We have seen here the excellent answer to the question: How would the Saturn V have differed if the first stage was also LH2/LOX? What if liquid methane would be used instead of kerosene? Would the tank for methane be smaller than a tank for LH2, but larger than a tank for kerosene?
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$\begingroup$ Related: space.stackexchange.com/questions/3161/… $\endgroup$– AntziAug 8, 2016 at 9:26
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$\begingroup$ For those who haven't seen it - could you embed a link to that answer in the text of your question? I think it's excellent too! The link is http://space.stackexchange.com/a/17633/12102. $\endgroup$– uhohAug 8, 2016 at 14:07
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Methane/LOX specific impulse is only slightly better than kerosene/LOX and it's about 25% less dense. In this case I think stretching the first stage would be more likely than fattening it; furthermore it might be possible to use a common-bulkhead tank instead of the separate tanks of the S-IC, (the temperature differential between liquid methane and liquid oxygen being relatively modest) so the external stage dimensions might not change much at all.
Methane wasn't popular as a rocket fuel at the time, of course, so there wouldn't be any viable candidates for engines to power the stage.
answered Aug 8, 2016 at 14:08
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$\begingroup$ @Russell Borogove can you describe with an example,let say if the F-1 engine would have used methane(in theory) and had the same thrust,but a higher Isp(an Isp typical of methane engines).For example since CH4 is less denser the 10.6m 1st stage in diameter would have been 30% taller (remember 1st stage dry mass will be heavier since is taller),but since higher Isp gives better performance,it would have less fuel so it would be 25% taller for the same performance with a normal Saturn V. Calculating height by calculating performance with the new Isp. $\endgroup$ Oct 11, 2016 at 18:54
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$\begingroup$ As I noted, it would make sense to use a common-bulkhead tank, so I'd have to do a lot of calculation of ellipsoid volumes, and make up specifications for a 1960s methane engine, and the net result would be some arbitrary value for the length of the stage that wouldn't tell anyone anything more interesting than "it'd be a little bit longer than the real first stage, but not a lot." It's not worth my time, and given some of the things I spend my time on, that's saying something ;) $\endgroup$ Oct 11, 2016 at 19:45
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$\begingroup$ Ok when you have those necessary elements,data or real values that would have those rocket part which will be different in methane lox stage, than you can complete your answer. But please don't forget ;) $\endgroup$ Oct 11, 2016 at 20:58
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$\begingroup$ They couldn't stretch the first stage much more and still fit in the VAB. $\endgroup$– JoshuaDec 7, 2016 at 19:36