NEW YORK CITY—I’ll probably never live out my childhood fantasy of riding in a fighter jet, let alone piloting one. But gazing down on a airborne F-15 Eagle from a cruising air tanker was more than enough to satisfy my adult self, who doesn’t mind vicariously taking in a thrill ride from a safe distance.

Then again, “safe distance” may be an overstatement here. From my windowed perch in a U.S. Air Force KC-10 Extender, essentially a flying fuel depot, the fighter plane bobbed and swayed in the air just 50 feet away, below and to the rear. I could easily see the fighter pilot’s helmet and visor, and felt that I could almost make out his or her face. With both aircraft moving at roughly 500 miles per hour, the KC-10 and the F-15 were each covering the distance separating them in about 70 milliseconds—faster, quite literally, than the blink of an eye. Thank goodness neither pilot made any sudden moves.

My August 14 ride-along in the KC-10, as it refueled three fighter planes running training missions out of Barnes Air National Guard Base in Massachusetts, came courtesy of the U.S. Air Force. The service invited dozens of media members onboard the KC-10 flight as a way to call attention to Air Force Week, which has taken place over the past few days in New York City. Air Force Week is the airman and airwoman’s answer to the better-known Fleet Week, during which uniformed sailors flood the streets of Manhattan.

The KC-10 is an impressive beast: its six tanks, located in the wings and under the floor of the cargo bay, can carry more than 350,000 pounds of jet fuel (as I learned, folks in the air refueling business measure fuel by weight, not by volume). That is roughly 50,000 gallons—nearly 10 times the fuel capacity of an F-15. During refueling, the KC-10 lowered a boom from the air tanker that connects to a refueling receptacle on top of the F-15. The KC-10’s boom operator, in a backward-facing seat at the lower rear of the aircraft, has the best seat in the house. His broad window looks straight down the boom and into the cockpit of the refilling aircraft, and at the broad expanse of blue ocean below. The rest of the air tanker, which is fitted with rollers for loading and unloading cargo, has very few windows [left]. I did not have much time shadowing the boom operator, but I was able to snap a few quick photos [above right] of one of the F-15s just after it had detached from the boom.

The purpose of air refueling, as a USAF media relations officer explained to me and a fellow journalist, is at least twofold. For one, it speeds long-range missions. Imagine, he said, if you could drive cross-country without ever stopping for gas—if a fuel truck pulled up alongside your car every few hundred miles and refilled your tank as you drove. Second, it allows fuel-hungry aircraft to stay aloft longer, sparing them dangerous takeoffs and landings in potentially hostile environs.

The KC-10 Extender on which I flew, part of the 514th Air Mobility Wing of Joint Base McGuire-Dix-Lakehurst in New Jersey, was in decidedly non-hostile territory at JFK airport last week. Before takeoff and after landing, airport staff buzzed about excitedly, hoping to snap a photo or even get a glimpse inside the matte gray bird docked at terminal 8. And once the KC-10 had disgorged its journalistic passengers and passed its safety checks, the air tanker received a sendoff I had never seen before. As the aircraft rolled out toward another takeoff, two fire trucks positioned on either side of the taxiway sprayed the tanker’s flanks with arcing streams of water. The ceremonial gesture, we were told, is called the “water cannon salute.