Chemical rockets are expensive but they can carry fragile cargo and people. Some guns are economical but most of them subject cargo to extreme acceleration. The following idea combines the gentle acceleration of a rocket with the low cost of a gun. It is exceptionally well suited for large cargoes that must be transported in one piece.
A hybrid rocket accelerates cargo to 2 km/s. Soon after the launch, the gun fires projectiles filled with solid rocket propellant. Far above the atmosphere the rocket docks with the projectiles and accelerates cargo to the orbital velocity. It would be impractical to carry liquid fuel or liquid oxidizer in the projectiles, because the extreme acceleration would generate excessive pressure. There is no bibliography. The minimum mass is only 10 tons.
The optimum flight profile of a conventional rocket launcher approximates a rather steep ballistic parabola. If the gun utilizes hydrogen injection or is suspended on balloons, the sounding rocket flight profile does not have to be altered to facilitate docking with the projectile. Otherwise the sounding rocket flight profile must be higher than the optimum.
The novel guns excite a researcher, but a risk averse administrator will not venture beyond the tried and true powder gun. Nitrocellulose powder is used to achieve projectile velocity up to about 2 km/s. Liquid propellants have a lower molecular mass, which increases the velocity to 3 km/s. Probably the best implementation of the powder gun is a cannon that is a fixed structural part of a submarine. Although the contraption is slightly heavier than a fixed cannon erected on a mountain side, it has the ability to sail to any latitude and aim at any angle. The cannon has the bore diameter of 2 meters and the length of 400 meters; large enough to fire 100-ton projectiles at 2 km/s. It is so large that it has to be cast in small segments. A recoilless cannon is cheaper than a recoil cannon because the axial force is lower and the joints between the segments do not have to be strong. Erosion of the internal surface of the cannon is reduced by encasing the projectile in a nylon sabot.
The success of the projectile-rocket relay depends on the cost of the gun. To reduce the cost, the mass of the gun and its projectile must also be reduced. In other words, a multitude of small projectiles must be used to launch the cargo. This is possible only if the projectiles are launched into Earth orbit and assembled into a cluster capable of docking with the rocket. Three clusters are plunged into the stratosphere. They orient themselves during atmospheric flight the same way as the Apollo entry capsule. They are slowed down by the drag, but they bounce off the stratosphere like a skipping stone. At the same time, a sounding rocket launched from the Earth accelerates cargo to 2 km/s. Far above the atmosphere the sounding rocket docks with the clusters at 2 km/s, 4 km/s, and 6 km/s, and accelerates the cargo to orbital velocity.