I would agree in part with Mike for the land warfare.
The only US Military advancement in the Revolution and the War of 1812 was eventually being successful in training citizen soldiers to standards where they could hold their own against a professional European Army using European weapons and tactics.
Until the American Army succeeded in doing that, we got our butts handed to us on a regular basis.
As far as weapons, the Americans were hard pressed to copy existing European designs. Not a whole lot of advancement to be seen there.
On the other side, the Ferguson breech loading rifle was advanced enough to have tipped the scales for the British, had its inventor not been killed at King's Mountain, preventing it from going into large scale production. It anticipated the Halls rifle by fifty years.
For the Mexican War-interchangeable parts used at the gov't armories. The real inovation however, was light artillery tactics, using European designed cannon in a new way. To a lesser extent, the successful development of the Colt's Revolver would have some impact on warfare worldwide over time, especially in the mounted arms.
For the Civil War-the telegraph and the railroad. There were plenty of weapon advances but they were mostly squandered by obsolete tactics. The Spencer and Henry Rifles would eventually lead to magazine fed cartridge weapons worldwide, but it was logistics and communication advances that would lead to the Prussian military model that would dominate the late Ninteenth and early Twentieth Centuries.
World War 1-Again, had to borrow weapons (tanks, airplanes, cannons) from other nations to get in the fight. We invented the submarine, but never followed it up. The Vickers, Lewis and Maxim machine guns were based on American designs that were never adopted by the US Army, so their inventors sold them overseas.
World War 2-Large Scale Mechanization, more vehicle transport and Self propelled Artillery than any other nation. The Garand Rifle. Small hand held radios (walkie-talkies). The Aircraft Carrier Battle Group (ironically forced upon us by the destruction of the Battleships at Pearl Harbor). The amphibious tractor (LVT) and DUKW.
Just My 2cts
MAJ, US Army (ret)
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