I just wanted to add to Troy's excellent anology and address barrel profile, length and accuracy.
In the theoretical vacuum Troy mentioned, not barrel profile, nor length would have any factor in accuracy. In this vacuum, where all things remain constant, every rifle will put the same bullet in exactly in the same place as the last one. However, in the real world, there are many evironmental influences to consinder, as Troy eluded to.
Let's first consider length. Length does two things that we should consider - stablization, and velocity.
Stablization occurrs by 'spinning' the projectile a certain number of revolutions prior to exiting the barrel to reduce 'wobble' in flight. 'Spin' is needed to keep the projectile moving in a straight line in relationship to its axis. The amount of spin needed depends on the velocity and weight of the projectile. Generally accepted is, the heavier the weight the more spin needed.
Velocity is the speed of the projectile. The faster it moves, the more stable on its axis, (if the correct spin is applied) and the less time it has to be affected by outside influence, i.e. gravity and wind. The velocity of the projectile is determined by the force created by the controlled explosion of the round + the time that force is allowed to push that round minus the friction created from them barrel. In other words, it takes a certain amount of time for the powder to completely burn, creating the peak force on the bullet itself. If the round leaves too early, and not all of the powder burns, you have less force. If it leaves too late, the friction of the barrel slows the bullet. In regards to the .223, the 16" barrel does not allot enough time to burn all of the propellant and create the peak velocity, thus reducing RPM's, thus reducing stablization in flight, thus increasing a greater impact from the environments. This principle is exacerbated with distance to impact.
Let's return to the barrel itself. Accuracy can only be determined by comparing more than one round fired. It begins with the explosion inside the cartridge which is determined by many things beyond the scope of this print - powder consistency, powder amount, case length, concentricty, neck tension, bullet weight consitency, aerodynamics consistency, etc, etc, etc. Bottom line, consistent chamber pressure applied to exactly the same projectile.
So, now, we have absolute consistent chamber pressure and concintricity of the bullet. Accuracy know is taken over by the device in which the projectile is propelled, the weapon. We have already determined that ballistics indicate the 16" barrel does not offer the projectile the amount of time needed to completely burn the powder, thus reducing velocity, thus reducing stablization, thus increasing environmental affects of the round.
The 16" barrel therefore, is less accurate than the 20" barreled weapon. The exact margin I cannot offer.
Barrel whip? Barrel whip is the result of the barrel vibrating under the stress of the chamber pressure caused by the explosion of the cartridge and the projectile traveling down the length of a tight barrel. Barrel whip will occur exactly the same if the chamber pressure and force exerted on it, is exactly the same, each and every time, without regard to the environment. See above.
The first two environmental effects of the round, while traveling the length of the barrel is harmonics (whip), and heat. As stated, the whip will remain the same, given consistent circumstances , However, enter heat. The heat created by the exposion will change the whip of the barrel. When metal heats, it's easier to bend. The heat generated from the first shot will affect the strike of the round of the exact same bullet we described earlier, simply because the barrel will flex differently with the subsequent round.
Whip is determined by the force applied. Whip is the bending of the barrel. Bending of the barrel increases with heat. Heat is created by the firing of the round. Heat increases with each round fired. Heat is dispersed by the amount of metal it is applied to, be it thickness or length. The more metal available, the less heat affects the bending of the barrel. The more time it takes to heat the barrel, the less deflection of the round.
Does length matter? Yes. So does circumference. At least as it is applied to accuracy.
I implore Troy, and other experts to clarify, expand on, or correct any points.
Semper Fi!