In Boston, air traffic controllers say morale at their control center ranks last in the country. In Los Angeles, controllers say they're tired of working six days a week. In Chicago, controllers say they've had more air traffic, but little relief since 1981 when their ranks were thinned by a bitter strike.

Little wonder, they add, that they are on the verge of organizing a new union.

"There's been tremendous interest in this," said John F. Thornton, national organizer of the National Air Traffic Controllers Association. "We can only hope they voted right."

Balloting over whether to recognize NATCA as the controllers' official bargaining unit ends today, and the votes will be counted Thursday to determine exactly how strong the call for a new union is.

The controllers have been without a union since 1981, when 11,400 of the country's 16,500 controllers were fired by President Reagan during the illegal strike.

Of the 12,768 controllers eligible to vote, more than 10,000 have returned ballots. Only a simple majority is needed to launch the new union, but Thornton said he wants to see at least 70 percent vote yes to give the new union some clout.

At Federal Aviation Administration headquarters, where a contingency plan for working with a unionized work force has been developed, FAA chief Donald D. Engen has declined to speculate about the vote -- other than to say he doesn't think the support for a new union is very strong.

In an effort to improve employe relations, the FAA organized human relations committees at control facilities. And, in a demonstration of its willingness to listen to its employes, FAA management has made a number of concessions in recent months. Perhaps the most dramatic example came in April when Engen reversed a decision to transfer the popular but controversial manager of the Leesburg Air Route Traffic Control Center after controllers began a petition campaign to retain him.

But controllers list dozens of other examples where FAA management has been less sensitive -- ranging from what management concedes was an insensitive investigation of alleged drug use among controllers in Los Angeles to the flap in Atlanta when three airport controllers were sent home because they did not wear socks to work.

"There's a facility where people are working six days a week and they're sending people home to put on socks," Thornton said.

Perhaps more significant is the viewpoint that the FAA, as a ward of the Transportation Department, is politically powerless to solve what is regarded as the most critical issue: manpower.

"Staffing is the number-one issue," Thornton said. "It has to do with the six-day work week. It has to do with traffic acceptance rates. It has to do, to a certain extent, with controller errors. It encompasses everything, and we've got a group of people who've been working like this since 1981 and you can only work people like that so long."

The Transportation Department announced last week it plans to hire an additional 955 controllers, supervisors and traffic management specialists next year -- at a cost of $51.5 million. The new controllers will need three years to complete their training.

The new union's constitution contains a no-strike clause, in part because controllers who crossed the picket lines in 1981 and went back to work have denounced the strike as a mistake.