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There and Back Again — A Rocket’s Tale

On Monday history was made. Returning to flight after six months on the ground in the wake of the failure of the CRS-7 mission, Elon Musk and SpaceX accomplished something most people in the industry thought was impossible. For the first time ever a rocket stage that delivered a payload to orbit turned around and returned, landing safely on its tail.

To get into orbit your rocket must overcome both gravity and drag. To do that it’s important to understand how the design of a rocket affects its flight, and why landing it again is so hard.

The center of mass of a rocket  is the point within your rocket where all mass is equally distributed around it. If the centre of thrust, and the thrust vector, is not in line with the centre of mass then your rocket will not flight straight instead it will pin wheel. This tendency to pin wheel is because you would be applying a sideways force to the rocket body.

The center of lift is the point where the sum total of all lift generated by parts — wings, control surfaces, and aerodynamic fuselage parts — balances out. Although its affect on a rocket’s flight is perhaps better understood by viewing it as a centre of drag. As a rocket launches the centre of drag will move in a way to place it directly behind the centre of mass. But as it burns fuel, the centre of mass will change. If centre of mass moves backwards behind the centre of drag, an initially a stable rocket will become unstable.

Getting to orbit is hard, but landing a rocket on its tail is harder because with almost dry tanks the rocket is much more unstable than when it launched. This wasn’t the first time that SpaceX had attempted to land their rocket, they’ve tried and failed on two previous occasions.

This time however, they stuck the landing, or as Jerry Pournelle once put it, landed a rocket on its tail “…just like God and Robert Heinlein intended it.

Both previous attempts to land the rocket were made on a drone barge out to sea, so this attempt, the first attempt on dry land had some advantages. Dry land doesn’t lurch around, and the newly built landing pad (LZ-1) at the Cape is a lot bigger — although to be fair this time around they nailed the landing right in the middle of the pad.

There’s a lot about the newly upgraded Falcon 9 that makes it unique . Most rockets need all their available fuel to get their payload into orbit, however the Falcon 9 was built with reusability in mind and an almost 30 percent margin in fuel, allowing it to deliver the SpaceX Dragon capsule, or another payload like the 11 ORBCOMM satellites lofted to orbit on Monday, and still return the first stage.

The extra fuel is needed to brake the first stage. After second stage separation and ignition has occurred, and whilst still hypersonic,  the first stage engines are relit braking and turning the stage back towards the landing site in a “boostback” burn. Later during reentry another burn is made, this time using just three of the nine engines — you can see evidence of this second burn in the long exposure photographs of the of the landing — followed be a “terminal” burn using a single engine to slow the rocket to a soft touchdown.

A long exposure image of the SpaceX Falcon 9 showing the launch, re-entry, and landing burns. (Credit: SpaceX)

A long exposure image of the SpaceX Falcon 9 showing the launch, re-entry, and landing burns. (Credit: SpaceX)

However extra fuel isn’t all that’s needed. The Falcon 9 has small foldable heat-resistant wings called grid fins, these are needed to steer the stage as it falls from the edge of space through the atmosphere. The stage also has cold-gas thrusters located towards the top rocket which are used to flip the rocket around so that the main engines can be relit and perform the boostback burn. Finally the stage is equipped with landing legs which deploy as it touches down.

Infographic showing the phases in the launch-and-landing of SpaceX's Falcon 9. (Credit: Jon Ross)

Infographic showing the phases in the launch-and-landing of SpaceX’s Falcon 9. (Credit: Jon Ross)

All of these systems are (and need to be) totally automated — reacting and adjusting their behaviours based on real-time data from onboard sensors.

So why is it so hard to land the rocket? It is down to the issues around of centre of mass and centre of drag that we talked about earlier. The Falcon 9 needs to be tall and thin (so it has a small cross-sectional area at launch) so that it can go up, however that’s a real problem when it comes back down.

Whilst the cold gas thrusters are used to rotate the rocket before the boostback burn, the Falcon 9 uses its gimballed main engines to provide the breaking thrust and (almost all) of the rotational (angular) thrust needed to land the stage back on the ground. In other words all the torque  to turn the rocket is applied at one end of the rocket far away from the centre of mass — without any balancing thrust at the other end. Just try balancing a broom handle on your finger tip to see how hard a problem this is going to be, it’s possible, but because you’re providing a force at one end it is very unstable and corrections need to be made continuously. However since the rocket engine providing these corrections (to keep the stage upright and stable) is also being used to break the falling first stage towards landing, and provide horizontal vectoring, doing so it a hard real-time computation problem.

The tipping point is the moment that the center of mass moves out beyond the edge of the tail of the rocket. Once that happens, unless it’s immediately pushed back in the opposite direction, the rocket stage will become unrecoverable. While a shorter, squatter, rocket would be easier to control but much harder to get into orbit in the first place because of the friction such a shape would generate on launch.

Of course this isn’t the first time a rocket has landed vertically. After the first successful landing of the Blue Origin suborbital New Shepard vehicle in West Texas towards of last month, Jeff Bezos took to Twitter, posting footage of the launch and landing of the vehicle.

Left unsaid was any mention of the failure of SpaceX to land its Falcon 9 — the five ocean water test decents, and the two failed test landings on the drone ship. This led to some acrimonious words between the two billionaires.

Ouch. However it really is the “flip” and boostback burn executed by Musk’s Falcon 9 that makes the landing a unique accomplishment. Getting to space requires speeds of around Mach 3, but getting to orbit requires speeds of around Mach 30, with the energy needed being the square of the speed. What SpaceX accomplished with the Falcon 9 is a lot tricker, breaking from orbital speeds to return the stage to the ground intact has never been done before.

Musk went on to point out that SpaceX had been flying sub-orbital test flights with their Falcon 9-R — code named “Grasshopper” — since 2013.

However after the Falcon 9’s successful landing on Monday, Bezos couldn’t help taking one last dig at Musk.

I don’t know how seriously Bezos and Musk are taking things, but personally I think trash-talking billionaires in a space race is exactly what we need right now. It’s certainly a whole lot more fun than the last space race, where two nuclear powers faced off over a bunch of ICBMs.

The returned Falcon 9 first stage is still sitting on the landing pad awaiting transport to the processing facility.

Whilst in the future the returned Falcon 9 first stages will be refuelled and reflown — slashing SpaceX’s operational costs as just 3 percent of the cost of building and launching it goes in spent fuel — it has been confirmed that this Falcon 9 at least won’t be reflown.

Following the unsuccessful CRS-7 launch, SpaceX’s Dragon is expected to return to flight in February with CRS-8. With the debut of the SpaceX Falcon Heavy, involving a ballet dance of three Falcon 9 first stage cores returning to the Cape, is scheduled for the middle of the year.

Alasdair Allan

Alasdair Allan is a scientist, author, hacker and tinkerer. In the past he has mesh networked the Moscone Center, caused a U.S. Senate hearing, and contributed to the detection of what was—at the time—the most distant object yet discovered.

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