It probably was the most unusual midair collision ever around Washington: Two veteran pilots, both working for the nation’s top aviation safety agencies, smashed their planes together 1,600 feet above Warrenton, Va., on a sunny Memorial Day afternoon two years ago.

Now, an exhaustive investigation has come to a startlingly simple conclusion: Somehow, they just didn’t see each other.

One of the planes, a Beechcraft 35, was chopped in two by the propeller of a Piper PA-28. With its tail cut off, the Beechcraft and the two certified pilots on board — James “Mike” Duncan, 60, and Paul Gardella Jr., 57 — spiraled down to their deaths.

The pilot of the Piper, Thomas R. Proven, 70, managed to bring his damaged plane down in a pasture, skidding through a narrow tree-lined path and clipping off the plane’s right wing.

Proven was an investigator for the Federal Aviation Administration. Duncan was chief medical officer for the National Transportation Safety Board, the federal agency charged with investigating airplane crashes. Gardella was a professional flight instructor and the region’s chief examining officer for the Civil Air Patrol.

Combined, the three pilots had 16,600 hours of experience at the controls of an airplane.

The Transportation Safety Board of Canada (TSB) was called in to handle the investigation, and the report it produced for the small-plane crash has a depth of detail normally found when a commercial airliner goes down.

The collision occurred in airspace that local pilots call the training ground, a swath generally free from airliner traffic where instructors bring fledgling pilots to practice, planes are taken to do testing and more experienced pilots go to log flying time that their certification requires.

The latter was what had Gardella and Duncan in the air that afternoon. They took off in the Beechcraft from Warrenton-Fauquier Airport for a flight review required of pilots every two years.

The TSB report says that 15 minutes after they were airborne, Proven radioed an air travel controller for clearance to land on runway 33 at the same airport. The controller responded and then turned to dealing with arrivals and departures of jetliners at nearby Dulles International Airport.

Both the Beechcraft and Piper were operating under what are known as visual flight rules: They were expected to be scanning the air for other planes.

Were they distracted by their cockpit gauges during the 37 seconds they were on a collision course? The TSB draws no conclusion.

At 4:04 p.m., the TSB said, the controller received an audio and visual warning on the computer screen of a possible collision between the two planes. The Beechcraft was 500 feet below and less than a mile away from the Piper. The controller assessed the situation and “assessed that there was no conflict” before returning to the airliners.

The two smaller planes merged at a 45-degree angle, and “the Piper’s propeller severed the Beechcraft’s fuselage just aft of the pilots’s seats.”

The TSB investigators said that “field-of-view analysis showed that there was a high likelihood that each aircraft was visible to the other, meaning that no aircraft structure would have obscured the view of either approaching aircraft.”

The report said that on board the Beechcraft, Gardella’s head might have obscured Duncan’s view, but Gardella’s view should have been unobstructed.

“There were no indications that either aircraft manoeuvered to avoid the other,” the report said.