A training flight that departed from the Vineyard ended in tragedy Sunday when the single-engine plane crashed into the icy waters of Cape Cod Bay, killing flight instructor Oulton Hues of Norwood and Edgartown and his student, Robert Walker of East Falmouth.

According to Martha’s Vineyard Airport manager Sean Flynn, Mr. Hues, 73, and Mr. Walker, 68, left the Vineyard at approximately 9:20 a.m. to practice holding patterns near Hyannis. Mr. Walker, an experienced pilot in his own right, was seeking advanced certification training from Mr. Hues. It is not known who was at the controls when the plane went down.

Shortly after 10 a.m., the pilot made contact with the Federal Aviation Administration to report that the cabin was filling with smoke, said FAA spokesman Jim Peters. The pilot then came back on the radio to report that the smoke had cleared, and he would continue practicing holding patterns. The FAA notified the Coast Guard at 10:23 a.m. that it had lost all contact with the plane.

That set in motion a nearly five-hour search by land, air and sea for the missing aircraft. State and local police and firefighters on Cape Cod also participated in the search. The bodies of the victims were recovered near the Saint’s Landing area of Brewster on Sunday afternoon.

Officials spent the week tagging and recovering wreckage from the plane on Cape Cod beaches, tidal flats and in open water. The debris is now being examined by the National Transportation Safety Board. A spokesman for the NTSB said an investigation to determine the cause of the crash may take several months to a year.

“It’s certainly not the outcome we were hoping for, but I just hope the families will be able to have some closure,” said Lieut. j.g. Jared Carbajal in a statement released by the Coast Guard after the search had ended.

In a conversation with the Gazette on Wednesday Mr. Flynn described the victims of the crash as generous, experienced and familiar to the Island aviation community.

Mr. Walker, who co-owned the 1961 Piper Comanche plane with his wife, volunteered his time with Angel Flight Northeast, a nonprofit organization that provides free flights to those in need of off-Island medical care.

“These pilots in that system are truly a lifeline for people who are suffering and require extensive treatments. This person did it with great frequency, him and his wife together,” said Mr. Flynn. “That will be missed. And I think this community will be at a loss because he’s no longer going to be there to do it.”

Angel Flight Northeast said in a statement this week that Mr. Walker and his wife had participated in nearly 90 such missions.

Of Mr. Hues the airport manager said that he was a loving husband, father and grandfather who traveled often by plane to his home in Edgartown and was quick to engage fellow pilots.

“Oulton was a fantastic member of our aviation community and our Island community as a whole,” said Mr. Flynn. “Though his love was aviation, he was much deeper than that. He was a good friend to all. He was extremely intelligent.”

“In your flying career you will have multiple flight instructors, and everyone said that he was one of the best.” Those who knew him are puzzled as to what may have caused the crash, he said.

“I think all of us are presuming that this was something that no human could have overcome, because if anybody could have managed an emergency in an aircraft, Oulton is the person who could have figured it out,” he said.

“We’re all sitting here waiting to see what that could be, because it must have been something so great that it could not be overcome by a human.”