# What is the minimal TWR of Falcon 9 booster right before touchdown?

A big point about Falcon 9 booster landing is that they need to stick the landing on the first try; they can't just hover and adjust position because even fully throttled single Merlin engine provides more thrust than the booster's weight.

But how much more? Does anyone have the number; what is the Thrust-to-Weight Ratio (TWR) of these boosters while landing?

Falcon 9's landing TWR will vary depending on the fuel mass remaining when the burn ends. This is typically close to zero, but we do know that excess fuel is vented shortly after landing. With a mass flow rate of ~250kg/s, the overall mass changes quite rapidly in the final moments before landing.

However, we can get an upper bound by just taking the empty mass of the first stage ~27200kg and the Merlin Engine's atmospheric thrust 845kN, giving us:

• $31ms^{-2} \Rightarrow$ TWR of 3.2 for single engine landing
• $93ms^{-2} \Rightarrow$ TWR of 9.5 for three engine landing

F9 v1.1 had a throttle depth of~70% it could go as low as a TWR of 2.2.

F9 v1.2 (FT) can apparently throttle to ~55% giving minimum terminal TWR of ~1.8.

Any remaining excess fuel on landing will lower this number further, but it will still be significantly higher than 1 - as mentioned, this excludes the possibility of a hover-landing.

However, since the purpose of using three engines is to maximise acceleration and minimise gravity losses, I would presume that the majority of the burn happens at maximum throttle.

It's worth noting that other small factors such as sea-level atmospheric pressure will affect this number a small amount. But since we don't know how/whether these are accounted for by F9's guidance, it's difficult to include them in any calculations.

• Block 9? I thought the current one is block 5? Jul 26 '18 at 13:45
• Spaceflight101 has the current Merlin throttle range as 55%-100%, rather than 70%. Not sure where they get their figures from, though. spaceflight101.com/spacerockets/falcon-9-ft Jul 26 '18 at 15:17
• @RussellBorogove I have found several conflicting sources on the throttle depth so I went with the official one. However, that is Oct 2015 so F9 v1.1... I believe the vacuum version can throttle to ~40% so maybe some of the confusion in the sources stems from there
– Jack
Jul 26 '18 at 15:28
• They've been extending the throttle range; the 2009 payload guide has the first stage engines unthrottleable! Jul 26 '18 at 15:30
• You need a TWR of 1 to be able to hover. Any larger and you'll thrust upwards, any smaller and you fall. Jul 26 '18 at 20:59