Here is some information on the great German cannon used to shell Paris during World War I. Ignoring air drag, what was the muzzle velocity required to have a range of 81 miles. What was the optimum launch angle? How much energy does the 210-pound shell have at launch? Asuming 4400 joules per gram of energy in gunpowder, how much gunpowder is required?
The Paris Gun was a weapon like no other, but its capabilities are not known with certainty. This is due to the weapon's apparent total destruction by the Germans in the face of the Allied offensive. Figures stated for the weapon's size, range, and performance vary widely depending on the source — not even the number of shells fired is certain.
The gun was capable of hurling a 94 kilogram (210 lb) shell to a range of 130 kilometres (81 miles) and a maximum altitude of 40 kilometres (25 miles) — the greatest height reached by a human-made projectile until the first successful V-2 flight test in October 1942.
The gun itself weighed 256 tons and was mounted on a special rail-transportable carriage mounted on a prepared concrete emplacement with a turntable. It had a 28 metre (92 ft) long, 210 millimetre (8.3 in) caliber rifled barrel, with a 6 metre (20 ft) long smoothbore extension. This barrel was placed inside a 38 cm Langer Max barrel, which in turn was placed on the carriage. The gun's barrel was braced to counteract barrel droop due to its length and weight, and vibrations while firing.
The projectile reached so high that it was the first human-made object to reach the stratosphere. This virtually eliminated drag from air resistance, allowing the shell to achieve a range of over 130 kilometres (81 mi). The shells were propelled at such a high velocity that each successive shot wore away a considerable amount of steel from the rifled bore.