What would have been the absolute maximum LEO payload of a two-stage Saturn V?

Question

I read about the Skylab 1 mission in which SA-513 was used to lob the Skylab OWS into orbit. One source (http://forum.nasaspaceflight.com/index.php?topic=12519.20) gave some payload masses:

• Total mass to LEO = 147,531kg
• OWS mass = 88,474kg
• S-II dry mass = 36,697kg
• S-II/OWS interstage = 3453kg
• Payload shroud = 11,630kg

The extra 7,000+ kg is redisual S-II propellant, and also the S-IC/S-II interstage that failed to separate after being damaged by debris from the OWS.

Excluding the S-II and its roughly 3t of propellant, but including the 4.1t S-IC/S-II interstage, the potential for usable payload was between 107t and 108t.

This payload was delivered to 50 degrees inclination at 434km in altitude. So, what could it have thrown to 185km and 28.5 degrees? Studies (From 1965, I believe) on the very similar Saturn INT-21 concept give that launcher a maximum payload of 115.7t (not including S-II) to 185km and 34.5 degrees. The date of those studies means that this may not factor in late-model weight savings and engine upratings made to SA-513, which went up in 1973. Could it have lifted more than 115.7t?

Some other sources give the Skylab OWS mass as being 75,000kg or even around 77t. I'm not sure of what figures are best.

Also, how tall was the Skylab/Saturn V combo anyway? I've found 333.7ft, 341.0ft and 343.8ft, but can't verify any of them.

Answer 1

The Silverbird calculator says about 107 tons payload plus the 11 ton payload shroud, for a total of 118 tons to 185km x 185km at 28.5 degrees.

I've been refining a general rocket launch simulation program over the last few years, modeling it on the work described here by Robert Braeunig.

According to my current version of the simulation, it's possible to launch 134,000kg of payload (including fairing mass) to a 185 km x 200 km orbit at 28.5º inclination on the INT-21, in addition to the nearly-expended S-II stage (another 43 tons) which ends up in the same orbit as the payload.

The simulation is time-stepped at 0.01 second intervals. It uses classic Runge-Kutta integration (RK4). It incorporates a drag model which varies coefficient of drag with Mach number and angle of attack. It incorporates varying specific impulse with altitude. The guidance logic uses linear tangent guidance with pitch rate limiting, beginning after a period of fixed vertical liftoff.

My INT-21 is using F-1 engines with the average performance of those actually flown from Apollo 9 to Apollo 14; the engines used on later missions were only a third of a percent more powerful. The Saturn V instrument unit would need to be replaced with something on the second stage, so I added 2500kg there -- 25% more than the 6.6m IU.

There are a few limitations of the sim which might be skewing the results slightly. The simulation does not yet incorporate body lift, which might reduce performance during negative-AoA periods, but the majority of the ascent is done with a small positive AoA, so it should be beneficial overall. The coefficient of drag calculation is based on a "generic rocket" body and may be somewhat inaccurate for the Saturn V. The guidance equation terminates when a certain minimum perigee and apogee are both reached, but doesn't guarantee hitting the desired eccentricity.

I'm not certain why my results are different from Silverbird. When the Apollo-Saturn stack is simulated instead of the INT-21, I observe slightly better performance than was seen in actual Apollo flights -- I reach 185 km x 238 km with more 3rd-stage fuel remaining than the actual missions did. My best guess is that the difference comes from the slightly different trajectory my sim flies compared to the real thing. I'm not certain if that means I'm exceeding the allowable limits of angle of attack or if requiring a circular insertion instead of the slight eccentricity I'm getting would eat up the margin -- more research is required!