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The grams was throwing me off, so I converted to grains to compare for the layperson who might not grok the difference.
3.5 grams is ~52 grains, which is lighter than the standard 5.56 loading of 55 grains. There is to my knowledge no blackpowder firearm ever manufactured that would fire such a tiny ball. Not a popgun, much less a musket, which historically would have been firing a ball weighing roughly between 500 to 600 grains. This is not a small difference, the listed weight is maybe 10% of the real weight. Nobody who knows a thing about blackpowder firearms would be fooled by a 52gr ball. Even modern blackpowder guns, which use more efficient powder and are smaller caliber, fire 300-500 gr bullets.
I could find a couple muzzleloaders, presumably meant for squirrel and groundhog, but they're extremely unusual even for muzzleloader toys, and notably I couldn't find a smoothbore one. So they're all rifles, not muskets. Which would have been a plausible mistake, but then the guy testified that they selected the ball first, and then made a simulated musket for it. And while it's hard to guess at the "simulated musket" efficiency without knowing any of its properties, either the powder charge was pretty light or they had a ton of venting, because 280 m/s is below the lower end for these squirrel guns. The Crockett's minimum recommended load ends up around 350+ m/s at the light end of its firing range.
My (simulated and very rough estimate!) numbers using this calculator say their shot was the equivalent of 8 grain FFFg black powder from a 9-inch barrel, or 6 grain from a 12-inch. You're not exaggerating when you call that a pop gun; for a flintlock, that's almost as much black powder in the pan as in the chamber. I'm not a muzzleloader guy, but there's really no defense of this experimental setup.
It's the thing that got me started down this rabbit hole. The rest of the weird experimental procedure stuff is embarrassing, but it has some plausible defenses and was at least locked behind a paywall. This one's just on the school's website! The round being lighter than a 5.56 NATO round is right there on the chart, you don't even have to know what the units are.
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Maybe a blunderbuss? Not a single ball, but maybe an 8-10 ball #00 buck load-out. Being fired from a blunderbuss would also explain the low velocities. Not all of us have stairs to mount a cannon loaded with grapeshot, so the blunderbuss is the next best fallback.
Tally ho lads.
A gentleman always maintains a staircase for his cannon.
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