KABUL, Afghanistan — A helicopter crash that killed 10 American troops last May was caused by a series of mishaps, a new report concluded. Problems included a nighttime landing on a small mountaintop zone, trees that were too close to the runway, and soldiers who lacked axes to cut them down.

A military spokesman at the American base at Bagram, north of Kabul, Major Matt Hackathorn, said yesterday that the May crash came “as a very hard lesson” in the difficulties of flying in Afghanistan.

The CH-47 Chinook — a large transport helicopter with two overhead rotors — had such a small landing zone that only its two rear wheels could touch down, while its front two wheels hovered off the mountain’s side, the report from the Accident Investigation Division of the U.S. Army Combat Readiness Center found.

Making matters tougher, it had to land at night between trees with only about 5 feet of clearance on either side of its rotors. Soldiers tried to cut down the most problematic tree but had no ax; instead they used a pick, hammer, and knife.

“The job proved easier said than done,” the report, which appeared in the October issue of Flightfax magazine, a military publication on Army aviation safety, said.

“They began hacking at the footwide tree trunk with the knife at a feverish pace, but after several hours, they were exhausted and had cut only halfway through,” the report said.”The soldiers were out of time and short on water, so they finished up the other [landing] preparations.”

The Chinook made one successful landing but, after 45 seconds, the crew saw “glowing spots” nearby and thought they were taking enemy fire. The chopper took off, but the crew soon realized the spots were only burning embers from a trash pit that had been stoked by the draft of the aircraft’s rotor wash.

When the helicopter came in for another landing, the rear rotor hit a tree. The Chinook then crashed on a nearby cliff and went up in flames, the report said.

The helicopter went down in remote Kunar province, killing 10 soldiers from the 10th Mountain Division, based in Fort Drum, New York.

A Marine platoon that arrived after the crash saw the partially chopped tree and took it down with a saw, the Flightfax report said.

“Within 10 minutes, they’d finished the job the ill-equipped soldiers had started earlier that day,” the report said.

The military spokesman, Major Hackathorn, said the military averages about 25 helicopter flights a day in eastern Afghanistan where most American troops operate. There has not been a helicopter crash since the May 5 accident.

“It was an extremely tough situation and in very difficult terrain in heavy wind … in that kind of altitude, 10,000 to 12,000 feet, there’s a lot of wind, so it’s very difficult,” Major Hackathorn said yesterday. “We use it, as indicated in the report, as a very hard lesson, and I’m sure that it’s something all of our pilots are looking at and studying.”

NATO and Afghan troops, meanwhile, killed 52 militants in a clash in southern Afghanistan, the alliance said yesterday, and three government officials going to investigate the burning of a school were killed by a roadside bomb.

The clash happened Sunday in Charchino in the southern province of Uruzgan after 20 militants fired on NATO and Afghan troops, NATO said.

A spokesman for NATO’s International Security Assistance Force, Major Luke Knittig, said the militant death toll from the hours-long fight was based on a “careful assessment” of direct reports from the battlefield.

It was impossible to independently verify the death toll.

In eastern Afghanistan, three officials — the district police chief, administrator, and intelligence chief — were killed by a roadside bomb that detonated as they were on their way to investigate the overnight burning of a school in Nangarhar province, the provincial police chief, General Abdul Basir Salangi, said.

Militants have been stepping up attacks across Afghanistan in recent months, including the use of suicide and roadside bombs. More than 150 schools have been attacked this year, education officials say.

In other violence:

• Two police and five Taliban were killed Sunday in a battle in Kandahar province near the Pakistan border, a border police commander, General Abdul Raziq, said.

• Armed militants kidnapped a Pakistani engineer working with a construction team in Kandahar. Police officers protecting the construction crew returned fire, killing two Taliban fighters, a Dund district chief, Hamed Wali, said.