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What could the link be between the «white performance bars show» below and the «actual size of the rocket»?

The quote below seems to imply there is one. But isn't that white scale purely arbitrary? It’s my current understanding that SpaceX could have increased the scale of the bar across the board so that Saturn V performance would also be above its height.

Vehicles by performance source page: 28 http://www.spacex.com/sites/spacex/files/mars_presentation.pdf

The white bars show the performance of the vehicles. In other words, the payload to orbit of the vehicle. What it represents is what the size efficiency of the vehicle is. And mostly including ours that are currently flying, including those; the performance bar is only a small percentage of the actual size of the rocket. With the interplanetary system initially to be used for Mars, we have been able to, we believe, massively improve the design performance. It's the first time the rocket performance bar will exceed the physical size of the rocket. -Elon
Source: https://diyhpl.us/wiki/transcripts/spacex/elon-musk-making-humans-a-multiplanetary-species/ or

This link illustrates my point in what is meant about not being correlated (its source is, somewhat ironically, this).

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    $\begingroup$ Good question. Seems like an arbitrary marketing ploy. $\endgroup$ – Organic Marble Jan 16 '17 at 20:45
  • $\begingroup$ Fully agree with Organic Marble for once. SpaceX is (and not for the first time) talking out of its ass. $\endgroup$ – Innovine Jan 29 '17 at 11:47
  • $\begingroup$ "The white bars show the performance of the vehicles. In other words, the payload to orbit of the vehicle." This is misleading at best. Payload to orbit (what orbit; LEO, GTO, GEO, MEO, ...?) is one relevant performance metric for a rocket. Delta-v capability after initial orbital injection is another. Payload to Earth escape velocity is a third. Ratio of payload capacity to dry or launch mass are another two. I'm sure there are more I'm not thinking of right now. Which of these makes the most sense to use depends entirely on what you are trying to accomplish. $\endgroup$ – a CVn Jan 31 '17 at 9:03
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Completing on Hobbes answer, user sol3tosol4 seems to have nailed my last misunderstanding.
A simple edit to Elon's quote, make it a nice gems of information:

«It's the first time the [ITS] rocket [... payload to LEO]
will [actually] exceed the physical size [dry mass] of the rocket»

Sometimes Elon tries to "dumb down" his explanations by using imprecise language, and when he does people tend to think he's gone crazy. Slide 28 "Vehicles by Performance" didn't make any sense to me either, so I decided to think about it for a while. Here's what I think:

When Elon presented that slide, he was trying to convey three pieces of information, and they got garbled together.

The first piece of information was the appearance and relative size of the different launch vehicles, which was copied over from the previous slide.

The second piece of information was the bar graph, which showed the relative amount of payload each launcher could send to low Earth orbit (LEO). The bar graph doesn't need a vertical scale, because it's relative amount of payload. For example, the proposed ITS (Mars Vehicle) could put up to 550,000 kg into LEO, and the Saturn V could put 135,000 kg into LEO. 550,000 divided by 135,000 is about 4.07, and the bar behind the ITS vehicle is about 4.07 times as high as the bar behind the Saturn V vehicle. The payload numbers are already printed below each launcher, but the bar graph makes the relative payload to LEO of each launcher visually obvious.

The third piece of information, which was not on the slide but which Elon described, was the "maximum payload to LEO" of each launcher, relative to the dry mass (the mass with no payload or propellant loaded) of the launcher. For example the ITS ("Mars Vehicle") can lift 550,000 kg to LEO, and the dry mass of the rocket (from other slides) is 425,000 kg, a ratio of 1.29: for the first time, a rocket can lift into orbit more than its own mass, which is a remarkable accomplishment. From what numbers I can find, the Saturn V could lift 135,000 kg into LEO and had 241,000 kg dry mass, a ratio of only 0.559, the Falcon Heavy a ratio of about 0.67, and the Falcon 9 Full Thrust a ratio of about 0.86 - very good but still less than one. What Elon said about that metric had nothing to do with the bar graph, and it was just a coincidence that the bar for the Mars Vehicle was taller than the picture of the rocket.

What Elon said was "It's the first time a rocket's performance bar will actually exceed the physical size of the rocket". Change that to "It's the first time a rocket's payload to LEO will actually exceed the dry mass of the rocket", and it makes sense. I'd prefer it if Elon didn't try to dumb down the terminology, since it's confusing, but I guess he thinks it's necessary when the audience isn't all rocket designers. At another point in the talk he started to discuss the TEA-TEB ignition fluid used by the Falcon rockets, but changed his mind and skipped that part.

Source r/SpaceX Official Mars Architecture Announcement/IAC 2016 Live Thread - Updates & Discussion from user sol3tosol4

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  • $\begingroup$ The true accomplishment, if even possible, would be when payload mass to LEO exceeds propellant mass required to get it there. $\endgroup$ – Anthony X Jan 28 '17 at 15:32
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    $\begingroup$ @AnthonyX: very unlikely to happen. Some 1400s of ISp at TWR>1 - we don't even have concepts of such engines. OTOH fuel is cheap, rockets are expensive. Improving dry mass to payload ratio is very beneficial. $\endgroup$ – SF. Jan 28 '17 at 22:00
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The white bars are payload in kg. They look roughly proportional to me, so in that sense they're accurate. The size of the white bars vs. the dimensions of the rocket is misleading. The performance bar is one-dimensional. The rockets, on the other hand, grow in 3 dimensions. So when you compare a Falcon 9 to a Saturn V, the performance difference is much larger than the height difference suggests. If you were to do a graph of takeoff weight vs payload weight for these rockets, you'd get a less misleading graph.

Now, there is a correlation between rocket size and performance. But that correlation seems to be fairly linear. Rocket stages of very different sizes have a mass fraction of around 95% (i.e. 95% of the stage weight is fuel).

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