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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.

Acceleration Matching for Space Elevator Grappling

10 June 2010

If you drop off a space elevator above 66% (23,600 km) without a reentry system, you will have to latch back on to get home. When your looping tour of Earth from high altitude (23,600 km) apogees to low altitude (185 km) perigees ends, your last excitement will be 1) matching your speed and position with the cable again and 2) grabbing on. I've talked about the "exciting technical challenges" this presents here and here.

Big delta-V budget.

I've focused before on minimal delta-V missions from the 66% level using sophisticated heat shields. But, a big delta-V budget opens up opportunities, and a big delta-V capability may be cheaper than a heat shield. This could become true in the "space elevator days" in a way we don't fully conceive of yet, since we are so used to delta-V always being the limiting factor. I still like bringing a heat shield along for safety when humans are on board, but it can be less sophisticated and lightweight if it doesn't need to perform multiple reentry aerobraking, high L/D inclination changes, etc. It can also be left behind on unmanned missions.

We are used to delta-V being the biggest constraint in designing missions. This may not be the case with a space elevator. Free-flight climbing to circular GEO from the "66% Tour" mission described above takes 1750 meters per second or 22% of the LEO orbital speed if you enter geosynchronous transfer orbit (GTO) from your perigee. That's a lot of delta-V. It's one of the costs to getting "down low" from a space elevator and then to latching back on at the easiest spot (GEO).

If we want to latch back on below GEO, probably at the level we dropped from (66%), it's trickier because we can't "sidle-up" next to the cable and casually dock. We need to get to our apogee at the same time the cable is there. The free vehicle and the cable will only match speed and position for one moment. We need to grab while the grabbing is good!

But, if we have a large delta-V budget, say on the order of 1000 m/s, it gets a whole lot easier. 1000 m/s may not be too unreasonable considering that 1) lifting mass is much cheaper on a space elevator, and 2) the alternative is 1750 m/s to get to GEO. So, large and/or frequent burns can enable the free-flier to get to the appointed spot much more readily (no integral fraction period matching needed). And also, the really cool thing is, when the free-flier gets to apogee it can stay there by hovering!

Hovering? By Rocket?

Hmmm... Yep. Rockets can and do hover. Here is a list of some "prior art" showing that this kind of technical risk is very low:

So, as long as we have a large fuel supply (delta-V) and the thrust is high enough to hold up the weight (at the effective gravity) we can have:
  1. The ability to hold up the free-flier's weight (hover) for a period of time while near the grapple point.
  2. The ability to maneuver to follow the oscillations of the grapple point.
  3. The ability to stay a minimum distance away from the cable while approaching it, then move in, or grapple from a distance.

How long can we hover?

The important minimum-drop-to-orbit point is 66% of the way from the surface to GEO. This level is useful because it results in a perigee right on the edge of the atmosphere - good for touring low levels, aerobraking to LEO, etc. Many free fliers will have initially dropped of from that point, and if they don't aerobrake they will want to reattach at that point. The higher up on the cable, the lower the "effective g". So, 66%, being the lowest point a free flying vehicle would likely want to attach to, is the reattachment point with the highest effective g, which is the most stressful point for hovering at grapple.

At the 66% level, the effective g is 0.0290 g, or 0.2845 m/s^2. So the thrust needed to hover is less than 1/35 of a g, not too difficult for smallish chemical rockets, but not "vernier class" (I think). Also, at that acceleration, 1 m/s of delta-V will last 3.5 seconds. If you have 800 m/s delta-V left in your 1000 m/s budget, that will last 2812 seconds, or 47 minutes. 47 minutes ought to be enough time to refine a position and "reach out and grapple".

If there is a failure to grapple, the cessation of hovering will result in the free flier simply continuing on its way in the same orbit as before, but with the apogee/perigee rotated by up to about 12 degrees.  That is, "fall from apogee" is simply delayed by the amount of time spent hovering. The free flier can then use its reserve one-time-use heat shield as a kind of "back up 'chute" to reenter. If the free flier is unmanned, it might be commanded to burn up or to continue to orbit until it can be retrieved some other way (interception or laser power). No big whup.

It might be preferable to use some of that delta-V to elevate the apogee (and perigee too so the horizontal speeds match at the new apogee) then reattach at a higher level with lower effective g, where the minimum hovering thrust would be less and the hovering time per delta-V would be more. I haven't looked at that tradeoff yet - more to come on that.

This hovering business, and the existing technologies (cited above) may also be just what's needed to solve the problem of grappling on at GEO when the system is undergoing its normal sway.


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