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Do larger rockets tend to have a better mass ratio due to the square cube law? I mean, larger tanks have a better surface-to-volume ratio, so their weight-to-volume should be improved

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    $\begingroup$ It's not as simple. Larger tanks have a better surface-to-volume ratio, but they also need thicker walls for several reasons. $\endgroup$ Commented Oct 11, 2023 at 17:44
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    $\begingroup$ You might be interested in the charts on pages 5 and 6 of this NASA document: ntrs.nasa.gov/api/citations/20090037584/downloads/… $\endgroup$ Commented Oct 11, 2023 at 21:32
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    $\begingroup$ There are aspects where the square-cube law acts in your favor as you scale up (surface-to-volume ratio, maximum combustion chamber pressure, fluid flow, etc), and aspects where the square-cube law acts in your detriment (overall structural strength, notably). $\endgroup$
    – TLW
    Commented Oct 12, 2023 at 14:20
  • $\begingroup$ What does "better" mean in this case? $\endgroup$
    – Stef
    Commented Oct 13, 2023 at 10:29
  • $\begingroup$ @Stef it means "higher", of course. $\endgroup$
    – RonJohn
    Commented Oct 14, 2023 at 11:19

3 Answers 3

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It doesn't really work that way, because a tank isn't just a volume; the tank itself is a structural member that needs to support the mass of the material contained inside it (and in most cases the tank also partially supports the rocket itself, so add in the mass of the upper stages and the aerodynamic forces). A larger tank needs walls that are proportionally thicker to keep its structural integrity.

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    $\begingroup$ @Krzysiek " booster without pressure inside can't even support its own weight. " True of some, but not most. $\endgroup$ Commented Oct 11, 2023 at 18:22
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    $\begingroup$ It's fair to say that many rockets depend on their tanks' pressurization for structural support, but IIRC usually that's more for stiffening against aerodynamic side loading rather than weight. You do want to be able to set the rocket upright prior to fueling, after all. $\endgroup$ Commented Oct 11, 2023 at 18:33
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    $\begingroup$ @DarthPseudonym: Falcon 9 uses aluminium-lithium tanks, Starship and Super Heavy is stainless steel. $\endgroup$ Commented Oct 11, 2023 at 20:01
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    $\begingroup$ @DarthPseudonym: IIRC Starship was originally planned with carbon composite tanks but then they switched to stainless steel because of easier/faster manufacturing and better thermal properties. Rocketlab uses carbon composites in their Electron rocket. $\endgroup$
    – Michael
    Commented Oct 12, 2023 at 7:57
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    $\begingroup$ @supercat: Given how efficient balloon tanks are, and how rarely they are used nevertheless, I imagine there must be significant obstacles to solving the problem with an exoskeleton, otherwise they would be in use already. But I am also curious what those obstacles are. $\endgroup$ Commented Oct 12, 2023 at 16:29
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The walls of pressurized tanks in particular need to get thicker as the pressurized volume increases, so the tankage mass still increases pretty close to linearly with the tankage volume, and tankage is most of the mass of an orbital launcher.

Larger rockets do still have a few scaling advantages. Avionics doesn't scale up with rocket size; cable runs scale 1-dimensionally; aerodynamic drag is generally proportional to cross section and to surface area rather than to volume, etc.

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    $\begingroup$ another possible advantage is that high-accuracy inertial navigation systems are generally much larger and heavier than less accurate ones, so a good one won't take up as large a fraction of the weight budget of a heavier rocket. $\endgroup$
    – Ryan C
    Commented Oct 12, 2023 at 14:34
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    $\begingroup$ IIUC the required sturdiness is based on the depth rather than the volume of the tank. So theoretically, you could allow for thinner tanks by making short, stubby rockets. But then you would drastically increase the cross-sectional area and consequently the drag. $\endgroup$ Commented Oct 12, 2023 at 16:35
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Unfortunately, it works the other way around: Structural stability requirements grow with the mass and hence the volume and hence the cube of the linear size, while the means for stability are cross-sections of structures and hence only grow with the square.

At some point, like the large dinosaurs, a rocket would not even be able to stand, let alone accelerate and withstand dynamic loads. (This is the primary reason we don't have space elevator towers.)

The main advantage of larger rockets is a lower air resistance per mass, which probably means that very small rockets have a disadvantage in the atmospheric phase of the ascent.

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    $\begingroup$ There are many other disadvantages of smaller rockets, not just air resistance - for instance max combustion chamber pressure is smaller in a scaled-smaller rocket, resulting in a lower specific impulse. $\endgroup$
    – TLW
    Commented Oct 12, 2023 at 14:18
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    $\begingroup$ I'd be curious which one of the simple truths in this answer did not find the approval of the audience. $\endgroup$ Commented Oct 12, 2023 at 14:50
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    $\begingroup$ "The only advantage of larger rockets is a lower air resistance per mass" is incorrect and hence not a "simple truth", for one. $\endgroup$
    – TLW
    Commented Oct 12, 2023 at 23:35
  • $\begingroup$ @TLW Ah, the avionics and cables. Well, true. $\endgroup$ Commented Oct 13, 2023 at 5:46

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