Catching a Falling Rocket
On 13 October 2024, a rocket booster as tall as a 20-storey building fell back from the edge of space toward its own launch tower. The booster didn't land on legs, and it didn't splash into the sea. The tower swung two giant steel arms together and caught the booster in mid-air.
The booster was the bottom half of SpaceX's Starship, called Super Heavy: about 70 metres tall and 9 metres wide, with 33 engines. SpaceX calls the tower's arms the chopsticks. Less than seven minutes passed between liftoff and the catch.
Make your guess. Why go to all this trouble, instead of letting the booster fall into the sea?
- To keep the sea clean
- The booster costs far more than its fuel, so flying the same booster again could make spaceflight much cheaper
- A booster that hits the water explodes and puts ships in danger
Show answer
B. The booster costs far more than its fuel, so flying the same booster again could make spaceflight much cheaper
The fuel is the cheap part. Elon Musk has said that the fuel for a launch of Falcon 9, SpaceX's smaller rocket, costs a few hundred thousand dollars, while the launch sells for tens of millions. Throwing a rocket away is like scrapping an airliner after one flight. A caught booster can fly again.
Before any explanation, try the catch yourself.
Catch it yourself
Your goal: press Start the fall. Hold Burn to slow down, steer with Left and Right, and reach the arms slower than 4 m/s before the fuel runs out.
Most first tries end in a crash or an empty tank. Light the engines too early, and the fuel runs out high above the arms. Light the engines too late, and no amount of burning can save the booster.
SpaceX's engineers play a harder version of this game, with a real booster at stake. So why bother? Why not build a new booster for every flight?
Rockets you throw away
For most of the space age, every rocket flew once, then fell into the ocean or burned up. Picture an airline that scrapped each plane after one flight: a ticket would cost about as much as the plane.
For Falcon 9, SpaceX has put the first stage alone at well over half the cost of the rocket. In 2018, Harry Jones, an engineer at NASA, compared what each kilogram cost to lift into low orbit:
The surprise is the Shuttle. Most of the Shuttle was reused, yet the Shuttle cost the most of all. Between flights, each Shuttle needed months of inspections and repairs by thousands of workers. Reuse only saves money if the reused part is quick and cheap to fly again.
So SpaceX wants the launch tower itself to catch the booster. A caught booster is already back at the pad, with no landing legs to carry, and SpaceX hopes one day to fly a caught booster again within hours.
To be caught, the booster must reach the arms almost perfectly still. How do you stop something falling at hundreds of kilometres an hour, at exactly the right spot?
When to light the engines
A falling booster gains about 10 m/s of speed every second, from gravity. The booster's engines push harder than gravity pulls, so once the engines light, the booster slows down. The whole question is when to light the engines.
Your goal: slide the height where the engines light, let go, and find the height where the booster stops exactly at the arms.
Only one height works: about 202 m above the arms, in this example. Light the engines higher, and the booster stops in mid-air. Light the engines lower, and the booster slams into the arms.
With the same engines, a booster falling twice as fast needs how much room to stop?
- The same room
- Twice the room
- Four times the room
Show answer
C. Four times the room
Four times. At twice the speed, the booster takes twice as long to stop, and during that time the booster also moves twice as fast on average: 2 × 2 = 4. A car braking at a red light follows the same rule.
In symbols: if the booster falls at speed \(v\) and slows by \(a\) metres per second every second, the stopping distance is
The flight computer keeps redoing this sum on the way down, so the engines light when the stopping distance matches the height left. But if the booster does stop too high, why not just hover and sink down gently, like a helicopter?
Why not just hover?
Rocket engines can turn down, but only so far. Below a certain setting, called the minimum throttle, an engine can't keep burning steadily. And by landing time, the booster has burned nearly all of its fuel, so the booster is very light.
A landing Falcon 9 booster is in exactly this spot: by most accounts, even one engine at its lowest setting outpushes the nearly empty booster. The engine must bring the booster's speed to zero at the very moment the booster reaches the ground. Fans call this a hoverslam.
Super Heavy's landing burn starts on 13 engines and ends on the 3 in the centre, and the booster almost pauses beside the tower. Still, as Lars Blackmore of SpaceX has written, every second spent hovering is wasted fuel: fuel the rocket could have spent lifting cargo.
So the plan has to be nearly perfect. But no plan survives a gust of wind, or an engine that pushes 1% weaker than expected. How does the booster fix mistakes that nobody predicted?
The autopilot
The flight computer doesn't blindly trust its plan. Many times a second, the computer measures where the booster is, compares that position with where the booster should be, and steers to shrink the difference. Then the computer measures again. This cycle is called a feedback loop.
Most autopilots are built from three simple rules. Try them on a booster in a crosswind.
Your goal: turn on rule 1 and watch the blue path. Then add rule 2, then rule 3, and get the miss under 3 m.
Rule 1 alone swings the booster past the line again and again, like a marble rolling in a bowl. Rule 2 calms the swings, but the steady wind still parks the booster a few metres off. Rule 3 notices that the booster has been off to one side for a while, and pushes a little harder until the miss is gone.
Together, the three rules have a name: a PID controller. P stands for proportional (rule 1), I for integral (rule 3) and D for derivative (rule 2).
How it really works (the math)
- Stopping distance. Engines that slow the booster by \(a\) every second take a time \(t = v/a\) to stop the booster. During that time the speed falls steadily from \(v\) to 0, so the average speed is \(v/2\):
\[ d = \frac{v}{2} \cdot \frac{v}{a} = \frac{v^2}{2a} \]2. The slowing, from the engines. Engines that push with force \(F\) on a booster of mass \(m\) slow the booster by \(a = F/m - g\). In the game, \(F\) is twice the weight, so \(a = 2g - g = g\). As fuel burns away, \(m\) shrinks and \(a\) grows, which real guidance has to track.
- The one perfect height. In the game the booster starts 300 m up at 45 m/s. Falling freely to height \(h\), the booster reaches \(v^2 = 45^2 + 2g(300 - h)\). A perfect stop needs \(v^2 = 2ah\) with \(a = g\):
\[ h = \frac{45^2 + 2g \cdot 300}{4g} \approx 202\text{ m} \]4. The three rules as one formula. Call the miss \(e\). The autopilot steers with
\[ u = -K_p\,e \; - \; K_i \int e\,dt \; - \; K_d\,\frac{de}{dt} \]Rule 1 alone gives \(\ddot e = -K_p e\), the equation of a mass on a spring, so the booster swings back and forth forever. Rule 2 adds friction, so the swings die away. With a steady wind push \(W\), rules 1 and 2 settle where the steering cancels the wind: \(K_p e = W\), so \(e = W/K_p\), about 4 m in the widget. Rule 3 keeps growing while \(e \neq 0\), so the only resting place left is \(e = 0\).
- Real guidance does more. A real booster doesn't pick one ignition height in advance. On the way down, the flight computer keeps solving for the path that uses the least fuel and still ends at the target. Lars Blackmore has described how SpaceX uses convex optimization, a kind of math a computer can solve reliably in a fraction of a second.
- Why fuel is precious. The rocket equation says how much speed \(\Delta v\) a rocket can gain or lose by burning fuel, with \(v_e\) the exhaust speed:
\[ \Delta v = v_e \ln \frac{m_{\text{full}}}{m_{\text{empty}}} \]The logarithm means that each extra bit of speed costs more fuel than the bit before. Fuel kept for the boostback and landing burns is fuel that didn't push cargo toward orbit.
Rockets that land themselves took decades to get right. Who did it first?
The first catches
Rockets that land upright are older than SpaceX. In the 1990s, a small US test rocket called DC-X took off and landed on its tail several times, and SpaceX's own test rocket, Grasshopper, hopped hundreds of metres up and back in 2012 and 2013. But no booster had yet come home from sending something to orbit.
| When | What happened |
|---|---|
| Dec 2015 | A Falcon 9 booster lands upright after sending satellites to orbit: a first |
| Mar 2017 | A landed Falcon 9 booster flies a second time |
| Oct 2024 | The tower catches a Super Heavy booster, on the first try |
| Nov 2024 | A check on the tower fails, so the catch is called off and the booster splashes down at sea |
| Jan, Mar 2025 | Two more boosters caught |
| May 2025 | A caught booster flies a second time |
Today one Falcon 9 booster has flown more than 30 times.
The feedback loop that steers Super Heavy is far from rare. Where else does a feedback loop show up?
Where it shows up
- Cruise control. A car measures its speed many times a second and opens or closes the throttle to hold the speed you set, uphill and downhill.
- Drones. A drone hangs still in the wind by measuring its tilt and correcting the speed of each propeller, hundreds of times a second.
- Your phone's camera. A tiny motion sensor measures your hand's shake, and the camera moves its lens or sensor the other way, so the photo stays sharp.
- Heating. Many heating systems use the third rule, so a room doesn't settle a degree too cold on a freezing day.
- Braking at a red light. Every driver and cyclist does the stopping-distance sum: twice the speed needs four times the room.
The catch, explained
Now you can explain the catch. Fuel is cheap and rockets are expensive, so flying the same booster again could make space far cheaper, as long as the booster is quick to fly again.
To be caught, the booster must lose all of its speed exactly at the arms. Twice the speed needs four times the room, so the engines must light at one precise height, and a nearly empty booster can't simply hover to fix a mistake.
A feedback loop fixes the mistakes instead: measure the miss, steer to shrink the miss, repeat, using three rules. The next time a drone hangs perfectly still in a breeze, you'll know the drone is doing the same thing.
Where to go next
The catch is a doorway to a lot of other ideas. Here are the questions this page opens up:
- How do engineers choose the strength of each rule in a PID controller?
- Why does reaching orbit take so much fuel, and what is delta-v?
- Could the tower catch the Starship upper stage too?
- How does a drone know which way is down?
- Why was the Space Shuttle so expensive to fly again?
Ask Phy
- Explain a PID controller using a shower where I'm trying to get the temperature right.
- Walk me through the rocket equation, and why most of a rocket is fuel.
- How does Super Heavy steer in the last seconds before the arms catch it?
- Starship's Fifth Flight Test (SpaceX, YouTube) — The first catch, filmed by SpaceX
- Starship flight test 5 (Wikipedia) — Timeline of the first catch
- SpaceX Super Heavy (Wikipedia) — Size, engines, landing burn and later catches
- The Recent Large Reduction in Space Launch Cost (H. W. Jones, NASA, 2018) — Cost per kilogram for the Shuttle and Falcon 9
- Autonomous Precision Landing of Space Rockets (L. Blackmore, SpaceX, 2016) — Why hovering wastes fuel, and how landings are planned
- Falcon 9 flight 20 (Wikipedia) — The first landing of an orbital booster, December 2015