Huh, somehow I always though the first stage would orbit the earth once and then land. I never considered that it doesn't have enought speed or fuel to do so even if forced.
If the 1st stage could make orbit, it would constitute an SSTO craft. You have to have higher ISP than kerosene and higher fuel mass fraction than aluminum can provide to do that.
Not strictly true. The Saturn V first stage could have been used as an SSTO, and it used kerosene and aluminum. The payload would be extremely small, though, so it's not worth it.
Are you familiar with Apollo 13's pogo oscillation? Money quote:
"The engine shutdown was determined to be caused by severe pogo oscillations measured at a strength of 68 g and a frequency of 16 hertz, flexing the thrust frame by 3 inches (76 mm)."
It was this close to ripping the whole rocket apart, but it managed to withstand some incredible shaking until the engine shut down.
Are you familiar with Apollo 13's pogo oscillation?
One of my friends in Houston was dealing with pogo in rockets specifically. So yes, I am familiar with pogo in general, and I had heard of it during the Apollo program.
Neat. Apollo 13's is one of my favorite little-known facts, so I thought I would mention it. They came so close to being famous for a completely different (and equally, perhaps more, catastrophic) reason.
