In carefully choreographed killings of tactical commanders like Mr. Qayum, use of heavier ordnance to beat back Taliban attacks, and efforts to keep roads clear of improvised fertilizer bombs, conventional American warplanes are integrated into the finest details of ground war. These missions, distinct from the C.I.A.-run drone program, have allowed a relatively small Western combat force, with just tens of thousands of troops actually patrolling each day, to wage war across a sprawling nation of 30 million people.

The tactics for air-to-ground war have greatly evolved since the war’s start in 2001. One pilot, saying that he dropped just a single 1,000-pound bomb during a six-month deployment, recalled that at the war’s outset, planes would take off with more bombs than they were allowed to return with for landings. “When this kicked off, they were launching aircraft with unrecoverable loads,” said the pilot, Lt. Cmdr. Peter Morgan. “Basically, you had to drop. That’s all changed.”

A Sophisticated Balance

F/A-18 strike fighters are among the world’s most advanced military aircraft, with a price of roughly $100 million each and operating costs estimated at $18,000 to $20,000 per flight hour. Their sorties from the Stennis, each often lasting eight hours round-trip, almost always passed without violence.

Part of this was the nature of an experienced foe. The Taliban have spent years learning to mask their movements and intentions from aircraft, making themselves hard to spot.

Another part was the nature of the rules. Even when Taliban fighters were visible, Western military restrictions devised to prevent harm to civilians and minimize damage to infrastructure, codified after prominent and deadly mistakes that fueled Afghan public outrage, sometimes limited a pilot’s options. Just last month, commanders again tightened the rules for use of air power in civilian areas, after Afghans said a NATO airstrike killed 18 civilians in an eastern village.

In all, Navy pilots released missiles or bombs, or fired their aircrafts’ 20-millimeter cannon, on 41 of the 892 F/A-18 sorties from the Stennis to Afghanistan in late 2011 and early 2012, the carrier air group’s data shows.

This roughly aligns with the use of air power in the recent war. In 2011, for example, the data shows that NATO fixed-wing aircraft dropped ordnance or strafed on 5.8 percent of 34,286 combat sorties flown.