Smoothbore ball velocity

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Said the **** well skinned I’m a hat on his head
Cause I simply forgot about well alloyed lead
With me said the deer my insides were wrecked
By ballistic co efficient and corllies effect
And legions of soldiers with their read coats and gear
all shook their heads and agreed with the deer
‘‘Twas not through skill or bad luck we encountered deaths path
But simply because that guy knew his math”
 
I observed an interesting, to me, thing when I was into paint ball.
Your paint ball was spinning when it left the barrel, not along the direction of travel like a rifled bullet, but at an angle to it. That causes exactly the thing you describe, and is called the Magnus effect. You can see the same thing exactly simply by throwing a ping-pong ball with spin, straight for a bit, then sharp swerve up, down, right left.

Benjamin Robins did the same thing with musket balls in 1730 or so.

Spence
 
An interesting debate, involving both internal and external ballistics!

My penny's worth is that the rifling in a gun will reduce the energy available for velocity due to the need to deform into the rifling and the increased friction due to the larger surface area in contact with the projectile. That said, the contact area with a round ball and that of a cylindrical projectile is significantly different. A round ball has a minimal contact depending on fit. Energy is also translated into the rotational momentum of a spun projectile.

The air resistance of a projectile is down to its mass, cross section and shape and varies with velocity. This is usually expressed as the ballistic coefficient, which is a value that expresses the "slipperyness" of a projectile. At slow, subsonic velocities, most of the resistance is caused by the turbulence at the rear of the projectile (hence the value of boat tails to subsonic projectiles.. A smooth ball, if it is not spinning on its axis may drift (hence the pits on a golf ball!) and a rough ball may fly straighter, however a smooth ball will offer less skin resistance. A bare ball fired from a rifle will have rough rifling marks, whereas a patched ball may not..!

The energy of a moving projectile is expressed as half mass times velocity squared, therefore for a given calibre and velocity, the only way of adding more energy is to increase the projectile mass. This means going from a sphere to a cylinder or moving to a denser material. regrettably cylinders are not ballistically stable, so we either have to spin it or put a tail on it..! The longer the cylinder, the faster we have to spin it.. spun balls are the easiest case and do not have to be spun much..!

Modern tank guns are now (mostly) smoothbore because to get the required energy in the projectiles, they have to use long, thin penetrators that cannot be spun stabilised.. so they now fire darts! The guns do produce less bore resistance, however they are also using some pretty sexy materials for driving bands and bore rider sabots..

To return to the subject however, I would think there is not actually much to choose between the velocities of smooth or rifled barrels for the same loading, however I would turn the argument the other way up. It is generally considered that accuracy increased with velocity in a smooth bore system however there is less velocity required for spun projectiles to achieve similar results. In other words the advantage of rifling for round ball is that you can achieve accuracy at lower velocities and lower loadings than the equivalent in smooth bores..
 
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