why do shotguns have a shorter range?
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The real answer is because they are designed without range optimization in mind.
Basically they operate at a much lower pressure than high-powered rifle rounds. This is accomplished with the large bore and the relatively small powder charge.
The projectile(s) contributes to this as well. A large, unaerodynamic slug would need a magnitude more pressure behind it to get it to go as close as far as a large rifle round with any accuracy. And buckshot pellets are both less aerodynamic and lower mass, meaning they carry less momentum to travel distances.
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