Stuff Happens…
In the tail end of 2021, SpaceX launched a commercial resupply mission to the ISS. That mission used Booster B1069, which landed successfully on the drone ship. Unfortunately, by the time it returned to port, something had happened, damaging most of the engines and likely requiring at least significant repairs. This led to the following question, given that SpaceX’s HLS bid is estimated to require 14 refuelings, how many launches, super-heavy boosters, and tanker Starships will be necessary?
Probabilities
Starship is currently under development, and as such, it will be assumed to be similar in reliability to Falcon 9.
SpaceX, in its history, has had three failures on its Falcon 9 Vehicle. One partial failure to deliver the payload to target, one explosion on the launch pad (AMOS-16), and one explosion in flight (CRS-7). Over 138 attempts, this is an impressive success rate of 97.8%. Additionally, this indicates that if the mission is not successful, SpaceX has a 66% probability of the entire rocket being destroyed.
Additionally, SpaceX has attempted to land 31 boosters in the last year, with 29 of them being in re-flyable condition, leading to a landing success rate of approximately 94%. Unfortunately, this is a small sample size, so let’s bake in some conservatives using the one-sided lower bound success rate at 90%. This provides a new rate of 88%, which we’ll use as the probability of successfully landing the superheavy booster.
Unfortunately, landing Starship is entirely unprecedented. Because it needs to re-enter the atmosphere from orbital speeds, it will likely have a lower success rate than the booster. For this post, I’ll say it has a success rate of 79% (aka 90% of the booster’s success probability).
Simulating Launches
Now that we have our baseline probabilities let’s simulate launches. To stimulate one launch, we will draw four random numbers from a uniform distribution. The first determines the success of the mission, the second determines the success of the booster recovery, the third the success of Starship recovery, and the fourth is used to determine if the rocket exploded during the launch. Launches are repeated until 14 successful dockings are achieved, and new boosters/starships are built as necessary to replace unsuccessful recoveries. (Note after the final refueling, the successful recovery of the booster or starship are not required) . The number of launches, boosters, and starships needed is then recorded. This Monte-Carlo is run a million times to calculate the distribution of
Results
The figure below shows the distributions for the number of launches, super-heavy boosters, and tanker starships required. For launches, thanks to SpaceX’s current track record with Falcon-9 successes, it’s improbable that this will require more than 16 launches. This result aligns well with the expectation from NASA’s OIG and serves as a good reality check that we haven’t done something massively wrong. We should expect either 2 or 3 boosters to be needed for an average HLS mission. However, we shouldn’t be surprised if it requires six boosters if they get unlucky. Similarly, due to the increased difficulty of recovering the tanker variant of Starship, we would expect either 3 or 4 to be required per HLS mission. There should be much doubt regarding the tanker Starship distribution, as recovering a starship from orbital velocities has never been done.
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