Well this was assuming low risk open cycle engines like F-1 and H-1 which 4
stages would have been necessary, maybe 4-1/2.
The Russian N-1 had 4 stages and used closed cycle NK-33 engines.
Ken
On Sat, Apr 29, 2023 at 3:33 PM Henry Spencer <hspencer@xxxxxxxxxxxxx>
wrote:
On Fri, 28 Apr 2023, roxanna Mason wrote:
Nova, with eight F-1 engines, may have become a reality if LH2 wasn't
adopted because an all kerosene vehicle like Russia's N-1, would have
needed a 4th stage to get to escape with any usable payload.
Mmm, I don't think that's necessarily true. If all that effort hadn't
gone into LH2 upper-stage engines, there would surely have been more work
on high-performance kerosene upper-stage engines. (Proton, roughly the
Russian contemporary of the Saturn IB, had staged-combustion engines
throughout -- NTO/UDMH for the three main stages, LOX/kerosene for the
optional maneuvering stage.)
Cautiously figure the S-IC as the first stage: call the average F-1 Isp
280s (actual numbers: sea-level 263s, vacuum 304s), and the stage mass
ratio was 14:1 (yes, 93% propellant at ignition -- impressive for a
conservative design from the Von Braun Iron Works :-) ). Add a
LOX/kerosene second stage with the same mass ratio but the vacuum Isp of
Proton's maneuvering stage, 263s; that Isp may be a bit optimistic, but
the mass ratio should be a bit pessimistic given more aggressive design
(the Titan II first stage was 25:1...) and less need for high thrust, so
call it a wash. Split a 9km/s delta-V 4/5, and I get 74t to LEO -- about
the same as the N1's three stages. (Korolev didn't have the manufacturing
capability to match the Saturn V's big cylindrical tanks, hence the
mass-inefficient spherical tanks on the N1.)
A TLI stage with the same mass ratio and Isp as the second (could probably
do a bit better on both) would push 27t to escape. That's a bit over half
of a complete Apollo, but close to twice Korolev's LOK/LK.
If you insist on a full Apollo :-), add a bit of EOR: a second launch
carries up a big drop-tank set for the TLI stage.
Henry