Unguided orbital insertion (cheap upper stages)

On Feb 25 2002 John Carmack started a thread by this name. Google
won't let me reply to that thread so I am starting another by the
same name.

John Carmack:
It seems to me like it is possible to put something into a 200km (or
whatever) circular orbit with a simple unguided, spin-stabilized
second stage, even when launched from an straight up/straight down
booster with a 100km apogee.

The idea would be that the X-Prize vehicle would have the passenger
cabin replaced with a fairing over a 300kg, non-streamlined second
stage mounted on a platform that could spin up and precisely aim it
(nearly horizontally) before firing it while the booster still has
significant upwards velocity. The complex stuff comes back down to
be reused, and the second stage is basically a piece of ammunition.

This is an interesting and fun problem, so I played with it a bit
in my simulator. With a high G spin stabilized rocket I can get
an orbit with a 90 km perigee. Depending on how high the apogee
is, the mass, and the drag, this can last for a bit (just over a
day in one sample I did). With a small thruster (Hall thruster
/ion-drive/arcjet) on the payload it can easily raise the perigee
and circularize the orbit.

I don't think that with a spin stabilized rocket aimed at one point
alone you can get into a 200+km circular orbit starting from a
minimal X-prize vehicle (i.e. goes to just over 100 km). If you
aim below horizontal by much you just hit too much air. If you
aim above then as you start to go around the Earth the angle seems
higher and higher relative to your velocity, which is not what you
want. It makes it as if your orbit came from inside the atmosphere,
and so after you get most of the way around that is where you will
be.

One trick (from Henry Cate) is that you could have your apogee
kick motor in front of the payload aimed the opposite way so
that when your spin stabilized vehicle got to the other side of
the Earth it would be aimed the right way. I did this in one
sample below. If spin stabilizing something can last for 40
minutes this could work.

You want high G thrust, so you may need to go to solids. And if
you go to solids you probably need 2 stages. But it seems like
2 spin stabilized solids and a small motor aimed backwards, or
an electric thruster on your payload, and you could get to a stable
orbit from an X-prize vehicle. This could be very cheap, and so
seems like good idea.

See samples 78 to 81 named "X-prize to orbit ..." in Java applet at:

http://spacetethers.com/spacetethers.html

-- Vince