Ok, look, I have this argument with my wife about comparing real world with theoretical ideal conditions all the time. It is important to understand when you’re using which. In this case, I’m talking about a theoretical ideal condition.
A trajectory is a special case of an orbit, its path can be accurately described by orbital equations, except that the path intercepts the surface of the Earth. For this question, as I said, that is the MAXIMUM possible range. This is assuming the following:
1) Assuming no air resistance.
2) Assuming the projectile is fired from the surface of the Earth.
3) Assuming the projectile does not travel high enough for there to be a significant difference in gravitational acceleration. (If this one is not true, then the range would increase.)
The range of a projectile in these conditions is given by R=Vo^2 sin(2Q)/g, where Q is the angle of launch relative to the horizontal, Vo is the muzzle velocity, and g is the gravitational acceleration at the surface of the Earth (9.8 m/s^2)
The value of the sine of an angle can vary from 0 to 1, with 1 being the value of the sine of 90 degrees. For any given muzzle velocity the maximum range is reached when the sin (2Q) equals 1, which is obviously when Q equals 45 degrees, since that’s when 2Q would be 90.
1200 fps is 366 meters per second (meter = 3.281 feet). Vo^2 = 366 squared, which is 133,956. divide by g gives 133,956/9.8= 13,669 meters. Divided by 1000 (1000 meters per kilometer) give 13.7 km. 1 km = 0.61 statute miles, so 13.7 km = 8.4 statute miles.
Thus the MAXIMUM POSSIBLE range of a projectile with a muzzle velocity of 1200 fps is 8.4 miles. It doesn’t matter if you used 40grains of ffg or a big rubber band, use a round ball or a cube, a projectile starting with a velocity of 1200 fps has a maximum possible range in **theoretical ideal conditions**, on the Earth, of 8.4 miles.
Now, what I said was:
“This is the MAXIMUM range. In real life the drag on the ball (a sphere is not a very aerodynamic shape) will decrease this range noticeably.“
Notice the “”¦will decrease this range noticeably” part. Not only is a sphere not very aerodynamic, it starts out traveling faster than mach 1, which REALLY increases the drag.
Without going through the calculations to include a constantly varying velocity, and first supersonic transitioning to subsonic drag ratios, I’d guess, offhand, that the real life maximum distance of a round ball would be maybe an 8th of that or less.
But I also said:
“But for safety sake I’d go with the maximum range.”
So it depends on how safe you want to be. But it is physically impossible for a projectile going 1200 fps to go farther than 8.4 miles, so you know you would be safe, absolutely, if you used that as a maximum range.
HOWEVER, as has been pointed out, the best thing is to know what’s behind your target in case you miss. I personally never take rifle shots when all that’s behind the target is open sky, but that’s just my own safety practice, others will undoubtedly differ.
