SpaceX And/Or Rocketry In General

Tonight's Launch

A lot about how things work in space is counter-intuitive, as all of our intuition is gained from daily experiences where the air is thick, gravity doesn't seem to change and movement is relatively slow. We do see lots of movies about space, but, unless you're watching an IMAX documentary, they vary from slightly wrong, like The Martian (good movie!), to mostly absurdly wrong, like Red Planet (don't watch this, it will hurt your brain), which also doesn't help intuition.

​Gravity Never Stops

The most important concept to appreciate is that the range of gravity is infinite. This sometimes comes across as mind-blowing, but is pretty easy to understand once you know how to imagine it. Think of space like a very slippery (no friction), stretched sheet with objects of various sizes dropped on it. Each of those objects creates a funnel shape in the sheet, with the size of the funnel proportionate to its mass, so a tiny object makes a tiny funnel and a giant object creates a giant funnel.

Now imagine placing a marble somewhere on that slippery sheet -- it is guaranteed to fall into one of the funnels. The shallow part of any given funnel gets really, really shallow, but it has no limit, so anything with mass has a gravity field that extends to the far reaches of the Universe, including you! Here's the weird thing: if you and your pet were the only objects in space and you had no relative motion, you would eventually collide even if you started off millions of light-years apart. This why it is velocity that matters, not distance. There is no such thing as "escape distance", only "escape velocity".

The only way that the marble is not going to fall into one of the funnels is if you spin it around a funnel, like the ball on a roulette wheel, so that it orbits around the center.

Getting back to everyday reality, the impression that most people have is that gravity stops once you reach a certain altitude above Earth, at which point you start floating around in "zero g", but, as we just talked about, this is obviously not true. The force of gravity drops proportionate to the square of the distance between the centers of two objects. This makes total sense when thinking about gravity wells like funnels -- if you moved the marble 2% further away from the center of the funnel, it would still fall in, just very slightly slower.

Earth is a slightly squashed sphere with an average distance from surface to center of 6,371 km (3,959 miles). That means if you were in a spacecraft hovering 100 km above the surface, the force of gravity would only drop by the ratio of the squares of the distance or about 3%! This is why you don't experience any weight loss flying in a plane at 10 to 15 km altitude or climbing a mountain -- you are technically slightly lighter, but not enough to notice.

Velocity (how to make what goes up, stay up)

So why are the astronauts in the Space Station, which is at just under 400 km altitude (~90% of surface gravity), floating around in what looks like zero g? This is because they are actually moving around Earth's gravity funnel at the blistering speed of 27,000 km/h (17,000 mph), completing a round-the-world trip every 90 minutes!

The reason they are floating around is that they have no net acceleration. The outward acceleration of (apparent) circular motion, which wants to sling them out into deep space, exactly balances the inward acceleration of gravity that wants to pull them down to Earth.

Kinetic Energy

Almost all two stage rocket systems have a staging altitude of around 100 km, plus minus 20 km. Therefore, the critical figure of merit for a rocket booster is how fast it can throw a payload of what mass at roughly 100 km. It is important to note that the amount of energy needed to achieve a given velocity increases with the square, so going from 1000 km/h to 2000 km/h takes four times as much energy as going from 0 km/h to 1000 km/h, not twice as much.

In the case of the Falcon 9 rocket, the boost stage is able to accelerate a payload mass of 125 metric tons to 8000 km/h and land on an ocean platform or to 5000 km/h and land back at the launch site. The second one is lower because the rocket is moving super fast away from the launch site, so it has to do a screetching U-turn with nitrogen attitude thrusters, then fire the engines to create a reversed ballistic arc, then reorient again for atmospheric entry and have the engines pointed in the right direction for the landing burn. Since the propellant is liquid, it wants to centrifuge out during these maneuvers, so there has to be a system of baffles and internal holding tanks to keep it in place. It also needs three axis control surfaces that don't melt easily and work well from hypersonic through subsonic speeds.

For a sea platform landing, the Falcon 9 figure of merit is therefore roughly 300 gigajoules (GJ) of kinetic energy and for a return to launch site landing, the number is about 120 GJ. These are fairly sizable by terrestrial standards. To put it into perspective, the city of San Francisco uses about 1 GJ per second of electricity, so the Falcon 9 booster transfers enough energy to power a city of almost a million people for five minutes.

When trying to understand the value of a reusable rocket booster, the kinetic energy transfer at a 100 km reference altitude is what matters. That altitude is the equivalent of the starting line of a race. The race itself is the kinetic energy.

SpaceX Reusability Progress to Date

We've done several vertical take-off and landing flights with the same Falcon 9 first stage test rig, called Grasshopper. These were important to ensure that the final velocity attenuation algorithms worked properly. In particular, we needed to prove out a hard slew maneuver and a high acceleration landing. The first is important because the rocket is still moving sideways before landing, so we need to zero out lateral velocity, and the second because landing slowly takes a lot more propellant than landing fast. Landing at 2 g's is 10X more efficient than landing at 1.1 g's, because anything below 1 doesn't count. Those tests all worked out and Grasshopper is currently parked in a field at our central Texas development facility.

We could have gone a lot higher, but it didn't really matter without the right atmospheric entry velocity vector, which can't be enveloped safely over land. Also, given that we had a high upcoming cadence of orbital launches with exactly the right conditions, it made sense to end over-land tests and switched to over-water tests.

The first attempt to touch down softly on water failed, as we tried to control the rocket with small attitude thrusters alone. While it works well for a smooth, blunt body shape like Dragon, that turns out to be a hopeless proposition for something the shape of a rocket booster. Falcon spun out of control and smashed into the water at high speed.

We then added four grid fins in an X-wing configuration to give us the necessary three axis control under high dynamic atmospheric pressure, which peaks at 1.5 tons per square foot.

This solved the control problem and we were able to do two successful soft landings in the water. Max altitude of the rocket stage was 210 km, which doesn't matter a lot, and max transfer kinetic energy was 200 GJ.

The rockets were not designed to survive in water, so only lasted for about 7 seconds after landing before we lost telemetry.

Droneship Landing

The obvious next step was to build an ocean landing platform that could hold station, so we built an autonomous droneship called Just Read the Instructions. This gave us a landing area of 150 by 250 feet. The leg span is about 60 ft, which meant that the margin of error in the worst direction was less than the leg span. Adding to the complexity, Falcon was coming in on a diagonal at extreme deceleration towards a heaving ship in high winds. This is a lot like landing a plane on an aircraft carrier vs a normal runway. A lot less room for error.

The first one hit really hard and exploded immediately on impact. The second one did land, but slightly too hard. Two of the legs broke their stops on landing, so it tipped over and exploded.

New and Improved!

The Falcon 9 rocket we are about to launch has higher performance than the prior version due mostly to increased boost thrust, deep cryo oxidizer and a much larger upper stage engine bell. It also has a number of reliability enhancements, such as a redundant stage separation system and greater structural safety margins.

This should, if all goes well, give us enough performance to deliver eleven satellites to orbit and bring the booster all the way back to Cape Canaveral to Landing Zone 1 (LZ-1).

T-zero in 15 minutes, so have to sign off. Apologies for any typos in the above.

-- Elon

Great stuff, mostly, but I suggest you rethink your mass ratio/stoichiometry comments

I understood from the beginning that sea recovery had to have a substantial fuel need/available delivery smash advantage over the return to launch site, but Elon's numbers are far more dramatic than my intuition.