Ram Rocket Altitude

Let’s say a Ram Rocket (Air Augmented Rocket) was traveling straight up at 100,000 feet when the oxygen becomes too thin for the rocket to provide thrust anymore. How fast would it have to be going to reach suborbital altitudes of 50 miles and 100 kilometers? I think the theoretical max speed for such rockets is around Mach 5. Would that be anywhere near fast enough to reach suborbital altitude? How much is drag an effect in the stratosphere?

I think you’d have a shot. The boosters in the first two Mercury missions cut out at about 40 miles altitude, which is admittedly higher than the 100000 feet you’re positing. But the upward component of their velocity wasn’t much more than Mach 5. They reach 110 miles or so in altitude.

DISCLAIMER: The above statement is provided for discussion purposes only and should not be used in planning actual flights.

Thanks Spectre. That’s a good lead to follow up on. I’m curious about the practicality of air-breathing propulsion as part of space flight. A ram rocket provides a very efficient propulsion system for a narrow range of altitude and velocity. It needs it’s own booster stage to reach mach 1.2 in order to use shock wave compression of intake air, has a top speed of mach 5, and at some altitude won’t work when the air gets too thin. 100,000 feet is a WAG. Even if it was practical for sub-orbital flight, that seems to have limited application for weapons, research, and now, space tourism. But if it needs an additional conventional rocket stage to reach just 50 miles it becomes a pretty complicated multi-stage rocket with limited utility.