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Well, more specifically, using a counterweight like you'd find in a non-space elevator to give the rocket a little acceleration before firing up and spending all that fuel-to-lift-the-fuel-to-lift-the-etc.
I understand from here and here that doing all the acceleration through non-rocket methods would be prohibitively difficult.

That said, would it be feasible to reduce the loaded-fuel requirement of a launch significantly, by keeping the rocket engines off until the craft's velocity reached some acceptably higher positive number?

Or, to put specific numbers on "significantly": how much extra delta-v would we need to add through non-rocket methods to reduce the carried fuel by, say, 10%?

The image I've got in mind here is the rocket being pulled up along a partial space elevator (supposing that building a complete space elevator in one go turns out to be just too much), by the action of a counterweight. - I have no idea whether there's anything strong enough to even be used as a cable (or set of cables, or pulley system) here, given how massive spacecraft apparently are.

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    $\begingroup$ I'm confused what you're asking. Can you clean it up a bit and ask a question in the title? $\endgroup$ – Scott Oct 18 '14 at 4:41
  • $\begingroup$ Sorry, I suppose that was partially me thinking out loud - it's quite possibly two or three related questions stuck together. See [here][1]space.stackexchange.com/questions/3770/… $\endgroup$ – Stephen Voris Oct 18 '14 at 5:21
  • $\begingroup$ @Scott ...It's sort of like this question, except without the requirement of abandoning rockets entirely between "takeoff" and orbital circularization. I'll try to get it more coherent after I get some sleep (this was originally supposed to be an edit to the last comment, but took too long). :P $\endgroup$ – Stephen Voris Oct 18 '14 at 5:28
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It's theoretically possible, but ludicrously impractical and missing the point.

I don't like to say things are impossible, but as another answer mentions, the numbers involved are too extreme.

You won't be limited by the speed of sound with a big enough counterweight, but the size of the counterweight, the height to which it must be stably lifted, and just the general engineering pretty much rule this out.

But, all this is missing the point. The hardest part of getting a rocket to orbit is to accelerate it horizontally, not vertically. If you start from a standstill in LEO, you're still going to need a rocket almost the same size to get enough speed.

If you want to escape the Earth's sphere of influence, an elevator-catapult makes a little more sense--but still only as much sense as a monumental tower-of-Babel-type-nonsense slingshot hurling a billion dollars of spaceship onto an escape trajectory could sound like.

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Are you thinking of a gravity gradient vertically stabilized tether?

enter image description here

Unlike a Clarke tower, the elevator pictured isn't moving one circuit per sidereal day but with an orbital period of 2.15 hours. The tether "center" is about 2070 km above the earth's surface. Not really the center of the tether as the length above 2070 altitude needs to be longer to balance the portion below.

The tether foot is at an altitude of about 200 km and moving 5.4 km/s. The tether top is at an altitude of 4265 km and moving 8.6 km/s which is escape velocity at that altitude.

To rendezvous with the tether foot would take less delta V than achieving orbit.

Catching a sub-orbital craft at the tether foot subtracts momentum. Repeated sub-orbital catches would eventually bring this tether down. But there are ways to restore momentum.

One way would be to run a current through the tether as it passes through earth's magnetic field. This would be an electrodynamic tether.

Another way to preserve tether's momentum is to make super-orbital as well as suborbital catches. Super-orbital catches from a higher orbit (like from the moon or an asteroid parked in lunar orbit) would boost momentum. If super-orbital catches are balanced with sub-orbital catches, momentum can remain the same over time. Other momentum changing maneuvers are releasing payloads from the tether foot or from the tether top. Balancing these can also preserve momentum.

Not only is this elevator far shorter than a Clarke Tower, but endures much less stress. No scrith or Bucky tubes needed, Kevlar with a taper ratio of 5.2 could do the job.

However rendezvous with the tether foot at low altitudes would be very hard. In this NasaSpaceFlight thread, Jim explains some of the difficulties.

Also the tether is passing through space with a relatively high debris density. It would likely be severed.

Alas, it seems such elevators would impractical for mitigating the ~9 km/s needed for achieving LEO.

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No.

There are several problems here:

  1. If you use a counterweight, the maximum speed it can reach in freefall is Mach 1 or 300 m/s. Orbital speed is around 7 km/s, so you've reduced the speed requirement of the rocket only by a bit. This means the rocket still weighs almost as much as a ground-based rocket. A Soyuz rocket weighs around 600 tons at liftoff. Let's say you can save 100 tons. That still means you have to lift 500 tons, plus several times that for the counterweight. See this related question, and this one.
  2. The counterweight must be connected to the rocket by a cable. If you separate the rocket from the space elevator at an altitude of 10 km, the cable is 10 km long. That's several times longer than the highest elevators in use today.
  3. How do you separate the rocket from the space elevator? The elevator must be strong enough to withstand the rocket exhaust. For ground-based launches you have hundreds, if not thousands of tons of concrete and steel for the launchpad, and hundreds of tons of water to reduce the damage done to the pad. All of this would have to be accelerated along with the rocket, and then braked to a standstill after separation.

All in all you'd have to construct a tower 10 times higher than the highest skyscraper in use today, and build it strong enough to carry several thousand tons at the top.

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