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I read it in James Forsyth 19th century classic "The sporting rifle and its projectiles". I heard it is mentioned in the Greener's "The gun and its development" and some other 19th century books. I also recently read it repeated on one reputable hunting website that for a given bore size, projectile weight, powder load and gun weight the felt recoil is less in smoothbores than rifles.

Personally I think it is a myth. I have never observed it and I don't understand what kind of mechanism could cause a reduction in felt recoil in smoothbores. 19th century sources claim that as a rifled barrel resists the projectile movement it somehow makes the "push back" of recoil stronger. Although on first look this sounds logical it is not how recoil works. There are multiple components to recoil.
One, the momentum of the bullet being propelled forward against the breech of the gun has to be matched by the gun. Here only weights and velocities of both items matter. The resistance in the barrel plays no role whatsoever.
Second, once the projectile exits the barrel we have a rocket like effect of gasses exiting the barrel pushing back. Again no way "resistance" can come into it.
Third, the momentum of the burnt and unburnt powder being propelled forward has to be matched by the gun going backwards. Also no relation to rifling.

The only actual difference in recoil when shooting a rifle vs smoothbore is the angular component. When the projectile starts being spinned up by the rifling the gun acquires the same twisting momentum at opposite direction. Basically we have the rifle trying to be rotated by recoil somewhat. I've noticed this, but overall I don't think this effect is responsible for the existence of the myth of lower recoiling smoothbore.

Am I mistaken about this? Am I missing something? I'm surprised that seemingly wrong statements from 19th century books are repeated verbatim in various places without being challenged. Finally, if "classics" are wrong about this, what else they are wrong about?

I would be very interested to find out what others think about it.

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