What we need now: Guidance system and other issues

[pyramids]

There's less than 180 days left and hence apparently not even enough time to, for example, go through the paperwork process for launching at ESTEC (unless the same rocket design was flown there before). Let's take stock and see what can still be done! The following is what little I have happened to find out:

1. Guidance System
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I haven't seen any discussion about guidance systems on here (thanks to Paul for pointing out that this is not entirely true). So either everyone knows a solution, or nobody has gotten this far. In principle, you could use MEMS sensors (accelerometers and gyroscopes) to build an inertial navigation system, but what is cheaply available (e.g. http://www.chrobotics.com, USD 125) or even just barely possible by building a similar circuit (I tried) will give you at least, and probably much more than, 10 degrees of angular error over the time of a launch, completely unacceptable for reaching a target orbit unless, maybe, you're willing to provide significant extra delta-v for such a high orbit that the rocket will still be guaranteed to miss earth on its trajectory. And that is not counting the adverse effect of vibrational noise in a rocket on the performance of INS sensors!

The way to build a working, cheap guidance system would appear to provide additional circuitry to augment the usual INS sensors. Using the earth's magnetic field is possible in theory, but with magnetic weather in the ionosphere being quite unpredictable, I'm tempted to call people trying that illinformed (but I would gladly be convinced otherwise, if anyone has a good argument). Yet either a GPS or a sun-tracking camera would seem to do the trick. GPS units have the problem that just about everything one can buy and afford is intentionally limited to not work for most of the rocket's flight, a requirement for selling from inside to outside the Wasenaar nations (still known in the trade by the obsolete term COCOM limits). Still many of the low power, low cost GPS modules and chips could be reprogrammed for our purpose, but existing such projects seem limited to obsolete chips and adapting or redoing it for current hardware requires documentation (trade secrets, I think) which the manufacturers seem unwilling to share unless you're a big volume manufacturer (does anyone have superb communication skills for negotiating an exception, guys?). It could of course be built with discrete hardware, a feat done at NASA to much higher capability, weight and power consumption than we would be interested in (google "Building a GPS Receiver for Space Lessons Learned" if you are interested), but even when recreated with the latest tech to our less demanding requirements, this approach will still be more wasteful in space and electric consumption than we should be willing to accept.

The other option is sun (or maybe star) tracking. A cheap webcam should be quite enough or maybe even an array of photodiodes could be enough because centroid estimation (calculating the center of the blob of light that is the sun) can be surprisingly accurate if you get a good signal-to-noise ratio. Note that there are launch constraints due to weather (visibility) and time of day. Also, condensation shock waves may impair the sensor's ability to see; maybe (I'm not quite sure) it will be enough to use a COCOM-limited GPS for the lower part of the trajectory where this is of gravest concern, or maybe one would have to take the possibility of condensation shock waves into account when designing the optical arrangement or when chosing permissible launch weather conditions. And then you may need careful caibration or superb optical design to not have your sensor irritated by seeing bits of the fireball that is your exhaust plume...

In either case, space applicaions usually require some kind of analysis of radiation hardness because electronic circuits are prone to malfunction when bombarded with ionizing radiation found in space. Judging on the fact that sometimes certain regular computer chips are found adequate for commercial satellites and the brief duration of our space mission (only the launch phase matters, after all!), there's a good chance to be fine without considering this point. Yet depending on the reliability we want to aim for, it may be worth to be mindful of not choosing a particularly ill-performing part or even designing for redundancy. Remember that even regular computer chips are manufactured to minimize the use of naturally radioactive ingredients to improve reliability as highest integration unfortunately tends to imply highest susceptibility.

2. Launch Method
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Surprisingly, with the extreme level of optimism we need to even think about the N prize, just about anything might work. I wrote an ascent simulation that indicates a delta-v of less than 9 km/s is enough to reach low earth orbit even with a not fully optimized trajectory of an equatorial sea-level launched 100 kg rocket, providing that a slenderness corresponding to maybe 3m total rocket length and very good aerodynamical fairing is used. For that I assumed one could reach drag coefficients of 0.05 (subsonic), 0.2 (transsonic) and 0.1 (supersonic), which should be realistically achievable for a fully streamlined body, but, ALERT, I have not considered plume effects and, frankly, I am not quite sure what is realistic when accounting for that. If the situation gets much worth, a balloon or other high altitude launch may indeed be neccessary. Another ALERT: I'm reciting these numbers from memory; sorry about having put the program with details only on a computer I left abroad. Also note that starting from sea level requires you to make sacrifices about the nozzle expansion ratio and hence achievable ISP in the first stage, especially if your combustion pressure is low. So if altitude comes free (mountain top? zero cost balloon?), you want to not only use it, but design the first stage nozzle for it.

By the way, almost any propellant will work! Even just hydrogen peroxide as a monopropellant (ISP up to ca. 1.8 km/s) could just about fit into the budget in a many-stage design as it allows very good mass fractions. But that is no longer true if you use the (expensive) catalysts that http://www.peroxidepropulsion.com used to sell before, sadly, their factory blew up (destilling peroxide is dangerous as the pure gas phase is an explosive at ambient pressure; don't try it at home, not even if you are unafraid of being arrested for bomb building intentions; google Sauerland Group for news on how terrorists tried using this stuff to fabricate much worse). Of course, peroxide and gasoline is nevertheless one of the particularly appealing bipropellant combinations for virtue of high ISP (around 3km/s), comparatively low flame temperature, storability without refrigeration, and, for rocket fuels, comparatively good handling safety (do remember not to boil it and be extremely mindful of unintentional catalysts such as wrong container materials, dirt, or residues of cleaning agents). Yet there are many other possibilities. The problem, of course, is that developing one's own rocket motor takes lots of time and testing for which it is too late now. At least for a sea level launch, you'd probably want your first stage throttleable, though, to stay in the sweet spot trade-off between gravity and air drag losses, and, of course, to limit aerodynamical forces to what your structure is designd for.

In stages that don't use a solid propellant (which may be attractive for the upper stages), you probably want a pressure-fed system. Unfortunately, you cannot achieve the full tank pressure in the combustion chamber as pogo oscillations result; I think I've somewhere seen the recommendation to use half this pressure as a rule of thumb, and I think constant flow valves (which can be no more than cleverly shaped pieces of an elastomere) might help in keeping this required head pressure as low as possble, maybe in addition to the usual baffles. Fortunately, small rocket motors apparently tend to be a bit more benign regarding all kinds of oscllations than big ones. And sorry for still getting too carried away over it, now that we really need to piece together what proven stages the community has produced rather than designing new ones!

3. Orbit Planning
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There's actually alot of man-made things in space nowadays, and it would really suck if our rocket made an unplanned rendezvous with something else on the way. Whilst chances for that may be much worse than winning the lottery, I could imagine that insurers for commercial satellites or operators of military ones or of the ISS take a different view of such chances than we hobbyists do. But, obviously, with a guidance system presumably chosen for being just cheap enough to achieve just any kind of orbit, there may be limited technical possibilities for chosing an orbit well enough to guarantee steering clear of even just the functional and in-one-piece satellites over our heads. Has anyone thought about this yet? There are tracking services, some not just limited to proper satellites but also including debris, of course, if only we had a sufficiently good guidance system to launch into the empty regions of space.

4. Orbit Validation
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This should be easy if we can motivate the hobby astronomy scene to help out and make the satellite visible from the ground. Mirroring the sun in an Alumnium foil extended by shape memory wire as sole satellite components should be capable of a ground visibility not too far away from an Iridium flare (do google if this is new for you), but the ground track covered by this reflection is limited and the satellite might have to be released in a spin-stabilized state. But with intentionally adding surface imperfections or wrinkles, it is possible to reach just about any compromise between covered ground track and apparent brightness. Sadly, just using a balloon would seem to reduce the brightness to no longer visible to the unaided eye.

About me
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I am one of these people who have lots of good ideas all the time but can only communicate them to others really interested in how things and nature work. I have a PhD in physics and secretly hope that I am a silicon valley type, but I am far too inhibited to find and motivate the collaborators needed to get just about anything worth thinking about actually started. So all this is to heal my inhibitions and become comfortable talking about ideas again. And...dare I say it...to hopefully find people interested in doing equally fun projects with economic potential. I mean even beyond turning the cheap N prize rocket launch into a service to provide artificial falling stars (customers paying more to get their cremated remains put into a falling star already exist).

[pauldear]

[pyramid] and I have exchanged a couple of emails already, and I was discussing optical guidance systems which he mentions. In other discussions, people have suggested that this would be too slow to correct instability in the rocket, but I don't see why this has to be the case if a simple sensor system (instead of video and a processor) is used.

Once above most of the atmosphere, the sun is basically the only significant light source (by several orders of magnitude).

Imagine three opaque discs, intersecting at right-angles to form the shape of a sphere. Now put 8 simple light sensors, one in each of the 8 "corners" where the discs intersect. At any orientation, a maximum of four sensors will see light; if four of them see equal light, you're pointing exactly along one of the intersection lines between the discs (I hope that made sense). Such a system would need clever design to null out errors (instead of trying to eliminate them, which would be difficult), but could then give you more-or-less instantaneous corrective data (response times on the order of microseconds).

Anyway, I'll shut up and let [pyramid] talk, since he knows way more about this than I do.
Cheers
Paul

[pyramids]

Hi Paul,

your argument is basically correct but depends heavily on the questionable assumption that the sun indeed is the only significant light source, where the significance lies in total flux (not just brightness) received by the sensors. With the assumptions that seem reasonable to me, we will have three such significant sources: the sun, the earth and the exhaust plume of our rocket. Unfortunately, all may create a roughly comparable signal in the detectors you described.

The sun is probably obvious. But it is immensely bright only because it covers a small part of the sky. A sensor that does not resolve this will see the sun and a nearby illuminated plane as essentially equally radiant. Hence a cloud covered earth, seen from a rocket at low altitude (let's say 300 km, small compared to the earth's radius) will give amost as much signal from the earth as from the sun. Another problem is the rocket plume, which, depending on propellants, can be no problem at all (a hydrogen flame is hardly visible outside the UV range) to roughly as bright as the sun plus covering a larger portion of the sky as seen from the rocket because at altitude, all rocket nozzles are underexpanded and the plume still expands lots behind the nozzle.

I'd still say the optical system is quite a viable option, but we need some processing or clever sensor orientation to exclude at least the effects of earth, clouds and plume. If the launch is done and timed such that the sun is far above the horizon and never behind the rocket, this should be doable even with photodiode sensors (with carefully designed angular openings), once we are well above the troposphere with its clouds. Of course, the camera option would allow lots more software processing and, because of the then availble brightness rather than total flux infomaion, very reliable operation.

That brings us to the time issue. Smaller rockets turn about faster, hence we need fast feedback loops. Neither photodiode nor camera solution seem to be good candidates, the first because of the difficulties encountered at launch when the earth fills (the bottom) half of the sky and is additionally illuminaed by the rocket's exhaust, and the later because something like 30 fps may indeed be marginal or even insufficent, at least for a tiny upper stage. MEMS gyros would help, and for an INS, you'll hardly get around them anyways, unless someone wants to build the world's smallest mechanical or laser gyro...? I'm fishing for more ideas here, dear fellow enthusiasts!

Unfortunately, I haven't found the other discussion that Paul mentioned. Searching for "sun" does not work in this forum, and other words I thought would be likely didn't seem to occur in that discussion. Could someone give me a hand in this?

[pauldear]

The "earlier discussion" was not on this forum (I think), but in any case it did not get very far. And point taken about the earth/clouds/plume distracting the sensors. However, I'm assuming that a forward-looking system will not see its own plume, and that once above the clouds (as in a rockoon launch, for instance), they wouldn't be an issue. That just leaves the earth, but this could be avoided provided that some fairly crude system keeps the rocket pointing in at least approximately the right direction, with the optical sensors doing the fine-tuning and stabilisation. Interesting problem, though, and probably far more complex than I imagine!

[pyramids]

Not really more complex than you imagine: I think you summarized the key points!

Just remember for "forward looking" that a typical rocket launch has the rocket turn through 90 degrees of angle, so what used to be up at launch (and even from a 30 km rockoon ignition height you still need to go up alot before you can consider even getting close to orbital speed) is pointing more or less at the horizon when orbit is attained (assuming you can do without a second firing for orbit circularizing). So to continue using sensors looking well away from the earth, you'll have to disable some depending on current rocket attitude.

Another counter-intuitive point that maybe should be mentioned is that the two angles we get from looking at the sun are insufficient to completely measure the three angles determining our rocket's attitude in space. That can be dealt with by taking a second sun angle measurement after intentionally rotating the rocket about by a known angle around a suitable, known axis; the real point is that even for this maneuver, one needs an alternate INS (but with quite limited requirements, hence a cheap MEMS based system is probably fine). And to conserve fuel, one should make this INS sufficiently good to not need this maneuver every few seconds...

Pity we couldn't raise anyone else's interest in this!
I suppose everyone is busy getting launch permits instead?

[DaveHein]

A rockoon launch would require sensors to orient the launch pad, and sensors in the rocket to provide a 6D IMU. The launch pad could use a combination of magnetic and gravitational sensors plus a gyro and a sun detector. The sun detector for the launch pad could use a digital pinhole camera to measure the sun's position to within a fraction of a degree. This would all be processed by a Kalman filter to provide an accurate indication of the launch pad orientation. A GPS receiver would provide an accurate measurement of the altitude and location.

The rocket could use similar sensors if spinning is not required for guidance. Electronically controlled flaps could be use to de-spin the rocket below 60km, and small pressure-fed thrusters could be used above that altitude.

If the rocket requires spinning for stability then a single photo-transistor with a slit aperture would provide an angular reference for the sun and horizon positions. The width of the horizon pulse would indicate the angle relative to the horizon. However, a camera in the tip of the nosecone with a small fish-eye lens would provide a more accurate measurement. Integrated over one rotational period, a bright ring would give the sun angle, and a dark circle in the center would yield the horizon angle.

[ThomVincent]

[pyramids]

Good stuff, Thom, thanks!

Just a tiny correction:
Sparkfun's 9 degree-of-freedom IMU actually does have 9 degrees of freedom; in addition to the usual 6, it features a 3d magnetometer. As I said in my original post, I fear this may be fairly useless once the rocket reaches the ionosphere, as I suspect (without knowing for sure) that there are enough unpredictable magnetic field variations to render navigation by earth's magnetic field essentially impossible.

[DaveHein]

I think Thom's description of the "9DOF" sensor is more accurate. A "degree of freedom" implies an independent parameter, or dimension, so there are only 6 degrees of freedom. It's clear that the gyro and magnetometer provide information about the 3 degrees of information involving orientation. The gyro tells us the rate of change of the 3 dimensions of orientation. The magnetometer gives us an absolute direction of the field lines, which really only provides 2 dimensions of information. If a rocket were pointed in the direction of the magnetic lines we would know its yaw and pitch, but could not determine it's roll from the magnetic data.

[ThomVincent]

Dave (KE5LOL),

I see you have been involved in rocketry for awhile. Do you by chance have an HPR license from Tripoli or NAR? Just curious.

I just got interested again in rockets again a few months ago when I heard of N-Prize. I am contemplating going for Level 1 and Level 2 HPR licenses this year, but haven't decided yet on it.

~Thom (KJ4IKJ)