Ironclads were commissioned in the U.S. Navy during Adams’s term.
1822 ironclads!!!!
OK, this has turned into fantasy. Practical iron-clads require screw propellers and those weren't developed until 1838. If the incident aboard the USS Princeton in 1843 is butterflied away, I could see an experimental ironclad maybe by 1850. Several more butterflies might bring an ironclad into being by 1840, but not in 1822.
Robert Fullton had laid down his own ironclad warship in 1809. It was never completed. And why would an ironclad warship need a propeller. A paddlewheel would work just as good.
Paddle wheels are horribly vulerable to enemy fire as it is impractical to armor all of that exposed machinery. By contrast, with a propellor you can place the machinery below the waterline where it is safe from enemy gunfire. In addition, screws have a higher power to weight ratio than do paddles which is also important for armored war ships. Finally, there is the fact that paddlewheel vessels are less seaworthy than either sailing or prop-driven vessels.
The advantage of paddlewheels is that they can handle poorly charted shallow draft rivers much beter than screw propellors, but absent a Civil War the US doesn't need a riverine ironclad.
