Date: Tue, 12 Jun 1990 17:05-EDT From: space-tech-request@CS.CMU.EDU To: ~/st/lists/stdigest Subject: Space-tech Digest #63 Sender: mnr@DAISY.LEARNING.CS.CMU.EDU Contents: Bruce Dunn Why bother endcapping gun barrels Doug Reeder Tether thesis available in LaTeX and PostScript Joe Pistritto AMSAT asteroid mission? Philip Fraering Minicomets Joe Pistritto Orbital Mechanics revisited [long discussion] Kevin Ryan Re: Orbital Mechanics revisited Paul Dietz Re: Orbital Mechanics revisited Joe Pistritto Re: Orbital Mechanics revisited Paul Dietz Re: Orbital Mechanics revisited Pete Thomas Re: Orbital Mechanics revisited Paul Dietz Re: Orbital Mechanics revisited Dan Briggs Numerical Recipies and adaptive stepsize ------------------------------------------------------------ Date: Tue, 5 Jun 90 12:41 PDT Apparently-To: space-tech@cs.cmu.edu Subject: Why bother endcapping gun barrels From: Bruce Dunn The main purpose of evacuating a gun barrel is to avoid the problem of gas compressing in front of the projectile, slowing it down (at least I think this is the problem). Maybe we are looking at the problem the wrong way. If the gun barrel were filled with a gas which is easily liquified under pressure, then the advancing projectile might simply collect the barrel gas as a thin layer of hot liquid at the front of the projectile. I propose filling the upended gun barrel with butane, which is heavier than air. Butane is easily liquified under pressure, at least as long as the temperature does not get too high. Can anyone comment on whether this is feasible, considering what might happen to the temperature of the butane as it is compressed? A side benefit of this scheme, should it be feasible, would be a muzzle flash of stupendous proportions.. -- Bruce Dunn Vancouver, Canada a752@mindlink.UUCP ------------------------------ From: oresoft!reed!reeder@uunet.uu.net To: space-tech@CS.CMU.EDU Subject: Tether thesis available in LaTeX and PostScript Date: Mon, 11 Jun 90 01:30:00 MDT I recently finished my undergraduate thesis entitled "Tethers for Space Propulsion Without Reaction Mass". If you want a copy, I can e-mail you the LaTeX source, or mail you one of the leftover copies. It's primarily of interest because it's a technical paper by someone you sort of know about a subject you may be interested in. The main topic is the question of stability of two connected masses, along with an introduction to electrodynamic tethers. It's oriented toward someone with a bachelor's degree in physics or engineering, and no particular knowledge of the subject. p.s. I can also send you the .dvi file or a copy translated into PostScript. I'm working on translations into Pascal and Serbo-Croatian as well. Doug Reeder USENET: ...!tektronix!reed!reeder from ARPA: tektronix!reed!reeder@berkeley.EDU BITNET: reeder@reed.BITNET Things ain't what they used to be... and they never were. ------------------------------ Subject: AMSAT asteroid mission? To: Space-Tech Mailing List Date: Mon, 11 Jun 90 15:10:09 MESZ From: Joseph C Pistritto Mailer: Elm [revision: 64.9] Is there anyone out there who has the facts on a proposed Ariane 4 mission to the asteroid Belt by AMSAT? I have the following citation from the AIAA aerospace literature abstract database about this: A84-11762 The AMSAT mission to the asteroid belt MEINZER, K. International Astronautical Federation, International Astronautical Congress, 34th, Budapest, Hungary, Oct. 10-15, 1983. 4 p. Anybody know how to get in touch with this guy, or have a copy of the referenced paper, or know anything about it? I'm writing an article on the topic and was looking for some data... -- Joseph C. Pistritto (bpistr@ciba-geigy.ch, jcp@brl.mil) Ciba Geigy AG, R1241.1.01, Postfach CH4002, Basel, Switzerland Tel: +41 61 697 6155 (work) +41 61 692 1728 (home) GMT+2hrs! ------------------------------ Date: Tue, 12 Jun 90 12:42:17 -0500 From: 9240 Fraering Philip To: space-tech@CS.CMU.EDU Subject: Minicomets Does anyone out there know the status of the theory(theories) about minicomets entering the earth's atmosphere at the rate of several thousand (or more) per day? Philip Fraering dlbres10@pc.usl.edu ------------------------------ Subject: Orbital Mechanics revisited To: Space-Tech Mailing List Date: Mon, 11 Jun 90 15:05:51 MESZ From: Joseph C Pistritto Mailer: Elm [revision: 64.9] A lot of the 'orbital mechanics' we all know and love deal with the situation most common today, the use of big rockets with lots of delta-v potential. In particular, stuff like the calculations for Hohmann ellipse transfer orbits assume instantaneous (or near enough) delta-v insertion/circularization burns. Does anyone have equations to cover the situation where thrust is low, but continuous, as in for ion engines or solar sailing? I did a simulation this weekend of an ion engine on a spacecraft deployed at 300km LEO and the results say that using an ion engine, I have to expend fuel equivalent to 6500 m/sec delta-v in order to build up the 3500 m/sec or so to escape from the Earth. Part of the problem is the moon, if you go fast, you can arrange for it to be out of the way, but if you 'spiral' outward, as happens with low thrust, then it turns out to be a significant problem, (as the spacecraft approaches lunar orbit distance, but is not moving fast enough yet to escape the earth's pull). Unfortunately, doing this the simulated way, (compute all forces, project velocities, step forward n seconds, do it again...) takes a LONG time, particularly when I'm using an 8Mhz AT. I was wondering if there were general purpose equations to deal with the situation, in the same way we can easily calculate a Hohmann orbit, etc. -jcp- -- Joseph C. Pistritto (bpistr@ciba-geigy.ch, jcp@brl.mil) Ciba Geigy AG, R1241.1.01, Postfach CH4002, Basel, Switzerland Tel: +41 61 697 6155 (work) +41 61 692 1728 (home) GMT+2hrs! ------------------------------ Date: Mon, 11 Jun 90 10:19 EDT From: KEVIN@a.CFR.CMU.EDU Subject: Re: Orbital Mechanics revisited To: space-tech@CS.CMU.EDU X-Envelope-to: space-tech@CS.CMU.EDU X-VMS-To: IPROUTE"space-tech@cs.cmu.edu",KEVIN > Problems of calculating low-thrust spiraling orbits, particularly in > regards to the Moon getting in the way... This weekend I saw a presentation by the Canadian Solar Sail Project, discussing among other things the planned orbits. Solar sailing is as low-thrust as anything else, such as ion propulsion, with even more limitations due to the reliance upon sun angle. They showed plots of an orbit spiraling up and away from earth (starting from a 1000km orbit, which they calculate is the minimum needed to prevent air friction from overcoming solar propulsion), and using the moon for a gravitational assist. They aren't certain if they can control the sail closely enough yet - they would need to get within ~100km for best effect, with a 120m sail, but they're checking on it. Apparently using a gravity assist will cut ~20 days off travel time to Mars. The Moon is a help, not a hindrance. The Canadian project is one of about 14 entrants proposed for the 1992 Columbus memorial Mars race. There are entrants from MIT (heliogyro style, very small at 80kg projected weight), Italy (_very_ well funded), I believe John Hopkins has two, although I might be wrong, Britain has one (the folding of the sail was designed by an origami expert - 200 meters across), Canada (rated the most manuverable), etc.. The competition is to race a solar sail ship, 500kg maximum, to Mars. Start is hoped to take place in 1992, only required payload is a 1kg plaque. kwr Internet: kr0u+@andrew.cmu.edu ------------------------------ To: space-tech@CS.CMU.EDU Subject: Re: Orbital Mechanics revisited Date: Mon, 11 Jun 90 11:25:02 -0400 From: dietz@cs.rochester.edu Joe Pistritto wrote: A lot of the 'orbital mechanics' we all know and love deal with the situation most common today, the use of big rockets with lots of delta-v potential. [...] Does anyone have equations to cover the situation where thrust is low, but continuous, as in for ion engines or solar sailing? [...] Unfortunately, doing this the simulated way, (compute all forces, project velocities, step forward n seconds, do it again...) takes a LONG time, particularly when I'm using an 8Mhz AT. There are some numerical techniques from astrodynamics for computing an orbit with perturbations. Normally, the perturbations are from things like the moon and sun, but they could also be accelerations from low-thrust engines. The technique you described goes by the name of Cowell's method. (I hope you used a good numerical integration scheme; see "Numerical Recipes" for some good off-the-shelf routines.) According to my copy of Bate, Mueller and White ("Fundamentals of Astrodynamics", Dover, ISBN 0-486-60061-0, $7.95 paperback), "this method is approximately 10 times slower than Encke's method. It has been found that Cowell's method is not the best for lunar trajectories. Even in double precision arithmetic, roundoff error will soon take its toll in interplanetary flight caculations if the step size is too small." In Encke's method, the difference between the primary acceleration (due to the earth, in your case) and perturbing accelerations is integrated. One calculates how far the spacecraft is diverging from the reference orbit it would have followed had there been no perturbing accelerations. When the discrepancy is too large, the reference orbit is updated ("rectified") and the calculation continued. More generally, one can continuously vary the orbital elements. That is, you can express the rate of change of the orbital elements with a set of differential equations, then numerically solve these equations. Bate, Mueller and White go into detail on Encke's method (pages 390-396) and this more general method of variation of parameters (pages 396-412). I have some C routines for doing some orbital mechanics calculations (not this particular one, though). It would be nice to have a library of public-domain routines for all the standard problems. For example, if you can solve for position and velocity as a function of time and orbital elements, and can solve the "Gauss problem" (given two positions and times, find an orbit connecting them), then you can find and optimize interplanetary trajectories that apply thrust only at the start and end of the trip. Paul F. Dietz dietz@cs.rochester.edu ------------------------------ Subject: Re: Orbital Mechanics revisited To: dietz@cs.rochester.edu Date: Tue, 12 Jun 90 10:09:08 MESZ From: Joseph C Pistritto Cc: space-tech@CS.CMU.EDU Mailer: Elm [revision: 64.9] Well thanks to Paul Dietz for his usual learned reply. I'll try to get ahold of Bate, Mueller, + White, it sounds like a good book to have, and not even expensive... Under Cowell's method, the adjustment of stepsize is a delicate compromise. If it gets too small, then accellerations fall off the end of the double precision arithmetic, if it gets too large, then inaccurracy results due to large changes in the 'net G' forces during a step. Also, the shape of the orbit involved makes a big difference. A step size that is very tolerable in an almost circular orbit becomes horrifically inaccurate in an elongated, highly elliptical orbit (a good test orbit, by the way, is GTO, Geosynchronous Transfer Orbit, 300x35800 km). In the Earth/Moon system, it that it is still usable, on truly interplanetary trajectories though, it seems doubtful (as the forces become dramatically smaller). I'll have to look into adopting Encke's method, and see what the differences really are. At the moment my simulation, by the way, runs at about 100x real time, which means multiple DAYS of execution time for typical ion engine situations. Yes, it would be really neat to have some public domain set of libraries for doing these sort of thing. On the subject of which, I wonder if the programs used by JPL, etc. are available, most government software is, if you know how to ask... Maybe I'll try asking on Compuserve, where I know a guy who works in the JPL public affairs office. I managed to get some papers on gravity assists out of him last year... Orbitally yours, -jcp- -- Joseph C. Pistritto (bpistr@ciba-geigy.ch, jcp@brl.mil) Ciba Geigy AG, R1241.1.01, Postfach CH4002, Basel, Switzerland Tel: +41 61 697 6155 (work) +41 61 692 1728 (home) GMT+2hrs! ------------------------------ To: bpistr@ciba-geigy.ch Cc: space-tech@CS.CMU.EDU, dietz@cs.rochester.edu Subject: Re: Orbital Mechanics revisited Date: Tue, 12 Jun 90 08:50:02 -0400 From: dietz@cs.rochester.edu Joe Pistritto wrote: Under Cowell's method, the adjustment of stepsize is a delicate compromise. If it gets too small, then accellerations fall off the end of the double precision arithmetic, if it gets too large, then inaccurracy results due to large changes in the 'net G' forces during a step. I hope you use adaptive step size. Not only does this improve the "quality control" of the code, it makes it more efficient, in some cases by a factor of 100 or more, over the "dumb" routine with fixed step size. "Numerical Recipes" has all the code you need for fifth-order Runge-Kutta with adaptive step size. Versions of the book are available for Fortran, Pascal and C, and you can get a diskette with each that has the routines all ready to use. I have heard many people recommend this book; I do also. It's invaluable. Paul F. Dietz dietz@cs.rochester.edu ------------------------------ Date: Tue, 12 Jun 90 12:42:04 -0400 From: "THOMAS, PETE (TEACHING ASSISTANT" MMDF-Warning: Parse error in original version of preceding line at CS.CMU.EDU To: cgch!jcp@CS.CMU.EDU, space-tech@CS.CMU.EDU Subject: Re: Orbital Mechanics revisited > particularly when I'm using an 8Mhz AT. I was > wondering if there were general purpose equations to > deal with the situation, in the same way we can easily > calculate a Hohmann orbit, etc. Hmmmmm--just completed a course in orbital mechanics. The last topics we covered were low-thrust alternatives (mainly solar sail and ion propulsion). The gist of what Dr. Flandro said was that the trajectories are fairly hellacious, most people choose to use numerical analysis, and that the "sphere-of-influence" and "patched-conic" assuptions collapse under constant low thrust conditions. What is probably particularly difficult is the inverse problem; we can solve for where the craft goes--but are we going to be able to solve for the optimum trajectory based on an origin and destination? I too am interested in what ideas people have on solving these problems--I've just started studying orbital mechanics, and these sort of situations are one of my biggest "question-mark areas." --Pete ------------------------------ To: "THOMAS, PETE (TEACHING ASSISTANT" Cc: cgch!jcp@CS.CMU.EDU, space-tech@CS.CMU.EDU, dietz@cs.rochester.edu Subject: Re: Orbital Mechanics revisited Date: Tue, 12 Jun 90 14:39:57 -0400 From: dietz@cs.rochester.edu Concerning low-thrust, long duration engines, Pete Thomas wrote: What is probably particularly difficult is the inverse problem; we can solve for where the craft goes--but are we going to be able to solve for the optimum trajectory based on an origin and destination? I don't know how the "pros" solve these kinds of problems, but here's a simple idea that springs to mind. Consider the following problem: find a trajectory that moves an ion-engine propelled spacecraft from position p_0 and velocity v_0 at time t_0 to position p_n and velocity v_n at time t_n. Suppose the spacecraft is in orbit around the sun, and ignore the gravity of other bodies. We can set up an optimization problem. Divide the time interval (t_0,t_n) into n-1 points. At each of the n-1 points are six unknowns: position and velocity of the spacecraft. n is chosen to be large enough so that the spacecraft does not move far in one step. The "cost" from time t_i to time t_{i+1} is a function of the acceleration the engine must provide to get the spacecraft to p_{i+1}, v_{i+1} (which we can compute, given that the steps are small). If this acceleration is more than the engine can supply, a very high artificial cost is imposed. Otherwise, the cost is something like the amount of reaction mass consumed. (You could probably get by just specifying the positions p_i, and solve for the velocities.) We start with an artificial, and probably impossible trajectory. Then, use a multidimensional optimizer (conjugate gradient?) to minimize the total cost of the trajectory. A more general technique might use orbital elements instead of positions and velocities, and/or might use adaptive time steps. Paul F. Dietz dietz@cs.rochester.edu ------------------------------ Date: Tue, 12 Jun 90 13:04:07 MDT From: Dan Briggs To: space-tech@CS.CMU.EDU Subject: Numerical Recipies and adaptive stepsize Paul Dietz wrote: I hope you use adaptive step size. Not only does this improve the "quality control" of the code, it makes it more efficient, in some cases by a factor of 100 or more, over the "dumb" routine with fixed step size. "Numerical Recipes" has all the code you need for fifth-order Runge-Kutta with adaptive step size. Versions of the book are available for Fortran, Pascal and C, and you can get a diskette with each that has the routines all ready to use. I have heard many people recommend this book; I do also. It's invaluable. While I personally agree with what Paul just said, you should also be aware that many professional numerical analysists do *NOT* like _Numerical Recepies_. The motivation for these feelings is essentially that a little knowledge can be a dangerous thing. The routines that you will get out of NR tend to be *good*, but that's about all. They are not necessarily state of the art! I like NR because the text of the book gives me a pretty good understanding of what the routine is doing. The routine is not a black box, so I can adapt it to my problem as needed. This is a great advantage, but the price you pay is using a routine that may not be the best available. The brutal fact is that numerical analysis can be a very tricky, sophisticated subject. The routines to deal with the nastier problems are not pretty things at all, and certainly not the sort of things that you would publish in a cookbook. You can go a long way with the routines in NR, but sometimes it is better to use a routine from IMSL or NAG. If those fail you, it's time to consult an expert. On the subject of adaptive stepsize, a couple of years ago I did a comparison between the 4th order RK with fixed step size, the 4th order RK with adaptive step size, and a 4th order predictor corrector ODE integrator. These were pretty much the same routines that are found in Numerical Recipies. I tried a number of different systems, including the third order Lorenz model. This last system is a horribly ill conditioned system that exhibits chaotic behavior. That is, it should prove a substantial challenge to any integrator. I was astonished how little difference there was between the integrators. For a constant number of CPU cycles, they were pretty much equivalent. They all had problems with the Lorenz system, and produced different answers. Thing is, the two RK integrators diverged from the "right" answer in about the same place. To this day, I don't know why this was the case, since a system like this is precisely the sort of problem that an adaptive integrator is supposed to be good at. BTW, the system is pretty simple. See Bender & Orzag, _Advanced Mathematical Methods for Scientists and Engineers_, pp.192 for details. The gist of it is that dx/dt = -3(x-y) dy/dt = -xz + rx - y dz/dt = xy - z r is an arbitrary parameter, and the system will exhibit different behavior in the regions -inf < -1 < 1 < 21 < +inf. Try r = 17, x(0) = z(0) = 0, y(0) = 1. Then try r = 26, x(0) = z(0) = 0, y(0) = 1. Anyway, I ramble on. The point that I am trying to make is that numerical analysis can be subtle, and you can get into real trouble thinking that one book like Numerical Recipies makes you equipped to handle all of the problems that you might run into in every day work. ---- Daniel Briggs (dbriggs@nrao.edu) New Mexico Tech / National Radio Astronomy Observatory P.O. Box O / Socorro, NM 87801 (505) 835-7360 ------------------------------ End of Space-tech Digest #63 *******************