0.5cm isn't even well defined, considering that the rocket itself is probably out of round by larger tolerances, not to mention issues of thermal expansion.
I would suspect it's some average of many points that the control systems try to track, because the rocket is not a point, and the press wants to quote a single easy number.
I'd expect that the rocket has a ton of sensors, and a ton of passive and semi-active tracking devices all over the body.
E.g. I'd put a bunch of NFC-type responders in a number of key positions, responding at different frequencies. Then a typical sweeping-frequency radar pulse would activate them all, and the response time and the Doppler shift would tell about positions and speeds of many points on the rocket. I'd do a similar thing with reflectors and IR/optical tracking.
All these points should follow some reasonable trajectory for some point the top of the rocket, near the chopsticks, would move towards some desired catch location point. Probably this motion is where "with precision of whatever cm" relates to.
is "surface amplitude" vibration? I could see vibration being graphed over time as a wave with an amplitude and frequency. I can't really comprehend the size of super heavy combined with the energy density of just one turbo pump on one raptor engine (let alone 33x2) and then the precision of control needed to catch the whole thing with chopsticks. Not many things do i admit are just beyond me period but this is for sure.
/raptor 3 pumps look like you could hold them in your hands but iirc they deliver over 100k horsepower each.
It's probably defined by the catch points as that's what matters: whether the catch points end up where they belong (good) or not (disaster). The catch points are not "out of round".
I should have mentioned that the catch points are on one long bar that goes atop the booster. They are not simply attached to the sides of the booster. Booster shell flexing does not affect the catch points at all.
I'd expect that the rocket has a ton of sensors, and a ton of passive and semi-active tracking devices all over the body.
E.g. I'd put a bunch of NFC-type responders in a number of key positions, responding at different frequencies. Then a typical sweeping-frequency radar pulse would activate them all, and the response time and the Doppler shift would tell about positions and speeds of many points on the rocket. I'd do a similar thing with reflectors and IR/optical tracking.
All these points should follow some reasonable trajectory for some point the top of the rocket, near the chopsticks, would move towards some desired catch location point. Probably this motion is where "with precision of whatever cm" relates to.