Sorry, but this comment is rather long.
Regarding the Saturn V LEO payload questions...
Check out this source:
The Saturn V launch vehicle was upgraded throughout its lifetime. Its engines were uprated and numerous measured were taken to reduce the weight of the rocket. Thus, by the time Apollo 17 came around, the Saturn was quite an improved machine. The link above details its LEO throw weight as having been 140,893kg. Some sources indicate lower or higher than this value, but this one was at hand when I wrote this.
So yes, the Saturn V was capable of delivering over 140t to LEO, but we must remember that this was after a bit of improvement. The final Saturn Vs were pumping out very close to 7.9 million pounds of thrust, which is also a lot more than is usually quoted (7.5 million). I believe the initial lunar landing missions involved LEO masses of somewhere around 133t, with less powerful Saturns.
Also, we must outline what makes up the LEO payload. The 140,893kg figure includes the partially-fuelled S-IVB third stage of the Saturn V. However, upper stages are usually excluded from earth orbital mission payload masses. So why is it included in the LEO payload…
Because Apollo 17’s mission was to go to the moon!
This is where the Saturn V’s quoted LEO payload definition differs from other launch vehicles. In the case of lunar landing missions, LEO is not the end of the line; something is needed to push the Apollo hardware to TLI. This is the S-IVB’s purpose. Upon reaching its low-earth parking orbit, the third stage is still fuelled and is not just inert mass. It still constitutes usable payload, as it is used to go to the moon.
Another important matter to consider is the height and inclination of the earth parking orbit. Early Apollo lunar missions entered LEO at around 185km at around 28.5 degrees. But on later ‘Apollo J’ missions, higher masses were delivered to LEO partly because they orbited at a lower altitude. Apollo 15, 16 and 17 parked at around 167km with similar inclination, meaning there would be more fuel left in the S-IVB upper stage for the TLI burn.
Now for the other values (127t and 118t respectively)
127t is the LEO payload mass given for the Saturn C-5… Take note!
The Saturn C-5 is not the Saturn V!
The Saturn C-5 was Von Braun’s initial design, developed while Apollo mission planners were still deciding on a basic method with which to reach the moon. When ‘Lunar Orbit Rendezvous’ was selected as the way to go, the Apollo CSM and LM combo was developed in greater detail. The payload weights grew, however, and eventually the original Saturn C-5 was found to be too weak to deliver them to TLI. Thus, the C-5 was improved and became the Saturn V. The first stage was kept very nearly identical, but the second stage was lengthened by around 3.5m for increased propellant. Also, the third stage was increased in diameter, again to hold more fuel.
The Saturn C-5 was able to deliver up to 127t (including the third stage) to a 185km LEO, and around 41t to TLI. The later Saturn Vs were able to deliver over 140t to a 167km LEO, and almost 50t to TLI.
118t (and 120t) is up for debate, as far as I know. Some say that it is the theoretical usable LEO payload of the Saturn V three-stage vehicle if the third stage is not included and is depleted upon reaching earth orbit (Apollo weighed up to 48.6t in total, leaving fuel left over for TLI, whereas 118t of payload would not). This is explored in the link at the top of this comment.
However, I have been led to wonder if this could be the maximum 185km LEO payload of a Saturn V two-stage vehicle to LEO, similar to the approach that would have occurred with non-TLI Saturn MLV-V-1 and Saturn MLV-V-3 launches (look these variants up, they’re brilliant). Such a rocket was designated the Saturn INT-21 and was never launched, although the Skylab Saturn V was essentially just that. Yes, the Skylab launcher didn’t deliver that much usable payload to its orbit, but it launched to 434km and over 50 degrees inclination, which requires more performance than 185km at 28.5 degrees. For this orbit, the INT-21 was quoted for 255,000lbs, or 115.7t… Pretty close, and that was studied before even the early Saturn Vs and as such did not include late model uprated engines and weight savings.
In summary, things to remember:
Think about what the mission requires. Missions going beyond LEO can still include the mass of the upper stage and its fuel for their quoted LEO masses. Missions only going to LEO cannot if the upper stage is depleted, because there is no more use for the empty fuel tank and engines.
Consider the altitude and inclination of the payload’s orbit. Higher orbits require more energy to achieve, and as such less mass will be delivered for a given rocket. Also, higher inclinations take more energy for a given altitude.
Think about developments and improvements made to the model of rocket. A rocket that has been in service for a long time will generally be more capable later in its operating life than its initial variants.
For error margins, I can’t say a whole lot on that subject. However, I would believe that it is recommended not to load a rocket to its designated limit. Safety margins are included, and as such a rocket should launch with a little bit more fuel than is absolutely needed, just in case something doesn’t turn out as planned. This would allow the vehicle to reach orbit even in the case of, let’s say, a single engine failure on a multi-engine upper stage (maybe, kind of like Apollo 6).
For historians, I would say that average payload for a launch vehicle variant over its lifetime would be useful knowledge. However, I would say that whatever the current LEO payload rating is for a rocket is the more important value. Assuming the vehicle has been improved over its lifetime (likely), it will generally be more capable than its earlier iterations. But that’s just my opinion.
If you have read all of this, thank you for taking the time to do so. Any feedback is welcome. If you notice anything incorrect about the information listed, please let me know.
Sorry for the ‘essay,’