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A problem that frequently shows up is estimating the mass of the propellant tanks of some hypothetical rocket configuration. This need arises from the important role of the dry mass in a rather famous equation.

Two assumptions that are often made:

  1. Tankage mass is proportional to propellant mass. ("the mass fraction is scale independent")
  2. Tankage mass and propellant mass have a square-cube relationship.

The actual values obviously differ both by propellant type, and by rocket configuration (launch vs. deep space). But the problem is still:

How well do the two assumptions above compare to real-world data?

And if those don't fit well at all, what better heuristic can be made?

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  • $\begingroup$ Doesn't propellant volume play a role also? The development of cryogenics was essential to the success of the Saturn program, as using gaseous propellants would have made the tankage impossibly big $\endgroup$
    – Ludo
    Oct 8 '20 at 9:11
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    $\begingroup$ @Ludo Implied by "propellant type". Gaseous oxygen is something else than liquid oxygen. $\endgroup$ Oct 8 '20 at 9:15
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    $\begingroup$ I would predict a square/cube relationship if tanks were spherical. Once your tank stops being spherical, you can only increase the propellant mass by making the tank longer. Thus, each marginal increase to propellant is effectively a disc of propellant surrounded by a ring of tank, which is a constant ratio no matter how long the tank grows. $\endgroup$ Oct 8 '20 at 19:22
  • $\begingroup$ RO/RP-1 dev team, is that you? $\endgroup$ Oct 10 '20 at 22:01
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NASA TM-78661 TECHNIOUES FOR THE DETERMINATION OF MASS PROPERTIES OF EARTH-TO-ORBIT TRANSPORTATION SYSTEMS agrees with the "proportional" method

Main propulsion system tank mass, if non integral, is much more sensitive to vehicle physical size and varies as Lr3 or directly as propellant mass since tank mass is approximately equal to a constant times propellant volume for any given shape.

(Lr is the vehicle reference length, emphasis mine)

This slide from Mass Estimating Relations shows linear fits that appear to be based on real world examples of tanks (the points on the graph), although frustratingly they don't say what tanks were used in the analysis. They derive slopes of 9.09 kg/m³ for hydrogen and 12.16 kg/m³ for other propellants. (It also references TM-78661)

enter image description here

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    $\begingroup$ Nice! They even offer two concrete such values: 9.09 kg/m³ (hydrogen), 12.16 kg/m³ (other propellants) $\endgroup$ Oct 8 '20 at 13:05
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    $\begingroup$ @SE-stopfiringthegoodguys yes, that presentation looks pretty helpful. Some of the other references might be useful as well. $\endgroup$ Oct 8 '20 at 13:05
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    $\begingroup$ Reading further, the presentation still goes into square-cube territory with insulation for cryogenic propellants (2.88 kg/m² for LH2, 1.123 kg/m² for LOX) $\endgroup$ Oct 8 '20 at 13:08
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    $\begingroup$ @SE-stopfiringthegoodguys that's for the mass of the insulation, no? Which makes sense because it would be applied to the surface. $\endgroup$ Oct 8 '20 at 13:09
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    $\begingroup$ This 2009 study uses "empty mass less engines" rather than "tank mass", so will include insulation as well as structural mass, equipment, etc, but does have details on a stage-by-stage basis. $\endgroup$
    – Andrew
    Oct 8 '20 at 16:29

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