Arthur B. Alphin is well acquainted with the trigonometry of terror.
The retired Army lieutenant colonel and West Point graduate, who has a mechanical engineering degree and specialized in ballistics, has testified in many multiple-shooting cases.
What he sees so far about Las Vegas shooter
Once the trigger was pulled, simple laws of physics and trigonometry sealed the fate of more than 500 people who would fall wounded in the ensuing fracas — 59 of them fatally.
"He had a huge area of three, four or five football fields with people standing shoulder to shoulder," Alphin said. "He was not aiming at any individual person. He was just throwing bullets in a huge 'beaten zone.'"
Beaten zone is an infantry term dating to World War I. Shaped like the area a searchlight casts across a flat surface, it represents the area where bullets can strike, and moves substantially with tiny changes in the tilt of the gun.
If the shooter shifted by about 1 degree, or the width of two fingers held at arm's length, Alphin said, the beaten zone would fall outside the crowd.
"That's all the distance you have to move and you aren't hitting anybody," Alphin said. "So he had to be pointing or aiming at the very center of mass and then bouncing all over with the recoil."
From a perch 320 feet above ground in a hotel whose base was about 1,050 feet from the concert venue, Paddock was firing down the 1,098-foot hypotenuse of a right triangle — and would have to adjust his aim for the arc of the bullet over that distance.
Alphin said there was "no way" the shooter maintained such a steady kill zone by dumb luck. Steady nerves and planning are a better explanation for the casualty rate, he said.
"How did this guy get trained that well? Where did it come from?"
At least one of the 23 rapid-firing weapons authorities found in the hotel room had a bipod stand to hold it steady, according to law enforcement authorities.
Paddock also may have fitted weapons with a device to make it cycle rounds more quickly into the chamber for firing, or converted some to fully automatic firing, potentially adding as many as eight rounds per second, Alphin said.
There may also be expertise at work in deciding when to switch rifles, Alphin said. Gun barrels expand as they heat up, and the bullet can lose contact with the grooves that spin it and keep it point-forward. Without the spin, it will tumble.