First off, I feel that I need to define what a gun launched rocket is as I've run into a remarkably large portion of people who seem to think that gun launched and tube launched are the same thing. They aren't.
A gun launched rocket is a rocket that is launched from a gun. That is to say, launched from a heavy walled pipe (we'll call it a barrel) that is closed at one end. Within the barrel, there is a charge of black powder. This charge is ignited, shooting the rocket out the open end of the barrel at high speed. Only after the rocket has cleared the barrel is the rocket motor ignited.
A tube launched rocket is a rocket that is launched from a simple tube that is open at both ends. In other words, the tube is just a nice place to store the rocket prior to launch and has little if any effect on the rocket's velocity.
Confused? Please notice the sketch included below...On top is a gun launched system (Notice that the rocket isn't ignited until after it leaves the barrel.). Below is a tube launched system (The rocket is ignited immediately.).
Now that I'm sure you're clear on the concept... The design I ended up with seems to work quite well. It is finless, spin stabilized, and has a measured muzzle velocity of up to 800 fps (mach 0.75). Sadly, I've no idea how high/fast it goes as onboard instrumentation packages are beyond my budget (And I doubt any HPR based accelerometer sets could handle the (roughly) 2,500 G accelerations within the gun.)
In case any of you are wondering, I plan on pushing the gun launch concept further. To include...