Question about SpaceX Falcon reusable first stage

[metaphor]

So, the Falcon 9 and Falcon Heavy first stages are planned to be made reusable sometime in the future. They're planning for the first stage to detach from the vehicle at Mach 6, and then use thrusters to land back at the launchpad.

What I don't really get is how will the stage negate is huge horizontal velocity away from the launch site, since the first stage separation will take place a while after the gravity turn has started. In

, at about the 2:40 mark, you can hear the announcer reading the spacecraft stats, 51 km in altitude, 59 km downrange, and velocity 1.8 km/s. The first stage separates about 40 seconds later in that video, at around Mach 10, but the reusable stage separation would occur at Mach 6, which is about 1.8 km/s. So I'm guessing the reusable spacecraft would also be at around 51 km altitude and 59 km downrange at that point.

It seems to me that it would require a huge amount of delta-v for the first stage to come back to the launchpad. First it would have to zero its 1.8 km/s forward speed, then it would have to cover the 59 km back to the launchpad, not to mention braking and hovering as it gets close to landing. That would require a large amount of fuel left over in the stage after separation. Am I missing something here? Anyone have an insight into how this would work?

[K^2]

Are we sure it will return to the same launchpad? That would be the easiest solution. Otherwise, other than doing gravity turn after the first stage separation, I've got nothing.

The part about braking is easy, though. Air will do most of it. You'll have only about 200m/s to kill before landing. And if the programming is done right, there should be almost no hover time there.

[N_las]

The ascente profile will be slightly different, so that the horizontall velocity isn't that high. And keep this in mind. If you shut down the first stage if its nearly empty, you lose a few deltaV (say 100 m/s, just for the thougt experiment). But after the detachement of the secon stage, the same fuel gives the now much lighter first stage (because the mass of the second stage is gone) a much bigger deltaV (like 800 m/s or something).

That means if we cut the sum deltaV of the Rocket by only 100 m/s, we give the first stage an additonal 800 m/s deltaV to return.

Second: The majority of canceling the horizontal velocity can be done with the atmosphere. And once the vessel dosen't have any horizontal velocity anymore, one can steer it back using lift forces.

If you do the complete Math you see, that you can land on the same launchpad and the Payload to orbit is approximatley only cut in half. The second stage can land on the same launchpad without problems because it reaches orbit first. It just needs a heat shield.

[B787_300]

i dont know when they plan to release the first stage on the Falcon 1.1, but i do know it will have more powerful and efficient engines, and it is a larger stage than Falcon 1.0, to carry the extra fuel that is needed to land back at Kennedy.

But before they land at Kennedy, they are going to try a couple of propulsive landings in water off the coast of florida to test out the mechanics. They have already done tests where the one engine was used to lift a firststage with weights off the ground and then hoverslamed it down, and they have proven that it can hold up in decent winds (latest test to 250m)

[metaphor]

The easiest solution would be to put another pad 150-200 km downrange for the first stage to land on, then it would only need the ~200 m/s delta-v for final braking and touching ground. But they specifically said it would land back on the original launchpad.

The Grasshopper test vehicle is just being used for testing the final ground approach and landing, I'm more interested in what they do right after stage separation.

As for the atmosphere killing the horizontal speed, at 50 km altitude the atmosphere is very thin, and the rocket is still going up so it would run into even less atmosphere. The terminal velocity at 50 km is around 3 km/s, so the stage would basically have to go up to its apoapsis and then come back down into the atmosphere to be slowed appreciably. By that time it would be about 150 km downrange from the launch site.

It might be that the first stage has a lot more delta-v without the second stage attached to it, but it would still have to accelerate quite a bit to get back to the launch pad.

I've looked and haven't found anything about this online, or other specifics on the reusability plan, so I guess it's like a trade secret and we have to just wait and see how they do it.

[Nibb31]

Elon has stated that his plan is for both the first and second stage to return to the launchpad, although this would effectively require a lot of delta-v.

They do have a launch site in Texas, which would put the ballistic trajectory somewhere in the Gulf. It might be easier boost forward towards Florida or the Keys rather than back to Texas.

[B787_300]

they are not lauching from texas yet, and flights over pop centers are not allowed, and i know the second stage would go once around before derbiting and landing