About a quarter century ago, Rodenberger carried out preliminary tests on a novel chemical-propulsion gun for accelerating a practical-sized projectile to muzzle velocities on the order of several kilometers per second in a cylindrical tube, within conventional peak-barrel-pressure constraints. The tube was continuously lined with a thin film of solid propellant that underwent very-high-burn-rate deflagration immediately after projectile passage. The generation of combustion-product gases along the tube was to maintain a higher pressure on the base of the projectile than was attained by the conventional procedure of confining the propellant to the breech. We undertake simple approximate analysis for a similar thin film of solid propellant, through one that sustains a relatively slow detonation wave. We suggest: (1) the thickness of the propellant lining should be tapered with distance along the barrel, but either the variation of the circumferential packing of propellant or the composition of the propellant may be designed to compensate, so that the mass of solid propellant per length of gun barrel is invariant, or even increases, with distance along the barrel; (2) a prolate conical base, not a flat base nor a recessed conical base, accommodates the objective of maintaining a constant base pressure on the projectile, since combustion-product-gas generation at a site along the tube is initiated immediately after projectile passage; and (3) relatively modest, partial evacuation of gas from the portion of the tube ahead of the projectile significantly alleviates the shock-induced pressure on the projectile nose, which acts counter to the accelerating pressure. We arrive at these considerations by examining a tractable inviscid model of the expansional flow of the combustion; generated gas near the base of the projectile, in conjunction with projectile dynamics.