Mathematical Proof The Eagle In The USPS Logo Is FAST!

The logo for the United States Postal Service is a mean-looking eagle. But a true fluid dynamics geek might look at it and realize that eagle is moving so fast it’s causing a shock wave. But just how fast is it moving? [Andrew Higgins] asked and answered this question, posting his analysis of the logo’s supersonic travel. He claims it’s Mach 4.9, but, how do we know? Science!

It turns out if something is going fast enough, you can tell just how fast with a simple picture! We’ve all seen pictures of jets breaking the sound barrier, this gives us information about the jet’s speed.

Mach Lines

How does it work?

Think about it like this: sound moves at roughly 330 m/s on Earth at sea level. If an object moves through air at that velocity, the air disturbances are transmitted as sound waves. If it’s moving faster than sound, those waves get distributed downstream, behind the moving object. The distance of these waves behind the moving object is dependent on the object’s speed.

This creates a line of these interactions known as a “Mach line.” Find the angle difference of the Mach line and the direction of travel and you have the “Mach angle” (denoted by α or µ).

There is a simple formula for determining the speed of an object using the Mach angle, the speed of sound (a), and an object’s velocity (v): sin(µ) = a / v.  The ratio of to a is known as the Mach number, (M). If an object is going exactly the speed of sound, it’s going Mach 1 (because v = a).

Since Mach number (M) is v / a, we can plug it into the formula from above as 1 / M and use [Andrew]’s calculation shown in the image at the top of the article for a Mach angle (µ) of ~11.7°:

\bf \sin ( \mu ) = \frac{1}{M} \\ \\ M = \frac{1}{\sin(\mu)} \\ \\ M = \frac{1}{\sin(11.7)} \\ \\ M = \frac{1}{0.202787295357} \\ \\ M = 4.9312753949380048

The real question is, did the USPS chose Mach 4.93 as a hint to some secret government postal project? Or, was it simply a 1993 logo designer’s attempt to “capture the ethos of a modern era which continues today”?

Designing Space-Rated PCBs

We’ve reduced printed circuit board design to practice so much that we hardly give a thought to the details anymore. It’s so easy to bang out a design, send it to a fab house, and have ten boards in your hands in no time at all. All the design complexities are largely hidden from us, abstracted down to a few checkboxes on the vendor’s website.

There’s no doubt that making professional PCB design tools available to the hobbyist has been a net benefit, but there a downside. Not every PCB design can be boiled down to the “one from column A, one from column B” approach. There are plenty of applications where stock materials and manufacturing techniques just won’t cut it. PCBs designed to operate in space is one such application, and while few of us will ever be lucky enough to have a widget blasted to infinity and beyond, learning what’s behind space-rated PCBs is pretty interesting.

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Rocket Science With The Other SpaceX

When you say that something’s not rocket science you mean that it’s not as hard to understand or do as it may seem. The implication is that rocket science is something which is hard and best left to the likes of SpaceX or NASA. But that’s not the hacker spirit.

Rocket science with BPS.Space[Joe Barnard] recently had an unsuccessful flight of his Falcon Heavy’s second stage and gives a very clear explanation of what went wrong using those two simple concepts along with the thrust, which in this case is just the force applied to the moment arm.

And no, you didn’t miss a big happening with SpaceX. His Falcon Heavy is a homebrew one using model rocket solid boosters. Mind you, it is a little more advanced than that as he’s implemented thrust vectoring by controlling the engine’s direction using servo motors.

And therein lies the problem. The second stage’s inertia is so small and the moment arm so short that even a small misalignment in the thrust vectoring results in a big effect on the moment arm causing the vehicle to deviate from the desired path. You can see this in the first video below. Another issue he discusses is the high drag, but we’ll leave that to the second video below which contains his explanation and some chart analysis.

So yeah, maybe rocket science is rocket science. But there’s no better way to get your feet wet then to get out there and get building.

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Books You Should Read: IGNITION!

Isaac Asimov described the business of rocket fuel research as “playing footsie with liquids from Hell.” If that piques your interest even a little, even if you do nothing else today, read the first few pages of IGNITION! which is available online for free. I bet you won’t want to stop reading.

IGNITION! An Informal History of Liquid Rocket Propellants is about how modern liquid rocket fuel came to be. Written by John D. Clark and published in 1972, the title might at first glance make the book sound terribly dry — it’s not. Liquid rocket fuel made modern rocketry possible. But most of us have no involvement with it at all besides an awareness that it exists, and that makes it easy to take for granted.

Most of us lack any understanding of the fact that its development was the result of a whole lot of hard scientific work, and that work required brilliance (and bravery) and had many frustrating dead ends. It was also an amazingly dangerous business to be in. Isaac Asimov put it this way in the introduction:

“[A]nyone working with rocket fuels is outstandingly mad. I don’t mean garden-variety crazy or a merely raving lunatic. I mean a record-shattering exponent of far-out insanity.

There are, after all, some chemicals that explode shatteringly, some that flame ravenously, some that corrode hellishly, some that poison sneakily, and some that stink stenchily. As far as I know, though, only liquid rocket fuels have all these delightful properties combined into one delectable whole.”

At the time that the book was written and published, most of the work on liquid rocket fuels had been done in the 40’s, 50’s, and first half of the 60’s. There was plenty written about rocketry, but very little about the propellants themselves, and nothing at all written about why these specific substances and not something else were being used. John Clark — having run a laboratory doing propellant research for seventeen years — had a unique perspective of the whole business and took the time to write IGNITION! An Informal History of Liquid Rocket Propellants.

Liquid rocket propellant was in two parts: a fuel and an oxidizer. The combination is hypergolic; that is, the two spontaneously ignite and burn upon contact with each other. As an example of the kinds of details that mattered (i.e. all of them), the combustion process had to be rapid and complete. If the two liquids flow into the combustion chamber and ignite immediately, that’s good. If they form a small puddle and then ignite, that’s bad. There are myriad other considerations as well; the fuel must burn at a manageable temperature (so as not to destroy the motor), the energy density of the fuel must be high enough to be a practical fuel in the first place, and so on.

The actual process of discovering exactly what materials to use and how precisely to make them work in a rocket motor was the very essence of the phrase “the devil is in the details.” For every potential solution, there was a mountain of dead-end possibilities that tantalizingly, infuriatingly, almost worked.

The first reliable, workable propellant combination was Aniline and Red Fuming Nitric Acid (RFNA). “It had the one – but magnificent – virtue that it worked,” writes Clark. “Otherwise it was an abomination.” Aniline was difficult to procure, ferociously poisonous and rapidly absorbed through skin, and froze at an inconvenient -6.2 Celsius which limited it to warm weather only. RFNA was fantastically corrosive, and this alone went on to cause no end of problems. It couldn’t be left sitting in a rocket tank waiting to be used for too long, because after a while you wouldn’t have a tank left. It needed to be periodically vented while in storage. Pouring it gave off dense clouds of remarkably toxic gas. This propellant would go on to cause incredibly costly and dangerous problems, but it worked. Still, no one wanted to put up with any of it one moment longer than they absolutely had to. As a result, that combination was not much more than a first step in the whole process; there was plenty of work left to do.

By the mid-sixties, liquid rocket propellant was a solved problem and the propellant community had pretty much worked themselves out of a job. Happily, a result of that work was this book; it captures history and detail that otherwise would simply have disappeared.

Clark has a gift for writing, and the book is easy to read and full of amusing (and eye-widening) anecdotes. Clark doesn’t skimp on the scientific background, but always in an accessible way. It’s interesting, it’s relevant, it’s relatable, and there is plenty to learn about how hard scientific and engineering development actually gets done. Download the PDF onto your favorite device. You’ll find it well worth the handful of evenings it takes to read through it.

How To Hack A Spacecraft To Die Gracefully

Last week, the Rosetta spacecraft crashed into comet 67P/Churyumov-Gerasimenko after orbiting it since 2014. It was supposed to do that: the mission was at an end, and the mission designers wanted to end it by getting a close look at the surface of the comet. But this raises an interesting problem: how do you get a device that is designed to never stop to actually stop?
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Paddy Neumann’s Bounce Per Ounce Is Better Than NASA’s

[Paddy Neumann] is an Australian physicist and founder of Neumann Space, a space start-up with a record-breaking ion drive.

The team at Neumann Space built an ion engine that broke the previous specific impulse (bounce per ounce) record. NASA’s HIPEP thruster previously held this record with a specific impulse of ~9600 seconds (+/- 200 seconds). The Neumann Drive’s specific impulse as recorded by the University of Sydney was ~14,690 seconds (+/- 2,000 seconds). This all equates to better efficiency by the Neumann Drive, however its acceleration does not match that of the HIPEP.

Simplified ion engine diagram courtesy of Neumann Space

The Neumann Drive has another unique advantage in its range of usable fuels. In comparison to the HIPEP which uses Xenon gas as fuel the Neumann Drive accepts a variety of metals including: Molybdenum, Magnesium, Aluminum, Carbon, Titanium, Vanadium, Tin, last and also least according to Neumann Space is Bismuth.

Interestingly, Neumann offered his intellectual property (IP) to the University of Sydney, since the research was done at the University but they passed on the offer. This allowed the IP to be returned to Paddy and he subsequently applied for a patent and began the search for funding for continued research.

Here at Hackaday we like space, in fact we’ve offered to send you to space more than once with the Hackaday Prize. We also enjoy amateur rocketry and young rocket scientists.