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Endless Skyway

As I was walking that ribbon of highway I saw above me that endless skyway...

19 May  2010   Space elevator to low orbit?
23 May  2010   Space Elevator and The Dynamic Grapple!
  8 June 2010   Hooking on when you're off GEO - an even more dynamic grapple.
10 June 2010   Acceleration Matching for Space Elevator Grappling.
  1 Dec  2012   U-Fly-It Satellite and Space Elevator Simulator.


Hooking on when you're off GEO - an even more dynamic grapple.

8 June 2010

Space elevators will have a sway, called "libration", with a period about 7 or 8 hours. This upside-down-pendulum-like motion will cause the GEO point to reach speeds up to 160 mph and to always be accelerating, ruling out a normal rendezvous as we think of it today. Rendezvous with a space elevator at GEO will be a dynamic thing (see here ). Rendezvous with the cable at points other than GEO will be even more dynamic, but they may be possible or even operationally desirable.

Get your kicks off level 66 - The best glider ride.

Neglecting the pendulum-like sway for now. When you kick off a space elevator from at or about 66% of the way up from the surface to GEO, you enter an orbit with a useful perigee - one that ranges from a little below the top of the atmosphere to a little above the top of the atmosphere. That perigee is easily adjustable with small amounts of delta-V. If you drop off from a little higher than 66%, your perigee will be well outside the atmosphere. You will make a super fast low level flyby of the planet (at LEO altitude), then you will swing right back up to the altitude you dropped off from, 6.9 hours later, and close to the very same spot you dropped from. By that time, the elevator cable will have advanced from between a quarter to a third of the way around (29%), so it won't be there any more. You can go around as often as you want, alternately seeing the planet from near and far. Then you can use a little delta-V at apogee to reduce your perigee for a one-shot reentry or for a sequential apogee knock-down with aerobraking during successive perigees. You might even use lift during aerobraking to alter your inclination up to about 14 degrees and land in your (tropical) back yard. Yeeeeee! Haaaaaaah!

Stopping off at LEO.

If you choose to sequentially aerobrake, sloughing off a fraction of your 5100 mph excess speed at each perigee, you can use a little delta-V at a now-low apogee to circularize and enter LEO. The only new technology here is a heat shield that works repeatedly for the sequential aerobraking, allowing the jets to work afterward, then functioning as a reentry shield. It's never been done publicly, but it's readily doable. That is, its technical risk is low. After you are in a near-circular, stable LEO, you will need to use a little more delta-V to again adjust your perigee downward for the final reentry. What a great tour for the delta-V of two de-orbit burns!

What? No reentry system?
 
If you have no reentry system, or one that you prefer not to use, you will need to reattach back onto the cable to come home. A huge delta-V (1750 m/s or 22% LEO speed) would enable you to get to circular GEO where it would be the easiest to latch back on. But, with only a little delta-V, reattachment below GEO might be possible, but it would be a tricky one-shot maneuver.

Latching on like a Velcro suit.
In 1984, David Letterman jumped onto a wall wearing a Velcro suit. At his apogee, the suit latched on and he was suspended on the wall. I'm not saying that Velcro should be used to grapple (although I wouldn't rule it out), but the way he approaches the wall is similar to the way a free vehicle dropped from a space elevator from below GEO would/could approach it for reattachment.

David Letterman in ballistic orbit at apogee---moments before grappling on to space elevator ribbon.

A dropped free-flying vehicle with a LEO-perigee could maneuver (with small delta-Vs) so that its apogee would meet again at a grapple point somewhere above the minimum drop-to-orbit point on the cable. At apogee, the horizontal speeds and positions match. The vertical speeds match too (zero), but only for a moment. The free flier would grab on at that point like a hat hung on a rack, or like Letterman sticking to the wall.

From the point of view of the grapple point, the free flying vehicle would approach from below and to the west. It would then appear to slow its approach toward the cable as it changed its relative direction to up the cable. It would arrive at the grapple point vertically and stop its ascent just at the grapple point. There, like a ball thrown up with just the right upward speed to someone on a ladder, it can be plucked from "mid-air", right at the top of its flight. If the grappling/plucking didn't occur, the free flying vehicle would begin its fall downward which would gradually shift to a progression eastward in a fashion symmetrical to its approach. Oh yeah! it's tricky, and risky!

Only at that one-time same-space-at-the-same-time opportunity could a grappling take place. At the moment of grapple, the horizontal velocities would match and both vertical velocities would be zero. The grappling would exert no east-west forces on the cable, but would be like a weight being quickly hung on the cable at the grapple point, just like the original drop was a weight being released from the drop point.

If there was a miss, at the next apogee the cable would have advanced about a third of the way around. How far exactly depends on the actual specific drop-off level, which affects the perigee and period. If you dropped from 71%, your perigee would give you a 1300 NM flyby each time, and every three times around the planet you would meet up with the cable again at apogee. Drops from between 66% and 71% give lower perigees, but no easy apogee re-matchups with the cable. Under these conditions, a reattachment try would come at a cost of some maneuvering delta-V or enough time until another near-matchup occurred, or a tradeoff between the two. Grapple points and orbits might be adjusted (with small delta-Vs) so that the period of the free vehicle is an integral fraction of a sidereal day, permitting another try just one day later.

I don't imagine such risky sophisticated maneuvers would be done in the early years of an orbital cable, if ever. Carrying a heat shield, or reattaching at GEO seems a lot safer and worth the extra weight or propellant. However, if or when it can be done safely, this kind of dynamic grappling may be compelling for minimal-fuel transfers between an Earth cable and a Moon Cable.


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