The convenient arrangement that permits airlines to decide among themselves who shall fly at what hours to Washington National and three other major U.S. airports is under serious threat from the gentle breezes of airline deregulation.

The result, in the opinion of both the airline industry and the airport operators, could be a chaotic return to overtaxed airspace, jammed terminals and increasing noise burdens on communities near airports.

For Washington National specifically, the change could mean an increase in the number of flights by commercial airlines and the elimination of the 650-mile limit on nonstop flights to and from National.

Both the quota and the 650-mile limit are mainstays in National Airport's delicate efforts to balance the demands of congressmen who want quick flights home and litegious residents along the Potomac River who would prefer no flights at all.

"Frankly, we're scared to death," said one Federal Aviation Administration official. No one would comment at National Airport, which is owned and operated by the FAA. The other airports affected are Chicago's O'Hare and New York's John F. Kennedy International and LaGuardia.

The fears are unfounded, according to the Civil Aeronautics Board (CAB), which is considering a change in the rules in the interest of promoting competition. Promoting competition is the guideline principle under which the CAB will be abolished on June 1, 1985, under legislation President Carter is expected to sign next week. Airline deregulation was a major legislative goal of the president.

All four of the airports have quotas on the number of commercial airliners that can take off and land during certain hours. At National, 40 commercial airliners per hour are permitted between 7 a.m. and 11 p.m.

The airlines allocate those slots in meetings that, under normal circumstances, would be a violation of the antitrust laws. They are permitted to meet only because the CAB waives the law. The waiver technically expires Wednesday, although it will remain in effect until the CAB acts formally.

If the CAB removes the waiver, who allocates the slots?

"I don't have an answer for you.

We're struggling," said Roland Eckert, special counsel to the FAA administrator. It took the FAA and its parent Department of Transportation five hours to decide who would say there was no answer.

In New York, Richard Zinser of the port authority, said "I don't know what we'd do." The port authority runs both La Guardia and Kennedy.

Michael E. Levine, director of the CAB's Bureau of Pricing and Domestic Aviation, sees no problems. "We don't object to the quota," said Levine. "The number (of flights permitted) may be wrong but I don't know and I don't care."

Two possible suggestion that have come from the CAB are higher landing fees for peak-hour slots or an auction. In other words, airlines would pay more to land at National or would bid for the slots.

Who would conduct the auction or supervise the fees?

"We don't have the methodology," said Levine.

The Air Transport Association of America, the airline lobby, has filled comments with the CAB in which it states that "none of the cost mechanisms," such as preferrential landing fees, "can guarantee the FAA that its slot limitation will not be exceeded tomorrow, next week or next year."

An auction, presumably conducted by the FAA, would mean that "big airlines with high-density airplanes would buy out all the space and small airlines serving short-haul routes would be forced out," according to the New York Port Authority's Zinser.

Washington National officials have made similar arguments in the past in defense of the 650-mile limit, among other things. That limit, according to the CAB's Levine, is "irrational. If an airline wants to come in nonstop from Denver, why shouldn't it do so and move its flight from Charlotte" to another airport, such as Dulles International, Levine asked.

Then there is the Texas International problem. Texas International wants to fly nonstop from New Orleans (beyond 650 miles) to Washington National and has applied to do so. If it is granted the authority, it does not have a slot at National under the present quota system, or a counter in the terminal, which is full.

That raises more questions that do not have answers, which is one of the reasons the FAA was reluctant to comment yesterday.

"As a matter of policy we do not want to create another CAB over here," said the FAA's Eckert. The FAA also is anxious not to appear to be opposed to one of the president's favorite causes - deregulations.

The airlines' scheduling committee has "worked well for 10 years," said the Air Transport Association, and is in the public interest.

But Levine asked: "If you have a scant resource - slots - should you let the airlines make an anticompetitive arrangement and not offer (slots) to everyone and not pass them on?"