Rocketdoc Notes – Week of October 18, 2020
Space-X Starship by the Numbers
In my last note I summarized what I learned at the Mars society Convention a week ago. My analysis of the Space-X Starship and what it offers was a quick sketch, so this week I dug in and did an in-depth analysis of the Starship and the real advantages it brings to human space settlements. I think you will find this both interesting and exciting.
To status Starship I watched a U-Tube (https://youtu.be/sOpMrVnjYeY) and I recommend you do the same. In the U-tube Elon Musk is standing in front of the Starship prototype in Bolsa Chica, Texas; and explaining to a crowd of visitors how far they have come, what comes next, and where it is all leading. Interesting stuff.
Space-X has not published a detailed system description for the Starship, so I set out to put together a fairly detailed description using the few numbers Space-X has published and a launch systems preliminary design tool, BLAST, put together by myself and others thirty-five years ago while working at the Boeing Aerospace Company. BLAST stands for Boeing Launch Analyses and Systems Technologies. It is an Excel Spreadsheet and has since been adopted throughout the Launch System Design fraternity. The BLAST results for the Starship 1st stage is shown below.
Figure 1 BLAST Worksheet for STARSHIP 1st Stage
I have used Space-X published data for Gross Weight, empty weight, and takeoff Thrust to Weight (T/W) but most everything else is spreadsheet generated. The corresponding 2nd Stage data is shown below in figure 2.
Figure 2 BLAST Results for Starship 2ndStage
What we’re seeing in the BLAST data is; 1) a vastly larger than advertised payload to 28.5 degree LEO ( 180+ mT instead of 150+ mT mentioned in Space-X literature), 2) a total development cost of $1.92 B (2010$) of which $369 M is for the Raptor Engines, $785M is for the 1st stage, and $ 765 M for the 2nd stage and, 3) average unit production costs of just under $1 M per engine, $112 M for each 1st stage, and $139 M for each 2nd stage. All costs are in $2010 dollars because I forgot to update the program before I did the analyses. A 2010 dollar is worth 1.1916 2020 dollars.
I assumed a 20-year program life, 200 reuses for each engine (rebuild after 100 uses), 100 flights per vehicle before it was retired, and an average fleet size of 50 Starships and 40 1st stages (some Starship 2nd stages are going to left on the moon and Mars so it needs more produced). I ran numbers for two flight rates, 1000 flights/year and 1500 flights/year. These may seem extremely high relative to current launch rates, but remember Starship is completely reusable with quick turnaround so twenty-five or thirty flights/vehicle per year is really conservative.
If I total up the operating cost/flight from the spreadsheets I get about $3.5 M/flight for the booster and $2.4 M/flight for the Starship 2nd stage in 2020 dollars. If we amortize the development cost over the twenty-year life of the program (assuming 1500 flight/year) that adds another $ 76,200 to each flight (2020 $). If we amortize the average unit cost for the hardware over each flight assuming 100 flights/stage and 200 flights/engine I get approximately $3.4 M per flight to depreciate the hardware (2020 $). Our total cost per flight is $3.5 M+ $2.4 M + $0.076 M + $3.4 M = $9.38 M. Assuming Space-X wants to make profit on each Starship launch, why don’t I add about 28% for profit and sell flights for $12M each (after all this is a risky business).This works out to about $100/kg, assuming the 120 mT average payload with an average load factor of 0.80 (this about average for volume constrained launch vehicles).
Based on previous work I know that $100/kg will enable rapid development of LEO business parks and hotels, but how will Starship perform for exploitation of lunar and asteroid resources? To illustrate this, I have included the same Mars/Moon/ Earth Delta-Vs chart I showed last issue as figure 3 below. Using this chart you can trace that the Delta-V to get from Low Earth Orbit (LEO) to the lunar surface is 6.4 km/sec, the Delta-V to get from LEO to Mars surface is 5.2 km/sec, and the Delta-V to get from the Surface of Mars to Earth flyby is 7.0 km/sec. These numbers include no losses, so they are a bit optimistic.
Figure 3 Mars/Moon/Earth Delta-Vs chart
Using the data from figure 3 we see that if the Starship upper stage outfitted for passengers provides a Delta-V of about 6.95 km/sec from LEO with 100 tons of payload, that same Starship, if fully refueled in LEO, could deliver 140 mT to the lunar surface one way, or could deliver 17.3 mT the lunar surface and return to Earth empty. That same basic Starship configuration, if refueled in LEO, could also boost to Mars Transfer orbit (during the Mars Launch Window) and could aerobrake and land propulsively on the surface of Mars with 120 mT of mixed cargo, and if refueled on Mars could boost back to Earth with about 95 mT of cargo. This is very impressive performance, but how do the costs stack up?
Space-X’s plan is to refuel by launching and rendezvousing several Starship tanker-versions with the carrier Starship and transfer propellants in zero-gee. There are operational risks involved multiple propellant transfers, but it should be workable. Assuming Space-X can launch a tanker version of the Starship with 180 mT of transfer propellants into LEO, then a Mars mission requires four refueling launches and a lunar mission requires six refueling launches. If the refueling mission each cost $12M (2020 $) then 120 mT to Mars would cost $60M ($500/kg) and 17.3 mT to the lunar surface costs $98M ($5665/kg). As discussed last week if we start Mars Colonization with 500 people in one launch window then they will require 125 launches (four refueling launches for each of 25 Starships to Mars) and this costs about $ 1.5 B for ETO transportation alone. This is $3M (2020$) transportation costs for each colonist, and to that we need to add the purchase costs of the Mars infrastructure (habitats, factories, mining equipment, greenhouses, etc.). Obviously, some organization back on Earth needs to fund the colonization of Mars, and just maybe that’s what the Mars Society is all about.
The lunar delivery option has issues. Starship does great as a delivery device to the moon but needs refueling on the moon to become a cost-effective system. A better solution would be the system described in Chapter 8 of my book. Imagine a Starship transferring propellants and cargo to an Aerobraked Orbit Transfer Vehicle (ABOTV) in LEO which transports the cargo to Low Lunar Orbit which in turns transfers the cargo to a Reusable Lunar Excursion Vehicle (RLEV) which lands it on the lunar surface. The entire system is reusable and only requires one Starship launch to deliver 40 mT to the lunar surface.
Thanks for reading.