Comet C/2013 A1 (Siding Spring)

B plane plot - Red circle is Mars, green star is most likely trajectory (miss by 55000km), black ellipses are 1,2,3 sigma direct from JPL Horizons, blue dots are 3,892 Monte Carlo samples

What's in a name?

First off, the name is C/2013 A1, which means that it is a C/ non-periodic comet (this is the first recorded observation of the object) 2013 A discovered in the first half of January 2013, 1 first comet discovered in that part of the month. Siding Spring is parenthetical and not part of the name, just the name of the observatory that discovered it, but since it's easier to remember than a number, we will probably end up hearing a lot about comet Siding Spring.

Why do we care?

The comet is on a very close-approach to Mars. We care about Mars because we care about the spacecraft present in orbit and on its surface. Even more interestingly, the 1-sigma uncertainty ellipse currently includes Mars. There is about a 1 in 1000 chance of impact.

What are its effects likely to be?

1. If it hits Mars, it will almost certainly throw enough junk into low Mars space to kill all the spacecraft in orbit. It is also likely to kill any rover which happens to be within several hundred kilometers.
2. If it misses, well it's a comet visible from 7+ AU out. It's going to be a big'un. All the usual stuff that applies to comets will apply here. It is likely that Mars (and therefore all the satellites) will pass through the coma, and be subjected to a pretty good sandblasting. We will need to review our experience with the Halley armada, and consider that the closer-passing objects were armored.
3. If we decide that the comet is a hazard to spacecraft and other mechanical things, we have to decide what to do with Maven. Do we hold it until the next window? Is it worth firing to get a month's worth of data?

Details

I have been watching this for the past week, and while refined orbits have been produced, the nominal miss distance has been shrinking, and impact has not been excluded yet. The last solution I have seen gives a 0.016% chance of impact.

In particular, Horizons says that the 3-sigma uncertainty ellipse has a semi-major axis of 88000km, a semi-minor axis of 22000km, and that the smallest uncertainty ellipse which touches Mars has a value of 0.98 sigmas. Further, the ellipse is rotated 24.20deg from the line between closest approach. I ran all this through an IDL script and got the plot at the top of this article.


I believe that the documentation on Horizons is wrong, and that what is documented as the 3-sigma uncertainty ellipse major and minor is really the 1-sigma ellipse. With this change, the Monte Carlo samples (see below) match the error ellipses well. Otherwise, I can't reconcile the 3-sigma ellipse touching Mars with the reported Nsigma of 0.98.

A new and powerful tool

The Minor Planet Center collects observations, and in principle you can fit those observations yourself, if your name is Carl Friedrich Gauss. Or if you get Find_orb from Project Pluto. I'm still learning it myself and playing with it, but it has the ability to import observations in MPC format. The program is under active development, and appears to have accreted features as interesting real-world events have happened. For our purpose, the two best features are auto-fit and Monte Carlo. The latter is done in an especially clever way. The program creates a cloud of objects, but it doesn't require a covariance matrix. Instead, it adds a bit of noise to each observation in RA and Dec, then fits an orbit to those new observations and creates an object.

So, I got the observations for C/2013 A1 and dropped them in. After 5015 Monte Carlo samples, 7 of them hit Mars, for an impact probability of 0.14%, quite in line with the JPL Horizons number, but produced directly and solely from the observations. As seen above, they almost perfectly fit the JPL Horizons ellipses.

2012 DA14 in Celestia

1) Go to Horizons and get the spice kernel

telnet ssd.jpl.nasa.gov:6775

type 2012 DA14, and say yes to do a name search. Once it finds it, type s to get an SPK kernel. Give the following answers:

SPK text transfer format  [ YES, NO, ? ] : n
SPK object START [ t >= 1900-Jan-01, ? ] : 2013-Feb-01
SPK object STOP  [ t <= 2101-Jan-01, ? ] : 2013-Mar-01

Binary SPK will be created, you will be asked to add more objects, say n.

Now you will get a download link, copy it to your browser and save it. It will be named something like wld17761.16.

2) Install Celestia

3) Create an extra for Celestia
Create a text file 2012_DA14.ssc in the extras folder and create a data folder within that folder. I needed to run a text editor as administrator to do this.

In the text file, paste the following text:

"2012 DA14" "Sol"
{
    Class "asteroid"
    Texture "asteroid.jpg"
        Color [ 1.000 0.960 0.919 ]
    BlendTexture true
    Radius 0.025

    SpiceOrbit
    {
         Kernel "2012_DA14.bsp"
         Target "3599602"
         Origin "SUN"
         Beginning "2013 2 13"
         Ending "2013 2 17"
         BoundingRadius 1.5
         Period 1.0
    }
    UniformRotation
    {
    Period 5.918
    }

    Albedo 0.048
}

4) Copy the spice kernel wld12345.16 to the extras/data folder and rename it 2012_DA14.bsp

5) Start up Celestia and look for 2012 DA14 in the solar system browser. It should be the last item under Sol. If it's not there, use ~ to bring up the debug screen and up and down to scroll it, and see if there are any errors for 2012 DA14.

Closest observed distance is just under 30000km. It travels from south to north past the night side of Earth.

Gem of the Week - On-Demand Printing

The Big One, by Stuart Slade. World War II went very differently, with England basically surrendering after Dunkirk, immediately drawing the USA into the war. With the Western front secure, Germany was able to focus on the Russian front. They captured Moscow (and killed Stalin, good riddance) but were stopped short of the Urals by the combined Russian and American armies, where they stalemated for five years.

One day in 1947, that changed. On that day, over a thousand planes were launched from bases all along the East Coast of the United states, carrying over 200 Mark III atomic bombs. These were upgraded from the Mk3 used in our timeline, with a typical yield of 35kT instead of the 20kT of Trinity and Fat Man. The main bombers were B-36s, with four bombs each. Each bomber had two escorts, also B-36s.

That smaller plane to the left is a B-29. To put it mildly, the B-36 is a large aircraft.

Interestingly, once the bombers were over Germany, they turned on Salvage Fuses, which would set the bombs off once they reached 2000ft, even if still in the plane. So even shooting down a bomber won't save you. In fact, the second blast was due to this very effect. That's just mean...

One hundred fifteen bombs are accounted for in the book, including twelve for Berlin, eight for Munich, and twenty-five between Dortmund and Bonn. Two were in the Frankfurt area, one in Koblenz, one in Heidelberg, but none in Rothenberg. Estimated casualties are twenty million immediate fatalities and probably that many again from radiation, lingering injuries, illness, and the collapse of civilization and famine caused thereby. The population of Germany was about 60 million in 1945, real world timeline.

It's an interesting story, but it has some holes in it, like how in the world did General Groves keep Manhattan secret for two additional years while they built up the stockpile? I got the book largely to see the answer to that question, but I didn't find it. Also, I am surprised they didn't base in Russia. However looking at the map, it is almost as far from the Front to Germany as it is all the way from America.

But none of that is the Gem. I found out about the Big One on the TV Tropes Wiki in late January, and after failing to find the story in free form on the net, I decided to shell out and buy the book on Friday, 1 Feb 2013. The last page of the book is marked:

Made in the USA

Lexington, KY

02 February 2013

The book was made after I ordered it. It seems that it was literally made for me.

Gem of the Week - EEPROM I2C Memory

Of course I am designing a Rocketometer around the Propeller. How could it be otherwise?

In doing so, I have to get my own parts. The Sparkfun breakout is an interesting jumping-off point, but they don't even use bypass caps, so I added a set of those. Also one thing which concerns me about this whole endeavor is that all the memory is limited. Each cog gets 2kiB, for a total of 16kiB, but the images for each cog must be stored in main memory, which has 32kiB of RAM and 32kiB of ROM. There is no way that I am going to be able to get the program source code embedded with that little amount of memory.

This brings us back to the EEPROM on the breakout board. The bootloader burned into the Propeller knows how to bit-bang an I2C interface and read a memory on the bus. It treats the memory as a 32kiB byte-addressable memory with auto-increment, so it can set an address once, then read and read and read and fill main RAM. The Propeller documents say to use a 24LC256 or similar, so I got to looking at Digikey to see if they had that chip, and perhaps more interestingly, if there was a bigger chip which would still work. It turns out that the design of the EEPROM is the gem of the week.

First, the hardware. The 24LC256 is a 256kib memory organized as a 32ki x 8 (byte-addressable) memory. It is in a kind of large package, a whopping 5mm wide, with 8 pins. This is a lot for a device which is I2C and could in principle work with only 4 pins. But here is the cleverness. The device has three address pins, allowing the 7-bit I2C address to be anything in the range 0x50-0x57. So, you could just stack up to 8 devices on the bus, with only the address pins different, and get 32x8=256kiB of memory, at the cost of using 8 devices.

The 32kiB space is addressable with 15 bits, but the I2C protocol is byte-oriented, so you have to send 16 bits, of which only A0-A14 are considered, and A15 is ignored.

These facts work together to allow the address space to be easily extended. First, a 64kiB part is doable just by considering A15 in the address. Next, a device can internally answer more than one address, for instance by ignoring the A0 hardware pin and answering both 0x50 and 0x51. This of course means that you have to readdress the device when you cross from the address space covered by 0x50 and the one covered by 0x51. You would have to do that anyway if there were multiple real devices.

This all adds up to the STMicro M24M02, which appears to be compatible with the 24LC256, in that if you talk to an 'M02 like a '256, it will answer like a '256. So, you can use the larger device and the bootloader should happily just work. However, it is a 2Mib memory organized as 256ki x 8 (256kiB), eight times as much memory as the reference design, and approaching comparability with the LPC2148 and its 512kiB of Flash. Then when your application takes over, you can use your own bit-bang to access the full chip.

The 'M02 still has one address pin, so in principle you could make a 512kiB memory in 1 chip without changing anything. Going beyond this will break the nice de-facto protocol going on here.

Gem of the Week - the Parallax Propeller

I write this before ever using one, so consider this a review of the concept rather than the implementation. The Parallax Propeller is a microcontroller with a couple of interesting features, and perhaps more interestingly, a couple of intentionally missing features.

First off, it has no peripherals other than 32 GPIO pins.

Secondly, it has no such concept as interrupt.

Thirdly, it has eight independent processors, called "cogs", each with its own memory. Each one can run on its own resources without interfering with any other processor. Each cog is a 32-bit processor, and gets access to 2kiB of ram, shared between code and data.

Fourth, it has a set of resources that all processors can access, called a "hub". This basically consists of more memory and a round-robin memory controller which each cog can access in turn. The hub has 32kiB of ROM with the bootloader, Spin interpreter, and a couple of tables, and 32kiB of RAM.

The missing features are what make the controller interesting. Want an I2C? Write a program for a cog which can bit-bang it. Same for SPI, UART serial, etc. Presumably it could bit-bang low-speed USB, but high-speed would be difficult due to limited processor speed.

Further -- want an interrupt? Too bad. Instead, assign a cog to sleep-wait for the appropriate signal.

Programming such a beast is clearly a different problem than programming an ARM of any flavor. ARMs are all about peripherals, registers, interrupts, etc. Propeller is about bit-banging. Effectively you can use a cog as a soft-peripheral to do basically any digital process.

As I mentioned above, the processor comes with a Spin interpreter. Spin is a custom language for programming Propeller, which gets compiled into byte code and interpreted with the Spin virtual machine. Of course you give up performance, but they used an interpreter in the Apollo Guidance Computer. There, it was for memory saving - a single interpretive instruction could take the place of many instructions in AGC machine language. They gave up time to gain space. Spin could have similar benefits, but it seems like the main purpose is providing a language which natively handles the very different concepts needed to handle a processor as weird as the Propeller.

A Propeller program then consists of a bunch of Spin and machine language routines, all stored in hub RAM and copied from some external source whenever the chip resets. Aside from self-modification or using a cog to bit-bang a memory bus, this is all the space you get. This is a rather tight restriction, in fact less memory than in the AGC. But, they fit a full-blown Kalman filter into that.

Of course I have already designed it into a Rocketometer. It's what I do. One of the great things about the GPIO and bit-banging style of the Propeller is that I can put the SPI bus on the pins which are closest to their targets outside the chip. This makes routing the board MUCH easier.

So I will say for now that Propeller shows a lot of promise. The design is a gem. We will see about the implementation.

Can't... bring... the... funny...

Wonderduck has decided to drop Ben-To, which I only downloaded and watched on his recommendation. Thanks for that... Although I guess writing a careful episode-by-episode writeup isn't really a recommendation from him -- consider Rio Rainbow Gate, where it is more like a warning.

Anyway, the Anime of the Week then is Vividred Operation (vivid-red, in case you miss the space and can't parse the title). Episode 1 established that it was that kind of show. I mean magical girl -- what were you thinking of? Even though it is technological magic, it was still magic, since they still had the magical clothing change transformation sequence. That's right, the defining characteristic of a magical girl is magical clothing change.

Episode 2 can be subtitled "Friendship is insufficiently magic".

I thought about doing an episode writeup, but I only thought of a couple of jokes, and Wonderduck got them himself, so I will restrict myself to what I can do -- one line jokes.

Episode 3 features them skipping directly to "Form Blazing Sword", a clear violation of protocol since you are supposed to wait until you are almost defeated before pulling out your game-changing weapon.

Gem of the Week: The Free Market

Or:  They had Opportunity, in their very Community

Dear Princess Celestia,

Recently there was a severe shortage of apple cider here in Ponyville, which we had the opportunity to remedy, but because of short-sidedness on the part of some of your subjects and your apparent policy to grant monopolies in too many areas of the market, we chased that opportunity out of town.

In Ponyville, the cider franchise is granted to the Apple family of Sweet Apple Acres. Their orchard is a relatively small business and is incapable of supplying the demand. Cider prices are also too low, due to your policies of price control on cider, so the Apples are losing out as well. As a consequence, hundreds of ponies, a good fraction of the citizens of Ponyville, are deprived of cider, and those that do get it are forced to pay for cider with their time rather than with bits, by camping out at the gate. The time that they are granted, all those moments that will never exist again, they were forced to spend waiting rather than doing what they wanted.

If it seems cruel and heartless to give priority to ponies just because they have more bits, consider that your current policies are cruel and heartless as well to those who don't get any cider because they don't have as much time to waste in line. Even those ponies who do choose to spend those moments that will never exist again, pay for cider with both bits and time. Those customers spent that time to no benefit to anyone -- not themselves, and not the Apple family. If time were bits, it is as if those bits of time were carefully collected, from both the ponies who got cider and those that didn't, and dropped into Tartarus, never to be recovered, and never doing any pony any good. Even worse, those ponies who don't end up getting any cider pay time for cider they don't get.

A pair of entrepreneur ponies, the Flim Flam brothers, tried to remedy this, but because of the cider monopoly, they were unable to simply purchase the Apple family apples as a raw material and make the additional cider the market demands. The new business attempted to enter into collusion with the established players, but were unable to negotiate a cartel, which may have been even worse than the monopoly. By denying market competition, they were forced to compete in other ways, in this case a single-elimination to-the-out-of-business contest of pure quantity of production, rather than the ability to satisfy customer demand. In this competition, the Apple family was forced to work far beyond its sustainable capacity to near-exhaustion, and the Flim Flam brothers were forced to compromise their quality control, leading to inferior cider and tired, thirsty ponies.

If your policy of granting monopoly franchises was rescinded, the Flim Flam brothers could have just purchased apples from the Apple family or other suppliers at the market rate, and the Apples and Flim Flam could have worked together without having to collude. If your policy of cider price control was rescinded, the Apples could have raised the price of their cider to the point that some ponies would have decided that the cider wasn't worth it. The same number of ponies would have been served, the Apples would have made more money, and those ponies at the back of the line but more willing to pay would have been able to get their cider. With another supplier, more ponies would have been able to be served, and even if Apple family cider is better than Flim Flam cider, something is better than nothing, and the market would have decided that Apple family cider was worth more, and would have paid more. Those unwilling to pay that much would have been able to pay less to get Flim Flam cider.

They call it capitalism, but it isn't really an -ism of any kind, just the invisible hoof at work, ponies working towards their own benifit but supplying the needs of all ponies.

Please consider changing your economic policies to allow freedom to your subjects to pursue the interests that seem best to them.

It's a new world with tons of cider, fresh squeezed and ready for drinking -- and also plenty of quills, sofas, anemometers, and maybe even things nopony has even thought of inventing yet, but would if they had time to think and invent instead of waiting in line for cider.

Your Fellow Citizen,
St. Kwan the Just

Gem(?) of the Week - the Minkowski metric

The Pythagorean theorem is one of those gems that I won't go into a lot of detail about, because it has been so well-covered before by others. Let's just say that it is a property of Euclidean space, in particular a consequence of the parallel postulate. I just mention it here because it is an example of a topic I am going to go over in great detail.

In 2D Euclidean space, we can figure out the distance of any point from any reference point by setting up a rectangular coordinate system with the reference point at the origin. If there were just two points we cared about, we could align the axes such that the X axis went through the other point, and then we could just read the distance off that axis. That's not really exploiting 2D space, so we will think about one reference point but lots of other points all over the plane. We can use the Pythagorean theorem to measure the distance from the origin to any point in the plane:

\[s^2=x^2+y^2\]

With this coordinate frame you can figure the distance between any two points, even if one is not at the origin, as follows:

\[s^2=(x_2-x_1)^2+(y_2-y_1)^2\]

By using the standard delta-notation from engineering, we can simplify this back to 

\[s^2=\Delta x^2+\Delta y^2\]

Now what is true for 2D Euclidean space is also true for 3D. The Pythagorean formula works, you just have to extend it to cover the third dimension
\[s^2=\Delta x^2+\Delta y^2+\Delta z^2\]

Those crazy topologists have generalized the Pythagorean theorem to fit their weird bent rubber spaces. They say that any space, along with a function which takes two points as an argument and returns a number, is called a metric space, where that function is called the metric. The metric must obey certain axioms, most important of which is commutativity - the distance from point A to B is the same as the distance from B to A.
Some of the topologists twisted imaginings don't really admit such a thing as a straight line. They get around this by saying that if you look at any small enough piece of the space, it is close enough to flat that we can define a metric there. Some spaces are so bent as to not even permit this, but those spaces which do, are called manifolds. In a manifold we talk about points which are close together, and represent this in our metric with differential notation

\[ds^2=dx^2+dy^2+dz^2\]

Now on a manifold we can specify a series of points to draw a path through, find the distance between each, add them all up, and get the length of the path. In calculus-speak, we have every point on the path, and we integrate along the curve to get the distance. However for flat space, there is such a concept as a straight line, and it is the shortest distance between two points. If you take the delta-form above and integrate the differential form, you end up with the same thing. Because of this, we will just show things in differential form from now on.

The film Dimensions is all about extending the same concept to four- and higher- dimensional space. All the Euclidean axioms apply, and the fourth dimension is exactly like the other three, so it works into the metric the same way:

\[ds^2=dx^2+dy^2+dz^2+dw^2\]

One narrator talks about how 4D space is the prettiest, because it contains such things as the 24-cell. Also he says that it may be because real physical space is 4-dimensional also once you consider time. Blah blah Einstein aggressively ignore history blah blah blah. Spacetime is 4-dimensional, but here's the weird part.

Time is not the same as Space.

"Wait a minute" I hear you all saying - "Obviously time isn't the same thing as space. Duh." But, the whole reason we call time a dimension, and the same reason we don't call temperature a dimension, is that there are coordinate transformations that mix in time with space. I'm going off of memory, but this argument came to me through a little book called "Relativity and Common Sense". For instance, imagine a plane where every point is painted a different color. So, at each point we can measure three things, its x and y coordinate, and its color. If we rotate the coordinate frame, we mix together the x and y coordinates

\[\begin{eqnarray*}
x'=& &x \cos \theta&+&y\sin \theta \\
y'=&-&x \sin \theta&+&y\cos\theta\ \end{eqnarray*}\]

But, there is no rotation, no coordinate transformation which preserves our understanding of what coordinate transformation means, which can mix color and spatial coordinates. Color is not a dimension in this sense.

Well, Time is.

The transformation isn't just a rotation, but the Lorenz transformation from coordinates measured by one observer to coordinates measured by a relatively moving observer, depends on the relative speeds of the observers. And here's the weird thing - time is a dimension, but it is not just like the other three dimensions. In fact, the metric for the spacetime observing the Lorenz transformation is called the Minkowski metric, and it looks like this:

\[ds^2=dx^2+dy^2+dz^2-dt^2\]

See the minus in the time term? It says that the longer the time between two events, the shorter the distance, all other coordinates being equal.

It gets weirder than that. If the time difference is long enough, it drags the whole right side negative. The squared distance between two events is negative. The distance between two events is imaginary. In special relativity, we say that when \(ds\) is real and positive, it is called proper distance, and it is the distance between two events as seen by some observer who sees them happening at the same time. Further there is no way for a single observer to be present at both events without exceeding the speed limit in the space, which introduces its own problems. When \(ds\) is imaginary, the (real) coefficient is called proper time, and represents the time interval between two events as seen by an observer who sees them happening in the same place. A single observer can be present at both events without exceeding the speed limit.

See what I mean by weird? In Minkowski space, there is a speed limit imposed as part of the fundamental geometry of space. If we though of time as just a dimension like space, this is equivalent to saying that it is impossible for a line to exceed a certain slope (change in space dimension per unit change in time dimension). No such limit exists in Euclidean space. Spacetime is 4D, but not Euclidean. It is not the same 4D space discussed in Dimensions. The Pythagorean theorem is false, and therefore the parallel postulate is false. Minkowski space is the only flat (metric works across long distances) space I know of which is non-Euclidean.

Now the question is, are the regular polytopes the same in Minkowski space? Does it make sense to talk about polytopes? Is a polytope regular from one point of view but not from another? These and other questions can be answered by the Minkowski metric, but I don't know the answers. I was only recently even able to form the questions.

Let's finish this off with a visualization:

Putting my hardware where my mouth is...

I had been keeping this quiet, but it is the natural culmination of all that I have written on this blog.


At my day job, I work with space projects, but I have only been in the same room as flight hardware once, and that was purely as a tourist, to get my picture taken with it. I have written code that has gone into space, but never touched the hardware that carried it.

In October 2013, that will change. I am building space hardware. In a sense, that has already changed, since I have touched the hardware, but it's not space hardware yet. I have arranged for a version of the Rocketometer to fly on a rocket all the way into space.

The people I work for at my day job run an instrument in space that needs to be calibrated every so often. Every year or so, we fly a sounding rocket with a copy of our instrument, pop it up above the atmosphere for a few minutes, then let it fall back down into the atmosphere and descend on a parachute. It goes into space (well over 100km) but not into orbit.

On the campaign building up the rocket for the last flight this past summer, I was tinkering with my rocketometer (actually the 11DoF) and got to talking to my scientists about it. I told them about my daydream to actually get this thing on the rocket, and they said it was a great idea. Naturally it was far too late to get on board that last rocket, but with this next one I have plenty of time, especially considering that the hardware is finished, and I potentially could fly it now. The baseline mission is just to collect the data as fast as possible, and not bother with any on-board processing. That code was demonstrated with the speed test I did a few weeks ago.

My test plan and to-do list then looks like this:

1. Adapt the old code to the new hardware. A couple of the I/O lines were reassigned to simplify the board design.
2. Write an offline Kalman filter to process the data. IDL will work fine for that. Mostly I just need a set of equations of motion that allow the compass, gyro, and accelerometer to calibrate each other.
3. Calibrate the sensors. I have an old record player with no needle which will be perfect for this. I may be able to use some stuff in the labs at work to help with this.
4. Do a test flight in a model rocket. These generate a similar scale of forces and rotation rates, just for much shorter durations, seconds rather than minutes. The Rocketometer was designed to be carried in any rocket with a payload section 1" or larger in diameter.
5. Get USB Bootloader++ working. This is low priority, as I can program the part over serial as I have been doing for a while.
6. Consider on-board processing of the data.

I will be using the Rocketometer2148 with an MPU6050 6DoF sensor, an ADXL377 analog high-g accelerometer, an AD7991 12 bit ADC to read it, an HMC5883 compass, and a BMP180 pressure/temperature sensor.

With a couple of changes to main.cpp and gpio.cpp to tell it where the sensors and lights are on this board, the thing works! It may also be working at my goal rate of 1000Hz, attributable to a faster SD card, reading the compass only 1 of 10 times that the 6DoF is read, and not reading the HighAcc.

Things that there are never enough of, part 1

There is never enough bandwidth.

I can get an MPU6000 from Newark for about $39, or I can get an MPU6050 from Sparkfun for about $20. The only issue with the 6050 is that it runs on I2C, and maxes out at 400kHz. In burst mode, I can get a byte across in 9 clock cycles. An MPU6050 readout has three 16-bit gyro registers, three 16-bit acc registers, and a 16-bit temperature readout, a total of 14 bytes, plus addressing the part, for 15 bytes. Nine cycles each gives 135 cycles, plus a couple more for starts and stops, call it 140 cycles.

Is this enough? Of course not. There is never enough bandwidth. But is it enough? In 1 millisecond, there are 400 cycles, so in theory the MPU6050 being read at 1000Hz will use up 33% of the available bandwidth.

Now there is also the high-accelerometer, read out using an I2C ADC. The ADC has three 16-bit data registers, so 7 bytes counting address. 7 bytes at 1000Hz, call it 70 more cycles. Now we are at 52% bus usage. We need to throw in a compass read and pressure sensor read every once in a while, but it looks like enough to run the sensor at whatever rate I want.

So maybe there is enough. One way to get more bandwidth is to use the other I2C bus on the chip, but this involves a fairly heavy redesign of the board. We would put the MPU and compass on one bus, and the HighAcc and pressure sensor on the other bus.

Onto the measurements. I put together a program which reads the sensors with no delay, in effect as fast as possible with blocking. The program records the tick count (TC), which increments at 60MHz, before each reading, then reads the ADXL345, HMC5883, MPU6050, and L3G4200D in that order. So, the time spent doing the ADXL345 read is the TC of each HMC packet minus the TC of the corresponding ADXL packet, and so forth. The ADXL345 consistently takes 131 microseconds with a variation of less than 1 microsecond. The HMC takes 483 microseconds. And for the moment of truth, the MPU6050 takes 539 microseconds. All is fine and good, right? Nope. We spend most of our time waiting for the card to write out. On a good write, it takes 9 milliseconds, 18 times longer than an MPU read, to write a sector to the SD card. A lot of that could be gotten around by not busy-waiting for the card to finish.

In any case, there is plenty of bandwidth for the sensors, so there is no point in splitting up the traffic to two I2C buses. Reading twice as many sensors as necessary and producing more data than necessary (the real rocketometer will only carry one set of gyros), it still is reading out at about 300Hz.

Dual (or dueling) gyroscopes

The experiment that I wrote about yesterday was actually carrying two gyroscopes: The one in the MPU6050 discussed then, and the L3G4200D on board the 11DoF. This gyro was connected to the Loginator by SPI running at 1MHz. The 11DoF tab was oriented such that during the South integration, +X was East, +Y was Up, and +Z was South. In the same integration, the MPU tab was oriented such that +X was West, +Y was South, and +Z was Up (not Down as marked on the board -- the silkscreen is wrong, proven by the positive signal on the +Z MPU signal.)

So, we match up axes as follows:

MPU6050	11DoF
+X	-X
+Y	+Z
+Z	+Y

Therefore we just perform the calculation using +Z on the 11DoF just like yesterday we used +Y.

The result doesn't look so good. First, data from yesterday, showing what a detection looks like:

This shows 1 minute of data from before and after the rotation. The noisy part on both ends is 10 seconds of raw data, and the smoothed bit in the middle shows a 2000-sample (roughly 20 second) boxcar smooth. The white data was with +Y pointing north, and the red data was with +Y pointing south. In that middle region, the difference is due to the rotation of the Earth.

Now, the data from the L3G, also taken yesterday, but not reduced until today.

Since the signals cross, there is no clear detection, even with a 20 second boxcar average. Why not? As it turns out, this sensor was set to 2000°/s, its least sensitive setting, with 1/8 the resolution of the MPU. So,  it's not a fair test.

Detection of the Rotation of the Earth

Abstract: An MPU6050 6DoF MEMS sensor is used to measure the rotation of the Earth. The device is run pointed north for 1 minute, then south for 1 minute, taking 98samples/s during the runs. Actual rotation difference between north and south is 0.0063837°/s, taking into account the cosine(latitude) effect. Measurement is 0.0064822°/s±0.0015299°/s, representing a clear detection of the rotation.  The MPU6050 gyroscope is extremely accurate, probably sufficient for the Rocketometer mission.

This is also a review of the MPU6050 6DoF sensor. This part has a three-axis accelerometer with ranges ±2g, ±4g, ±8g, and ±16g, and a three-axis gyroscope with ranges ±250°/s, ±500°/s, ±1000°/s, and ±2000°/s. Since the intended mission is flying on a rocket, and certain rockets that may fly with this have been observed to accelerate at around 25g, it will need to be supplemented with a high-accelerometer, but the gyroscope will handle the 4.5Hz rotation expected.

The earth rotates 360° in 24h*60m*60s=86400s, or 1° in 240 seconds, or 0.00416666°/s. The gyroscope's most sensitive setting is ±250°/s and reads out at 16 bit resolution, resulting in 500°/s/65536DN=0.0076294°/s/DN, not quite enough to distinguish earth rotation from a standing stop, but enough to distinguish when one axis is pointing north, then south. Unfortunately, that presumes that the gyro is noise-free, which we will soon see is false.

The current experimental setup is on a breadboard connected to a version 1.1 Loginator by I2C at 400kHz, carefully aligned to true north by the following extremely accurate procedure: Since the walls of the secret underground laboratory are not aligned with true north, I pulled up the Google map of the lab and oriented the map such that the walls on the map were parallel to the real walls. The case of the phone was then aligned to true north. I put down a line of tape to mark this orientation. In this setup, the MPU6050 axes were aligned with +Z pointing down (thus we expect to see the 1g field read negative), the +Y axis pointing north first then south, and the +X axis pointing east first then west.

Of course, all measurements are contaminated with noise. This can often be beaten back by taking many measurements of the same thing. If you take into account a number of simplifying assumptions, the noise of the average of \(N\) measurements of the same quantity is \(\sigma/\sqrt{N}\). In short, if you take 100 measurements of the same thing, the average of them is expected to have 1/10 the noise of the original measurements. My previous efforts have taken data over very long stretches of time, hundreds of samples per second over hours. This time I decided to take data for 1 minute at a time. I sampled at 98samples/s (2samples/s were spent reading the pressure sensor, a topic for another day) for 1 minute with the Y axis pointing north, then 1 minute with the Y axis pointing south.

The estimated noise on each measurement, calculated with the standard deviation of all the measurements, was 11.02DN, or 0.084°/s, about 20 times that of the rotation of the earth, so it is obviously impossible to measure with one sample. But, I took 5880 samples, giving a predicted noise on the average of 0.14DN or 0.001°/s, plenty small enough to measure the rotation of the Earth. But did I? And if I did, why did I fail before?

Data:
Y north: -0.2217195°/s±0.0010972°/s (1σ)
Y south: -0.2282107°/s±0.0010972°/s (1σ)

Difference: 0.0064822°/s±0.0015299°/s (North is greater than South by this much)

Now, what is the expected value? First, is it positive or negative? Relative to inertial space, the device is rotating according to the right-hand rule around the Earth's axis. The device measures a right-handed rotation around an axis as positive, so the device should read more positive when pointing north than when pointing south, as it does.

Also, as mentioned above, the earth rotates at 0.00416°/s, but my Y axis is inclined 40° relative to the earth's rotation axis, so I should only expect to see \(\cos 40^\circ\) as much. Also, I would expect to see twice as much as that, because I am not comparing a standing stop to rotation, but rotation one way to rotation the other way.

Taking all this into account, the predicted measurement is....

0.0063837°/s.

My measurement clearly brackets this. In fact, the measurement is much better than I have any right to expect, being only 0.06σ above the expected value. I would have accepted any measurement with the proper sign and an error of less than 1σ.

Why did I fail before, with measurements taken over hours and hours? Gyro drift. Ideally, the zero point of the measurement would be zero DN, but we are happy if the zero point is just constant. But it's not. Temperature changes and other unmeasured effects cause the zero point to drift, and when measuring for hours and hours, this gyro drift swamps the signal I am trying to measure. To get a good rotation measurement, you want as many samples as possible, but taken over a relatively short time such that gyro drift is small.

So, back to the review. The MPU sensor is kind of noisy, with 11DN noise per sample, but can be read out sufficiently quickly and has sufficiently small gyro drift that it can measure the rotation of the Earth.

The USB protocol stack

SPI is a nice, simple, uncomplicated way of communicating between two or more embedded devices. Set a couple of registers defining clock rate, phase, and polarity, and you are ready to go at up to about 10Mb/s. It's a convenient way to talk to microSD cards, accelerometers, basically anything on board with an embedded device. Lots of device-defined protocols can be layered on top of it to do anything the host and device agree to.

USB is a nice, COMPLICATED way of communicating between a host and multiple devices, and multiple applications within the devices. It's not just a bus protocol, it's practically a network in itself. This has its advantages and drawbacks. If my device learns how to speak Mass Storage, any host computer in the world can use it. But, it is considerably more complicated. I can't just look up in a reference guide and bit-bang a protocol out like I can with SPI or I2C.

USB is in fact a stack of protocols, much like HTTP/TCP/IP/Ethernet. Some layers are handled by the hardware autonomously, some need the cooperation of the hardware and the firmware, and some is up to the firmware completely.

The USB project I had been working off of, LPCUSB, is a set of C routines with no readily apparent structure. You can trace through the handlers, to find handlers on top of handlers and handlers all the way down. For one thing, there is code just to work with the USB hardware, then there is code to implement the mass storage class and then code to implement the serial port class. Much of the interaction between these is through callbacks. In reorganizing it into C++, I had the ideal that the device could operate both as mass storage and serial at the same time. There would be a low-level USB class, and then on top of that, a Mass Storage class, and separately a Serial class, which could both be active at the same time.

I am going to abandon that idea for now. I don't know enough about the stack to do this yet. So, we do a USB class with several abstract virtual methods, then an MSC subclass which implements the virtuals purely as mass storage, without worrying about sharing. Likewise, we are going to have a USB control endpoint handler, then a MSC subclass which does what is needed for MSC.

Battle of Compression

Everyone else was doing it, so I might as well give it a try also. Here's my use case: I want to compress the C++ source code and anything else needed to rebuild my firmware (mostly Makefiles) into one tight little package, then append that package to the firmware itself. Naturally smaller is better. Especially I would like the Bootloader++ (I'll explain it when I'm ready to publish, but its a bootloader for a Logomatic-type circuit which handles fat32 and sdhc) code and source pack to fit within the 64kiB it has allocated for itself.

So, the test case. I already have a rule in my makefile to pack the code:
$(TARGET).tar.$(TAR_EXT): $(ALLTAR)
        $(CC) --version --verbose > /tmp/gccversion.txt 2>&1
        tar $(TAR_FORMAT)cvf $(TARGET).tar.$(TAR_EXT) -C .. $(addprefix $(TARGETBASE)/, $(ALLTAR)) /tmp/gccversion.txt

$(TARGET).tar.$(TAR_EXT).o: $(TARGET).tar.$(TAR_EXT)
        $(OBJCOPY) -I binary -O elf32-littlearm $(TARGET).tar.$(TAR_EXT) $(TARGET).tar.$(TAR_EXT).o --rename-section .data=.xz -B arm

I'm quite proud of the latter, as it packs the archive into a normal object file, which my linker script makes sure gets packed into the final firmware image, with symbols bracketing it so I can dump just the source code bundle.

Anyway, we will look at our challengers:

• No compression, just a tar file. This one is actually a bit bigger than the total of the file sizes
• gzip, the old standard, both with no special flags and with the -9 option
• compress, the really old standard .Z file using the (expired) patented LZW algorithm
• bzip2, the second generation compresion algorithm notable for both better compression and longer compression time than gzip, used both with no special flags and with the -9 option
• Lempel-Ziv-Markov algorithm, implemented as the Ubuntu command lzip and xz. third generation compression algorithm, once again better compression, once again longer time
• lzop, a compressor optimized for speed and memory consumption rather than size
• PKZIP, implemented via the zip command available in Ubuntu. This might not be a fair test, as it is not compressing the TAR file, but is in fact using its own method to compress each file individually. So, it has an index, plus each file is compressed anew, meaning there is no advantage from the previous file's compression.
• 7z, implemented via the 7z command available in Ubuntu. Same notes as with PKZIP.
• zpaq, a compressor which at each step tries several methods and picks the best. This one takes a monumental amount of time and memory, but seems to be worth it if minimum file size is the goal.

So, we notice a couple of things. One, sometimes -9 doesn't improve things measurably, and sometimes makes things worse. Next, zpaq rocks out loud as far as compressing C++ source code. It's still larger than the firmware binary image, which is 12423 bytes. It might take more time and more memory than any other compressor, but all that time and memory is in a beefy desktop machine, and not in the Loginator.

Gem of the Week - Kepler's and Newton's laws and universal gravitation.

The discovery by Kepler of his laws of planetary motion is one of the more amazing bits of observational science, made more amazing by the lack of tools which he had to work with. But, that's not our gem of the week. Instead, we will see how Newton deduced that there is such a concept as universal gravitation, and proved that it worked. Actually we won't see how he did it, but we will see how it can be done with modern techniques such as vectors.

Gem of the Week - Euler's Identity

I am going to present a new feature to all my 0 readers - the "Gem of the Week". This is a reprise of a sometime feature on my old private blog, "Chemical of the Day". I am expanding the topic somewhat from chemicals to anything I find interesting. None of these are necessarily news, but they might be.

This week, it's Euler's Identity.

Keeping secrets

I hate secrets.

Some people have to keep secrets because they are legally obligated. This includes any government classified information. Boy am I happy I don't have to deal with that headache. I bet Robert did.

Some people have to keep secrets because they are contractually obligated. Some projects LASP works on are with customers who treat some aspects as proprietary. For instance, I was brought in on Sentinel long before it was announced, in October of last year. Ball, perhaps under orders from B612, required us to keep the mission proprietary. It is a really cool mission, and I hated not being able to talk about it for months on end.

I keep some secrets because the time is not yet right to publish. I have something cool in mind for the Loginator, but I don't want to shoot my mouth off before I know that it is going to happen. So, watch this space...

File system driver

My C++ification of the Loginator code continues. As noted below, I have the startup code now in full C++ (with 18 lines of inline asm), and I have overthrown the tyranny of main() (that sounds familiar, have I written on this topic before?). I have taken Roland Riegel's sd_raw driver and heavily modified and simplified it. Basically I made it a pure block device. I have dropped all the buffering. You can open an SD card (SDHC fully supported), read a block, write a block, and get the card info.

I looked into extending c++ifying the partition and fat32 driver, but it looked too complicated and messy. One of the things I am dead set against is dynamic memory allocation in an embedded process. What if it fails? When that happens, the software crashes (it wouldn't ask for memory if it didn't desperately need it) and when that happens, it is a good possibility that the device it is flying crashes too.

So, I get to write a fat32 driver myself. Once again, only whole blocks at a time. And to start with, only that which the USB bootloader and Logomatic need: read a file, write a file, delete a file. Also to start with, we fully support FAT32, but do not support long filenames.

One area where I am going to get myself in trouble is writing the file. Sometimes when you write a file, you have to change the file allocation table. When you do so, you need to read the sector containing the change, make the change, then write the new sector. This is all easy, but you need a buffer to do it. Also, you will need to read the table to find the next cluster. What buffer do you use? I know that the LPC2148 is not really memory-limited, but it still seems a waste to set aside a whole block buffer for this.

I started by writing a partition driver. You pass it an open and started SD object and a partition number, and it reads the partition table to get the info for that partition. From then on, you use the partition object to read and write blocks.

A review of the ADXL345 and BMA180

First off, the ADXL345 is exactlty what it claims to be. It's my own fault for not reading the data sheet, or rather reading it but not comprehending the information in it.

So, my first experience with digital accelerometers was with the Bosch BMA180. The part had 14 bits of precision and 6 scale settings, from 1g to 16g. When you switched to the lower scales, you got more precision, as expected.

I finally got all 11 DoFs working on the 11DoF board. The first SPI part I broughs up was the ADXL345, so I learned about its SPI protocol that way. For one thing, those of you used to I2C, SPI is different! For instance, on both the ADXL345 and the gyro on the 11DoF, the L3G4200D, the register addresses are six bits. This is fine, since that is a big enough space. You send this address as the first word of any transfer in either direction from these devices. However, both devices use 8 bit words in the protocol. The other two bits control the direction of transfer for the other words, and whether the device is to expect more than one word -- that is, whether it should increment the register address pointer for the next words.

For instance, say you want to read all the measurement registers in the ADXL345. The register map says that this is registers 0x32 through 0x37. Since SPI is a full-duplex protocol, every time you send a byte, you receive a byte. So, send 0x32, ignore what you receive, then send six more bytes (doesn't matter what, I used 0) to read 6 bytes that you care about. Right? Almost, but not close enough. I did this first with the ID register, and it worked, sometimes. But, when I actually tried to read the data, I got back the same word six times. What gives? First, bit 7 of the address is read/#write. You have to set it to read the register, otherwise it interprets the MOSI data as data to be written to the registers. The data registers are read-only, so the part ignored me. Next, bit 6 is the multibyte flag. Set this bit if you are going to read/write multiple registers in one transaction (one continuous #cs assert). Doing this will cause the part to increment the address pointer each time it sends or receives 8 bytes. Since I set neither of these, my part became very confused, since I was telling it to write to a single read-only register six consecutive times.

tl;dr - Tell it you are using address 0xF2, then read 6 more times to get the 6 data registers.

This is an unnamed protocol layered on top of SPI, which by itself knows nothing of registers. It happens that the gyro uses the same protocol, so turning it on was a simple matter of verifying that the protocol was the same, and copypasting the code.

Now for the review. The ADXL345 has a programmable range, with choices ±2, 4, 8, and 16g. We will need 16g for the rocketometer. It has a readout precision of 13 bits, almost equal to the 14 bits the BMA180 gives. Now for the bad part. The readout precision is only 12 bits for 8g, 11 bits for 4g, and 10 bits for 2g. It is as if the part was always running at 16g, but reporting saturation if it was out of its current range.

I might as well use an analog part if I am only going to get 10 bits. I had always known this, but only realized the significance when I finally got it up and running, and only got about 250DN out of the part in the 1g field. So, the ADXL gets 2 of 5 stars, not recommended on the Chizumatic scale.

The BMA180 is what I used before, in flight. It has a programmable range, with choices ±1, 1.5, 2, 3, 4, 8, and 16g. It produces 14 bits of precision, and this 14 bits is constant across all ranges, so if you use the 1.0g range, you actually have zoomed in, and get better resolution than when you are at 16g. I can't speak to its accuracy, so it gets 4 of 5 stars, not recommended. Why not? The part was discontinued without a suggested replacement as of today, and is no longer available on Digikey. In fact, I am hoarding three of them still in their cut tape, purchased from Sparkfun today at great expense, not even on a breakout board. None of the other BMA accelerometers are as good, and none of the Analog Device accelerometers are as good either.

8 DoFs so far...

I have gotten the ADXL345 accelerometer, HMC5883L compass, and BMP180 pressure/temperature sensors working with the Loginator and 11DoF board. This means that all SPI and I2C signals work on both boards. Last thing to do is to get the STMicro L3G4200D gyroscope working.

I just saw a board basically identical to the 11DoF (same sensors except a BMP085). The problem is that it is all done up in I2C.

Starting up an ARM processor with 90% C code

Now why would you want to do a darn fool thing like that? Startup.S works fine, why mess with it?

One word: Understanding.

Let's face it: Assembly is hard to read. Especially ARM assembly, with its special registers, shift-operands, and treating memory (load/store) fundamentally different from registers (mov). You can't get more than a few lines through an assembly listing without having to crack the ARM ARM.

Besides, I have a philosophy to use a consistent language throughout a program to the extent possible. So, for the embedded stuff, it's C++ when you can, C when you have to, and asm only when you really have to.

So what stands in the way? Mostly it's the fact that the toolchain makes it difficult to put things exactly where you want:

1. The interrupt vector table. This is what keeps the code from being 99% C instead of 90%. On an x86 processor, the interrupt vector table is purely a list of addresses. Upon interruption, the processor looks up the correct vector, and loads it straight into the instruction pointer, causing the processor to branch to the handler. In many other processors, the table is actually code. When an interrupt happens, the processor jumps to the correct slot in the table and executes it. Usually this is a jump to where the handler really is. In ARM, there isn't enough space for a long jump in a single instruction, so each vector says to load the program counter with another value from memory, usually in a table located right after the true interrupt table. In any case, C just isn't a good language for building the table. What we do then is use inline asm. We make a function called vectorg which is purely inline asm. The first half is instructions, specifically the long jump instructions with embedded pointers to the second half, which is the address table. This is populated with symbols, so the linker can patch it up.
2. Putting things where we want. The old Turbo Pascal had a mechanism for assigning a variable to a particular point in memory. In asm, this is easy: just define a symbol with a hard-coded address. This just isn't possible in C. So, we need cooperation from the linker. We need to specify the linker script. In particular, we need to say that a particular named ELF section is to be linked right at the beginning of flash, and then make sure that the table is in fact in that section, at the beginning of it. The easiest way to do that is to turn on -ffunction-sections when compiling, then link .text.vectorg at the beginning. The source code and the linker script have to agree on this.
3. Registers - This is the other 1%. To set up the program, the reset handler has to set up the stacks, move the initialized data from flash to RAM, zero out the uninitialized data, and call all the constructors for global objects. But, in order to set up the stacks, the code has to be able to set the CPSR register, so it can flip through modes and set each mode's stack register. It also has to be able to write directly to the stack register itself.

Around the world in (considerably less than) 80 hours

A thought experiment. I would need to go home and throw some stuff in a backpack, and get my passport, but this is doable. It was 2012 Sep 19 11:00am MDT as I searched.

Layover	From			Depart		Arrive		Flight	Time
	Airport	TZ	UTC rel	Local	UTC	Local	UTC
	Boulder	Mountain Daylight Time	-6	2012 Sep 19 11:00AM	2012 Sep 19 17:00	2012 Sep 19 11:00AM	2012 Sep 19 17:00	Look up flight	00h00m
09h45m	Denver (DEN)	Mountain Daylight Time	-6	2012 Sep 19 08:45PM	2012 Sep 20 02:45	2012 Sep 20 12:35PM	2012 Sep 20 11:35	American 6169 as British Airways 218	08h50m
02h10m	London (LHR)	British Summer Time	1	2012 Sep 20 02:45PM	2012 Sep 20 13:45	2012 Sep 21 12:50AM	2012 Sep 20 20:50	Etihad 20	07h05m
01h35m	Abu Dhabi (AHU)	Gulf Standard Time	4	2012 Sep 21 02:25AM	2012 Sep 20 22:25	2012 Sep 21 03:25PM	2012 Sep 21 07:25	Etihad 424	09h00m
07h05m	Manila (MNL)	Philippine Time	8	2012 Sep 21 10:30PM	2012 Sep 21 14:30	2012 Sep 21 08:00PM	2012 Sep 22 03:00	Philippine 104	12h30m
09h50m	San Francisco (SFO)	Pacific Daylight Time	-7	2012 Sep 22 05:50AM	2012 Sep 22 12:50	2012 Sep 22 09:21AM	2012 Sep 22 15:21	United 729	02h31m
1d06h25m	Total Layover					Total trip time	2d12h36m	Total flight time	1d15h56m

Also as of 11:00am, this flight had a cost of $5,351.89. I couldn't swing that right now, and I have work to do for the next few days, but Phileas Fogg wouldn't have any such trouble. He had £20000 cash in his pocket, and this trip would cost about £55.16 There are probably possible trips with tighter connections. There are surely trips that are cheaper with a longer lead time -- I found one in January for ~$3500.

This trip is definitely around the world. It crosses all the meridians. But, it is only 32833km as the crow flies. I have heard that a trip around the world must cover a distance longer than one of the tropic circles (36787km). This trip doesn't cut it if it follows the great circle route, but if the actual routing is 10% inefficient then it counts.

Mathjax

Here is a new cool thing: MathJax

\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \M{A} \MM{P}{^-_i}\]

Mathjax is apparently a TeX implementation written entirely in Javascript. It looks like it scans the source code of your page, looks for delimited equations, then interprets the TeX within and renders it using math fonts.

Instructions for how to get it to work for Blogspot are here.

Now I get to go through all of my Kalman filter stuff and fix the math there into something actually readable.

Complete Precision

Project Precision has reached its successful conclusion. I now have a physical hardware clock with an hour, minute, second, and third hand, and enough accuracy to justify needing a third hand.

As I have mentioned before, I noticed that an Arduino Nano has precisely the pinouts necessary to drive a charlieplex with 240 lights. The interesting thing is how few leftover resources there are. There are two analog inputs that are useless in this design. Every single other pin is used. I even considered giving up the crystal inputs to get two more digital pins.I had to include a digital multiplexer since the ATMega only has one serial port, and it needs to listen to both the USB port and the GPS.

As I said before, I will not make one for you for less than $300. The parts alone cost almost that much. However, I am going to publish everything you need to make one yourself.

This is the Digikey part list:

Quantity	Digikey Part Number	Part	Value	Case	Placement	Price per	Min quantity	Ext Price
2	445-7483-1-ND	Capacitor	4.7uF	Ceramic 0603	C010 C418	$0.24000	1	$0.48
2	478-6025-1-ND	Capacitor	18pF 2% NP0	Ceramic 0603	C407 C408	$0.40000	1	$0.80
2	445-1316-1-ND	Capacitor	100nF	Ceramic 0603	C420 C502	$0.10000	1	$0.20
61	754-1359-1-ND	LED	Red 320mcd	LED 0603	D000-D059 D502	$0.14040	1	$8.56
60	754-1124-1-ND	LED	Yellow 150mcd	LED 0603	D100-D159	$0.11160	1	$6.70
60	350-2036-1-ND	LED	Green 300mcd	LED 0603	D200-D259	$0.51840	1	$31.10
61	350-2037-1-ND	LED	Blue 140mcd	LED 0603	D300-D359 D501	$0.48960	1	$29.87
4	CRA4S847CT-ND	Resistor Pack	47	CRA04	R1 R2 R3 R4	$0.04300	10	$0.43
2	P680GCT-ND	Resistor	680	SMD 0603	R501 R502	$0.10000	1	$0.20
1	CRA4S810KCT-ND	Resistor Pack	10k	CRA04	R606	$0.04300	10	$0.43
1	SW1021CT-ND	Switch	SPST	B3U-1100P	S429	$1.03000	1	$1.03
1	ATMEGA328P-15AZCT-ND	Microcontroller	ATMEGA328P	32-TQFP	U401	$6.45000	1	$6.45
1	768-1007-1-ND	USB interface	FT232RL	28-SSOP	U501	$4.50000	1	$4.50
1	NC7SZ157P6XCT-ND	Multiplexer	Noninv 2 input	SC-70-6	U602	$0.41000	1	$0.41
1	887-1319-1-ND	Crystal	16MHz	7M	Y401	$1.69000	1	$1.69
							Lights	$76.23
							Rest	$16.62
							Total	$92.85

This costs on the order of $100, but the vast majority of the cost is in the 242 lights (240 for the hands, 2 for the TX/RX indicator). I get the above prices today from Digikey with no tax or shipping added on.You can get cheaper lights if you are satisfied with not using green or blue.

You will also need some connectors for the boards:
Sparkfun Female Header Pack - a set of two 6-pin and two 8-pin sockets. You will need this complete set, plus another 6- or 8-pin that will be cut down to 4 pins. You might as well get two of these sets, since they are cheap
Two Arduino 6-pin stackable headers
A strip of male straight headers and male right-angle headers. You need 32 pins' worth of straight headers and 4 of right-angle headers.
A long USB-A plug to USB-Anything cord. You are going to cut the cord off as far from the A end as possible.You will also need a way to connect this to the 4-pin right angle connector. I used a 5x2 ribbon connector (yes, 5, even though only 4 are needed. It's what I had on my bench at the time.).

While we are going through the Sparkfun shopping list, I recommend getting the UP-501 GPS receiver. In principle, any GPS receiver can work, and you can even set the clock over USB and have it run free without any GPS at all, but then you don't get sufficient precision to justify the third hand. The socket on the circuit board is designed for this UP501, and it fits nicely on the back of the board in between the four screws. If you use another GPS, you will need to make a connector for it. Get one that runs at 3.3V (or has a voltage adaptor) and one that has a PPS signal.

Finally, you need the light pipe parts. Ponoko does great work, but it is quite a bit more expensive than just the bare plastic sheets cost. The light pipes as I designed them are exceptionally fragile, and I forgot to put tabs on the light pipes to connect them directly to the four screws. If I were to make another clock, I would fix the latter flaw. As it is, the light pipes have holes for each LED, and these are used to hold the hands in place.

The firmware is plain ordinary Arduino code. There are two separate sketches, one to test each light in a controlled condition, and one to actually be a clock. The Charlieplex driver is put into a library so that the test code tests the same code that the clock code uses.

AppArmor

AppArmor is one of those things that our distribution engineers like to put into our Linux distributions without telling us. If you don't know about it, it can cause some WEIRD errors.

First off, AppArmor is basically another more restrictive set of file permissions, based not on the userid, but the filename of the process itself. If a process is not allowed access to a file by AppArmor, it will fail, just as if the permissions were set wrong.

If you don't know about this, it can be a head scratcher. Like for instance, I just moved my MySQL tables from their natural home to the raid. All the permissions are set properly, because mv does that when it can, and because I was root at the time. But MySQL still wouldn't work.

There is a set of file restrictions in /etc/apparmor.d/ . Find the right file, named after the process path but with dots instead of slashes (/etc/apparmor.d/.usr.bin.mysqld controls access by /usr/bin/mysqld). Set the permissions in there, and things will work.

Resurrecting Omoikane

So, as you may or may not know, I ran a nice little Linux server with all my data on it, including a filesystem dating back to at least 2003 with files back to 1999. I used LVM to spread the file system across all the drives I had, so that I didn't worry about which file was on which drive. I let the filesystem driver handle that.

Well, a couple of months ago, one of the drives in Omoikane started emitting this terrible shaking noise, which panicked the kernel. When I restarted the system, that drive was dead.

So, now I get to learn more than I cared to about the LVM and ext4 filesystems, in order to recover what I can from the good drive. As it happens to turn out, the system was in five "stripes", continuous blocks of LVM extents. Three of them, including the first one, are on the good disk, representing 2TB of the total 3.5TB system.

First thing is to write a really primitive LVM driver. I used the LVM tools to get a map of the stripes, then hard coded that map into my recovery program. This means that my program is not directly applicable to your problem, if you stumbled across this looking for LVM-saving hints. But, I did learn something about LVM: It uses the first 384 sectors (512 bytes each, 192kiB total) of each physical volume to record info about the entire LVM system the volume is participating in. This means that if any drive is still good, I can use it to reconstruct the structure, and find out which stripes I have and which I don't.

After the LVM header, each physical volume is just a trackless waste of unstructured bytes. The stripe information in the LVM header is needed just to see the order of the LVM extents on the physical volume. This is actually good, as it means that I don't have to interpret anything in the sea of data, at least in an LVM sense. To find the Nth extent of a logical volume, use the stripe map to get which extent of which stripe on which drive, then seek to 384*512+M*65536*512 to get to that extent, where M is the physical extent number you get from the stripe map.

Next it's on to writing a really primitive ext4 driver. Ext4 is rather sophisticated, in that it keeps track of a lot of data and uses complicated algorithms to decide where and when to write what. The good news is that Ext4 is a straightforward extension of Ext3, which again is an extension of Ext2, which was quite a bit simpler. Because it makes an effort at backward compatibility, much of Ext4 is readable with the simpler Ext2 logic.

For instance: Ext4 is divided up into block groups, same as Ext2. Each block group has an inode table and some bitmaps to help the full-blown driver allocate things quickly and optimally. Some block groups, always including the first, include a superblock with information about the entire file system, and a table of block group descriptors. Each block group table contains descriptors for all the block groups. So, in the first block group, we find a superblock, descriptors of all the block groups, and an inode table which lets us start finding files.

Now here's the clever bit. For a variety of reasons, pointers in different structures may point to blocks in other groups. That's ok, because all block pointers are absolute, meaning that they are all relative to the beginning of the filesystem. In one of the ext4 sophistications, it groups block groups into metagroups, and combines the inode tables and bitmaps from several block groups into one contiguous stream. For instance on Omoikane, 16 contiguous block groups made up a metagroup, so that the inodes for all 16 groups are in the first group. My code doesn't care, because the inode pointer in the block group descriptor points to the right place inside the inode metatable.

Another clever bit is in the directory structure. As is typical with a Unix filesystem, all the important information about a file is in the inode, including the file's length, permissions, owner, and block map. Everything you need to read a file, in other words. The directory only contains the name and an inode index. This is how hard linking is implemented: If two directory entries point to the same inode, then the file has two hard links, and each entry has equal claim to being the true name of the file. The directory entries don't even have to be in the same directory.

Ext2 just searched each directory entry linearly. Ext4 has the option of indexing the directory file, but it is done in such a way that Ext2 logic will completely ignore the index. The index data is actually in the directory entry for '..' after the file name.

In ext2, the closest thing to a "file allocation table" analogous to FAT filesystems is the block map. This map starts in the inode, which has the index for the first 12 blocks used by the file. Files of up to 48kiB are accomodated thusly. If the file takes more than 12 blocks, the 13th entry in the index points to another data block, the indirect block, which is completely full of pointers to the actual data blocks, allowing 4kiB*1ki blocks=4MiB more data, with the cost of 4kiB extra index data. For larger still files, we have the 14th entry which points to the double indirect block. Each pointer in this block points to another block full of pointers to the actual data blocks. 4kiB*1ki blocks*1ki blocks=4GiB more data, at the cost of 4MiB+4kiB more index data. Similarly the 15th entry points to the triple indirect block, which allows 4TiB more data at the cost of 4GiB+4MiB+4kiB of index data. Each step means about 0.1% overhead in storing a large file. Larger block sizes make the indirect blocks able to hold more pointers, so the level factor is more than 1024.

However, in ext4, a new block index called an extent tree (not the same as LVM extents) is used. The block map tree is fairly complicated, and needs to mark every block a file uses. Extents basically run-length compresses this by using one extent entry for each contiguous stream of blocks the file uses.

I told you it would work!

The above image is a 256x256 thumbnail from one of the front Hazcams on the Curiosity Rover, and represents more science data than sent back by any surface mission not sent by Americans.

And then there was this:

 While recording the MSL entry data in canister mode, MRO also snapped this photo of MSL on its parachute. They said that this photo would be harder, because even though (or rather because) it's closer, the angular rates are higher. Well, this is a much better picture than that of Phoenix.

I gotta Feeling that Tonight's going to be a Good Night...

Go MSL! Stick the landing! Thousands of people have worked hard on you, millions are wishing you well.

Some humor:

When I say "overheard", I actually mean that I said that when I was working at a summer job at JPL. I'm not saying that I had any influence over arming the rover, but let's just say that all successful surface missions have been American.

Why do I do this?

I am throwing a zombified lobotomized Omoikane back into the atomic banana peeler, just for its compute power. I have Unplugged All the Things (drives) and am going to run it just off of a USB stick with Ubuntu Precise on it.

I'm no Dan Maas. I don't have the time necessary to give this the attention it deserves. I don't have enough computer power to get a full model of both the lander and the terrain into view at once.

What I can do is easy. Spice kernels take all of the work out of predicting where things are. I don't need an aero model, I don't need a guidance program, I don't even need a numerical integrator.

So why do I bother? Especially in the face of this?

Because I like it. I love doing computer animations. I love collecting data and models. It's tradition started from Phoenix. If I had MER data I would probably do them too. And above all, Absurd Accuracy is Our Obsession. I have seen how SUFR works and how the balance masses deploy. They look weird, but a bit of though suggests its probably right. I have seen the lander scream into Gale Crater and descend against the backdrop of Mt Sharp. I have seen the parachute deploy and the backshell swing on it. I have seen the Skycrane Maneuver, and it doesn't look half as crazy as it once did. To be honest, its the part of powered descent before the skycrane that has me most worried.

Besides, it's not all bad. I finally found a nice map of Gale crater. So, my model of Mars lacks in detail, dozens or hundreds of meters resolution in topography, smaller but still large blocks in image map. Better is available, but not in color and difficult to mosaic. Besides, I don't have the memory for better. POV is particularly inefficient with meshes, and the maps I do have tax Aika's memory.

Anyway, with that map in place, with the backshell scorched, and so on, it looks good to me. Maybe I am comparable to Dan Maas. A little more time, a little more greeblies on the descent stage and rover (and perhaps Santa will bring me a copy of SolidWorks to do it with) and a little more patience and memory, and I might have a world-class animation. I at least hope to have a LASP-class animation to show on Sunday night.