One of the many murder mystery shows on TV these days recently did an episode wherein an assassin shot his victim through the heart at a mile and a half with a single shot from a super-scary sniper rifle, complete with portable weather station, laser range finder and computer, etc. (sounds a bit like my setup). It reminds me of Henry (nostrilitis) Waxman’s attempt to scare children over the magical capabilities of the .50 BMG cartridge.
Knowing this claimed feat to be beyond ridiculous, and for fun I decided to test it using Joe’s exterior ballistics program. Using all the most generous figures: Caliber .50 BMG (loaded with the slipperiest small arm bullet, with a Ballistic Coefficient of 1.05) which I gave an impressive standard velocity deviation of only 5 feet per second, and an inherent accuracy of 0.5 minutes of angle (super, ultra special, custom ammo) with a wind estimation error of only 2 MPH over that whole mile and a half, and perfect assessment of temperature, humidity and barometric pressure. It turns out that the probability of a hit (any hit) on a 15 inch circle at that distance (2,640 yards) is from 1% to 8% (depending on which 100-shot simulation you go with– i.e. there were 100-shot strings in which only one bullet hit its target) assuming a perfect shooter with nerves of perfect steel, perfect optics and visual conditions that can resolve a 16-inch (a little over ½ MOA) wide target at 2,640 yards.
Using the more common, high powered, long-range 300 Winchester Magnum, with the same amazingly good velocity deviation and the same super 0.5 MOA accuracy, the hit probability went to about 0.6% on a 15-inch stationary circle. Bullet’s time of flight: 7.37 seconds.
On the TV show, the shooter did another amazing trick by timing his shot (from a mile and a half away) to exactly coincide with some blanks fired in a movie set dual. The time of flight for his (assumed) .50 BMG bullet at 2,640 yards is nearly 5 seconds, so the shooter would have to anticipate his victim’s actions with superb accuracy, five seconds in advance. Furthermore, he took the shot from an urban area, where the intense muzzle report from a necessarily very powerful rifle would have gotten the attention of people in a wide radius. The rifle was bolt action, and the ejected cartridge case was depicted as having melted into the outdoor carpet on the balcony that served as the shooting position– also preposterous, as the case sits in the chamber too long to leave it so hot upon ejection (the relatively cool barrel acts as a tremendous heat sink for the thin brass case). Only autoloaders spit out hot cases because they extract the case within milliseconds of firing. Oh and the target, being a human in the process of acting out a mock duel, was moving, making the probability of a hit even less (my simulations were done on a stationary target).
Now some would say, “Hey, its just a TV show. Its entertainment, Dude, lighten up.” I would agree if it were a science fiction series, or fantasy, but this stuff is put forth as serious, hard-hitting drama. To me its like a serious W.W. II drama in which people fly like superman, battle tanks travel at 200 miles an hour, and animals talk. It ceases being entertainment and becomes an insult.
