Surprise again! I completed this next course back in November, but I haven’t gotten around to posting it until now. Unlike with 6.002x, certificates with letter grades are not available, but they did provide this additional letter, to indicate that I completed the course “with distinction”.

With its next set of course offerings, edX is really starting to take off! I’ve signed up for four courses, because so many of them sound amazing, but in reality I may need to prune my selection at some point. I’m now registered for…

• CS184.1x: Foundations of Computer Graphics
• CS191x: Quantum Mechanics and Quantum Computation
• Stat2.1x: Introduction to Statistics
• 14.73x: The Challenges of Global Poverty

The statistics course and the graphics course could be redundant for me, but I’d like to check them out anyway. I have some limited background in quantum mechanics, but I expect to learn a whole lot from CS191x. And global poverty is something I’ve been devoting plenty of thought to recently, so I was excited when I saw that among the new courses offered.

OTHER NEWS…

Unfortunately, I’ve been laid off from my job at the Graybiel Lab due to unexpected research funding problems. This is cause for much sadness, but I think also a cordial invitation for me to move forward in my career. At the lab, I’ve straddled the boundary between software and hardware engineering. Now I see myself well situated for a transition into the control systems and robotics work I’d love to do. I may also find a job more directly related to space exploration!

I’ll keep you all updated on my job search. I also think I’ll put together a post to commemorate my unforgettable eight and a half years at the lab.

Surprise! I have some various, accumulating news I’d like to report. This post is about one news item; more will follow. For the past fourteen weeks, I’ve been taking an online class about electrical engineering! It was provided for free by MITx, which is now a part of edX (a collaboration between MIT and Harvard). The class is called “Circuits and Electronics”, frequently referred to by the code “6.002x”. It’s an adaptation of the MIT course of the same name (with code “6.002”, no “x”), which is a foundational course for MIT electrical engineering students. It was even taught by a professor who teaches that course at MIT. His name is Anant Agarwal and he is also the first president of edX.

I have to say, I’m really impressed with what the MITx group has been able to pull together. While a lot of people like to talk about the limitations of an online course format, I’d like to talk about the ways in which it can actually be superior to conventional coursework. For one thing, the course was available, free of charge, to anyone with an internet connection. That’s called a MOOC: a Massively Open Online Course.

The thing that really amazed me was that I found it easier to work with the online format, and I learned the material more thoroughly. The key was the way they set up the “lecture sequences”. Each one was a series of short videos with interspersed exercises. Most of the video segments consisted of the instructor’s voice, a slideshow presentation (similar to Power Point), and whiteboard-like markup that the instructor added as he spoke. Occasionally, there was a video demonstration of the concepts we were learning about in action.  Unlike in a conventional class, I could pause, rewind, and revisit videos. You probably guessed that much. I could also play the videos at slower or faster speeds (audio pitch was preserved). Captions scrolled by on the side so I could read what the instructor was saying, what he had said recently, and what he was about to say. I could click on any of those captions to jump the video to that moment.

My favorite parts were the exercises. I’d work on the problem, enter my answers, and then click the “Check” button to find out which answers I got right. Green check marks appear for correct answers, red exes for wrong. I could keep trying until I got it right. I never had to proceed with the lecture until I fully understood the material. The answer checking was pretty sophisticated too. The system used symbolic math processing to determine whether or not I entered a mathematical expression equivalent to the correct answer, even though there are countless equivalent expressions. (Well, I’m guessing that technically the number of equivalent expressions is countably infinite, but who’s counting? ;-) )

With lots of optional tutorials, circuit simulation software, a textbook (which was made viewable by students for free), message boards, and a class wiki, there were plenty of resources available to help me learn in a way that suited me. Plus, although I did have to meet weekly deadlines for submitting homework assignments and labs (and the midterm and final exams), I was free to manage my time in whatever way worked for me. I could watch the lectures when I wanted, spend extra time on parts that challenged me, and zip through parts that came easy to me.

My experience on this was not universal, but certainly common enough among the 6.002x students. Some students will find other formats easier and more effective for them. And I’ll also grant that all the automated checking and grading tools are only of use when the subject matter is math, science, and/or engineering. All the same, I think edX may become a tipping point for free and open education. It now has the potential to gain professional and academic credibility, and that could open doors for people in a very impactful way.

Here are some broad-stroked, but somewhat instructive statistics that MITx has released on their pilot run of 6.002x: “6.002x had 154,763 registrants. Of these, 69,221 people looked at the first problem set, and 26,349 earned at least one point on it. 13,569 people looked at the midterm while it was still open, 10,547 people got at least one point on the midterm, and 9,318 people got a passing score on the midterm. 10,262 people looked at the final exam while it was still open, 8,240 people got at least one point on the final exam, and 5,800 people got a passing score on the final exam. Finally, after completing 14 weeks of study, 7,157 people have earned the first certificate awarded by MITx, proving that they successfully completed 6.002x.”

And as you can see above, I am proud to be among the 7,157 to earn that certificate. And I got an A. Yes, you’re imagining the smug look on my face correctly. Hey, give me a break! I have a lingering phobia about taking classes again, but this made a big dent in that. Let’s see where it leads…

I’ll bet you forgot all about me, didn’t you?  Ha!  Back when you least expected it!

I’d like to tell you about a small bit of my time at Arisia 2012 this past weekend.  For those who don’t know, Arisia is an annual science fiction convention in Boston, MA.  Especially if you live in the Boston area, I highly recommend this convention.  Sci-fi conventions have a lot going on: a welcoming community, panels, parties, classes, art shows, sing-a-longs, movies, book signings, children’s programs, blood drives, readings, demonstrations, games, concerts, ….  I’ll stop right there, because that’s the particular thing I want to talk about today.

At Arisia, I went to see a concert given by two homegrown and delightfully geeky bands.  They are Stranger Ways and Sassafrass.  I thoroughly enjoyed the whole concert and there were several original songs that blew me away.  One of them is called “Somebody Will”, by Sassafrass, and it’s about humanity’s future in space.  More specifically, it’s about our practical and emotional relationship with that envisioned future.  For the most part, I’ll let this beautiful song speak for itself, but one little detail I’d like not to go unappreciated is that while looking to the future of humanity, the song includes a brief but profound nod to our past.  That’s all the commentary I’ll provide about the song.  Here it is…

You can listen for free, but if you enjoy it, I encourage you to purchase the music you like to help support these artists so there’ll be more where that came from!

P.S.  You can read the lyrics here.  Just scroll down.

Here I will repost an entry from my old blog which is relevant to human spaceflight…

Here’s my video! It’s far from flawless, but I’ve decided to stick a fork in it. Thank you to all who gave me some excellent constructive criticism. I’ll be sure to apply it to my next video!

… and tornadoes. My dad, Stanley Schleifer, happens to be the chair of the Department of Earth and Physical Sciences at York College, so he had a few things to say about the role of the Coriolis effect in weather systems. He prefers to think of it in terms of conservation of angular momentum. You know how figure skaters often start themselves spinning and then pull their arms inward to make themselves suddenly spin faster? That’s conservation of angular momentum. Angular momentum is defined as angular velocity times moment of inertia. Moment of inertia is sort of the angular equivalent of mass. “Conservation of angular momentum” means that the angular momentum of an an object won’t change unless it is subjected to a torque (angular equivalent of force). You can’t change your body’s mass without taking in or expelling material – an inconvenient prospect while figure skating – but you can easily change your body’s moment of inertia. When a figure skater pulls their arms inward, that decreases their moment of inertia. Since their angular momentum (angular velocity times moment of inertia) must stay the same, their angular velocity increases!

The same thing happens with the formation of hurricanes. When a very large region of low pressure air is surrounded by higher pressure air, the system will equalize the pressure – the high pressure air will flow inward. In other words, the weather system will “pull its arms inward” like a figure skater. So if it already has some angular velocity, it will be increased to conserve angular momentum. But why would the air already have significant angular velocity? Because the whole planet is spinning! In the case of a hurricane, the change in moment of inertia is so huge, that you end up with, well … a hurricane. Regarding the direction of rotation: when you view an analog clock from the front, its hands move clockwise of course. But if the clock face is transparent and you could see the hands from behind, you’d see them moving counterclockwise. It is for the same simple reason that hurricanes in the northern hemisphere rotate counterclockwise while their southern brethren rotate clockwise.

This same phenomenon can be understood from an Earth-fixed frame of reference by examining the Coriolis forces at work in the rotating environment that is the planet Earth. So now we see our low pressure air surrounded by high pressure air, and the air rushes inward. “Rushes inward”? That sounds like high velocity. And Coriolis forces are velocity dependent, right? The air will “feel” a Coriolis force in a direction orthogonal to the air’s velocity and orthogonal to the environment’s (Earth’s) axis of rotation. Since the air is moving inward, all those right angles push the air around in a circle and a hurricane is born.

If the scale is reduced, say to the size of a tornado, then the velocities involved are smaller and the distances over which the Coriolis force can accelerate the air are also smaller. For that reason, only about 70% of tornadoes in the United States rotate counterclockwise. That means that about 30% of the time, the air already has clockwise angular momentum strong enough to overpower the Coriolis force. Still, the Coriolis force can claim responsibility for the fact that there is a bias at all.

If the scale is reduced even further, say to the size of a toilet bowl, the Coriolis forces are even weaker. Contrary to popular belief, at this scale, Earth-based Coriolis forces are dwarfed by angular momentum introduced in the flushing process by asymmetries in the toilet itself – we see toilet water vortex in both directions in both hemispheres. But if the effect of these asymmetries is so variable, then why does the toilet water always vortex on its way down? Why doesn’t it sometimes go down without spinning at all (crazy toilets that flush super-fast notwithstanding)? Because even the tiniest angular momentum in the water will undergo a self-reinforcing amplification process enabled by the water’s viscosity and fueled by the gravitational energy released as the water descends. If that made no sense to you, please read it as, “There really is a good reason, but I won’t be fully explaining it here.”

YOUR HOMEWORK: Next time you use your toilet, take note of which way the water vortexes. Then include that information in a comment on this post along with the geographic region in which the aforementioned flush occurred. Let’s see for ourselves whether or not there is a latitude-based bias here!

And now… MATH!

But how do we know all this stuff about the Coriolis and centrifugal forces? Where did all this “right angles” and “distance from the center” business come from? It can all be derived mathematically! All we have to do is transform Newton’s famous equation, $\vec{F} = m\vec{a}$, into our rotating reference frame and the Coriolis and centrifugal force terms pop right out.

Rather than painstakingly entering my own derivation here in LaTeX, I’ll direct those who want to prove this to themselves to the derivation supplied by Wikipedia. The “Euler force” shown there does not apply to the situations I’ve described here, since I’ve only discussed environments rotating at a constant rate.

Finally, I’ll leave you with a link to an XKCD comic: http://xkcd.com/123/.

Image via Wikipedia

I’ve encountered some debate about the correctness / incorrectness of the terms “0G”, “microgravity”,  and “weightlessness”. Most people have some wrong ideas in their heads which I believe are the root of the problem.

We see images of astronauts floating around within spacecraft. We see that they are not falling to the floor of the cabin and I think most determine that there’s no significant gravity where they are. This intuitive conclusion is taken for granted and then we move on to the debate over terminology. We run into nuggets of common wisdom such as, “There’s no such thing as 0G, because the gravity from Earth gets weaker the farther away you go, but never goes away completely.”

The hidden assumption is that in LEO (Low Earth Orbit), where we often see our astronauts floating about, we have practically, if not completely, escaped Earth’s gravity. It’s true that Earth’s gravity gets weaker the farther away you go, but it doesn’t fall off that quickly! The fact is, at 500 kilometers above the Earth’s surface (where the shuttle likes (er… liked) to hang out) the strength of Earth’s gravity is still a little more than 80% of what it is on the surface. That’s a difference you might not even notice!

So what’s with all the floating, then?! Well, in a way, they’re NOT floating. They’re falling. It’s gravity itself that actually keeps things in orbit around the Earth. Without that 80%, the space shuttle would coast helplessly away from the planet and wouldn’t have the fuel capacity necessary to bring itself back! At any given altitude, the acceleration due to gravity is the same for all objects, no matter how much the object weighs. So one way to look at it is that the astronauts are most certainly falling toward the Earth, but the spaceship is also falling at the same rate. The trick is that they’re going so fast that their freefall trajectory never makes it to the ground! Gravity becomes like the force of a string on a ball that you’re swinging around in a circle.

Now we might easily think, “OK… so it’s microgravity, not 0G, since we’re still at 80%.” But let me float another idea out there for you (sorry … sometimes I don’t have the ability not to make puns). The moon is also just falling around the Earth. And the Earth and the moon together are just falling around the sun. And the the whole Solar system is in the same kind of freefall orbit around the center of the Milky Way. We are awash in all that gravity! But we can’t feel it at all, because our whole world is in freefall. It challenges the meaningfulness of that 80%.

Modern physics seems to have brought us to the realization that you actually can’t meaningfully discuss the absolute sum total of gravity at any location. You can only talk about gravity within a frame of reference. For example, the acceleration due to gravity in the reference frame of the orbiting space shuttle is zero. Sure, that may not be exactly true if you consider the air resistance due to the rarefied edge of the atmosphere present even at that altitude, gravitational attraction due to the masses within the ship itself, or tidal forces due to the slight difference in orbital altitude from one side of the ship to the other… but those accelerations are REALLY tiny.

Another part of the confusion is the notion that the “G” in “0G” stands for “gravity”. This leads us to interpret “0G” to be either the general concept of the absence of gravity or a zero measurement of the force of gravity. It is neither, in fact. “G” is actually a well defined unit of acceleration.  $1G = 9.8 m/s^{2}$. Or… 1G is the acceleration due to Earth’s gravity at sea level. Next one might argue that “0G” is still not an accurate description of the orbital environment because there are still some minuscule accelerations. Notice, though, that you never see “0.000000000000000000000000000G”.  ;-) “0G” has only one significant digit, which to a scientist means that the number doesn’t imply any claim that it is very precise to begin with.

Before this gets too long (too late?), the point I’m driving at is that “0G”, “microgravity”, and “weightlessness” are all correct terms to describe the environment within freefalling spacecraft.

Image via Wikipedia

Most people who’ve paid any attention to spaceflight have heard the terms “guided rocket”, “guidance systems”, “navigation and guidance”, “inertial guidance”, etc…. What these terms actually refer to is fairly straightforward, but I think most treat these concepts as untouchably complex. After all, it’s rocket science! And it’s true that the implementation can become extraordinarily complicated, but that’s no reason not to learn the basics. So I’ve read up on navigation, guidance, and control. In this post I will summarize the topic, including what I think are the most crucial / interesting points, hopefully in a way most readers can understand (follow the Wikipedia links if you need them!).

A “model rocketry” kit is a great way to learn what rockets are and the basics of how they work. Simply put, they provide a continuous force which accelerates the “payload” (whatever the rocket is carrying). That force is called “thrust”. But model rockets rarely follow the trajectory you want them to. To understand why, you can use something you probably have on hand already: a pencil.

If you mathematically model the pencil using Newtonian physics, you find that it should be possible place the pencil upright on a level surface such that it balances perfectly on its tip and stays that way until something else pushes it. In this idealized model, the pencil’s center of mass is exactly above its point of contact with the level surface. But good luck trying to make that work in real life! It is practically impossible to get that center of mass exactly lined up with with the point of contact. And if you could do that, the gentlest air current could still topple the pencil. If it’s even slightly out of alignment, then the force of gravity on the pencil is no longer in equilibrium with the normal force from the surface (i.e. the force that keeps the pencil from falling through the table). That non-zero net force causes the pencil to accelerate, moving it even further out of alignment. So that ideal balanced pencil is in what’s called an unstable equilibrium.

The balancing pencil is similar to the model rocket in that way. The rocket will follow the path we (probably) want it to if the thrust from its motor is perfectly aligned with a straight line drawn between the motor (really the center of pressure of the motor’s thrust on the rest of the rocket) and the rocket’s center of mass. If the direction of thrust is even slightly off, then some component of the thrust will become a torque (rotational force) on the rocket. So the rocket will start to rotate and the rotation will accelerate. And as the rocket turns, the larger linear component of the thrust will accelerate the rocket in an increasingly wrong direction. Another unstable equilibrium!

But going back to the pencil, you might find that with some practice you have more success balancing the pencil on your finger or palm than on the table. If you do manage to balance the pencil, even just for a few seconds, you’re doing it by reacting to the pencil’s motion with hand motion. In effect, the normal force from the table has been replaced with a dynamic force which changes as needed to counteract slight deviations from the unstable equilibrium. Engineers call this closed-loop control.

The same principle can be applied to rockets! In order to make it work we need three things…

1. Navigation: A way to measure that actual motion of the rocket, so we know how far off we are. This could include…
• Global Positioning System: Just like the GPS devices that now help us find our way on road trips, a spacecraft can use GPS to determine its current position, and by deriving over time, its current velocity. It cannot provide information about the spacecraft’s orientation. Also, GPS may not always be sufficiently precise and available, so practically it must be used in conjunction with some other source of navigational information.
• Accelerometers: An accelerometer is a sensor that measures the gravito-inertial acceleration to which it is subjected. Using a separate accelerometer for each of the cardinal axes, we can measure the spacecraft’s acceleration vector. By knowing the starting velocity and by integrating the current acceleration over time, we can know the current velocity. And if we know the starting position and we integrate the velocity over time, we can know the current position. So that gives us our position and velocity, but not orientation. By also using angular accelerometers (or three or more three-axis accelerometers in a known rigid configuration with significant distances between them), we could get orientation… but that suffers especially badly from the basic shortcoming of using accelerometers for navigation: accumulated error. The numerical integration we have to do in order to get velocity and position means that slight errors in the measured acceleration will, over a long enough time course, become very large errors in measured velocity and position. Hey! Wouldn’t GPS be great for providing occasional “reality checks” on our running integrals? ;-) Since the accelerometers only give us acceleration in the spacecraft’s local coordinate system, we need orientation information to interpret what the acceleration means in the outside world.
• Gyroscopes: By capitalizing on the gyroscopic effect, we can keep track of our orientation with very little accumulated error. It works by allowing full rotational freedom to a gyrostabilized platform (usually consisting of two gyroscopes) and simply measuring how it moves relative to the spacecraft. The platform will tend to maintain its initial orientation while the spacecraft rotates around it. This provides no position or linear velocity information. Incidentally, some systems do not truly give full rotational freedom to their gyrostabilized platforms. For instance, the Apollo spacecraft used three nested gimbals to provide freedom of motion. That does indeed allow the platform to be in any orientation, but in certain orientations it does not allow the platform to move in certain directions. In the movie Apollo 13, when they freak out about “flirting with gimbal lock,” that’s what they’re talking about. They were coming close to an orientation that would cause the loss of one degree of freedom. If that happened, the gimbals could end up “tumbling” the gyros – pushing them, and the orientation information they provide would no longer be trustworthy.
• Celestial Navigation: Just as sailors have done for centuries astronauts or onboard computers can use the positions of the stars and other heavenly bodies determine their orientation. This information may not be available at a sufficient rate to guide a burning rocket, but it can be invaluable for determining initial values if, say, your gyros have tumbled.  ;-)
2. Guidance: A way to determine how the thrust vector needs to change in order to correct our trajectory. This is a matter of computation. In some systems, a human operator can do this job by observing navigational indicators and adjusting flight controls to compensate for errors. But most of the time, with high-powered rockets, a human being simply doesn’t have the necessary accuracy and reaction time. That’s why the task is usually given to a computer. The algorithms for doing this can be very complicated, accounting for many factors. So I’ll substitute a simpler but analogous example of a closed-loop control system: a position servomotor. Suppose you want an electric motor to be able to rotate to any position on command. But the motor itself doesn’t take a position input – all you can control directly is, for example, the force the motor will apply. The only way to control the position is to measure the actual position of the motor shaft with some type of position encoder (analogous to navigation), decide what force is best to apply to get the shaft into the desired position (analogous to guidance), and send the force command to the motor (analogous to control – explained below). A simple algorithm for that: subtract the desired position from the actual position and multiply that by a gain constant to get the force. So if the motor is in the desired position, no force is applied. The farther it gets from correct, the more force is applied pushing it in the direction of the desired position. In practice, a damping constant would also need to be applied to keep it from oscillating around the desired position instead of settling there, but hopefully the simplified analogy helps you get the idea of what a rocket guidance system has to do.
3. Control: A way to actually change the thrust vector as needed. Here are some methods that have been used…
• Moving the whole thrust chamber / nozzle: This is what we’re all used to seeing in manned launches. All of the manned missions NASA has carried out have launched with gimbaled engines. The space shuttle also gimbals its OMS engines. So we’re controlling the thrust vector basically by moving the whole engine. With multiple engines, the gimbals can also be used to stabilize the roll (rotation around the axis of the rocket) of the spacecraft. This category also includes hinges and other types of bearings.  This category is more efficient than the others I’ll mention.
• Instead of moving most of the engine, we insert something heat resistant into the exhaust jet that can push the exhaust one way or another.
• Injecting a fluid into one side of the exhaust jet to redirect part of the gas flow.
• Firing additional, smaller thrusters in other directions for a deflected resultant thrust.
• Within the atmosphere, moving aerodynamic surfaces, such as “fins” can redirect the thrust (at the cost of additional air resistance).

Those three elements (navigation, guidance, and control) are so frequently discussed that they are often referred to together with the acronym “NGC”. This innovation was prerequisite to orbital spaceflight.

I have a couple more questions from readers queued up, but they are personal and/or philosophical in nature. I will happily answer them, but I’d also like to see some engineering questions. Click here to submit a question!

Sources:

Image via Wikipedia

I am the first to admit that there are some parts of my life that I don’t have entirely figured out yet. That includes some things that a good astronaut candidate should have a handle on. Since my goal is to make myself a more viable astronaut candidate, I’d best turn my attention toward those matters. One of them is sleep schedule.

I am not a morning person. But I really want to be one. I want to get up early and meditate, eat breakfast, do much of my exercise for the day, brush my teeth, shower, shave, dress, and go to work – all without any snooze-pressing or zoning out due to sleep inertia. I have work to do on this, but I’ve come up with a tactic that’s helping a lot. When my alarm clock sounds, I convince myself that A BOMB IS ABOUT TO EXPLODE! Unless I can disarm it in time … with push-ups! Fifty of them. That’s all I have to do and then I can get back in bed. But by the time I’m done with that, I’m awake enough that I can continue getting ready.

The name goes back to a national convention of my fraternity. I was staying at a hotel… well… cheap and creepy motel… with two other fraternity members and a ferret. No kidding. In any case, this was one of those few occasions when I was up bright and early and did not despise all I surveyed on general principle. I knew it was going to be a long and busy day and that I probably would not have another chance to get any exercise. So I rolled out of bed bleary-eyed, fell face-first (landing in the push-up position), and began my push-ups. At this point, the owner of the aforementioned ferret freaked out, eventually pointing at me and shouting, “Batman!” She was a major Batman fan and I had apparently replicated a scene from the movie Batman Begins.

So that’s what batman push-ups are: push-ups performed immediately after getting out of bed, preferably with the preceding fall. It helps me get up when I want to and it makes me feel like a badass superhero. Try it yourself and let me know what you think!