we see racing away? A series of sonic booms easily explains that.

  14. Thomas A. Fine (History)

    I’m pretty sure you are wrong about the shockwaves corresponding to features on the rocket. Since both the rocket and the shockwaves move at the speed of sound, the spread across all shockwaves would have to be the same size as the rocket, but the spread is clearly much much larger.

    The shockwaves must be separate events over time, probably all from the nose of the rocket.

  15. Geoff Forden (History)

    Perhaps you should look at this image:

    Now imagine the intersection of these shockwaves with a plane perpendicular to the axis of the aircraft.

  16. Barbara Tomlinson (History)

    I’m glad to see this discussion of my video, especially the explanation of the optical effects of the cloud layer. Somebody suggested to me that the ice crystals were tipped to reflect the sun to make the visible ripples but something about that seemed unlikely — that they’d just neatly stay aligned. Ordinary Snell’s Law seems so much more workable. Maybe it’s relevant to note that you can see a vapor cone forming around the rocket in this video. I zoomed in and slowed it down a lot in this version.
    I wonder if anybody has an explanation for the lines moving by to the left? Interference effects from the multiple wavefronts is all I can think of.

  17. Geoff Forden (History)


    Thanks for your comments and thanks for taking such an amazing and fun video! If I understand which lines you are talking about, they are just the other side of the shock cone “ring”. It is simply expanding radially, which makes it appear to be moving in the opposite direction when it is on the opposite side of the rocket. The vapor cone around the nose cone is another manifestation of the rocket going super sonic. Take a look at this image of a jet just crossing the speed of sound:

    By the way, since the vapor cone appears before the rings, that pretty much proves that the rocket was supersonic when the rings appeared.

  18. Mark Gubrud

    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.

  19. PinkyLeft (History)

    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?

  20. Mark Gubrud

    The slow-motion videos, such as this one:
    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.

  21. Geoff Forden (History)

    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.

  22. Mark Gubrud

    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.

  23. Geoff Forden (History)

    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.)

  24. Mark Gubrud

    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.

  25. Geoff Forden (History)

    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.

  26. Mark Gubrud

    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.

  27. ajm

    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.

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