AIUI, the Falcon rocket boosters (or the main first stage, for that matter) are mostly empty during their return flight: the upper stage has been delivered to earth orbit or beyond, and most of the booster’s fuel has been used during the ascent.
Here’s one image indicating the phases of the booster flight during which the main engines are burning fuel in quantity:
-boostback burn: the booster flips and thrusts to eliminate its downrange velocity. Consistent with other sketches I’ve seen, this one suggests that the boostback burn also adds some altitude, presumably so that a small westward velocity will have enough time to get the booster back to the barge or launch site.
-Reentry burn: I assume this is to cut down on the freefall velocity so that the booster doesn’t get cooked by aerodynamic heating.
-Landing burn: all the vertical velocity is scrubbed off for a gentle touchdown on the launchpad.
This video shows the landing burn, starting at 0:20. A sonic boom arrives several seconds later, which means they’re doing more than 760 MPH before that burn starts. Just ten seconds after ignition, they’re traveling at touchdown speeds, a few MPH.
So just how fast are they falling at the start of the landing burn? What sort of thrust-to-weight ratio do they have during the burn?
That is awesome, thank you. So it looks like it’s barely going Mach 1 when the landing burn starts. With a nice clean plot showing the acceleration I can estimate the landing burn’s thrust:weight ratio later today.
IIRC the Falcon booster rockets can adjust their thrust, but there’s a lower limit on their thrust that is significantly greater than their weight. This means that they can’t do a “smooth landing” where they reduce the thrust gradually as they land; they basically have to finagle things so that they reach 0 m/s just above the landing pad, and then turn off the engines and “drop” the remaining distance to the ground.
Check out Flight Club for detailed analysis of many missions.
For instance, Iridium NEXT-4. You can see from the acceleration chart that the booster never goes below 1.7 gees, and peaks at about 4.5. MikeS is correct that the stage just can’t throttle any lower; they just have to time it so that they reach zero velocity at zero height.
Also:
You can tell that they’re going over mach 1 just before the landing burn. You can generally hear a triple sonic boom before the engine noise ramps up. Sounds like dun…dundun. The first boom is from the bottom edge of the craft, and the next two closely-spaced booms are from the grid fins and the top edge of the craft. With the Heavy landing, you could hear six booms: two sets of the three.
