(Illustration near the end)
Reading Homo Excelsior, using that wonderful Omega Database (great work guys!), I came across the Lofstrom Loop concept, which seemed rather intriguing. There was not much detail on it, except that it used TWO space stations and one ground station, with an EM propelled/controlled "stream of bars", which I did not understand the purpose for, unless they can carry payload.Terry Egan:
Putting some old Thunkthussp onto the problem, I concieved another type of construction, that we could call a Lorrey Loop, if it hasn't already been thought of yet by someone else. (besides, it would really truck too!) ;)
Essentially, you have one station at geosynch, that is say a hundred miles long, containing a main EM rail system, and an accelerator/decellerator rail in parallel. On the opposite side of the planet, you've got a ground station, with a similar EM setup.
Now imagine a big loop going all the way around the planet, with its apogee at the geosynch station and perigee at the ground station. This loop, seeing as how it will be traveling quite fast at perigee and slow at apogee, would necessarily be actually simply a virtual path or corridor for a continuous line of "cars", as if it were a solid loop it would tear itself apart (solid orbital loops being quite impossible and unstable).
The cars would, when reaching the geosynch station, be traveling at the same velocity as the station, from which they can either dump their load, accept a load, or be switched to the parallel system for changeover to an accelerator for transition to higher orbit or interplanetary trajectory.
To build this system, you'd want a high altitude equatorial area for the ground station (Ecuador, Kenya?, maybe the Spine of PauPau New Guinea?)
Its a bit different from what I've seen in other concepts, which require either towers or actual vertical linkage (!!!) the stress alone would require materials at least a hundred times more structurally sound than those known today. using linear motors and orbital mechanics from geosynch to surface, a true sky hook could be possible.
For those who say ground based accelerators are impossible, I will direct you to study up on the papers of the late Dr. Gerald Bull (known as the father of the Supergun) who conclusively proved (on paper, and would have proved in practice if that darn pesky Gulf War and the Mossad haddn't gotten in the way) that using conventional materials and normal chemical artillery propellants, a gun could be constructed that would be capable of placing materials in orbit, with guns specifications similar to that quoted by H.G. Wells' old novel [Jules Verne's From the Earth to the Moon?]. If such things can be accomplished with conventional 19th century technology, certainly using 21st century superconductor technology we could do even better.
The Lorrey Loop would seem to require a vast amount of material.Michael Lorrey:
Actually, it could take less than any of the other [megaengineering projects]. it all depends on how many cars you want in the loop at one time. you could start with just one, and keep adding them. its essentially a huge juggling trick, so you can use that analogy to see how you could keep adding cars until you reach the capacity of the system to process them. What it will require is a vast amount of momentum put into the system, to keep things flowing. Once you get it going, the only energy you need to put in is that to match the momentum losses induced by new cargo put into the system. The cars would already have the momentum. Additionally, let me change the geosynch station, it would not need to be so big, unless it were handling a loop at full capacity.Michael Lorrey:
The cars would be going at their very slowest at their highest altitude (read keplers law) and fastest at the ground. I am actually concerned that they wont be going fast enough at geosynch, as they need to be going slow enough to fall back to earth, rather than staying in geosynch, even though at apogee they will be tangential to the geosynch orbit.Hal Finney:
Opening my Introduction to Space Dynamics by William Tyrrell Thomson, I see that my deduction is right. Essentially, the cars will be following a Hohmann transfer orbit, with lower orbit tangential point at earth ground (perigee) and upper point at Geosynch station, where the velocity of the cars would be less than the velocity of the station, so the station would catch up to the cars as they reach their peaks, add a little momentum to keep them, and then drop them off the back, regaining the momentum when they are returning a car. If you drop off a car every time you pick up a car, you lose or gain zero momentum at the station.
I do understand that the cars in the transfer orbit are going slower than the geosynch orbit at apogee. But I miscalculated the speed of the geosynch station. I now get a value of about 2800 mps. The differential clearly can't be greater than that.Michael Lorrey:
My new improved calculations suggest that orbital velocity at perigee is 10000 mps, and since apogee is about 6 times larger, by Kepler's law the speed must be about 1/6 as much or about 1700 mps. This would lead to a differential of about 1100 mps, with the station going faster than the cars in its orbital direction.
Actually I am not sure how the geometry will work in terms of the station "catching up" to the cars. During the transfer, the station and the earth will have rotated to new positions. That means that each launched car is in a different elliptical orbit (in the non-rotating frame). You will need to launch the cars from a point counter-clockwise from the point opposite to the station, and receive them from a point clockwise from the opposition point. How far these offsets are will depend on how long it takes to reach geosynch orbit, how much the earth rotates in that time.
After sleeping on it, doing some intentional dreamCAD, I decided that, yes, the cars, in an absolute sense are following a Hohmann elliptical orbit. However relative to the geosynch and ground stations, since we are dealing with the earth rotating, they will apear to follow a figure eight path, with the crossover point being that point at which the cars angular velocity is equal to the rotation of the earth. So, this will require good timing in geosynch traffic control to prevent car collisions in a high capacity Lorrey Loop.Hal Finney:
[DreamCAD] (-: That's an interesting design technique :-)Michael Lorrey:
I don't think ballistic cars will literally follow a figure eight trajectory in the earth's rotational frame of reference, although you are right that the orbit will have a loop in it. Rather, it will be more like a Spirograph pattern, because the orbit will not form a closed loop when it comes back to Earth. It will be in a different place because the Earth has rotated away. So left to itself the car would continue back on up, loop again, and come back down, repeatedly.
If the period of the elliptical orbit had some simple relationship to the 24-hour rotational period of the Earth, then eventually the ground station would catch up with the cars again. But it won't happen on the first orbit. This suggests that your "ground station" maybe would be better placed in low earth orbit, otherwise you'll have a lot of fireballs streaking through the equatorial skies all over the planet.
Another idea would be to put your high station not in geosynch orbit, but at whatever altitude gives the Hohmann elliptical trajectory exactly a 24 hour period. This way the cars all come back to the ground station, and you do have your nice figure eight relative to the rotating earth.
The only problem is that the high station's orbit would not be geosynch. You could have several high stations and time your launches so that one would be overhead when the cars get there, or you could have the high station be in a non-inertial orbit, actively thrusting to stay geosynch. Maybe the thrust requirements would be small enough to be satisfied by mirrors.
I'm not sure if I follow your reasoning at the moment....Remember, the ground station is rotating around the planet ina 24 hour period, as is the geosynch station. AHHH. actually, instead of being on opposite sides of the planet, the geosynch would be directly above the ground station. a car would get ahead of the two ( the relative path would be a O between the two stations, with the launch phase being the left side and return phase being the right side, looking down from above the north pole, now that I remember my Smoke Ring Rules of Living).Michael Lorrey:
Yes, the atmosphere is a problem, but I think that using javelin shaped vehicles, with power systems on them generating high external EM fields to the point of ionizing the air around them, would decrease resistance/sonic booms, etc. If you ionize the air passing the car to a higher degree than whould be achieved by friction, you effectivley reduce resistance (drag) as well as surface temperature problems. (a simple matter of magnetohydrodynamics). Sufficient ionization also can eliminate sonic shock waves (true).
While having the lower station in LEO would be easier on the cars, its not a launching system then (the prime goal), and you are hampered in getting material there to build it. If you build the ground station on earth first, you just shoot up cars with constrution materials, and thrusters to insert into GEO and then build the GEO station.
I personally like the Ecuadorian Andes for a ground station. You could definitely get those people interested, as they would think they were rebuilding Atlantis. (old memes into new!!!). Additionally, all that good ionization will be great for producing high altitude ozone to rebuild the O3-layer. Also, being in this hemisphere, your geosynch station would be in a prime position to provide greatly expanded comm services to North and South America, weather and geophysical observation, etc. Given NA being the prime market, it only follows.
After some discussions with Hal Finney, and some more involved calculations, I've developed a more final concept for the Lorrey Loop. Its rather convoluted, but actually a lot more feasible and basic than many beanstalk concepts out there. The attached diagram shows the path that the cars would take, relative to the orbiting GEO stations. NOTE: THe cars in an absolute sense will be following a classic Hohmann elliptical transfer orbit, which when viewed from a GEO station, would appear to cross over itself as the cars angular velocity drops below that of the rotating earth.
According to my caculations, this concept should fly.....
Anders and Shaun, would you mind compiling the gist of this discussion for inclusion in Homo Excelsior?