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Boy, Does This Need A Follow Up

ESMD has finally responded to Keith Cowing's questions to NASA PAO.

One bit of explanation is required, I think. When Keith refers to a "five-by-five" matrix, he's talking about the standard risk assessment tool that NASA (and ARES Corporation, for whom I casually consult, and others) use to track program risk.

Here's an example from the Mil Standard, but it's a five by four (five levels of probability, four levels of consequence). Anything that is in one corner (low likelihood, low consequence) can be ignored, and anything that is in the opposite corner (high for both) should be receiving the bulk of the program resources. Things that are in between are tracked, and measures are taken to move them down to the 1,1 corner of the matrix. Though I can't find an example of one at my fingertips, the five by five is a little more fine grained in consequence level.

It can be used either for safety issues (in which case, "catastrophic" corresponds to loss of mission or crew), or for programmatic issues, in which case "catastrophic" would probably be complete program failure. It's a little harder to evaluate in this case, though, because that depends on how "program failure" is defined. Does it mean that the program is cancelled? Or does it mean that the program is restructured beyond recognition? Ares 1 seems to me to be vulnerable to either one.

What exactly is the issue? The problem is that any structure has a resonant frequency at which it naturally vibrates. If you excite the structure at that frequency, you can develop a positive-feedback system that will literally shake it apart (the Tacoma Narrows Bridge is the classic example).

Solid rocket motors don't run particularly smoothly (compared to well-designed or even poorly designed liquids) and large solid motors provide a very rough ride. Everyone who has ever ridden the Shuttle to orbit has commented on how much smoother the ride gets after staging the SRBs.

Now, one way to mitigate this is to damp it out with a large mass. The Shuttle does this by its nature, because even though it has two of the things, they are not directly attached to the orbiter--they are attached to a large external tank with one and a half million pounds of liquid propellants in it, and it can absorb a lot of the vibration. Moreover, the large mass has a frequency that doesn't resonate with the vibration.

As I understand it (and I could be wrong, and I'm not working Ares, but this is based on discussions, many off the record and all on background with insiders on the program), there is a very real concern that the upper stage on top of the SRB in "the Stick" will be excited at a resonant frequency, but that even if not, the stage will be too small to damp the vibrations of the huge SRB below.

If this is the case, there is no simple solution. You can't arbitrarily change the mass of the upper stage--that is determined by the mission requirement. Any solution is going to involve damping systems independent of the basic structure that are sure to add weight to a launch vehicle that is already, according to most reports, underperforming. Or it will involve beefing up the structure of the upper stage and the Orion itself so that they can sustain the acoustic vibration loads. In the case of the latter, it is already overweight, with low margins.

So this constitutes a major program risk, that could result in either cancellation, or a complete redesign (that no longer represents the original concept, because the problem is fundamentally intrinsic to it).

Now, let's take apart the response a little:

Thrust oscillation is...a risk. It is being reviewed, and a mitigation plan is being developed. NASA is committed to resolve this issue prior to the Ares I Project's preliminary design review, currently scheduled for late 2008.

The problem is that NASA can "commit" to resolve it until the cows come home, but if it's not resolvable, it's not resolvable. They can't rescind the laws of physics, and we're approaching a couple of anniversaries of times when they attempted to do that, with tragic results.

Now this next part is (to put it mildly) annoying:

NASA has given careful consideration to many different launch concepts (shuttle-derived, evolved expendable launch vehicle, etc.) over several years. This activity culminated with release of the Exploration Systems Architecture Study in 2005. Since then, the baseline architecture has been improved to decrease life cycle costs significantly.

NASA's analysis backs up the fact that the Ares family enables the safest, least expensive launch architecture to meet requirements for missions to the International Space Station, the moon and Mars. NASA is not contemplating alternatives to the current approach.

The problem is that NASA didn't give "careful consideration" to the previous analyses after Mike Griffin came in. As far as can be determined, all of the analysis performed under Admiral Steidle's multiple CE&R contracts, performed by major contractors, was ignored, and put on the shelf to collect dust while NASA decided to build what the new administrator, along with Scott Horowitz and Doug Stanley, were predisposed to build. I have never seen "NASA's analysis" that supports this statement. Steve Cook made a valiant attempt to justify it at the Space Access Meeting last March, and was given kudos, at least by me, for having the guts to come in and defend it to a hostile audience, but no one was convinced, or even saw convincing data. He simply stated the conclusions, but didn't show the numbers.

But the most troubling thing to me is the end:

Thrust oscillation is a new engineering challenge to the developers of Ares - but a challenge very similar to many NASA encountered during the Apollo Program and development of the space shuttle. Every time NASA faces an engineering challenge - and it faces many - agency engineers examine all the options for addressing the issue. NASA has an excellent track record of resolving technical challenges. NASA is confident it will solve this one as well.

The problem is that, in reality, despite its confidence (or at least its stated confidence) NASA's record on this score is, at best, mixed. For instance, think about (as just two examples) the X-33. Or the OMV (I did a Google on it, and couldn't come up with any good histories of it--one needs to be written). Or many of the original space station concepts, which required complete redesigns. Sometimes engineering challenges are just too great to overcome, and a new approach is required to overcome a flawed concept. I don't know whether that's the case with Ares 1 or not, but this response doesn't instill in me any confidence that it's not.

Posted by Rand Simberg at January 17, 2008 04:02 PM
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Is there some reason why they can't/don't want to use the Atlas V or Delta IV?

Posted by rickl at January 17, 2008 06:48 PM

Apparently there is. Whether that reason would stand up to engineering or taxpayer scrutiny is a separate question...

Posted by Rand Simberg at January 17, 2008 07:00 PM

It would seem Direct would solve this issue.

Posted by Mike Puckett at January 17, 2008 07:08 PM

There are many solutions to this issue. The problem is that NASA, for whatever reasons, seems determined to make the Ares 1 the solution to the issue.

Posted by Rand Simberg at January 17, 2008 07:32 PM

That response is a complete non answer and the hope is that Cowing and the other space industry papers go after this one. Administrator Mike Griffin is wasting billions of dollars worth of taxpayer money on a system that he already knows is unlikely to be workable.

Many sources indicate that the engineering group at the Marshall Spaceflight Center would quit en masse if they could. Many engineers are trying desperately to find charge codes that do not have anything to do with Mike's stick.

Beyond this, Griffin is the laughing stock of even his headquarters operation. Everyone knows that no matter who is elected, Griffin is gone and so are just trying to lay low until this blessed event comes. The worst thing about this is that it is so bad that many are pining for the "good old days" under administrator Dan. Dan was crazy, but at least let the minions do their jobs. Mike thinks that he is the second incarnation of Von Braun, sans the good judgement.

Posted by Random Thoughts at January 17, 2008 09:13 PM

Is there some reason why they can't/don't want to use the Atlas V or Delta IV?

Yeah. The Senator from Utah wouldn't like it.

Posted by K at January 17, 2008 10:35 PM

There are no infidels in Baghdad

Posted by kert at January 18, 2008 07:40 AM

I got thinking about this statement:

What exactly is the issue? The problem is that any structure has a resonant frequency at which it naturally vibrates.

While it is true, it also is an extraordinary claim to make. So I got thinking about how to explain why this is true. So this is my first attempt at the matter.

Most mechanical systems (and most dynamical systems, that is physical systems that change over time) have the property that small inputs leads to small physical changes. That is, you're not looking at a system where the changes are big enough to instantly break the system (say as a house of cards can collapse or a pen precariously balanced on end can fall, if anyone jostles the table).

When you have that situation, then for small enough changes, the system will behave linearly. That is, the change in the parameters of the system with respect to time can be described as a linear function of the parameters. Second, that you can adequately describe your system using a finite number of objects. Third, that you have an equilibrium point. The Solar System can be described over small time steps linearly and knowing the center of gravity of the significant masses are usually enough for modeling purposes, but it doesn't have a stable point. Everything is always in motion. But a building normally does (ignoring structures that are intended to be in motion like carousels).

What this means is that at some point, you can describe small vibrations in a building by

dX/dt = A*X

where X is a list of n real number parameters (or an "n-dimensional vector") and A is a finite square matrix of numbers (there are n rows and n columns of numbers in this matrix). The product A*X is also a vector. The ith element of this product is the ith row of A multiplied component by component with the respective number in X and summed together. This is standard matrix multiplication for those in the know.

One property of multiplication by this matrix A is that there's at least one way (and usually there are a full and maximum n ways) in which multiplication of A looks like multiplication by a number. This number is a complex number, that is you usually need the square root of -1, "i" (engineers use "j") to properly describe it. In practice all complex numbers have the form "a + i*b" where a, b are real numbers.

What this means is that there's a perculiar choice for the parameters of X, which I will call "Y" and a complex number c, so that

A*Y = c*Y.

In other words, multiplication by A is the same as taking each number in the list of Y and multiplying it by c. c has the form

c = k + i*w.

where k and w are both real numbers, and i is the square root of -1 as described above.

Usually, Y doesn't make physical sense because it is composed of complex, but not real numbers. The trick usually is that there's also a second "c" which I'll call "c'" which has the form:

c' = k - i*w,

and a parameter choice "Y'" so that

A*Y' = c'*Y'

*and* so that the imaginary (the parts multiplied by i) parts completely cancel out. That is, Y+Y' is a list of real numbers. What happens is that whenever you have some bit of Y showing up in the vibrations of your building, it is always exactly matched by Y' so everything stays real.

So what does this mean for your building? It means that there's a vibration mode described by c,Y. Namely, that you have vibrations of the form

exp(k*t)*cos(w*t), exp(k*t)*sin(w*t).

The vibrating parts, cos(w*t) and sin(w*t) don't contribute much. They are bounded in size. "w" is just the frequency of the vibration.

If k were positive, then you'd have exponentially increasing vibrations. This is the special case of a positive feedback system. That is, when k is positive, you have positive feedback. In practice, this means that you quickly push the building out of the space where a linear approximation makes sense and it goes into some sort of non-linear dynamics. Also, this usually means that the building tears itself apart. I believe you'd need some sort of energy source (like a disfunctional active ounterweight system) to get a positive feedback system. In biology, you might see this sort of thing in growing populations due either to synchronized breeding, day/night cycle, or short term exhaustion of food supply.

When k is negative, you have an example of a damped system. That's because the vibration is decaying exponentially.So if there's no new inputs of energy into the system, your vibration eventually dampens out. As k gets closer to 0, the dampening gets weaker. Energy remains in that vibration mode for longer, if you will.

What actually happened with the Tacoma Bridge is not a case of positive feedback. That is, the bridge didn't have an exponentially growing vibration shake it apart. But instead, it had a vibration mode with weak dampening. k was too close to zero. So when there was an energy input to that frequency (from a strong wind at the time), the energy inserted by the wind was insufficiently dampened by the bridge.Further, it took the bridge out of a space where linear approximations make sense and put it in a non-linear space where things start to break and the bridge eventually collapse.

Fron the point of view of Ares 1, there is a heavy upper stage mounted via a small neck to the SRB lower stage which as Rand notes, generates a lot of vibration. As I understand it, the vibration mode is of the top stage moving transversally relative to the lower stage (think of it as a rocking dumbbell with the weights on the ends being the two stages and the handle in between being somewhat weak and flexible). The only place that can dissipate this vibration is the neck connecting the two pieces. k naturally is near zero for this sort of thing because you have a small region dampening the vibration. By adding mass, and either strengthening the neck or increasing the ways energy of the vibration mode can be syphoned away, you can move the "k" for this vibration mode away from zero and improve dampening of this vibration mode.

The problem is whether you have a usable launch vehicle after you've added the mass.

Posted by Karl Hallowell at January 18, 2008 08:28 AM

That rocked! I actually learned something out of that. Thank you...

/me nominates Karl's comment as Comment of the Year.


Posted by Michael Mealling at January 18, 2008 08:50 AM

As I understand it [snip], there is a very real concern that the upper stage on top of the SRB in "the Stick" will be excited at a resonant frequency, but that even if not, the stage will be too small to damp the vibrations of the huge SRB below.

Yep. Spot on. Orion and Ares I are very worried about it. One structures guy called Ares I a piece of spaghetti pushing a balloon with a lead weight on top.

Oh, and Orion contractor staff familiar with Atlas predicted this problem a year ago.

Posted by anon at January 18, 2008 08:50 AM

/me nominates Karl's comment as Comment of the Year.

Thanks Michael. BTW, can someone slip me that prize before something better comes along? :-)

Posted by Karl Hallowell at January 18, 2008 02:50 PM

Looks like the cat is finally out of the bag, and boy is he pissed. How long before the ESAS architecture falls by the wayside? Reports of a $700M dollar budget shortfall pushing the testing of the system into the next year, and increasingly confident reports that the Ares 1 is an underperforming vehicle along with an Ares V that is 13 tons shy of its desired performance.

When ESAS dies, what is going to be our path to the future? This should be thought about now, rather than later. Mike Griffin is headed for an iceberg at full steam with no clue what to do when his ship is ripped from stem to stern or even interest in jumping ship to another idea. He has staked all on this and what happens when congress figures out what is going on and stops it?

Posted by Random Thoughts at January 18, 2008 06:00 PM

I guess the Stick came out of the "lessons learned" of the two fatal Shuttle accidents -- put the upper stage on top of the solid booster so it can't get torched, and put the heat shield on top of the upper stage so ice or foam can't smack it. I get the feeling that apart from addressing those two concerns, the stick is a naive design.

As to either EELV, my understanding is that they are designed to take smaller payloads to GEO instead of larger payloads (the CEV) to LEO, so by and large their upper stages are seriously underpowered.

Don't know if this is under the rubric of Direct or what, but it seems the sensible thing would be to develope a single launch vehicle along the lines of Shuttle C, and launch everything with it.

This vehicle is now too powerful to launch the CEV-only mission? There once was talk that the separate Saturn-V Saturn-Ib was too expensive -- that it could have been cheaper just to make more Saturn-V's and launch all Apollo flights, lunar or Earth orbit, on the one rocket.

This vehicle has a pair of solid boosters next to the tank? Haven't they pretty much solved the leaking booster problem -- it seems that the foam problem and a host of other problems are without solution, but I haven't heard anyone worry about booster seals in a long time.

Posted by Paul Milenkovic at January 18, 2008 06:27 PM

The Ares 1 vibration story is listed on the main Yahoo! page as I write this ...

Posted by Jay Manifold at January 18, 2008 08:08 PM

The people who deride Ares as a "jobs program for NASA" will usually turn right around and cry about how there are so few people going into aerospace these days. Well, no shit Sherlock, there's nothing for them to do! What, you're gonna spend seven years in college so that you can go build radio satellites for the next forty years? Whoop-dee-fukkin'-doo.

You're right that Ares is a jobs program. It's a jobs program to attract students to an aerospace career. On the other hand, I can see how a bunch of old farts wouldn't want any of those young whippersnappers running around. By gaw, I was building rockets with my bare hands, biting holes in aluminum with my teeth, driving rivets by kicking them. MGSE? We just lifted the bastards onto the pad, and we used a garden hose and a hand pump for the IRFNA.

Posted by DensityDuck at January 21, 2008 03:45 PM

Duck needs to lay off the steroids. Steroids is why the Ares I will never fly.

If it walks like a duck, talks like a duck and quacks like a duck, it's a duck. Ares I is a duck.

And so are you. A duck. On steroids. Pretty ugly.

Posted by You Dawg Is Gawd at January 21, 2008 09:40 PM

What Karl so clearly explained there is the notion of an eigenvector and its associated eigenvalue. These are also sometimes called characteristic vectors and characteristic values.

Posted by Paul F. Dietz at January 22, 2008 12:25 PM

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