ArmsControlWonk.com

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Unfortunately, there was a mistake in the range of the original plots. (These things happen when you rush to get things put up on the blog as soon as possible. Im sorry about that!) The observed pitch angle is still very shallow but less so that I originally thought. However, I am still of the opinion that this trajectory is more consistent with an ICBM type flyout that tries to maximize range than a space launch vehicle. Here is my original post:

This question is not going to be answered with one set of data but the pitch program, as determined by the contrail observed in the DigitalGlobe/Globalsecurity.org image is more consistent with an ICMB trying to maximize its range than a space launch vehicle. The one remaining uncertainty, for me, was DigitalGlobe’s time of imaging. They reported 11:32:00 local time, which seems very round to me. So I thought I’d look at the effects of a 30 second uncertainty in when the image was taken. That is shown in the graph of trajectory above. It’s much shallower than I would have expected if it was trying to maximize the orbit. So I am now favoring the hypothesis that North Korea was testing both the missile and an important part of the guidance program of an ICBM with this test. Since the missile appears to have succeeded in second stage separation and ignition, then this was a highly significant accomplishment for them.

Update: I have come to realize, surprise, surprise, that I have not explained myself very clearly. I want to apologize to my readers; my only excuse is that I got very excited about this analysis. Hopefully, this image should help explain things.

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If you look at this image, the contrail, as projected against the ground is in the lower right corner and are represented as circular targets. ( You can find a GoogleEarth overlay of the contrail here.) The points in the “orbital plane”—the plane the rocket travels in, are shown as diamonds with little sticks connecting them to the ground (and are in the center left). These are the reconstructed points through which the rocket actually passed. If you were to connect the ground points with their corresponding trajectory point and continue on into space, they would all intersect at the location of the Worldview-1 satellites. And if you were to draw a line through the places where the space points’ sticks touch the Earth, it would pass through the launch pad, even if it doesn’t look like it would from this perspective.

Update: After discussions with David Wright, I went back and re-checked my calculations and, unfortunately, there was a problem with calculating the positions of the contrail from the alternate satellite positions. In particular, the position assuming the image was taken 30 seconds later than DigitalGlobe stated seems to indicate a considerably steeper raise to the missile so it is possible that could account for differences between this and David’s model. We will have to see if that timing is more consistent. The trajectory is so sensitive to this timing because the image is taken at such a slanting angle. I doubt that DigitalGlobe or any other image provider would normally take such oblique angles. However, it is also clear that DigitalGlobe was trying to maximize its chances of seeing the launch. I suspect all the different commercial (and governmental?) satellites were also imaging the launch pad at large angles. I would guess that DigitalGlobe could see the launch site for at about 5 minutes before and 5 minutes after it passes directly over the launch site. That in itself improves the chances of seeing the launch to about 1%. If you include the other photoreccon satellites, this probability could “climb” to 5% or greater. So this was hardly the “1 in a million” chance that some satellite would photograph it that has been bandied about.

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The amazing satellite image by DigitalGlobe and presented by GlobalSecurity.org of the Unha-2 in flight can be used to determine the portion of the powered trajectory as it crosses those altitudes where contrails are normally produced. The graph above, which I calculated from that image and the position of the worldview-1 satellite at the time the image was taken, shows some of the points that any simulation of the rocket will have to fit. This, together with the splash down zones will add significant constraints to certainly the first stage. Some wonk-readers have wondered about both the direction and position of the observed contrail as projected against the Earth’s surface. This can be simply explained by the oblique viewing angle of the satellite (which had a latitude of 33 N degrees and a longitude of 126.6 degrees E and an altitude of 489.7 km) at the time the image was take and the fact that the rocket itself was over 4 km above the surface of the Earth.

Comment [2]

Images from the ground of the Unha-2 launch are starting to come in. Besides an amazing satellite image by DigitalGlobe and presented by GlobalSecurity.org of the the Unha-2 in flight, there are North Korean television images starting to appear in the West. (I should mention that the flare at the of the rocket’s contrail is not the rocket plume but rather indicates that the CCD camera on board the satellite saturated.) I’m going to be analyzing these images and hope to write more but I wanted to get these out as soon as possible.

There are a few comments I’d like to make:

1) The first stage is not quite as large as I thought based on a slanted satellite view. It’s much closer to half the rocket length than the 2/3 that I originally thought. I think I was mislead by the projection of the interstage as seen from a funny angle.

2) While you cannot see the individual nozzles on these images, you have to say its more consistent with a cluster of engines than a single engine. ( See this image of the missile in flight.)

3) The diameter is the first stage appears quite large. More work needs to be done on measuring it.

4) No fins are visible on these images or the one the of the missile in flight. While fins are not needed to insure a rocket’s stable powered flight, some analysts had automatically put them on their models.

5) No clear indication one way or another (at least with the cursory viewing of them I’ve made so far) of vernier engines or gimbaled engines.

Update: It’s a cluster! I cannot tell for sure whether or not its 2 or 4 engines but it is definitely a cluster. New info is coming so fast and furious that it’s almost worth missing the Carnegie conference.

By the way, so many of you are viewing this site, I am having a very hard time posting updates! This must be a good sign, but it’s causing me a lot of problems with lost work.

Update: The cluster of engines seems to use a single turbopump. Its still possible, of course, that each nozzle has its own turbopump but given the location of the exhaust exit, Im guessing that its a single pump. This implies a both a reduction in weight and an increase in sophistication on North Korea’s part. This image is a lot more convincing when you look at it in the video because you can see the exhaust plume from the turbopump pulsing.

Update: Gimbaled engines or jet vanes? I cannot tell for sure (if you look at the image of the turbopump exhaust I point to above) there appears to be four (you can see two spaced approximately 1/4 the way around the stage’s circumference) members sticking down from the airframe to below the nozzles. These could be either structural members to support the rocket on the launch pad or extensions for bringing down jet vanes to the level of the nozzle exits. I frankly think the support structures is a more likely alternative so I’m guessing the first stage is guided by gimbaled engines.

Update: I didn’t mean to rule out vernier engines. They are certainly still a possibility.

Update: The DigitalGlobe/GlobalSecurity.org image of the Unha-2 contrail is going to prove to be an analytical goldmine! I have made a rough GoogleEarth overlay of it it. Now, to find out the exact time the image was taken and use these to triangulate the Unha-2’s trajectory during early flight!

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Screen Capture from a FNN Video, click here for the entire video.

So, for about five minutes this morning, the Japanese Self-Defense Forces thought North Korea had launched its satellite rocket. (Good thing they didn’t launch anything in response.) One of the interesting things about this false alarm was that it was reportedly seen by a radar that I and a few experts who know a lot more about radars than I do, weren’t aware of. It’s the J/FPS-5 radar and has been called Japan’s “next generation of ballistic missile tracking radars.” There is apparently a prototype near Chiba, near Tokyo, and one that just went operational in Shimokoshiki-shima [island] in Kagoshima Prefecture. (I’ve marked the general areas on a GoogleEarth image.) I think I would not have placed a radar all the down in Shimokoshiki-shima (if I have the right Island) if I was going to view missiles flying out of North Korea. Perhaps it might be a good place to observe (and direct?) a missile defense engagement?

ps As I write this, dawn must be coming to the Korean peninsula. It can get exhausting waiting for this thing to launch!

pps. Perhaps the existence of the J/FPS-5 is one reason why the Sea-based X-band radar hasn’t left Pearl Harbor?

Update: It must be a rule: as soon as you post something, the answer comes flying through the door. The J/FPS-5 is a detection radar and Japan will eventually surround itself with them. Take a look at this slide from an MDA briefing.

Update: (11:10 pm EDST) North Korea launched its Unha-2 rocket today at about 10:30 pm EDST. No word yet on if it put anything into orbit. Of course, if it did put something into orbit, it would be crossing the United State’s satellite tracking radar fence in Texas right about now for the first time. (Well, actually not. It would be at about 40 degrees South this time. So the US will either have to track it with other assets to determine its orbit—the most probable eventuality—or wait 5 or 6 hours for the US to pass underneath its orbit. Its late and Im tired.)

Update: (6:45 am EDST, 5 April 09) As of now, still no orbital object cataloged in the NASA satellite database as coming from this launch.

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In all the excitement and hubbub about Iran’s launch of the Omid satellite yesterday, there was other news that should warrant our attention. North Korea has, apparently, been seen shipping large missile bodies to its Western launch range. While described as a “Tae’podong 3” or upgraded Tae’podong 2, it already seems like old technology some how. What we should look for is signs that the North has imported technology from Iran and is moving away from stacking SCUD-type missiles on top of each other.

I’ve heard some interesting comments about this launch though I can’t seem to find the references when I need them. In particular, I’ve heard that launching from its new Western launch site would allow both the first stage to fall well short of Japan but also allow the upper stages to be considered already “in space” by the time they pass over Japan. I’m uncertain as to the space law involved but I would have assumed that the only meaningful milestone would have been for the satellite to already have reached orbital speed by the time it crosses Japan. Somehow I doubt that is will be the case. Furthermore, if North Korea does use a third stage, as it did with the Tae’podong 1, then the second stage would almost certainly not be “in space” as it over flew Japan.

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…and the middle one (after surveying all the beautiful Italian people) says “Know any good books about missiles?”

And the last one says “Why, yes! I like the books from the ‘50s and ‘60s.”

And the first one in says “And then the frog said, ‘I feel all white and fluffy!” But that’s another story.

So James has asked me what books I can recommend for learning about missiles and he also suggested that it would make a good easy blog. Here is my short list:

1) Handbook of Astronautical Engineering by Heinz Hermann (ed.) Koelle. Hands down the best book for actually learning about missiles. When ever I have mistakenly first tried a different book, I always come back to this one.

2) Aerospace Vehicle Design: Spacecraft Design (vol. 2) by K. D. Wood. If you want to calculate something quickly, this is the book to go to. Its just full of interesting and important empirical relations.

3) Rocket Propulsion Elements by George Sutton and Oscar Biblarz. Ok, they are always coming out with an new edition so perhaps its not really from the 60s any more, but people expect to see it in such a list. But seriously, If you have Koelle, you really don’t need anything else.

I like books written in the ‘50s and ‘60s because they weren’t pure mathematics and actually explained things. That, of course, is an interesting sociological “observation.” You might disagree and I’d like to hear your thoughts. Also, if you know of any other great books on missiles, let’s start a list! Of course, we all run the risk of starting a run on these books, so make sure you have your copy before posting it! Books from the ‘50s and ‘60s are starting to be worth their weight in gold.

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I remember having a conversation with a missile engineer some time ago about the North Korean Nodong missile; he said “no one in their right mind would field a missile that has only been successfully tested once!” At the time, that made a lot of sense to me. But exactly how many tests do you need? And more importantly, how do you decide how many tests you need? These questions should all be determined by the reason why tests are performed in the first place.

I think I understand bullet testing. When developing a new bullet, you test it millions and millions of times to make sure they work right in all imaginable situations and that you have a high degree of confidence that they will work. But, of course, bullets only cost a dollar or two each so there is little problem with running a standard quality control test program to allow you to achieve real confidence they are going to work. National missile defense tests cost about $100 million each so we are never going have the “95% confidence that the system works 95% of the time” that some critics of missile defense have been advocating. (I’m not against that in principle; I’m just saying it’s never going to happen. Any missile defense development program has to be adjusted to that reality.)

I was reminded of my conversation with the missile engineer when NASA announced it was awarding SpaceX part of a $3.5 Billion dollar contract to deliver supplies to the ISS based on a single successful test flight. SpaceX is quickly becoming my favorite sociological experiment in missile development. Touted as a more cost effective way of getting into space, SpaceX has hired former NASA engineers and uses government facilities without, I’m sure, contributing to paying off their development costs; just some sort of use fee. But now, it seems, that the real way they are going to save money is not to have the sort of expensive testing program we might expect from a government development program. This isn’t going to be a rant against SpaceX, which as I say, is one of my favorite sociological experiments (which also doesn’t imply that I think they are doing the right things!) The problem is, I’m not sure what the government would use that development program for, anyways. If we are not using flight tests to determine statistical reliability, perhaps only one successful test is really all that is needed. If so, what does that tell us about countries just starting the development of their missiles?

Tests Associated with Various Development Programs

Program	No. of Tests	No. Successful Tests
Falcon-1 (SpaceX)	4	1
W-76	4	2*
RS-24	3	3
Al Samoud I (Iraq)	37	33
Al Samoud II (Iraq)	24	22
Nodong (DPRK only)	2	1
Taepo’dong I (DPRK)	1	0**
Taepo’dong II (DPRK)	1	0

*I have arbitrarily dropped the two tests with anomalous results from the successful column. **First 2 stages successful.

Integration Tests

One reason I like the Falcon-1 test series so much is illustrated by the reason the third flight test failed. Developed by engineers and scientists who have had plenty of experience developing other missiles, this missile failed (I believe) because they were concentrating so much on economic factors, namely the reuse of the first stage engine. If you want to reuse an engine, you don’t want to go firing pyrotechnics that blow holes in the nozzle to quickly drain the fuel. On the other hand, if you don’t quickly and reliably shut the engine down, the remaining fuel might cause the first stage to continue to produce a little bit of thrust and hence risk bumping into the second stage engine and breaking it as they separate. That is exactly what happened. Could SpaceX have caught this error if it had run more ground checks? If so, were they cut to reduce design costs? I hope you see why I like it so much.

The RS-24 is another interesting case that seems to be devoted to testing an integrated system. Pavel Podvig has made a very convincing argument that the RS-24 is a Topol-M missile with more than one warhead uploaded onto its bus. In that case, perhaps it shouldn’t need very many flight tests to get it up to speed. In fact, one might think that only the post-boost bus needs testing. But perhaps even that doesn’t need much testing since some claim that the Topol-M’s bus was tested for more than one warhead without loading any more on it by simply maneuvering as if it did have the warheads. (Some Russians claim exactly the same thing for some US post-boost buses. The US responds to those charges by claiming that additional maneuvers were needed for range safety reasons. And so it goes.) On the other hand, as the Falcon-1 test series shows, integrating different components does introduce new modes of failure. Were three tests enough? Apparently so, since Russia has said they will now introduce the RS-24 into their arsenal.

Statistical Uncertainty

The US philosophy of testing nuclear weapons is perhaps the hardest to understand; not least because so much is buried in secrecy. One could have imagined that, since the US performed over 1054 nuclear explosion tests (it appears that some tests had more than one explosive device tested at a time) and “developed” a total of 112 nuclear weapons, they could have used these tests to establish a reasonable statistical reliability for each weapon. After all, this corresponds to nine tests per bomb design with a significant number left over for testing one-point-safety, which would be reassuring. Except that the US testing philosophy was never to test to this level.

Instead, our nuclear tests were supposed to develop weapon designers’ expertise; an expertise from which they could judge the reliability of a nuclear design without further testing. This must rely on two assumptions that are probably true most of the time: 1) that the non-nuclear components are tested individually and as a whole enough times to establish a statistical reliability for the non-nuclear functioning of the design and 2) the nuclear process involves so many “particles” that statistical fluctuations cannot have a significant effect on the design’s function.

Some doubt that the later is true for the W-76, a mainstay of the submarine leg of our nuclear triad. Critics have suggested that the possibility that a macroscopic instability exists that violates the second assumption. It is also one of the few warheads for which the US has released information on its testing. It had a total of four tests during its development and apparently two of them had “anomalies.” They could have had anomalously high yields, or anomalously low yields, or anomalies that didn’t affect the yield; the open literature doesn’t say. However, we know that one anomaly resulted in a retest and the other in a change in a component (but no retest). Fortunately, there have probably been enough tests of the W-76 with the few stockpile surveillance tests done in the later years of testing to establish a reasonable statistical reliability, especially when more than one warhead is devoted to each target.

Other Countries
Given these examples of developed countries’ R&D programs, Iraq’s development of the Al Samoud I and II are very reassuring. Not only did they use flight tests to iron out the bugs, they went on to what we would call an extensive operational test and evaluation series. The last 11 Al Samoud II flight tests were for verification of the “firing table,” determining the range under various conditions such as changes to the pitch program etc. (One of these failed, so the operation failure rate of the Al Samoud II was probably around 10%.) Still, I cannot help suspecting that somebody in a powerful position might have made a lot of money for each test flight flown. Hence their large numbers. Still, if other countries followed this sort of a testing program, we would never miss their development of an ICBM.

North Korea, on the other hand, doesn’t seem to need nearly as many flight tests. Apparently only one successful test was needed for DPRK to start selling its Nodong missile abroad. Various analysts have come up with ingenious reasons for this and they could very well be right. But, on the other hand, do we really understand why and how we test complex systems well enough to claim to understand North Korea’s? I am full of doubt.

Note added: Just to be clear, when I say I think there have probably been enough stockpile surveillance tests of the W-76 to give a reasonable statistical confidence to the W-76’s reliability, that was not the intention of the surveillance tests. In fact, this statement is based only on my estimates of the numbers tested that I derived from a correlation analysis and published in Jane’s Intelligence Review in July 2005. As I hope I made clear, the reliability of nuclear weapons is officially based on the judgment of the designers and not on tests. Perhaps not surprisingly, that is probably the case with all the other tests considered here.

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The currently active US early warning satellites, SBIRS and DSP: each satellite is removed one at a time to highlight its individual coverage. Orbits have been determined by the amateur satellite observer network, see-sat, with particular thanks to Mike McCants, Greg Roberts, Peter Wakelin, and Scott Campbell

Now a ‘days everyone seems to know that you need at least two DSP or SBIRS satellites to track a missile in stereo. (Actually, that’s not exactly true. If only the US and Russia had continued with their RAMOS project, we could have jointly developed the sensors necessary to determine the 3D position of a missile with only a single satellite. That, however, is a different blog altogether.) But that is far from the only reason why we need at least two satellites observing every point on the Earth’s surface. Perhaps an even more important reason for having multiple observations of a missile’s heat signature is to eliminate false alarms.

Most, but not all, of the background from reflected sunlight is eliminated by looking at the Earth in only a very narrow band tuned to the wavelengths absorbed by water. Yesterday, we considered in detail the image taken by SBIRS HEO 2. One of the features of that photograph was a thunderhead that in all likelihood extended high into the atmosphere, past where most of its reflected light would have been absorbed by the surrounding water vapor. Today, we are going to look at a different source of background, sunlight reflected off of low altitude clouds but with a geometry where the sun, clouds, and satellite nearly line up. This results in what is known as specular reflection as opposed to the more common diffuse reflection. The later reflects much less light into the sensor and is, therefore, easier to eliminate as background.

The SBIRS HEO-1 checkout photograph (taken on 14 November 2006 of the launch of the DMSP F17 satellite from the Vandenberg AFB) provides a good example of how bright low altitude clouds can get:

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The Delta IV rocket lifted off from Vandenberg on a generally southern heading (I estimate an azimuth of about 190 degrees, based on the 98 degree inclination of the orbit) which, in the image as presented above, makes it appear to go downward. There is a clear decrease in the track’s luminosity just below the upper part of the track (which is its start) that is a combination of the trough region, as discussed in my post on signal and background, and the 28 second gap between main engine cut off (MECO) and the ignition of the second stage.

The thing I want to discuss about this photograph, however, is the bright background near the top of the image. Again, this background has been “artificially” increased by combining the images taken over several hundred seconds while the signal has been smeared across a number of different pixels as the rocket moves across the scene. However, the clouds near the Earth’s limb are considerably brighter than the clouds appeared in the image taken on 11 June 2008 of the Delta II even though that image was taken at local noon. Here, the sun, Earth, and satellite have almost exactly lined up, producing the enhancement associated with specular reflection. If this had not been over the United States, and if the satellite had been searching for launches as opposed to waiting for an expected launch, it is possible other meteorological—in combination with the alignment—could have produced a false alarm and perhaps triggered a nuclear war. One possibility might be for a storm front to be moving obliquely across limb of the Earth and different thunderheads to be illuminated in turn. Of course, we are talking about a system that continuously watches the Earth for years at a time and is bound to see all sorts of different and unexpected phenomena.

That is exactly what almost happened in 1983 when specular reflection caused many people in Russia’s strategic forces to think the US had launched an attack of half a dozen or so missiles. Fortunately, Col Petrov, the officer in charge of monitoring the newly launched system, decided such a small attack could not possibly be used to start a nuclear war. He was court-martialed for his troubles but at least we didn’t all die.

It is an interesting question just how much this danger is reduced by the SBIRS very high revisit rates; I would guess that an image is taken at least once a second and added into these composites we see here. After all, with more points on the “trajectory” it becomes more difficult for a natural phenomena to fake a missile launch. However, it is best not to rely on that too much. Instead, the US can usually view the same launch from two or more satellites; in this case SBIRS HEO 1, DSP F14 and DSP F17 with a possible contribution from DSP F16 if it used its above-the-earth-limb sensor; a special sensor that is meant to view rocket launches at the edge of the Earth and which appear silhouetted against the black background of space. This is apparently the only why Russia views missile launches but they can still get into trouble from reflections off of clouds and hence maintain early warning satellites in both geostationary and Molynia orbits looking at the central US missile fields from two very different directions. There are still worries, however, that Russia is not maintaining a complete Molynia constellation of early warning satellites and, some fear, could accidently start a nuclear war triggered by some rare weather phenomena or other benign event.

If the US currently has enough early warning satellites for this overlap, some analysts fear that it might not in a few years as DSP ages. But that is another blog.

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The image on the left is a simulation of the Delta II powered trajectory in GoogleEarth, the red portion is the solid rocket boosters; the image on the right is the actual SBIRS photo with the outline of Florida highlighted.

The US Air Force released the on-orbit checkout picture for SBIRS HEO 2 on 20 June 2008, showing in remarkable detail what that satellite, in a Molynia orbit, can do. I would say it was unprecedented, but the Air Force had actually released a similar picture that was published in November 2006, as I blogged about last Friday. In the November 2006 press release, the Air Force emphasized that the picture had been doctored by removing all the stars visible in the image so as not to give away which satellite the SBIRS HEO sensor was riding on. Unfortunately, there are few, if any, secrets in space! Amateur satellite observers had long ago determined which satellites SBIRS was riding on and had even determined their orbital elements. It turns out that Keplerian dynamics were declassified about 400 years ago. Perhaps the people responsible for our military space infrastructure should start taking that into account?

However, just knowing which rocket launch was being imaged allows us to say quite a bit about the capabilities of the sensor, though perhaps not the minimum thrust detectable by the system; something I wont even attempt to do. Since the image was released on 20 June 2008, we can look back for US launches that took place shortly before that and see that the most likely target was the 11 June 2008 launch of the GLAST scientific satellite which went into a nearly circular orbit with an inclination of 26 degrees from Cape Canaveral onboard a Delta II 7920H. That orbital inclination corresponds to a launch azimuth of 90 degrees. From the publicly available information about the Delta family of launch vehicles, we can determine the timeline of important events for that launch and, in fact, simulate its trajectory with a high degree of certainty. These events are listed as the first comment in that section of this blog.

Simulating the GLAST launch helps identify the various phenomena discussed in the previous blog as well as the area of the Earth’s surface visible in the image. It appears to me that the outline of Florida is clearly visible in the image as is, perhaps, the Grand Bahamas Island. (I can’t be as sure about that later identification.) The SBIRS image clearly shows many of the phenomena we discussed yesterday. My identification of these features are shown in the picture below; what follows is a more detailed discussion of them.

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(note that this image has been rotated 180 degrees from the images above, so that the track starts on left and ends on the right.)

A) The Delta II 7920H has a total of nine strap-on GEM solid-propellant boosters. Six of them are lit on the ground after the main stage, or core, liquid propellant engines are started. Three are lit while the rocket is in the air, at 66 seconds into the flight and about 14 km up. These solid-propellant boosters have, as do most modern solid-propellant motors, a high component of aluminum mixed in. This serves to increase the combustion temperature inside the motor casing but as come out the nozzle as fairly large globs of liquid aluminum (on the order of 100 microns in diameter). This molten aluminum continues to oxidize after leaving the nozzle and helps produce this very bright segment of track. The main core liquid-propellant engine, which burns LOX and kerosene, probably has a very complete combustion inside the chamber. However, it does contribute to this part of the track if for no other reason than the reheating caused by shear-shock as it exits the nozzle and hits the surrounding atmosphere. The last three strap-ons burn out at about 68 km altitude (marked by B in the image).

B-C) This segment of the track is caused by the core first stage, with the predominant portion caused by the shear-shock reheating of the exhaust.

C-E) The missile has entered the “trough” region where plume brightness is minimal, at least partially because the exhaust gases come out of the nozzle almost at rest with respect to the surrounding atmosphere. (In other words, the rocket is moving at the speed of its exhaust gases and they enter the atmosphere almost at rest.)

D) This is almost certainly a thunderhead that has risen so high (some can reach 23 km) that it can reflect a lot of sunlight back to the sensor. There are no significant events in the rocket trajectory at anywhere near this time that could account for a missile generated event. If it is an illuminated cloud, it has been “integrated” over some 200 seconds by adding a whole series of frames together. Each individual frame from SBIRS would show a very low intensity cloud image here and the rocket exhaust plume would be considerably brighter, eliminating the problem seen here of tracking across the cloud.

F) The rocket has left the “trough” region and its exhaust is being reheated by the collapsing shockwave as the atmosphere rushes back into that space. There appears to a significant cross-track movement to the trajectory here. The things that occur to me are either jitter in the sensor—it has to keep pointing accuracy to something on the order of 14 microradians over several hundred seconds in this case—or it could be that the missile actually made a significant course correction here. Of course, the satellite does not need to point to that accuracy, it just needs to hold the image that still either mechanically, by a steering mirror, or digitally by adjusting some guide pixels. Both of these techniques have become familiar to owners of digital cameras in recent years.

G and H) G is almost certainly the tip of Florida and I have come to believe that H is the Grand Bahamas Island. The background, which has remained stationary in the frame, has been essentially “integrated” over some 200 seconds. This has allowed the very faint ground image to show up.

I) This is the end of the track shown in the image. Since the rocket coasts for some 10 seconds (which would correspond to some 450 km) it is not a brief increase in luminosity showing up as the second stage plume hits the first stage as it falls away. In fact, I am not 100% convinced that it is even the end of the first stage firing. It has proven very hard to get a good match up between the SBIRS image and the GoogleEarth position so I cannot say with certainty that it corresponds to MECO (Main Engine Cut Off). On the other hand, there is a definite increase in brightness that could be associated with MECO, though what exactly, I don’t know.

Tomorrow, I will look at the other SBIRS image, which shows the limb of the Earth in the field of view and very bright clouds. While it too has been integrated over several hundred seconds, it shows another reason why it is good to look at missile launches in stereo, and not just for tracking! See my CATO paper on Russia’s space-based early warning system and in particular, what I call the Autumnal Equinox Incident that almost started a nuclear war between the US and the Soviet Union.

Comment [8]

Before analyzing the two SBIRS-HEO images, its necessary to review a little of phenomenology associated with viewing rocket plumes in the infrared. That’s because there are some surprising effects that show up very well in both these photos that, perhaps, most people would not be aware of. In particular, I’m thinking of the “trough” a missile plume appears to go through when it passes through a region roughly 70 to 90 km high. If you look back to the first post I made on these images , you can perhaps see this trough as a dim spot in the plume’s trace as it streaks across the field of view. But I’m getting ahead of myself. Today, we need to discuss both the signal and the predominant background: reflected sunlight.

From the very start of the US space-based, early warning program, our satellites have reduced the background caused by sunlight reflected off of various things (clouds, snowfields, water) by only looking in a very narrow wavelength around 2.7 microns. This is the band at which water both radiates—when it is created in the combustion of hydrocarbons such as kerosene and acids such as nitric acid—and absorbs when it is in a more relaxed state, such as water vapor in the atmosphere.

What the world would look like to SBIRS if there were no atmosphere
If you were to stand 100 meters away from a Titan II missile (sorry, I know that’s rather an obsolete missile, but I happen to have the data for its plume radiance but not for more relevant rockets such as the Delta II) was firing, every thing else would appear dimmer than the plume. That is because sunlight reflected from a square meter is relatively weak as shown in the left side of this picture:

The right side of this picture shows a rather artificial comparison, namely if there were no atmospheric or dynamic effects. Here, a single pixel on the SBIRS sensor is assumed to be 0.5 km x 0.5 km on a side. In that case, you have no choice but to add up (or, as a techno-wonk might say, “integrate”) all the sunlight reflected to SBIRS that landed in that pixel. In this case, the sunlight is assumed to be reflected by something like white sand (white in the infrared(!), whatever color that corresponds to) and is “diffusively” reflected. If the sun, Earth, and satellite are aligned in the proper way, you could get specular reflection, when the Earth acts as a very good mirror, and get a considerable increase in solar power directed into the pixel and further worsening the signal to noise ratio. It doesn’t take ice or snow to give specular reflections, you can see from an airplane that trees, rocks, cornfields, clouds also give specular reflection—only in this case, specular backscatter—if you look at the bright circle around the plane’s shadow.

Adding in atmospheric absorption
Most of the sunlight, however, is reflected off of things fairly low in the atmosphere. Even most clouds are, almost by definition, in the “moist” part of the atmosphere where water vapor can absorb the same wavelengths of light that is generated by the water molecules in the rocket exhaust. The graph below shows the one-way absorption of light by the atmosphere for different heights that it originated. Sunlight reflected off of clouds would have to pass twice through this absorption and be even further reduced relative to the signal.

By the way, this atmospheric absorption worked so well and the DoD was so entranced by it that it apparently became very difficult for other sensors, that did not use this this absorption band, to be approved. Lets hope that the few military satellites that have flown with other sensors have convinced the powers-that-be that those wavelengths are valuable too!

Rockets move fast
This is not the complete story, however! There are other effects as the rocket moves through the atmosphere that also changes its signal. At low altitudes, there is enough oxygen for unburnt fuel to combust in “afterburning.” This, plus the shear-induced shock wave produced by the exhaust as it hits the atmosphere upon exiting the nozzle, increases the plume temperature and hence the signal at low altitudes. Even the aluminum particles ejected from most solid propellants continue to combust and radiate at these altitudes. These low altitude enhancements reach a maximum at around 20 km and can fall very quickly above that as the atmospheric oxygen drops off.

After the low altitude effects drop off, the plume is said to enter a “trough” region where the overall brightness of the plume drops to very low levels. In addition to a lack of oxygen for afterburning, the rocket is moving so fast that its exhaust gas comes out almost at rest with respect to the atmosphere. This reduces the shear shockwave effect that reheats the exhaust at lower altitudes, causing a further reduction in radiation. The trough occurs roughly between 40 and 90 km. Above this altitude the exhaust brightness increases again: the exhaust first displaces the very thin atmosphere as it comes out at temperatures lower than the ambient temperature. But as the rocket moves away, the atmosphere actually compresses the exhaust plume, creating a new shockwave that can reheat the plume up to temperatures near the combustion chamber temperature. These different regions are shown in the picture below:

Tomorrow, we will use these effects to understand the images taken by SBIRS-HEO 1 and 2. Until then, you might want to play around with the model of the Delta II 7920H that I’ve written to simulate the June 11, 2008 launch that SBIRS-HEO 2 imaged. There are, unfortunately, a number of approximations I’ve had to make to simulate this missile with its very complex flight that has both ground- and air-lit strap on solid-propellant boosters. I’ve included it as the first entry in the comment section. Remember, you can use GUI_missileFlyout to run that model.

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