# Why were three engines used for the F9 1st stage landing burn (BulgariaSat-1)?

As pointed out in the question What is the “emergency crush core”?, an Elon Musk tweet about the Falcon 9 1st stage landing following the BulgariaSat-1 launch says:

Rocket is extra toasty and hit the deck hard (used almost all of the emergency crush core), but otherwise good

An earlier tweet says:

Falcon 9 will experience its highest ever reentry force and heat in today's launch. Good chance rocket booster doesn't make it back.

The narrator in the SpaceX BulgariaSat-1 webcast says at around T -00:11:32 (about 04:56 into the video currently) that this is an extra-challenging, three-engine landing:

Our landing today involves some of the highest heating and structural loads on the first stage that we have seen to date, and it includes a three-engine landing burn. While it is still a secondary goal, this landing is going to prove to be extra challenging for us. But if we are successful, this will be the first rocket to land on both our East- and West-coast drone ships.

I'm fairly sure that burning three roughly ~650 kN Merlin 1D (throttle-able) engines to land a nearly empty rocket has something to do with the hot landing, and there must have been something about this launch that made the use of three engines necessary or at least the best option, but I don't know what it is.

Question: Why were three engines used for the F9 1st stage landing burn for BulgariaSat-1?

A short description of why the use of three engines for the landing burn makes the landing so challenging would be great as well.

Falcon 9 FT has demonstrated the ability to do a drone ship landing after launching a 5.3 ton payload into geosynchronous transfer orbit.

BulgariaSat-1 is only 3.7 tons, but was launched into a higher super-synchronous transfer orbit. (This allows it to do a plane change to an equatorial orbit using less fuel than it would at geosynchronous altitude.) This higher orbit requires more fuel expenditure from the first stage, and thus less fuel remains to execute the landing maneuver.

On the final landing approach, every second in flight accelerates the stage by another 9.8 m/s due to gravity's pull. You spend the least fuel by waiting until the very last instant to decelerate. If you decelerate on three engines, you can wait longer than if you decelerate on one engine.

The downside is, doing the terminal burn on three engines means everything is happening faster; there's less time to correct for any measurement errors or irregularities in throttle response. Note that hitting slightly faster than planned and expending the "crush core" is preferable to the alternative, which is to run out of fuel while still above the pad.

On a one-engine landing, things are a little more leisurely and SpaceX has no trouble hitting the bullseye.

(We went over some of this last year.)

• Excellent answer, thanks! The choice of super-synchronous orbit for this mission instead of a more typical GTO sounds like an interesting, but separate question. – uhoh Jun 24 '17 at 18:52
• Iirc someone on reddit computed that the savings on gravity losses are equivalent to about 1.5s of S1 ascent burn (9 engines on 100% thrust) which is quite significant velocity difference on MECO. – jkavalik Jun 24 '17 at 22:24
• Does S1 not throttle down at the end of the burn prior to staging for g-limiting? – Russell Borogove Jun 24 '17 at 22:58
• Elon Musk tweeted before the flight: Falcon 9 will experience its highest ever reentry force and heat in today's launch. Good chance rocket booster doesn't make it back. – DarkDust Jun 25 '17 at 9:24

I've speculated, and SpaceX's comments seem to concur that fuel burn is not linear as you throttle the engine up... so, having to run one engine a higher throttle for longer apparently actually burns more fuel that running three engines at lower thrust for a shorter time. And, the stage seems to be at terminal velocity anyway coming down, so waiting a few seconds more won't increase its speed much, just decrease the distance it has to decelerate to zero. Three engines provide about 3X the deceleration of one engine, so say, 1/3 the burn time, and since they are running at lower throttle, net-net, less fuel consumed to decelerate the same amount.

• This might be similar or identical to what is discussed in this answer, that when you are decelerating in an external gravity field it's better to do it quicker. If the acceleration due to thrust is less than that of gravity, you actually accelerate. This is not due to a nonlinearity of engine behavior, just the algebra of adding up all sources of acceleration. – uhoh Feb 24 '18 at 0:01