WASHINGTON — During a training course on defending against knife attacks, a young Salt Lake City police officer asked a question: “How close can somebody get to me before I’m justified in using deadly force?”

Dennis Tueller, the instructor in that class more than three decades ago, decided to find out. In the fall of 1982, he performed a rudimentary series of tests and concluded that an armed attacker who bolted toward an officer could clear 21 feet in the time it took most officers to draw, aim and fire their weapon.

The next spring, Mr. Tueller published his findings in SWAT magazine and transformed police training in the United States. The “21-foot rule” became dogma. It has been taught in police academies around the country, accepted by courts and cited by officers to justify countless shootings, including recent episodes involving a homeless woodcarver in Seattle and a schizophrenic woman in San Francisco.