[Recoil42]

Ten seconds seems like an incredibly liberal estimate. You need a pretty decent "margin of error" reserve. I'd wager we're looking at something more like 30-60s of fuel during the last stages of landing, at least. So let's call it something like 2-3% of the fuel.

[avmich]

SpaceX claims that Falcon-9 first stage has a pretty good mass ratio - meaning that the fuel weights many times more than the tanks and engines (and everything else).

However, even if we assume 30 as the ratio of loaded vs. dry mass, which is better, for example, than Titan II first stage, which has pretty good mass ratio, we need to add the mass of landing legs - something unique for the Falcon. Suppose legs halve the mass ratio, making it 15.

9 engines are capable of lifting the dry first stage, the fuel in it, and the second stage plus payload. That means 9 engines can lift much more than 15 times the dry mass of the first stage. Dividing the thrust by 9 makes the thrust much more than necessary to support the dry stage.

In other words, even the thrust of a single Merlin engine is more than enough to brake the dry weight of the first stage. That means when first stage lands the engine is throttled - spending less mass of fuel per second than it does when Falcon lifts off. The better mass ratio of the first stage, the smaller flow of fuel is needed to decelerate it - so less fuel is needed to brake. It's not enough to count seconds of thrust - how big the thrust is should also be taken into account.

[ceejayoz]

I'd imagine it's nowhere near full power for most of that, as it's an empty shell of a craft and thus quite light.

[JshWright]

The engine can only throttle down to about 70%. For the final landing, the first stage will only use the center engine (leaving the other 8 shut down).

Even with only one engine at 70%, the thrust to weight ratio is greater than 1. That means the rocket can't hover, they just have to time the burn perfectly so the speed reaches 0 at the moment it reaches the ground.

[grinich]

Why can they only throttle to 70%? Is that related to old-school turbopumps?

[Mvandenbergh]

Most rocket engines don't throttle down well. The main reason isn't the turbopumps (although that can also be an issue) but combustion instabilities in the chamber and flow separation in the nozzle.

Nasa overview of liquid engine throttling:

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2010003...

[grinich]

Exactly the answer I was looking for-- thanks!

[Serow225]

That's a very readable reference, thanks.