QUESTION:
I have a theory about horizontal takeoff. I believe that if a
customized space vehicle was in a tunnel on a hill, when its rocket
ignites, the pressure will build behind the spacecraft. It will shoot off
at a 135 degree angle. Do you think that my theory is possible?

ANSWER from Rich Hogen on November 29, 1999:
My guess is that you were watching some launches and found yourself
wondering, "Isn't allowing all that pressure to dissipate into the
surrounding air wasteful? Would the rocket have more power if its exhaust
were constrained to the space immediately below/behind it?"

You've hit on an a fairly subtle aspect of rocket design, which is the
exhaust pressure "at the nozzle" compared to the ambient air pressure. This
is actually more of a fluid dynamics issue while the rocket is in the
atmosphere than a question of thrust or horizontal versus vertical takeoff.

There's an important thing to remember about rockets: thrust exists whether
or not there's an atmosphere. People used to say that Goddard's ideas about
sending rockets into space were silly because in space there's no atmosphere
"to push against". But it isn't the atmosphere that's providing the
rocket's thrust, it's the flow of material from inside the rocket out to the
surroundings (whatever they are) that's providing the thrust. That's why
rocket engines work in space!

Here's a simplistic description. A spacecraft with some kind of rocket
engine is in outer space (i.e. out of the atmosphere). It turns on its
rocket engine, which means that mass is being thrown out of the spacecraft
(along the exhaust vector). Pushing that mass out the engine means there is
an "equal and opposite" reaction to the pushing, and the spacecraft is
pushed in the opposite direction (along the thrust vector, which is in the
opposite direction from the exhaust vector). It does not matter that there
is vacuum outside the spacecraft, because it's the act of throwing mass out
the engine which is providing the thrust. Within the atmosphere the
situation is the same. The thrust is provided by throwing mass out the back
of the rocket, not by the exhaust hitting the atmosphere.

But back to the subtlety brought out by this question, for rocket engines
that have "bell nozzles" the thermodynamics and velocity of the exhaust are
coupled to ambient pressure to some extent (that's the fluid dynamics part),
so that the maximum thrust is a function of both ambient pressure and shape
of the engine bell. Since atmospheric pressure drops off exponentially as
you rise from the surface, most of the atmosphere is close to the ground.
This means that many engine bells on rockets are optimized for a particular
atmospheric pressure, resulting in a total, integrated thrust over the
entire launch trajectory that is optimal. (I would imagine that
dramatically _increasing_ the atmospheric pressure surrounding a rocket
engine might actually be detrimental by obstructing the flow of exhaust
thereby forcing a completely different optimization at the launch pad than
in the air or in space)

The X-34/Venturestar design does not use engine bells in its rocket engines.
Instead, it uses linear aerospike engines (similar to the exhaust design in
the SR-71 aircraft), which result in optimal thrust for any atmospheric
pressure. Thus, no design optimization for a specific altitude is required
and you get the best performance all the way up.