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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

uhoh
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Krzysiek
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    It's not as simple. Larger tanks have a better surface-to-volume ratio, but they also need thicker walls for several reasons. – leftaroundabout Oct 11 '23 at 17:44
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    You might be interested in the charts on pages 5 and 6 of this NASA document: https://ntrs.nasa.gov/api/citations/20090037584/downloads/20090037584.pdf – Organic Marble Oct 11 '23 at 21:32
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    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). – TLW Oct 12 '23 at 14:20
  • What does "better" mean in this case? – Stef Oct 13 '23 at 10:29
  • @Stef it means "higher", of course. – RonJohn Oct 14 '23 at 11:19
  • @RonJohn Sorry if I wasn't clear. I was asking for clarification from the OP, not for a guess by someone else. – Stef Oct 14 '23 at 23:35
  • @Stef "higher" isn't a guess, it's many decades of experience as a native speaker of English. – RonJohn Oct 15 '23 at 00:25
  • Where do the Answerers below get the idea that more capacious tanks requiring thicker walls will significantly drag down the mass ratio due to the square cube law?

    Of course thicker walls matter, but by exactly how much?

     – Robbie Goodwin Oct 16 '23 at 22:12

3 Answers3

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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.

Russell Borogove
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    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. – Ryan C Oct 12 '23 at 14:34
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    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. – Charles Staats Oct 12 '23 at 16:35
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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.

Darth Pseudonym
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  • I thought the same way, but I have been searching for information on various rocket tank thicknesses, and I didn't find a good example that would confirm it.

    For example, starship has a diameter of 9 meters, and its tanks have a thickness of only 4 millimeters. A booster without pressure inside can't even support its own weight.

     – Krzysiek Oct 11 '23 at 18:15
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    @Krzysiek " booster without pressure inside can't even support its own weight. " True of some, but not most. – Organic Marble Oct 11 '23 at 18:22
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    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. – Darth Pseudonym Oct 11 '23 at 18:33
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    @DarthPseudonym: Falcon 9 uses aluminium-lithium tanks, Starship and Super Heavy is stainless steel. – Jörg W Mittag Oct 11 '23 at 20:01
  • Did they used to use CF and changed it later? I'm sure I remember a spacex rocket several years ago that sprung a fuel leak on the ground and one of the going theories was CF delamination on the tank. – Darth Pseudonym Oct 12 '23 at 05:31
  • I guess let's just say tank materials can vary and have different structural characteristics, so you can't necessarily compare the thickness of rocket A's tank to the thickness of rocket B's tank on a one-to-one basis. – Darth Pseudonym Oct 12 '23 at 05:33
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    @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. – Michael Oct 12 '23 at 07:57
  • @DarthPseudonym you're thinking of the AMOS-6 mission. The tank that exploded was indeed carbon fibre (a composite overwrapped pressure vessel), but it was only a small helium tank. These are at much higher pressure than the main tanks, which increases the advantages of composites over metal. – leftaroundabout Oct 12 '23 at 14:19
  • @DarthPseudonym: Would there be any particular difficulty designing a rocket with an exoskeleton that could supply structural support prior to pressurization? Such support wouldn't be needed once the rocket started its liftoff (which would only happen when the tank was pressurized), and having it on the exoskeleton would mean it had to be included in ground transport vehicles' weight budget, but no fuel would need to be spent accelerating it. – supercat Oct 12 '23 at 14:52
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    @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. – Charles Staats Oct 12 '23 at 16:29
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    @supercat I'm not any expert on the matter but I would guess that support structures would have to be extremely accurately fitted, which is a potential source of error, and the tanks themselves are light but very difficult to build and work with due to the thinness of the walls so the savings may not actually add up to much. I mean, how many hundred pounds of extra lift capacity would you really be able to get that way? – Darth Pseudonym Oct 12 '23 at 20:42
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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.

Peter - Reinstate Monica
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