In Could any existing gun reach the Karman Line?, Richard Graf's Kickstarter campaign for his Starfire space-gun is referenced & discussed. Setting aside my native skepticism for a project with such scanty technical details, I have another problem: anytime I hear the word "suborbital," the words that follow come out "blah blah blah."
Let's face it, most useful science that can be accomplished through suborbital flights has been done years ago, and, unless you're going to make your space-gun many, many kilometers long, it's not going to be suitable for space tourism. From John Hunter's presentation this past summer at the Starship Congress (starting at 37:40), we hear that you cannot fire a projectile high enough for it to not eventually come down somewhere. So, if space-gun technology is ever to reach LEO, a boost near the top of the projectile's parabola needs to be employed.
Let's assume two things to make it simple: 1) The max G-force sustained by the booster/projectile will be 10,000 Gs (Graf's Starfire claim), 2) To reduce moving parts, let's make it a solid fuel rocket. Can such a booster be designed to strap on the back of our projectile with current technology?