How high can a sounding rocket launch and for how long time can it put a payload in freefall microgravity?

Question

Sounding rockets or suborbital launches basically go straight up and then fall down without entering orbit. That requires much less fuel mass than to achieve 8,000 m/s or so orbital velocity.

• For how long could such a launch put a payload in freefall microgravity (which could be of interest to science, manufacturing, tourism)? I suppose that there won't be much microgravity once atmospheric braking sets in below 100 km altitude or so.
• How would today's most powerful launcher, Delta IV Heavy, perform as a sounding rocket in terms of altitude and payload time in freefall? Or a Saturn V? The EFT-1 with Orion on a DIVH lasted for over 4 hours, but was actually designed to accelerate the payload down through Earth's atmosphere.

Answer 1

A good start is to find the upper limit, so I am going to first oversimplify it.

If I launch a rocket straight upwards with the same $\Delta v$ as required for a circular orbit, my free-fall time is $\frac{\pi +2}{2\pi}$ times the orbital period of the circular orbit.

That means that the maximum amount of time I can spend in free-fall is about 80 minutes, before it makes more sense to launch into orbit instead.

Does the atmosphere actually matter? At $8 km/s$ the last 100 km is only a loss of thirteen seconds, negligible compared to the total flight time. Of course the $\Delta v$ lost at ascent is significant, but a rocket launched to orbit also experiences that drag. Thus, the longest meaningful free-fall time a suborbital launch can give you is a little more than an hour.

As for what payloads modern rockets can set into this trajectory, the $\Delta v$ required for the longest meaningful free-fall time is the same as for a launch into orbit. Simply use their payload capacity into LEO. As for a minimal sub-orbital launch, about $1.4 km/s$ of $\Delta v$ is required. For such low requirements, the launcher's thrust to weight ratio is the limit.