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Since both Kerosene (RP-1) and liquid hydrogen (LH2) continue to be important liquid fuels used with liquid oxygen (LOX), something can be learned by comparing how they are used. This is covered well within questions and answers here this stackexchange. One recent question piqued my interest.

In the Saturn V, RP-1 was used in the massive first stage, but the 2nd and third stages used LH2.

In this answer to the question, it's pointed out that the low density of the Hydrogen will have a penalty on the structure (the giant LH2 tank?) somewhat increased drag (again the giant LH2 tank?) and would require either a larger chamber size, or possibly more engines.

If the Saturn V did have to use LH2/LOX in the first stage, roughly how much different would it look? Just a little bit taller and wider, or really totally different?

How much larger would the total LH2/LOX storage on the ground be? 5x? 25x?

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  • $\begingroup$ What engines would it hypothetically use? I don't think there were really big LH2/LO2 engines then. As you know, Isp is key to answering this question. $\endgroup$ – Organic Marble Aug 3 '16 at 13:08
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    $\begingroup$ There'd probably be more changes due to reworking the engines. You'd probably need a few M-1's or 10-15 SSME-class engines. $\endgroup$ – DylanSp Aug 3 '16 at 13:11
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The requirements of the first stage are that it deliver about 3340 m/s of delta v to a 690 ton payload (the upper stages and spacecraft), with an initial thrust-to-weight ratio of at least 1.16:1.

The best candidate for a first-stage hydrogen engine in the Saturn era would be the never-completed M-1. At sea level, it would be much less powerful than the F-1, but with better specific impulse - 310 seconds vs 263. Without going into too much detail, the result is that the first stage carries 1730 tons of LH2/LOX rather than 2160 tons of kerosene/LOX. However, depending on the exact mixture ratios in use, kerosene/LOX is about 3.5 times denser than LH2/LOX, so even with less fuel mass, the stage needs to get a lot bigger. If the 10 meter diameter is retained, the stage gets stretched from 42m to 92m -- a very long and skinny stage. More reasonable would be a 12-meter diameter, 63 meter long first stage. The overall rocket, all-up for an Apollo J mission, masses 2593 tons instead of 2970 tons. It might look something like this:

enter image description here

The drag penalty wouldn't be terribly severe. About 50 m/s of the Saturn V's total potential is lost to drag; the larger diameter stage would probably incur another ~25m/s hit, but I don't want to go back and recalculate.

To achieve the initial TWR requirement, 8 M-1s are needed, granting 1.21:1 TWR. As fuel mass was consumed and specific impulse (and thus thrust) increased, 2 or 4 of them would likely be shut off over the course of the burn to limit acceleration for crew comfort, with the remainder left running til fuel-out. Acceleration-by-time curves are shallower for higher Isp engines, so we may have a less efficient ascent than the Saturn V. Engine shutdown might therefore be delayed to make up some speed; this could mean a higher peak acceleration than Saturn V.

Total hydrogen carried by the rocket would be about 4x that of the Saturn V; presumably that would quadruple the ground storage requirements.

Bear in mind that even though this rocket masses less in total, it probably costs much more because of first stage construction and transport logistics, engine complexity, and hydrogen handling, and on that basis it's somewhat inferior to the Saturn V.

Another possibility would be using 16x SSME instead of 8x M-1. This probably couldn't have flown until the 1980s, but the sea level specific impulse is far better, 366s instead of 310s. This would further reduce the first-stage fuel mass but probably add a lot of cost -- the entire shuttle program only built 42 of those engines.

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  • $\begingroup$ Why shut off two of the engines? $\endgroup$ – uhoh Aug 3 '16 at 16:20
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    $\begingroup$ Limiting the acceleration for crew comfort. Saturn V shut down the center engine late in the burn of the 1st and 2nd stages for this reason. $\endgroup$ – Russell Borogove Aug 3 '16 at 16:24
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    $\begingroup$ Yep, this just illustrates why Saturn V didn't have a hydrogen first stage, and why it's very common practice to have solid rocket boosters on launchers, paired with kerosene or hydrogen -- they're cheap, compact, and high-thrust. $\endgroup$ – Russell Borogove Aug 4 '16 at 13:25
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    $\begingroup$ The mass of insulation is accounted for in my design using the assumption that the tankage proportions are similar to the second stage. This is conservative; insulation scales with surface area rather than volume. (The first stage volume and dimensions are rough estimates only.) $\endgroup$ – Russell Borogove Aug 5 '16 at 15:59
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    $\begingroup$ I believe that's an error in Wikipedia; that's the correct thrust for the upper stage version firing in vacuum. Astronautix.com has much more detail and claims the first stage version would be 3865kN (310s Isp) at sea level and 5336kN (428s) in vac due to use of a shorter nozzle. astronautix.com/m/m-1.html $\endgroup$ – Russell Borogove Oct 20 '16 at 14:29

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