Issue 039 - Rocket reusability - Manufacturing mass
How much rocket hardware does reusability save?
Chinese startup LandSpace successfully recovered the first stage of its Zhuque-3 orbital rocket this week. The 66-meter stainless-steel rocket is designed so its first-stage booster can eventually be reused up to 20 times.
The problem
Estimate how much rocket hardware would have to be manufactured and discarded if 20 Zhuque-3 launches used a fresh first-stage booster every time, compared with reusing one booster for all 20 launches.
Use the result to put the savings in physical context: is booster reuse saving something closer to the mass of a few cars, a commercial airplane, or an entire building's worth of manufactured material over 20 launches?
As an additional scale check, Zhuque-3 can carry about 14.2 metric tons to low Earth orbit in its expendable configuration.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
This is kind of cheating, but one of the ways I imagine scale is by using memory pegs for each order of magnitude. At the 10^6 kg magnitude, I remember the launch mass of the Space Shuttle stack, boosters plus shuttle, and I imagine Zhuque-3 being somewhere near one-third the mass of the Space Shuttle plus launch rocket. That would put it around 3 x 10^5 kg.
If we are only concerned with the reusable booster portion, I imagine that accounts for at least two-thirds of the mass of the full Zhuque-3 launch structure, or about 2 x 10^5 kg.
Zhuque-3 launch mass guess ~= 3 x 10^5 kg
booster wet mass guess ~= (2/3) x 3 x 10^5
~= 2 x 10^5 kgThe reality check indicates 14.2 metric tons could be carried to orbit, which is something like 8% the mass of the booster. That feels about right given how much the mass of fuel in the booster accounts for overall rocket mass.
Calibration Score
Matt's Calibration Score: 70 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 10/30. Booster wet mass was reasonable, but dry hardware mass was not carried through in the first pass.
Model: 30/30. Comparing expendable booster hardware with reusable booster hardware is the right model.
Math: 10/10. The arithmetic was clean once the dry-mass step was supplied.
Result: 20/30. The inferred hardware-saved estimate would have landed within an order of magnitude.
Grounding facts
The 14.2-ton expendable payload figure is useful for perspective. If the saved hardware is about 840 tons, then across 20 launches:
hardware saved / payload per launch ~= 840 tons / 14.2 tons
~= 6 x 10^1 payloadsIn other words, the dry booster hardware not thrown away over a 20-flight lifetime could weigh on the order of 60 Zhuque-3 expendable LEO payloads. That is one reason reusability changes launch economics even before considering factory time, engine production, inspections, supply chains, launch cadence, and learning curves.
After checking sources
Check and recalibrate
Matt's scale for the wet booster was pretty good. The missing step is that reusability does not save the propellant burned on each launch. It saves the dry first-stage hardware: engines, tanks, structure, landing systems, avionics, plumbing, and thermal-protection or recovery hardware.
Public launch summaries put Zhuque-3's liftoff mass around the mid-500-ton range. Use 5.5 x 10^5 kg as a rounded full-stack wet mass. For a two-stage rocket, the first stage often dominates the wet mass, so assume roughly 75% to 85% of the full stack is first stage. Use 80%:
rocket wet mass ~= 5.5 x 10^5 kg
first-stage share ~= 8 x 10^-1
booster wet mass ~= 5.5 x 10^5 x 8 x 10^-1
~= 4.4 x 10^5 kgNow remove propellant. Rockets are mostly propellant. Falcon 9's first-stage public mass figures are about 25.6 tons empty and 395.7 tons of propellant, meaning dry hardware is roughly 6% of first-stage wet mass. Zhuque-3 is stainless steel and reusable, so a dry fraction around 8% to 12% is a reasonable Fermi range. Use 10%:
dry booster mass ~= 4.4 x 10^5 kg x 1 x 10^-1
~= 4.4 x 10^4 kg
~= 44 tonsIf 20 launches require 20 fresh boosters in the expendable case but only one booster in the reusable case, the ideal hardware saving is 19 dry boosters:
hardware saved ~= (20 - 1) x 4.4 x 10^4 kg
~= 8.4 x 10^5 kg
~= 840 tonsA reasonable central answer is therefore about 8 x 10^5 kg, or 800 metric tons, of manufactured first-stage hardware avoided across 20 launches. A broad credible range might be roughly 4 x 10^5 to 1.2 x 10^6 kg, depending on the actual booster wet mass and dry mass fraction.
That is not the mass of a few cars. It is also much more than one commercial airplane's empty mass. It is closer to a small building's worth of manufactured metal, engines, tanks, and machinery, avoided by making one booster survive many flights.
Post-check reflection
Matt's reflection
Looks like I was mostly on point, but did not take the additional step of estimating the hardware mass if fuel was removed. I think I would have ended up near the correct answer after doing so, since I was aware that fuel made up about 90% of launch mass.
My guess at 2 x 10^5 kg booster launch mass would have become about 2.2 x 10^4 kg hardware mass per launch, and saving 19 of those, since we still need to manufacture one, would have given me a guess of about 4.2 x 10^5 kg of hardware saved. With the answer nearer to 10^6 kg, that puts me within an order of magnitude and just under half the reference number. Not bad.
These news items are important because booster reusability is central to making entering orbit, and exiting it, much more economically feasible than it would be if each launch required a new booster.
Recommended memory peg
For reusable rocket problems, remember: orbital boosters are mostly propellant. A first-stage dry mass around 5% to 10% of wet booster mass is a good starting peg, and hardware saved by reuse = avoided boosters x dry booster mass.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.