How stable would a Falcon 9 first stage be after it has landed on a drone ship?

Question

Presumably, the booster would be a very light, very tall tube (Most of the fuel spent) standing on 4 fairly small legs on a ship in the middle of the ocean. It would also still contain some LOX and RP1 that would start boiling fairly soon after landing. The booster appears to be fairly prone to exploding based on the past 2 landing attempts.

My question is, what steps will be taken to secure the booster to the ship and drain the fuel and how likely is it to fall over or explode before this is done?

Answer 1

There's not much reliable data out there to estimate this ourselves, and SpaceX isn't exactly forthcoming with details. Or perhaps they would be, but media aren't asking the right questions during press conferences. So far, the only somewhat reliable data point is the canceled recovery attempt during the DSCOVR launch on February 11, 2015;

According to SpaceX press release:

The drone ship was designed to operate in all but the most extreme weather. We are experiencing just such weather in the Atlantic with waves reaching up to three stories in height crashing over the decks. Also, only three of the drone ship’s four engines are functioning, making station-keeping in the face of such wave action extremely difficult.

This would suggest that SpaceX are confident they could land and keep the first stage stable on the drone ship as long as it can provide a stable surface to land on and smooth out the swelling of the sea during strong lower atmosphere winds.

Now for a bit of speculation on my part; Stability of the landed first stage, assuming weather permits it and all four of its landing legs are properly extended and on the platform, shouldn't be such a big deal even with occasional (not gale force) gusts of wind. Practically exhausted of propellants, with perhaps up to a few seconds of literally fumes of kerosene remaining (that's why it appears to explode so fast once the propellant tanks are breached on impact, or what Elon Musk called closer to a fast fire than an explosion), the first stage's center of gravity would be low. If position of the landing legs' mount points suggest where exactly, and those are quite low, it would have to be in the lower 1/3 of its length, possibly quite a bit lower, since lateral pressure on the truss increases with mount point's distance to CoG (law of the lever).

Sadly, I can't estimate this analytically, because ideal pressure angle isn't known. For structures that can withstand pressure equally both in lateral and long axis direction, that would be 45°. But rocket stages can't be built like that, so this angle would be substantially higher, in favor of pressure along the long axis (vertically). If we knew that angle at legs' mount point ring (that's got to be reinforced for lateral forces, but how much?), and exact point of CoG, and we already know rough total weight of near dry landed stage (it was mentioned during the CRS-6 post-launch news conference), stage's height, how much legs extend and how high they suspend the stage (can be estimated through photographs), we could extend stress line from CoG, at that given angle, towards the landing surface and compare that to stage's total height. Then, with its know weight and surface area, we could calculate wind shear it could withstand laterally before it tips over. Sadly, as we lack crucial data, not even such estimates could be done.

Anyway, I wanted to write this so we identify data that we still need to (roughly) analyze landed first stage's stability, and why with too many unknowns, it can't be done. I'll trust that SpaceX can do, and did do, extended analysis on (to them) known structural properties of their first stages and will take their word for it - that if the barge can handle it, landed first stage should too. But I wouldn't rule out possible future use of mobile anchor shoes to clamp landing legs in place with their weight, or some other means of achieving this as the barge heads back to land with recovered stage on it, or prior to refueling and flying it to shore, as SpaceX indicated they eventually intend on doing. Of course, ultimate goal is still landing on terra firma, once they demonstrate to FAA and other authorities that it's safe. But that's a different story.

Answer 2

That is my estimation of CoG of nearly empty Falcon 9 booster. On the left is GoG with legs opened, on the right with legs retracted.

The landed vehicle is pretty stable. It could withstand the winds of 50 m/sec (97 knots!), if sliding is prevented. There are relatively narrow limits on horizontal component of landing speed as well as on rotational velocity at touchdown which are not unusual for vertical landing craft.

Answer 3

In order for such an object to be stable, it has to have it's center of mass over the area of it's base. It's a bit tricky to know exactly where the center of mass is in such a rocket, but it must be fairly low, as there is little fuel left and the engine is one of the heavier parts of the rocket. Wind is also a factor in how stable it must be, as that will tend to tilt the rocket. My guess is it has to remain vertical with a few degrees of tilt allowed. From Wired's analysis, it seemed to lose control when it hit more than 5 degrees of tilt, with a high degree of uncertainty. Still, I'd say that the rocket must remain within a few degrees, or else it will not remain steady.

As for what can be done, there are a large number of things. The basic idea is, if you can fix the rocket to the barge, then it's the center of mass of the barge that makes a difference. If you can fix the rocket, then you could simply release the oxygen to keep the rocket from exploding. The kerosene is not as dangerous to keep around for a while, so presumably someone could help with that, or it could wait for the drainage of the oxygen.

Answer 4

The landing legs spread out pretty far. 60 feet or more in total around the core. The center of mass is fairly low due to the mass of the engines being right at the bottom and the rest of the cylinder is very uniform and light.

Thus once it is down, SpaceX expects it to be very stable. Their bigger concern is slipping around. Initially they said they would weld placeholders over the feet to secure it to the deck. Then people started reporting that they would use chains to secure it.

After the CRS-8 mission, Elon Musk (transcript not yet available) said they would be welding shoes over the feet. Upon reaching port a high resolution photo shows that they also chained it down to the deck via the launch mounts

The deck has been shown in detailed photos to have lots of tie down points (like on an aircraft carrier) so both options are likely possible.

Answer 5

This article says

Recent information notes that the rocket will be “tied down” via chains that extend from the engine section to the deck.

but doesn't give any sources. It's not clear if the chains are already present on the F9, or are part of the structure of the barge platform.

Since SpaceX refers to the barge as a drone, it's not clear how the chains would be secured.

Answer 6

Elon Musk gave some interesting information about it relating to the CRS-8 booster landing. When it was on the ground, it suffered 50 miles per hour winds, which tilted it about 2-3 degrees. He said that the maximum tilt the booster could support would be about 3 times that, so somewhere between 6-9 degrees. Presumably it could also take more than 50 miles per hour winds to do so as well.

The next step is to weld special containers around the feet to the drone ship, known as "Steel Shoes".

Answer 7

Using spherical cow physics, ignoring momentum and sloshing (because the time scales are so different) I just looked at where the cm is for an empty F9 1st stage of uniform density, and one with 5% remaining propellants. I get static tip-over angles of 15° and 18°, respectively.

Additional remaining propellants bring the center of mass even lower.

Counting localized masses like bulkheads and engines would further lower the center of mass. See this answer above!

That's not inconsistent with Musk's comments that 8-9° would be possible, which probably includes various non-spherical-horse factors like dynamics, leg strength (especially if there turned out to be more fuel than expected) and others.

NOTE: All numbers are the ones I used for this quick calculation - they are not necessarily correct so don't use them!