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Why It’s So Hard to Land a Rocket on Its Tail
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. Photo courtesy of SpaceX

On Monday, Elon Musk’s SpaceX accomplished something most people in the rocket industry thought was almost impossible: For the first time ever, a rocket stage that delivered a payload to orbit turned around and returned to Earth, landing safely on its tail.

Getting a rocket off the ground is difficult enough, but the science is well understood and the physics are fairly basic. The reverse of that, though, is challenging. Landing a tall, skinny craft safely is an entirely different problem.

Leaving Earth

First, a primer on the easy part. To get into orbit, a rocket must overcome both gravity and drag. Designing a rocket to be good at that, unfortunately, makes landing it again hard.

The basic rocket physics are the same for a NASA rocket or a model rocket launched by a 9-year-old. The center of mass of a rocket (the point within the rocket around which all the mass is evenly distributed) has to be lined up with the center of thrust and the thrust vector. If not, the rocket will pinwheel instead of flying straight.

Rocket designers also have to think of the center of lift, which is the point where the sum total of all lift generated by parts — wings, control surfaces, and aerodynamic fuselage parts — balances out. It’s easy to think of it, actually, as a center of drag. As a rocket launches, the center of drag will move in a way to keep it directly behind the center of mass. A rocket flying in that configuration will be stable.

But as a rocket burns fuel, the center of mass will shift. If the center of mass moves backwards behind the center of drag, a rocket that was stable will become unstable. A lift vehicle that’s done its job is likely very close to being in this unstable configuration, due to all the propellant being expelled in launch.

Coming Home

Getting to orbit is hard enough. But landing a rocket on its tail is harder, because with almost dry tanks, the rocket is much more unstable than when it launched. The December 21 SpaceX landing wasn’t the company’s first attempt at this: They’ve tried and failed on two previous occasions.

Both previous attempts to land the rocket were made on a drone barge out to sea. This was the first attempt on dry land, which 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 SpaceX’s credit, they nailed the landing right in the middle of the pad.)

There’s a lot about the newly upgraded Falcon 9 that makes it uniquely capable of landing after launching. Most rockets need all their available fuel to get their payload into orbit. But the Falcon 9 was built with reusability in mind, and an almost 30% 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 have enough fuel to 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 main thrust engines. Finally, a “terminal” burn uses a single engine to slow the rocket to a soft touchdown.

But it’s not just extra fuel that’s needed. The Falcon 9 also has small, foldable, heat-resistant wings called grid fins. These are needed to steer the stage as it falls, tail-first, from the edge of space through the atmosphere. The fins put the drag behind the downward vector of the rocket, keeping the engine pointed into the flight vector, where just minutes prior, every law of physics was making the rocket fly in the exact opposite configuration.

The first stage also has cold-gas thrusters located towards the top of the 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: SpaceX)
Infographic showing the phases in the launch-and-landing of SpaceX’s Falcon 9. Image courtesy of SpaceX

All of these systems are (and need to be) totally automated — reacting and adjusting their behaviors based on real-time data from onboard sensors. Things happen far too fast, and the rocket is far too twitchy, for a human to operate it. It’s a job best left to a computer.

The reason the rocket is difficult to control in landing configuration has a lot to do with the centers of mass and drag that we talked about earlier. The Falcon 9 needs to be tall and thin so that it can be an efficient launch vehicle, but that exact configuration makes it a beast to control as it comes back down.

While the cold-gas thrusters are used to rotate the rocket before the boostback burn, the Falcon 9 uses its gimbaled main engines to provide the breaking thrust and (almost all) of the rotational (angular) thrust needed to steer and 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, without any balancing thrust at the other end. Just try balancing a broom handle on your fingertip, head-side up, to see how hard a problem this is.

It’s possible, but because you’re providing a force at one end, it is very unstable and corrections need to be made continuously. And since the rocket engine providing these corrections (to keep the stage upright and stable) is also being used to brake the falling first stage towards landing, and also provide horizontal vectoring, doing so is a hard real-time computation problem.

If the rocket tips too far and the center of mass moves out beyond the edge of the tail of the rocket, unless it’s immediately pushed back in the opposite direction, the rocket stage will become unrecoverable. A shorter, squatter rocket would be easier to control for landing, but much harder to get into orbit in the first place due to aerodynamic drag, not to mention being less stable on the ascent.

In sum, the SpaceX tail landing is a triumph not just of rocket design, but of software. It’s just not easy to balance a moving, unstable stick on its tail all the way down to a safe landing at a very specific location.

But it’s not the first

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 the end of last month, Blue Orbital founder Jeff Bezos took to Twitter, posting footage of the launch and landing of the vehicle.

Graciously left unsaid was any mention of the failure of SpaceX to land its Falcon 9 — the five ocean water test descents, and the two failed test landings on the drone ship. Nonetheless 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, where the required energy is proportional to the square of the speed (E ∝ v²). What SpaceX accomplished with the Falcon 9 is a lot tricker: breaking from orbital speeds to return the stage to the ground with rocket 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. It’s certainly a whole lot more fun than the last space race, where two nuclear powers faced off over a bunch of ICBMs.

Its Final Voyage

The returned Falcon 9 first stage is currently 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% 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 an unsuccessful CRS-7 launch, SpaceX’s Dragon is expected to return to flight in February with CRS-8. 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.

12 thoughts on “Why It’s So Hard to Land a Rocket on Its Tail

  1. I still don’t understand, if it’s so hard to land a rocket on it tail, why on Earth would they first attempt to land one on a moving barge?

    There must be a really good reason…

    1. beacuse it is not so safe to land that thing on land where it can kill people or destroy stuff. I think first they needed to show NASA and FAA that they could hit a target “safely”.

      1. So they satisfied NASA and FAA by blowing up the barge a couple times?
        Also, why didn’t Bezos’ Blue Origin try to land on a barge first as well?

      1. Plus it’s unknown how many failures Blue Origin had out in the remote desert. They only released one nicely produced video of a success.

        Another point not mentioned in the above discussion is the thrust to weight ratio of a single Merlin engine to the first stage weight plus whatever propellant remains. It is my understanding that the Merlin can only throttle between a range of 70 – 100% and that 70% of a single Merlin ( Merlin 1 D ThrustSea Level: 654kN – Vac: 716kN http://spaceflight101.com/spacerockets/falcon-9-v1-1-f9r/ )
        is still greater than the weight of the first stage and remaining prop ( Inert Mass~23,100kg (F9R: ~25,600kg) http://spaceflight101.com/spacerockets/falcon-9-v1-1-f9r/ ) . This means that it can’t hover because if it reaches zero downward velocity before touching down it will start accelerating upwards again at an ever increasing rate as propellant is burned off, until it’s depleted, then boom. So the timing of the start of the last burn is critical. I assume they initially aim for a point some distance below ground if only minimum thrust was used then modulate the engine thrust upwards so as to produce zero downwards velocity right at touchdown then shut down the engine. Add wind and pitching seas and one can see why landing on the drone ship is such a challenge. Although the future Falcon Heavy center booster will likely be too far down range and moving too fast to return to the launch site so the autonomous drone ship is the only option.

        I can only assume Grasshopper had different thrust and mass quantities as it was clearly able to hover.
        Any corrections appreciated. ☺

        1. Yup. Bezos operates in what Carmack calls a “cone of silence.” Since their first launch back in 2007, http://www.dailyack.com/2007/01/first-launch-for-blue-origin.html, there’s really only been a couple of press releases out of Blue Origin. There has been at least one known (total) vehicle loss to my knowledge. It’s really only recently they’ve started to open up, a little bit, as they’ve started to work with outside partners like ULA.

          You make a good point about the Merlin throttle range, your argument seems fairly solid. Makes sense. However SpaceX’s publicity suggests that the central core of the Falcon Heavy will head back to the Cape.

          https://www.youtube.com/watch?v=4Ca6x4QbpoM

          Although I’d presume it’s down to whether or not the Heavy is heading to GTO and the parameters of the mission.

          1. They can still return the Falcon Heavy core from downrange because of the drastic change in thrust to weight ratio when they’ve burned off the bulk of the fuel and decoupled from the upper stage. Sure, it took 90% (made up numbers) of the fuel to get going that high and fast, but to return you’re dealing with a tiny fraction of the mass that went up.. So a tinier amount of thrust is able to reverse course and get the stage heading back to the cape.

  2. The unasked question, why?

    My understanding is 50% of the cost is fuel.

    Then of the rest, the body of the rocket, not much, that leaves the engines.

    So why not just parachute back the engines?

    Why not concentrate on making cheap engines?

    Look at modern technology. Lots of that is throwaway because its cheap.

    Strikes me the reuse argument is the wrong approach. Instead ask why the costs are so large.

    1. Your estimate of 50% for fuel cost is way over. During his conference call Monday night, Musk said a Falcon 9 currently costs about $60 million to build and launch. But propellants (fuel) only account for about $200,000 of that total. And that, he said, “means that the potential cost reduction over the long term is probably in excess of a factor of 100.”

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Alasdair Allan is a scientist, author, hacker and tinkerer, who is spending a lot of his time thinking about the Internet of Things. 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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