The booster was falling at 4500 Km/h 30 seconds before the catch with 2-3% fuel left. How is that amount of fuel remotely enough to stop the downward momentum?
Going by the telemetry of the seconds before the landing burn and noting the speed vs time, it seems drag was around 40 m/s^2 when it was going at around 3000 km/h. Since drag depends on velocity squared though, it had reduced to just above 10 m/s^2 just before the engines lit at 1250 km/h, and so would quickly become negligible once the engines lit.
Going by Wikipedia, the Super Heavy[1] has 3400000 kg of fuel at launch, so 3% of that is about 102000 kg. For the landing burn, it used 13 Raptor v3 engines[2] to scrub speed. Each Raptor flows about 650 kg/s max, so 3% fuel is enough for about 12 seconds for the 13 engines.
The empty mass of the Super Heavy is about 275000 kg, so about 377000 kg before the landing burn with 3% fuel.
Using the sea-level vs vacuum performance of the Raptor v2 engines, one can estimate that each Raptor v3 produces about 2.45 NM of force at sea-level. So 13 of them would produce about 31.85 MN of force.
Using Newton's second law, F=ma, this gives an initial deceleration of about 84 m/s^2 and about 104 m/s^2 when empty. If we do a rough spreadsheet integration, we get that a burn of roughly 4 seconds is needed to scrub the speed assuming no other forces.
Now, comparing this with reality, the full 13 engines were lit for a little over 5 seconds.
In my simplified calculations I was assuming full throttle the whole way, which obviously isn't realistic, and I also assumed 3% fuel. So over all I think that's a pretty decent estimation.
[1]: https://en.wikipedia.org/wiki/SpaceX_Super_Heavy#Engines
So, 34M kg of fuel has to be burned (in this booster alone) to facilitate a flight ... and I see that the propellant is CH4 / LOX[1].
Burning methane is much, much better than simply releasing methane but the release becomes CO2 instead ...
What is the back-of-the-envelope conversion of 34M kg CH4 vs., for instance, 34M kg of kerosene/JP ?
[1] https://en.wikipedia.org/wiki/SpaceX_Super_Heavy#Engines
[1] https://www.engineeringtoolbox.com/co2-emission-fuels-d_1085... [2] https://x.com/elonmusk/status/1298426245991063554?lang=en
IIRC there's a tradeoff between efficiency and thrust as well. Heavier fuels aren't quite as energy-efficient, but it's easier for them to develop a lot of thrust, which is important for the initial stages of launch. If I'm remembering events described in Ignition! correctly this led to "thrust density" being something that was optimized for - to the point that there were experiments with mixing mercury into the fuel!
[0]: https://world-nuclear.org/information-library/facts-and-figu...
Long ago though so rusty, $dayjob doesn't involve any advanced math at all.
edit: To expand, the "rough spreadsheet integration" was just the Euler method[1] assuming a constant acceleration. So
v(t+dt) = v(t) + a * dt
v(t+dt) = v(t) + F/m(t) * dt
m(t+dt) = m(t) - 650 * dt
Using dt = 0.1 seconds, I got almost exactly 4 seconds until the velocity reached zero.
That should of course be 13 * 650 * dt.
Anyway, plugging in the Raptor V2 thrust numbers the approximation increases to 4.25 seconds. This is in line with the thrust I used for the V3 being ~8% higher than the V2 thrust figures.
Fuel is the vast majority of the vehicle weight at launch, kind of like an empty vs full can of soda.
They ignite a subset of engines just a few seconds before landing for the final slowdown and maneuvering.
Edit: here is a video from further away that shows the rocket gliding in under control of the grid fins before the engines light and execute the final landing maneuver:
They sure made it look easy...
Surprising to see this work first time though - I don't recall them doing any hover and lateral movement tests, but I assume they must have done.
What's also wild is that the booster isn't being caught/supported by those giant grid fins, but rather by small lifting pins just below them, and seems to only have two of these (one on either side), so it also has to get it's rotational position right so those pins engage with (are supported by) the arms.
Watching the video, it looked like the bottom of the rocket was glowing hot, but the engines were cool. I imagine that means they were probably running some amount of methane through the engine bells to cool them.
Also I don't think the telemetry on the feed is that accurate, so with all of the atmospheric braking, it was probably going a bit slower than the 1200km/h at engine reignition.