Does the SpaceX Starship plan to have landing legs?
And if so, how many and where will they be located on the body of the rocket?
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At the moment, all Starships have 6 landing legs located on the inside of the skirt. For transport, launch, and flight, they are folded up 180° inwards. It is believed that the legs are designed to crumple to absorb the deceleration, meaning they are not reusable.
During landing, they are deployed using a simple gravity system (in other words, they just fall down using their own weight) and locked in place. Or not, as happened with SN10, where you can clearly see at least 2 legs not locking and swinging freely back and forth during landing.
However, Elon Musk has tweeted multiple times that these are simply interim placeholder legs solely for the current phase of the test program.
Almost nothing is known about the final leg design, which many analysts take to mean that SpaceX hasn't actually figured out yet what they are going to do. The number (3, 4, 5, and 6) and location (outside and inside the skirt as well as on the body) has varied greatly between different designs (at one point, the body flaps were also the legs, for example).
It is known that the legs are supposed to be self-leveling, which they need to be in order to land on unprepared surfaces on the Moon and Mars.
As part of the recent #dearMoon announcement, new renders of Starship have appeared on the #dearMoon website, showing four "pods" near the bottom of the fuselage which could contain four large landing legs. But there are no renders actually showing legs, and it is not clear whether these renders are "artist impressions" or whether they represent actual engineering models.
So, to recap: at the moment, they have 6 small landing legs on the inside of the skirt possibly with a non-reusable crumple zone that are deployed via simple gravity drop and then lock in place.
In the future, things will be different, but we don't know how.
SpaceX are focusing on doing R&D "just-in-time", only designing the parts they actually need right now, and focusing on the hardest to design parts first. In this case, the hardest parts are aerodynamic control during the belly flop, the flip maneuver, and Raptor reliability.
Landing legs are something that can relatively easily be changed very late in development: SpaceX changed the Falcon 9 landing legs while Falcon 9 was already well operational, for example. (And of course Falcon 9 didn't have landing legs at all in the beginning, those were added later.) They are only landing on prepared landing pads and they are not landing large masses. They won't actually need the full capability of the landing legs until they land a large payload mass on the Moon or on Mars, so probably not for another 5–10 years. There is no need for them to develop the landing legs right now. The landing legs really only need to be good enough so that the vehicle is in one piece and can be picked up by a crane.