I want to calculate the size in cubic meters of Starship's propellant tanks. The only figures for LOX I can find are at −183 °C. 1141.7 kg/m³ at −183 °C. Could somebody please calculate it at −206 °C, the temperature SpaceX uses? (Perhaps sub-cooled is the proper term.)
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The US National Institute of Standards and Technology (NIST) is pretty useful for that. They offer a free tool that allows you to calculate a lot of useful properties of multiple interesting compounds including e.g. oxygen, nitrogen, helium, hydrogen, methane and propane:
https://webbook.nist.gov/chemistry/fluid/
E.g. we can plot the density of Oxygen at 0.3 MPa / 3 bar and a temperature betwen 54 K and 90 K
For -206 °C / 67 Kelvin we can get:
Temperature (K) 67.132
Pressure (MPa) 0.30000
Density (kg/m3) 1250.4
Volume (m3/kg) 0.00079972
Internal Energy (kJ/kg) -172.29
Enthalpy (kJ/kg) -172.05
Entropy (J/g*K) 2.4445
Cv (J/g*K) 1.0330
Cp (J/g*K) 1.6772
Sound Spd. (m/s) 1088.2
Joule-Thomson (K/MPa) -0.36071
Viscosity (uPa*s) 451.36
Therm. Cond. (W/m*K) 0.18464
Phase liquid
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2$\begingroup$ Excellent answer! There are some other scrappy bits of information in Does the NK-33 engine require subcooled kerosene so cold that it turns to wax? $\endgroup$ – uhoh Dec 13 '19 at 8:52
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1$\begingroup$ Thanks for the useful link to the property tables. $\endgroup$ – Organic Marble Dec 13 '19 at 14:50
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1$\begingroup$ Thank you for the thorough answer, and the link. The only calculator I found did not calculate such a low temperature. Now I can calculate it for methane myself. (Will post it here.) You used 3 bar; do you have any idea what the Starship tank pressure will be? Or the Falcon 9 tank pressure? The only figure I could find, 10 bar, is 5 years old. $\endgroup$ – SpaceInMyHead Dec 13 '19 at 17:40
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1$\begingroup$ @SpaceInMyHead To be honest I'm not sure on that but we can find a reasonable lower limit by observing that they probably don't want buckling in their tanks so the total force on the bulkheads will probably be bigger than total force of the engines. For superheavy that would mean 72,000 kN/(9m*9m*pi/4) = 11.3 bar as lower limit. This pretty much scales linear with height (for the same type of fuel at least). For Falcon 9 we get around 7 bar. $\endgroup$ – Christoph Dec 16 '19 at 11:40
