On Friday, SpaceX made the news again with the successful launch and recovery of their upgraded Falcon 9 booster, the Block 5, this time carrying a Bangladeshi telecommunications satellite into orbit.

Like many tech breakthroughs, the success of the Falcon 9 series has almost become routine to the point that it doesn’t get any attention any more, but aside from spearheading the commercial space revolution, SpaceX deserves a lot of credit for tackling, and overcoming, significant technological challenges in order to maximize the reuse of spaceflight hardware.

I hope you’ll indulge me this week as I stray from outdoor/nature topics and get more into the engineering of SpaceX’s accomplishment, particularly from the aspect of guidance and control.

Why Do It?

Elon Musk’s stated goal, all along, has been to reduce the cost of space flight.  This isn’t to say SpaceX has made it CHEAP – gravity is harsh, the spaceflight environment is dangerous, and getting anything out of Earth’s grip takes a lot of fuel and energy, which adds weight, which requires more fuel and energy, etc.  So the goal of all engineers developing rocketry systems is to keep them light, while making sure they are sufficiently redundant, reliable, and with sufficient control and guidance systems to put a payload where you want it, EVERY TIME.

Certainly, improvements in materials have allowed us to build aerospace structures significantly lighter without sacrificing strength.  Miniaturization of electronics allow accelerometers and rate sensors to take up far less size, weight and power (referred to as SWAP) than they used to.  These advances have shrunk the payloads as well, which certainly helps as the probes and instruments we launch now can match the performance of those launched on the Space Shuttle, but with far less weight.  Rocket fuels have become more efficient – but not extremely so, as you can still only extract so much chemical energy from a propellant, we’ve just learned how to do it in a more controlled fashion than we used to.  Despite all these advances, one of the primary challenges has been recovery and reuse of the equipment itself – and this is where SpaceX placed its bets.

The Challenge

The challenges of recovering a large, hypersonic object re-entering the atmosphere from a sub-orbital trajectory are many – but chief among them are being able to properly orient, maneuver and control an object through a dynamically changing environment, from near-vacuum and extremely high speeds, through hypersonic (above Mach 5) flight in a very thin atmosphere, to zero velocity in exactly the right spot back on the surface.  To do this, the system must be observable (that is, you can tell where it is, how it’s oriented, and where it’s going), and controllable through the entire flight, recognizing that classic aerodynamics won’t work for the high altitude portions.

There’s also a significant tradeoff in propulsion here – if you hope to use your engines on the descent, you’ll have to carry extra fuel for that purpose, which makes your vehicle heavier…  So this approach is only worth the effort if you can do it very efficiently, minimizing fuel use.  You can’t afford a system that spends a lot of time maneuvering around to get the landing just right — a successful recovery is more like drifting your car sideways at top speed into a parallel parking spot, rather than precisely and carefully backing in.

SpaceX originally announced its intention to reuse both stages of the two-stage Falcon system, including the protective payload fairing (the “bulb” at the top of the rocket that protects the payload while in atmospheric flight).  So far, they’ve focused on the challenge of recovering the first stage, and the fairing.  The second stage is still  “disposable”, though they’re not done yet.  SpaceX recently announced its intention to recover the second stage using a “giant party balloon”, which is still in the conceptual design phases.

How They Do It

Ideally, if you’re trying to lower a cylinder vertically, upright, onto the ground, you want to control it from the top.  This puts the center of mass below your primary control and force generator, and results in a system that is statically stable.

(Statically stable systems tend to return to their reference condition when disturbed.  Picture a marble in the bottom of a bowl – if you move the marble, its tendency is to return to its start point.  In the case of a booster under a parachute, it acts like a pendulum.  It may swing to one side, but its tendency is to hang straight down.  Move the point you’re hanging from, and the booster/pendulum will follow).

The problem here is that parachutes don’t work at high altitudes and high speeds where there’s no air.  If you wait until atmospheric conditions support parachute deployment (like the Sold Rocket Boosters on the Space Shuttle, and really every recovered vehicle since Gemini), you don’t have time or altitude to do anything more than slow your descent – placing the payload where you want it is not really an option, as the system just isn’t sufficiently controllable.  “Splashdown”, somewhere in a big target area, becomes the only real solution – and while the Shuttle’s SRB’s were “reusable”, they really didn’t save much.  Dunking flight vehicles into salt water is not great for their long-term health, though recovering the boosters certainly taught NASA a lot about what was going on through launch.

The alternative to this is to control from the bottom, but that’s not easy.  The engines and their gimbals provide a lot of force, and a lot of control power, but the system is unstable.  In addition, controllability requires that your engines can change force output on command, including that they be shut down and re-lit as required.  This drives you to a liquid fuel setup, which is more volatile and hard to work with on the launch pad, but much more operationally flexible than a solid fuel booster.

Regardless of the control power, you’re still dealing with an unstable system.  This is a classic inverted pendulum – like balancing a baseball bat on your finger.

(Statically unstable systems tend to diverge from where you want them.  The marble in this case is carefully balanced on the top of an upside down bowl – breathe on it, and it’s gone…)

With an inverted pendulum, you can’t just move the system where you want it to go.  If you want to move right, you must push the bottom of the cylinder LEFT, so the center of mass starts to FALL right.  Then you push the bottom back to the right to keep up with the tendency to fall that way, and either keep up (to keep sliding in that direction), or counteract the movement and balance straight up again.  In essence, every movement of the rocket requires three controls – start in the wrong direction, move back in the right direction to control the movement, then counter that movement to stop again.  This is the same thing you do balancing a baseball bat, or in fact, WALKING, but your brain makes these changes quickly.  Making these corrections quickly with hardware requires good sensors, and fast actuators, and would have been impossible to pull off before the computer age.

The Falcon 9 also has another trick, and that is the use of grid fins.  These are perforated plates, about 4 ft by 5 ft, that extend from the top of the rocket and articulate in roll and pitch.  These add drag and slow the vehicle like a parachute, but more importantly they also can create aerodynamic forces and moments, even when the rocket is still supersonic, to help control the vehicle from the top.  SpaceX states that the grid fins, by themselves, can create enough control power to change the orientation of the rocket by 20 degrees in any direction.  This takes a lot of work off the engine, but the coordination between these effectors is what controls engineers call a dynamic allocation problem.  With roughly 6 controls to use (engine thrust, engine gimbal, and the roll angle of four independent grid fins), knowing which tools to use, in what combination, and to what degree, is another problem for the computers, which constantly adjust based on rate, attitude, speed, dynamic pressure, to get the system where you want it.  Tweaking these algorithms, based on lots of simulation and test flight data, has been the role of many SpaceX engineers since this system was initially developed.  (Here’s a good, short video showing the grid fins in action on an early test).

Finally, there’s the landing.  Falcon 9 uses a very wide (stable), forgiving landing leg system that extends to cushion the hopefully-gentle touchdown.  But the location of that landing is also critical.

SpaceX has put Falcon 9’s back on land, both in low altitude test events, and then quite dramatically during the launch of the Falcon 9 Heavy, which uses three 9’s strapped together.  In that launch the two boosters pulled off simultaneous returns to the pad, while the center section crashed on the drone ship offshore.  Yes, the “Drone Ship”.  This is an unmanned barge, equipped with a totally different kind of thruster (the water-jet kind), to maintain position in current, wave action, and wind, about 200 miles offshore at a precise location, give or take 10 feet.  Having a landing platform autonomously station-keep is another thing we couldn’t have done 20 years ago.

Putting it All Together

So a typical profile looks like this:  Main engine ignition, all nine of the Falcon 9’s Merlin engines ignite for liftoff and acceleration.  Assuming this is a launch intended to put the payload into Low-Earth Orbit (LEO), the rocket rolls east and starts to accelerate downrange as it climbs.

Falcon 9 recovery profile.  Click for larger view.

At an altitude of about 70 km (~43.5 miles, or ~230,000 ft), and travelling at about 12,000 km/h or 7,600 mph – equivalent to roughly Mach 10 at sea level – the rocket experiences Main Engine Cutoff (MECO), and the stages separate.  The second stage lights off and continues, while stage one relights only three of its nine engines, and begins the “boostback burn” to maneuver back to the touchdown area.  Initially, the rocket flies like you would expect a rocket to fly (i.e. engine in the back), but after getting the rocket flying in the right direction toward the touchdown point, it will turn around and fly engine-first, starting the “inverted pendulum” phase.

Gradually slowing, and and with dynamic pressure increasing due to a thickening atmosphere, the grid fins are extended to slow and control the descent.  Ground-based observers will hear 2 sonic booms – one from the rocket body, one from the fins – as the rocket continues to slow gradually.  Make no mistake, this thing is still coming down fast, well above Mach 3.

Fine guidance corrections begin, putting the rocket above the Drone Ship, and establishing a vertical attitude (straight up and down).  At the last minute, the thrust is ramped up to achieve a last-second stop, just in time for a gentle touchdown.  Observers then (carefully) approach the Drone Ship to secure the vehicle for post-flight return to shore.

Meanwhile, the payload fairing deploys a parachute, and glides to a landing, also to be recovered.

Someday, the second stage will be recovered as well – but that’s still in the future.

Does it Work?

Writing as of May 13, 2018 – Since June, 2010, SpaceX has launched the Falcon 9 55 times, with 53 full mission successes (96.4% success).  Booster recoveries have been attempted 31 times, and were successful 25 of those times (80.6% success).  Of those, eleven boosters have been reused, three have been refurbished and are awaiting a second flight, and two more have been recovered and are awaiting refurbishment.  So not only has SpaceX recorded a significant number of launches, with a high mission success rate, they have repeatedly demonstrated the ability to reuse launch hardware.

Additionally, while cost estimates depend on a lot of factors, and aren’t always directly available, the approximate launch cost per kilogram of payload for the Falcon 9 is down to about $2,700.  This compares to roughly $10,000/kg for the Space Shuttle program, and is significantly lower than other available modern launch vehicles.  The development of the Falcon 9 Heavy variant, and continued work on recovery of the second stage aim to bring costs down to $1,100/kg.

So, while there are certainly haters and nay-sayers out there, and many turned off byt he cult of personality around Elon Musk himself, it is hard to deny that SpaceX has developed a business with a list of paying launch customers.  They’ve done it by tackling some of the hardest problems in rocketry, and systematically built a reliable system that does what no other launch platform can do.  Best of all, the majority of the drama seems to be waning, such that both flights and recoveries are now “routine”.  This is surely an indication that the Falcon 9 and SpaceX have achieved what they set out to do, even if they’re still making improvements.

I’m curious and excited to see the next developments.  Audacious accomplishments like this inevitably drive competition and innovation across the industry, and those who first achieve a breakthrough rarely hold onto a unique monopoly for long.  It will be interesting to see what improvements are made, now that more and more commercial companies are getting into this game!

Get Out There
Troy
http://www.flying-squirrel.org

(Note: All images are public domain, courtesy of SpaceX)