I didn’t disagree with your statement that air resistance is proportional to the square of the speed.
However, the fact that air resistance is proportional to the square of the speed doesn’t tell you how far a bullet will travel before it hits the ground.
A bullet, or rock, will have dropped 1 foot in 0.25 sec. Assuming the lower edge of the barrel is held horizontally, 12" above ground level, and the ground is perfectly flat, the bullet will impact the ground 0.25 sec later.
How far away from the barrel that impact will occur depends on muzzle velocity and the bullet’s ballistic coefficient ratio.
I don’t have access to an exterior ballistic trajectory program but I do have olde-skool exterior ballistic tables.
Assuming a muzzle velocity of 1300 fps:
A bullet with a BC of 0.13 will take 0.1240 sec to reach 50yds and 0.2638 sec to reach 100yds.
A BC of 0.21 = 0.1208 sec to reach 50yds and 0.2519 sec to reach 100yds.
A BC of 0.23 = 0.1203 sec to reach 50yds and 0.2502 sec to reach 100yds.
A BC of 0.30 = 0.1192 sec to reach 50yds and 0.2458 sec to reach 100yds.
Well, yes and no. If you know all the forces on a bullet (including air resistance), you should be able to predict how far it will go. It’s more complicated than the parabolic trajectories you might learn about in an introductory physics class, and the calculations are extremely time-consuming; you either need to have a computer or, well, a computer to do them. But it can be done, starting from the principle that the air resistance is proportional to the square of the velocity.
Those tables may well have been compiled by computer calculations (computers of the second type, if they’re sufficiently old-school.)
It’s been a long time since James M. Ingalls first published his exterior ballistics tables in 1918. Many others have made repeated modifications to keep abreast of the latest changes to bullet design.
Among other things, there are multiple “G” form drag models to consider:
G1.1 - Standard model, Flat Based with 2 caliber (blunt) nose ogive
G5.1 - For Moderate (low base) Boat Tails - 7° 30’ Tail Taper with 6.19 caliber tangent nose ogive
G6.1 - For flat based “Spire Point” type bullets - 6.09 caliber secant nose ogive
G7.1 - For “VLD” type Boat Tails - long 7° 30’ Tail Taper with 10 caliber tangent nose ogive
GS - For round ball - Based on measured 9/16" spherical projectiles
RA4 - For 22 Long Rifle, identical to G1 below 1400 fps
GL - Traditional model used for blunt nosed exposed lead bullets, identical to G1 below 1400 fps
GI - Converted from the original Ingalls tables
Shortly after WWII, the U.S. Army’s Ballistic Research Lab (BRL) compensated for the substantially increased air resistance encountered above the speed of sound. Smart bomb tech eventually outmoded the BRL at Aberdeen but firearm component manufactures still publish exterior ballistics tables in their reloading manuals.
For general firearm use, those tables are more than adequate. Additional PC software is available for anyone who wishes to make their own projectiles or participate in very long range shooting competitions.
And it’s all based on the fact that air resistance is proportional to the square of the speed.