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I was trying to find out more about the Space-X booster return system, and
I am fully aware of apparently silent videos about it and showing it, but as
I cannot see these i wondered if there is a discussion of the concepts and
shape of the system the size and the methods used somewhere?

Not that I'm aware of, so I'll give this a quick shot. Bear with me
since things like this are hard for me to describe in text.

The entire two stage Falcon 9 Full Thrust is a cylinder 12 feet in
diameter and 230 feet high. It's really tall, but relatively small in
diameter so its individual (fully assembled and tested) stages can be
shipped via semi-truck (i.e. "wide/oversized load") instead of being
shipped by much more expensive means like many launch vehicles.

In a nutshell, the Falcon 9 first stage is about 2/3 of the height (I'm
eyeballing a picture for this number) of the launch vehicle and looks
more or less conventional. In rough terms, it is a long, skinny,
cylinder that is 12 feet in diameter and with 9 engines on the bottom
(one in the center with 8 around the outside). The engines are attached
to the stage via a thrust structure that SpaceX likes to call the
octoweb. Because this is so strong, it has four hardpoints built into
it, equally spaced around the bottom of the stage. These hardpoints are
where the booster sits when on the launchpad and are also where the
landing legs attach.

The landing legs number four (since they each attach to two adjacent
octoweb hardpoints at the bottom). The legs are roughly a very long
triangle whose short side attaches to the hardpoints at the bottom of
the stage and whose point is attached to the side of the stage. When
landing, the legs are forced outwards by very large pistons made up of
several nested cylinders, similar to an old style extendable portable
radio antenna. The pistons lock in place when fully extended.

The top of the stage comes back with the interstage adapter ring
attached (inside of that ring is where the upper stage Merlin engine
occupies space before stage separation). Attached to the outside of the
interstage adapter are four movable grid fins. for launch they are
folded (down) against the vehicle to minimize drag. When folded down,
they look like the end of an old school fly swatter with slightly bigger
square holes in the face of the swatter. Also, the face of the swatter
would need to be maybe 1/2" thick or more (instead of thin and floppy)
to look the same.

So when coming in for a landing, the grid fins are extended very high up
in the atmosphere and are movable so that they help keep the stage
stable during its descent. When the stage is getting close to the
ground, the landing legs are extended and locked and only the center
engine is firing at its lowest thrust level. The center engine gimbals
and the grid fins keep moving in order to stabilize the stage.

I really hope this helps. I'm an engineer, not a writer, so I'm used to
drawing things on a white board while describing them to other people.
If anything is unclear, just ask.

Jeff
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