Saturn V had RP-1/LOX 1st stage with 5 F-1 rocket engines. The 2nd and 3rd stage used LH2/LOX J-2 rocket engines, 5 and 1 respectively. At that time NASA had an advantage to launch heavy payloads because it was successful in the production of LH2/LOX rocket engines. What situation would it be if even the 2nd and 3rd stages of Saturn V would have been with RP-1/LOX engines? I am speaking for that situation where the 1st stage remains the same. What configuration would the Saturn V have had for the 2nd and 3rd stages (with what rocket engines, how many of them, what amount of fuel in their tanks, or even a possible 4th stage) and what performance? Probably it would have lower payload values and would be a shorter rocket since RP-1 is denser than LH2, but what would be the values and how would it look like?
If we hold the loaded masses of the Saturn V's three stages constant, but switch to kerosene tankage, engines, and propellants for the upper stages, we get a rocket that can send perhaps 55 tons to LEO and 9 tons translunar -- not enough for a crewed landing mission, but certainly enough for a flyby and possibly a crewed lunar orbit mission. Two launches and an Earth orbit rendezvous could possibly get a bare bones, Soyuz/LK lander mission, and three launches and EOR could probably pull off an Apollo CSM/LM mission.
First stage remains a 5-engine S-IC, 2148 tons propellant, 132 tons dry.
Second stage would be 447t propellant, 34t dry, 1x F-1 engine.
Third stage would be 106t propellant, 9t dry, 1x H-1 engine.
For translunar flight, the third-stage H-1 would have to be modified to provide restart capability; it would burn once to get into LEO and then again for TLI, like the J-2 on the Saturn V third stage.
All-up launchpad mass would be 2885 tons for the translunar mission, 2931 tons for 60t to LEO.
The upper stages would be much more compact than on the Saturn V, as you note. The second stage would be about the size of the Saturn V third stage, in fact, so the stack could look rather like the proposed Saturn INT-20 configuration.
(Amended tonnages to reflect more conservative fuel tank mass fractions.)
According to my spreadsheet estimates, a four-stage kerosene rocket 3 times the size of Saturn V could do it.
The translunar stage, S-IV-K, is 138 tons propellant, 12 tons dry, 47 tons payload (Apollo CSM and LM). 1x H-1 engine (as used on the Saturn 1B).
Third stage, S-III-K, 465 propellant, 35t dry, 1x F-1 engine.
Second stage, S-II-K, 1674t propellant, 126t dry, 3x F-1 engines.
First stage, S-I-K, 6392t propellant, 408t dry, 16x F-1 engines.
All-up mission launch mass of this "Saturn XVI" would be 9297 tons.
First 3 stages produce ~9600 m/s of delta-v, taking the beast to a 185km circular orbit. Fourth stage produces ~3400 m/s to send the spacecraft to the moon.
The mass could be brought down substantially with more optimized engines; both the F-1 and H-1 were designed as first-stage engines. Larger nozzle extensions, particularly on the 3rd and 4th stages, would improve the specific impulse, without requiring all-new engine designs. With an "H-1V" producing 320s ISP and an "F-1V" producing 337s, total launch mass could be brought down to 6820 tons or so, with "only" 12 engines on the first stage.
Both my answers are, obviously, merely rough Kerbal-style feasibility estimates.
(Amended tonnages to reflect more conservative fuel tank mass fractions.)
Yet another approach to the answer is to look at the Soviet N-1 rocket, which evolved in fact to attempt a Soviet version of the Lunar Orbit Rendezvous strategy accomplished by Apollo. The Soviets lacking a good developed hydrogen engine, it was all kerlox.
Their approach took several measures to greatly lighten the spacecraft involved, a version of Soyuz and a lander called LK that relied on a kerosene-oxygen "crasher" to take the LK down from orbital speed to a half kilometer or so above the landing site--and more importantly than losing altitude, took off most of the orbital speed. Thus the LK itself was a single stage unlike the American LM, basically a smaller analog of the LM ascent module with extra fuel for final descent, hovering and landing. (It also had a complete backup engine in case its main engine failed, of the same thrust but with no throttle ability, for abort or as a backup ascent engine). The LK could only handle one cosmonaut, for a much briefer stay on the lunar surface, and upon returning to the Soyuz in orbit (and to board it to descend) the cosmonaut had to spacewalk--no transfer tunnel.
Using more efficient pumped kerosene-oxygen engines than the American pressure fed hypergolics, the Soviet approach required a lighter stack to be launched to the Moon, but even so due to the lower efficiency of kerosene compared to hydrogen, the fourth stage that would serve to send that stack to encounter the moon had to be larger in proportion. Counting the kerosene-oxygen "D" block as a fifth stage, the attempt to get the Lunar mission done with a single launch was very marginal despite the fact that the five-stage rocket outmassed the Saturn V by a considerable margin. To try to lighten it enough to enable the mission they took all sorts of dubious weight-saving expedients, such as removing most of the telemetry. The earliest version of N-1 was not expected to boost more than 45 or so tons to low Earth orbit. Between adding engines, raising the dimensions a bit, and these weight trimming and propellant maximizing expedients, it was to put 95 tons into LEO in the Lunar version that was tested several times. Each attempt led to failure, and had they succeeded in getting a manned Lunar stack on the fourth stage, to inject it on to the Moon, I fear the corner cutting would have spelled disaster sooner or later, probably sooner.
Had they gone over to a two-launch strategy and made fewer heroic efforts to maximize payload and made it somewhat more robust, I think they could have pulled off a Moon landing with margin to spare--indeed the escape/survival modes enabling the crew to return despite major failures might have been far superior to Apollo with a two launch plan. An Alternate History timeline I much enjoyed was written several years ago on this premise.
But looking at the huge size, numerous engines and many stages of the N-1 as built, compared to a much more meagre tonnage to low lunar orbit, illustrates the huge advantage the Americans enjoyed in developing hydrogen upper stages. With kerosene alone, it would have been possible to achieve greater efficiencies than our program accomplished with that fuel mix--the Soviet pumped kerosene engines in their N-1/LK program were all notably more efficient than the best American kerosene engines, though none came close to matching the sheer mighty thrust of the US F-1 engine.
But even so, with markedly superior ISP kerosene engines, the Soviets, or Americans foregoing development of hydrogen engines, would have had to launch a much greater tonnage off of launch pads to achieve comparable results in terms of a moon landing. If the goal were merely to build space stations or the like, the tradeoff is much more reasonable.
But then again, one disadvantage hydrogen burning rockets have is the difficulty of storing the hydrogen for a long time. In space, it is not that difficult to keep LOX liquid and stored for a long time, but hydrogen boils off (or the tanks explode!) Centaur has demonstrated that one can retain enough fuel after several days to be worthwhile, so in principle the Apollo stack might have been braked to low Lunar orbit insertion by such a stage with some savings in weight, but the design was frozen in the early sixties around using nothing but pressure fed hypergolic engines after TLI, and TLI would be initiated just hours after reaching the parking orbit.
So, the drawback of hydrogen boiling off is not a problem if one is using the hydrogen to put something into low Earth orbit or plans to use it pretty soon after that. Thus to argue ker-lox would be better than using hydrogen upper stages one would have to look closely at the structural fixed mass penalties that hydrogen storage imposes. But with good design these are not terrible; look at the STS fuel tank, that massed 36 tons dry but held something like 750 tons of oxygen and hydrogen. Or, the S-IV third stage of the Saturn V (also the second stage of Saturn 1B) which massed 9 tons or so dry, including the engine, but held 120 or more tons of propellant-these are dry weight fractions well under 1/10, while few ker-lox or hypergolic stages actually used were dramatically lower than that.
Another penalty of using hydrogen is that the ratio of thrust to engine weight is also inferior to what a similar state of the art investment can achieve with less energetic but cooler-burning and denser propellants. The Shuttle SSME had a good thrust/weight ratio compared to first generation kerosene or hypergolic engines, but this was accomplished by heroic and expensive to develop, build and maintain methods involving extremely high pressures and temperatures. The tradeoff between efficiency and thrust is inherent in the basic physics; to get a faster exhaust one operates at higher temperatures; to get decent thrust against high sea level atmospheric pressure one uses high pressure; a lower energy per kilogram propellant mix burns cooler and trades off higher mass flow for lower power for the same thrust. If thrust is the goal, it often makes sense to burn something cooler and use simpler, cheaper machinery.
Bottom line is, that initial boosting off the launch pad, the job of a first stage, is a task accomplished by use of massive thrust, and the benefits of using hydrogen are most marginal there, while the advantages of less ambitious fuel mixes in simpler but stronger engines are greatest, especially factoring in easier storage. Vice versa, once raised off the ground, out of the lower atmosphere and boosted to modest speeds that buy time for weaker but more efficient hydrogen based engines to work, at much lower thrusts orbit can be achieved with lower overall upper stage masses and fewer stages. Thus the design of the Saturn V was a good synergy. Note that the first stage is more massive by far than any upper stages--Saturn V had roughly a factor of 5 jump between the third and second stages, but the first stage was something between 3 and 4 times the mass of the entire upper stack, of two stages and a 45 ton Lunar stack all put together. To move this huge total mass engines creating tremendous thrust were required; even if the great challenge of making hydrogen engines that could produce that thrust were met, the drawbacks of storing huge quantities of hydrogen versus compact volumes of kerosene would have offset much of the advantage to be gained by higher efficiency faster exhaust speeds. They economized on these where it counted the most, in the first stage. A mixed stack, despite the problems of managing several types of propellant instead of just two, was the superior way to go.