Missiles and Rockets

Missiles and Rockets was a magazine that ran from the mid 1950's to the mid 1960's at the height of the Space Race. All the issues are available on the internet archive. It's neat to see some of the old concepts (like the manned rocket bomber above), and the advertisements in the early issues by companies trying to hire engineers and scientists so they can cash in on the flood of funding in the early gold rush days are pretty entertaining.

Some interesting aerodynamics & control details on the re-design required for the Falcon Heavy at 15:20 or so. Great launch!

Starscraper Sounding Rocket Kickstarter

The Boston University Rocket Propulsion Group (BURPG) is developing a sounding rocket designed to top 150km and funding it partially through a kickstarter campaign. They plan on launching from Blackrock next year like Qu8k, but this is a more ambitious and complex effort.

The rocket will be controlled using fluid injection thrust vectoring. The thrust levels of their hybrid motor are comparable to Qu8k, but it is a significantly larger (30 vs 14ft long, 12 vs 8in diameter) and heavier (1100 vs 320 lbs) and aims higher (150km vs 120kft). It's hard to tell, but it also seems to be an order of magnitude or so more expensive.

The advantage the BURPG folks claim for their concept over traditional solid fuel sounding rockets is a gentler ride for payloads on the longer, smoother burning hybrid.

Funding for US Government Launch-Related Activities

As part of a broader effort looking at impediments to launch services procurement, the GAO summarized US government-wide budget requests for space launch-related activities (pdf). The purpose of the GAO's broader effort is to provide short- and long-term assessments examining impediments to economical procurement of government launch vehicles and launch services across government.

GAO reviewed FY14 through FY18 space launch-related President's Budget (then year dollars) request by NASA, NOAA, and DOD including military services and other offices.

US Government Launch Procurement Budget Requests

(then-year $M)	FY14	FY15	FY16	FY17	FY18	Total
Procurement	4981.4	5819.7	5816.2	5914.4	5915.5	28447.2
RDT&E	2469.0	2473.0	2414.6	2073.9	1834.0	11264.5
Other	1053.5	774.3	770.7	790.0	762.5	4151.0
Total	8503.9	9067.0	9001.5	8778.3	8512.0	43862.7

Total funding seems pretty flat accross the five years examined. Both DOD and NASA are acquiring launch vehicles by launch services contracts. Procurement is about evenly split between DOD and NASA (slightly more by DOD). The bulk of RDT&E dollars are spent by NASA: $10.5 billion over the five years vs. $718 million.

On the slide detailing the RDT&E spending this report cites another GAO report about the FY10 National Defense Authorization Act requirement for the Department of Defense and the Director of National Intelligence to issue a space science and technology strategy every 2 years. GAO recommends DOD coordinate more with NASA and NOAA to leverage their significant RDT&E investment.

I am interested to see what "impediments" GAO finds as a result of their broader effort.

SCRAMSPACE: Launch Anomaly

Tough day at Andoya Rocket Range for University of Queensland SCRAMSPACE team. My heart goes out to these guys; they put a lot of good time, effort and smarts into their experiment.

Here's the official statement:

“The rocket carrying the scramjet launched at 3pm (Norwegian time, 11pm Brisbane time), however the payload failed to achieve the correct altitude to begin the scientific experiment as planned.

“The SCRAMSPACE payload, according to our data, was operating perfectly and performed extremely well before and during the launch, and we received telemetry data all the way into the water.

“Unfortunately the failed launch meant we could not carry out the experiment as planned.”

“The team is very disappointed. The project represents a lot of time, effort and money by a committed consortium of partners and sponsors.”
University of Queensland Hypersonics Chair Professor Russell Boyce

Orbital Sciences Antares Launch Success

A New Nuclear Rocket Concept

The folks at University of Washington and MSWNW LLC. have a new Fusion Driven Rocket concept. It combines magnetic and inertial confinement to achieve fusion and subsequent fuel heating for high exhaust velocity.

HIFiRE-5 Flight Test Preliminary Results and Video

Check out the preliminary results on AIAA's ARC site: HIFiRE-5 Flight Test Preliminary Results

Nuclear Rockets Petition

As reported by NBC there is a petition on WhiteHouse.gov to rapidly develop and deploy a nuclear thermal rocket for both manned & un-manned space missions. I signed it; why not? Here's the short url: http://wh.gov/UVuD

Nuclear rocketry seems to be a popular topic of late. Gary Johnson has a recent post about nuclear rockets. The NBC article mentions NERVA. There is also the more recent Project Timberwind and Space Nuclear Thermal Propulsion program effort to develop nuclear upper-stages.

Falcon 9 Flight 4, CRS-1

Congratulations to SpaceX on their successful launch of the first commercial resupply mission to the International Space Station!

Rocket Risk

As reported on ParabolicArc, NASA awarded SpaceX a contract to launch one of their science payloads. The topic of NASA's assessment of launch service provider risk naturally came up. NASA has published payload value, and risk rating guidelines.

If we assume that each launch has the same probability of success, then these are simple risk calculations to make, e.g. see these slides. The posterior probability of success, \(\theta\), is
\[ p(\theta | r, n) = \mathrm{Beta}(\alpha + r, \beta + n - r) \]
where \(r\) is the number of successes, \(n\) is the number of trials, and \(\alpha\) and \(\beta\) are parameters of the Beta distribution prior. What values of parameters should we choose for the prior? I like \(\alpha=\beta=1\), you could probably make a case for anything consistent with \(\alpha+\beta-2=0\). Many people say that risk = probability * consequence. I don't know what the consequences are in this case, and under that approach NASA's chart doesn't make any sense (you could have a low risk with a high probability of failing to launch an inconsequential payload), so I'll stick to just the probabilities of launch success, and leave worrying about the consequences to others.

Since NASA specifies a number of successes in a row (consecutive) then there is already an indication that assuming the trials independent and identically distributed (i.i.d.) is unrealistic. If your expensive rocket blows up, you usually do your best to find out why and fix the cause of failure. That way on the next launch your rocket has a higher probability of success than it previously did.

HIFiRE 2 Videos

Lug camera video of the HIFiRE (Hypersonic International Flight Research and Experimentation) flight 2 launch:


Multiple high-speed views:


Additional coverage on Parabolic Arc.

Second Falcon 9/Dragon Launch

Successful launch of the Falcon 9/Dragon to the International Space Station for COTS demo flight 2.


Lots of coverage on Parabolic Arc and Nuite Blanche.

Sears--Haack Body for Mini-Estes

We have a little company here in Dayton that does print on demand (Fabbr) with Makerbots. They specialize in printing RepRap kits, but I think I'm going to see if they can print me a little rocket to use with Estes mini-motors.
The 1/4 and 1/2 A motors are 13 mm in diameter and 44 mm long.

The first thing you need to print a part with these hobby printers is an stl file. I followed a some-what torturous route to generating one.
First I made a little python script to find the minimum volume Sears-Haack body that would fit a 13x44 mm cylinder. The bold black curve is the minimum volume body; it happens to have a length of twice the motor length.

As you can see in the script, I also dumped an svg file of that curve. This is easily imported into Blender. Then the svg curve must be converted into a Mesh, and the Spin method applied to generate the body of revolution.

I played with the number of steps to get a mesh that looked like it had surface faces with near unit aspect ratio (not that it really matters, but old habits die hard).

Now I should be able to add some fins and export an stl from Blender for my rapid prototyping friends to play with. The design goal for this rocket will be to have positive static margin with the motor in the rocket, but neutral or negative static margin once the ejection charge pops it out the back (that way it does a tumble recovery).

Qu8k Accelerometer Data

There was a pretty cool amateur rocket shot recently that was an attempt to win the Carmack micro-prize. The rocket is called Qu8k, designed and built by Derek Deville and friends. One of the stipulations of the prize is collection of a GPS location by the onboard avionics at an altitude above 100kft (as long as the velocity is low, this should theoretically not require an unrestricted GPS).

Of course, since the other stipulation of the prize is a detailed report about the shot and the data collected, this gives us number crunching nerds a neat data set to play with. Derek posted a spreadsheet of the accelerometer data, along with a simple first order integration (twice) to get velocity and altitude. I tried an FFT-based method to compare against the first order approach in the spread-sheet, and a second-order trapezoidal rule integration. The python script to do the integration and make the two plots below is on github.

The errors in the numerical integration are not terrible (the plots of the trajectories using the different approaches are indistinguishable in the eye-ball norm).

One of the cool things about Python is the array masking capability. That makes implementing the temperature ratio component of the 1976 US Standard atmosphere (to estimate Mach number) 7 lines of code.

J2X Time Series

I thought the intermittent splashing of the cooling water/steam in the close-up portion of this J2-X engine test video looked interesting.

So, I used mplayer to dump frames from the video (30 fps) to jpg files (about 1800 images), and the Python Image Library to crop to a rectangle focused on the splashes.

When a splash occurs the pixels in this region become much whiter, so the whiteness of the region should give an indication of the "splashiness". I then converted the images to black and white, and averaged the pixel values to get a scalar time-series. The whole time series is shown in the plot below.

Also, here's a text file if you want to play with the data.

Here's a PSD and autocorrelation for the section of the data excluding the start-up and shut-down transients.

Here's a recurrence plot of that section of the data.

This is a pretty short data set, but you can see that there are little "bursts" of periodic response in the recurrence plot (compare to some of the recurrence plots for Lorenz63 trajectories). I'm pretty sure this is not significant to engine development in any way, but I thought it was a neat source of time series data.

Second HTV-2 Flight Test

The second HTV-2 test flight experienced a loss of telemetry about 9 minutes into the flight, very similar to the first test-flight. The post-flight analysis from the first flight indicated that inertia coupling caused the vehicle to depart stable flight (which lead the autopilot to terminate the flight). Here’s a relevant snippet from Bifurcation Analysis for the Inertial Coupling Problem of a Reentry Vehicle,

Inertial coupling has been known since around 1948 [1]. It is essentially a gyroscopic effect, occurring in high roll-rate maneuvers of modern high-speed airplanes including spinning missiles designed in such a way that most of their masses are concentrated in the fuselage. For such an airplane, a slight deviation of its control surface angle from the steady-state angle may lead to a drastic change in roll-rate, causing damage on its empennage; known as the jump phenomenon. Nonlinear analyses to elucidate this problem have been reported in [2, 3], for example. However, the airplanes treated in these works are stable around the equilibrium point of level flight. On the other hand, an intrinsically unstable reentry vehicle, if combined with a malfunction of its AFCSs, may result in a catastrophe once it falls into a high roll-rate motion.

This does sound an awful lot like what happened to both of DARPA’s HTV-2 vehicles. Departure from controlled flight due to inertia coupling was the cause of a loss of crew in the early X-2 testing [4].

Simple explanations are usually not the reason for flight test accidents or mishaps. Experience has shown that there is usually a chain of events that lead to the mishap. Day gives a great summary of the combination of contributing factors that lead to the fatal X-2 test [4],

• Optimum energy boost trajectory.
• The rocket burn was longer than predicted by 15 sec and positioned the pilot further from Muroc Dry Lake than expected.
• Decrease in directional stability as speed increased.
• Decrease in directional stability with increased lift, leading to a reduced critical roll rate for inertial coupling.
• Adverse aileron control (control reversal).
• High positive effective dihedral.
• Rudder locked supersonically.
• Mass properties in window of susceptibility for inertial roll coupling.

Day describes the result of hitting an unstable region in the control parameter space:

At critical roll velocity, violent uncontrollable motions characteristic of inertial roll coupling occurred about all three axes.

At low-speeds this might be recoverable, but it is simply intractable to design a hypersonic aircraft to handle the loads this kind of rapid motion imposes on the vehicle structure. Eventually something gives, and this “jump” leads rapidly to catastrophic failure.

Day summarizes the reasoning for not modifying the X-2 for manned hypersonic flight,

The X-2 was unfortunately in the twilight zone of progress where rocket power, structural integrity, and thermodynamics were sufficiently advanced to push the aircraft to supersonic speeds. However, hydraulic controls and computerized control augmentation systems were not yet developed enough to contend with the instabilities.

And a relevant snippet from the more recent bifurcation analysis,

If it has unstable dynamics in the neighborhood of a trim point, a slight external disturbance or a slight deviation of control surface angles from their precise values at the trim point cannot allow the vehicle to stay at the trim point [5].

The flight regime that HTV-2 is operating in is unknown enough that it is difficult for designers to know before flight if the flight profile will put the vehicle into an unstable region of the control space. I thought the language that the program manager (a fellow AFIT alum btw) used to describe the post-flight analysis was interesting,

“Assumptions about Mach 20 hypersonic flight were made from physics-based computational models and simulations, wind tunnel testing, and data collected from HTV-2s first test flight the first real data available in this flight regime at Mach 20,” said Air Force Maj. Chris Schulz, HTV-2 program manager who holds a doctorate in aerospace engineering. “Its time to conduct another flight test to validate our assumptions and gain further insight into extremely high Mach regimes that we cannot fully replicate on the ground.” DARPA Press Release

I've noticed physics-based is a common meme for climate policy alarmists trying to shore-up the credibility of simulation predictions. There’s that same tone of, “The Science Says...”, which leads to unwarranted confidence in a situation of profound ignorance (unquantifiable uncertainty). I’ve also observed that program managers seem to take great comfort in the aura of a model that is “physics-based” as a talisman against criticism (“just look at these colorful fluid dynamics, you must be really stupid to question Physics…”). Of course, “physics-based” can be said of all sorts of models of varying fidelity. It is a vague enough moniker to be of great political or rhetorical use. Not that I think Schulz is one of these shady operatives since he goes on to say,

“we wouldn't know exactly what to expect based solely on the snapshots provided in ground testing. Only flight testing reveals the harsh and uncertain reality.”

As DARPA has been well informed by recent experience, ignorance becomes apparent only when confronted with the reality of interest. “Physics-based” is no guarantee of predictive capability.

References

[1]   Abzug, M.J. and Larrabee, E.E., Airplane Stability and Control. A History of the Technologies that Made Aviation Possible, Cambridge University Press, Cambridge, U.K., Chap. 8, 1997.

[2]   Schy, A.A. and Hannah, M.E., “Prediction of jump phenomena in rolling coupled maneuvers of airplanes,” Journal of Aircraft, Vol. 14, pp. 375–382, April 1977.

[3]   Carrol, J.V. and Mehra, R.D., “Bifurcation analysis of nonlinear aircraft dynamics,” Journal of Guidance, Control and Dynamics, Vol. 5, No. 5, pp. 529–536, 1982.

[4]   Day, R.E., Coupling Dynamics in Aircraft: A Historical Perspective, NASA Special Publication 532, 1997.

[5]   Goto, N. and Kawakita, T., Advances in Dynamics and Control, CRC Press, Chap. 4, 2004.

Falcon 9: Lift Off!

Falcon 9 launch successful on first test flight.  Wow!

First Stage In Flight

Successful Stage Separation

Second Stage Burn

Yeah, yeah, it's just a test.  But the cost of the entire development program (~$335M) for Falcon 9 is the same as a single test flight for Ares I-X (~$445M)...

From my perspective (as someone who's sat in the hot seat conducting flight tests), the really impressive thing with the SpaceX operation was their ability  to light the engines, auto-abort, and turn a new countdown/launch at the end of their range time.  There was clearly a whole lot of work in the design phase leading up to the impressive execution today that made saving the mission possible.  Nice.