I was under the impression (remember new reloader here) that if my group size was 1" at 100 yards I could expect 2" at 200 yards and 3" at 300 yards and so on.
That's not what you should expect. If you were shooting in a vacuum that would be the case, but bullets have to fly though the atmosphere. Ballistic computer programs are a decent approximation of the bulk effect of the atmosphere on a bullet, but most only take into account the effect of drag and crosswind. Even with hat simple model the effect of crosswind and velocity dispersion increase more than linearly with distance since bullets slow down with distance. Vertical dispersion caused by bullet muzzzle velocity variation must increse with the square of the time of flight, which must be greater than the square of the distance. So for long range the linear approximation is not realistic. Winning group aggregates at 1000 yards (nearly) always much more than ten times the size (in inches, not moa) of winning aggregates shot at 100 yards,
But the real picture is much more compliicated. All spin stabilized bullets which have forces on them other than directly along the spin axis will precess. Precession is the way a toy gyroscope behaves if it's spinning staniding on its spin axis. If you bump it the axis will rotate slowly (much slower than the top is spinning) and it will slowly stand back to vertical agian. If its not spinning fast enough it will roatate slowly as it falls over on it's side Bullets do esentially the same thing.
The forces whiich arren't along the spin axis come from several sources. They can be initial condiitions from forces applied as the bullet leaves the muzzle. These may come from the bullet being asymentric, the muzzle blast being asymentric, from crosswind as the bullet leaves the muzzle, or in all cases except shooting vertically the force can come continuously along the trajectory from the acceleration of gravity pulling the bullet(downward) while the bullet tries to fly nose first into the air. . In all cases these asymentric forces cause the bullet nose to precess with a relatively slow conical motion, resulting in the bullets path being helical around what it's trajectory would be as calculated by drag and crosswinds alone. The diameter of the helix depends on many factors. For short low drag benchrest bullets it can be tiiny, in the order of a millimeter. For very heavy long VLD bullets it can be inches.
If all of the forces were identical with each shot then each bullet would precess exactly the same and all bullets would inpact the same spot. It's possible to come close to doing that as benchrest shooters regularly demonstrate, even at 1000 yards. It's also possible though, as in the case of the top standing back upright for a bullet to reduce the diameter of the helix with distance. That does not override drag or wind defelction, it just adds to it. It is a common phenomina when shooting at moderate distances with low drag bullets to see smallest angular group sizes at some intermediate distance, You can be sure if you shot at even longer range the groups will open up again due to geometnry, wind deflection, and velocty dispersion.
The common ballistics programs say nothing about precession effects. THere are programs which do calculate bullet precession, , but the results are so sensitive to initial conditions that it's useless for actually predicting point of impact. It can be useful for predicting the diameter of the helix, but even that doesn't offer much aid to a shooter in achieving better accuracy compared to just loading for consistancy.
For an excellent mathematical dissertation on the above subject i recommend Robert F. McCoy's book "Modern Exterior Ballistics". Don't read it if you want to be a better shooter. At best it will cause you worry and at worst you'll give up hope of ever shooting well. If you design bullets and rifles it's worth studying.
