Landing a Spaceship on its Tail is Really Hard
On April 14th, SpaceX tried to land another rocket on its tail. They failed spectacularly, but it was damn close! Why are they having so much trouble?
The problem is rooted in the most basic factors that shape the silhouette of a rocket ship. When launched from Earth's surface, the hardest part of a rocket's job is to overcome Earth's gravity and leave its atmosphere. For a reusable craft, the trip back down is brutal, too.
The ship is hindered by all of the air molecules it crashes into on its way up (and down). This aerodynamic drag adds to the rocket engine's massive burden. Drag resistance from air increases as you go faster through it. But it doesn't increase gradually, or even proportionally: doubling speed quadruples drag. If a rocket travels 50 times faster than a Ferrari, the rocket faces 2500 times the drag of the car. A narrow, sleek, pointy profile is absolutely critical for a rocket launching from an object with as much atmosphere as our planet.
The atmosphere creates a second obstacle for rockets. The extremely high velocity of the craft going both up and down causes the impacted air molecules to impart not only not only drag but dangerous amounts of heat to the ship. Small damage to the heat protection of a spaceship can turn its re-entry into a catastrophe. The necessity of a long pointy design to lessen air impact is thus doubly important. This physical form does come with one large cost.
Imagine if we took the rocket and laid it lengthwise across a huge balance beam. If we gradually moved the balance point of the rocket from the tail to the nose cone, we'd find a place along the length where it would balance perfectly suspended above the ground--if it didn't crack in half! This point would be the vertical location of the center of mass, or equivalently center of gravity, of the ship. This point is way high above the ground when the rocket is standing upright. Its altitude would also measure much higher than the width of the ship.
A high center of mass in a narrow object gives its upright stance a very tenuous balance. If carefully set perfectly on the tail, the ship will stand. But, shake up this configuration even slightly and the rocket tips over. The crucial tipping point is the moment that the center of mass tips out beyond the edge of the tail of the rocket on the ground. Once that happens the ship is doomed to fall unless it's immediately pushed back in the opposite direction.
A short, squat ship with a low center of mass point could lean much further before that low point could get far enough out from the center of the ship to project beyond the edge. As you shrink the diameter relative to the height however, stability drops quickly. On the far end of the narrowness spectrum, a hair-thin needle is likely to tip over with even a feather's touch. The rocket with its very thin aspect ratio is much closer to a needle than a coin.
SpaceX of course is well aware of this. They build small rocket thrusters, called attitude control thrusters, into the top of the rocket to push back against tipping. When the ship starts to tilt, one of these rockets can fire to give the top a little push back. In the most recent landing attempt you can see one of these thrusters firing on the left side of the nose at nine seconds in:
The ship almost rights itself, but it has just picked up too much momentum pushing it over. The firing thruster isn't strong enough to push the center of mass back over the tail.
Don't jeer these failures. Salute SpaceX for trying something so hard and nearly succeeding. They will probably make a successful tail landing soon. Progressing from one safe landing to nailing it every single time will be an even greater challenge. Still, their accomplishments are the most exciting news going in space travel right now.