One of the most impenetrable fogs in months, if not years, settled over Washington yesterday, restricting visibility to about 100 yards and disrpting the plans of thousands of air travelers and those waiting for them.

With both National and Dulles airports shut down from midmorning to late afternoon, and airports in Richmond, Baltimore and Philadelphia shut down as well, many Washington-bound travelers found themselves shunted to such unexpected destinations as Detroit, or Bangor, Maine.

With each announcement at National Airport of an additional delay, sad choruses of sighs and moans swelled from throats of hundreds of stranded would-be travelers, as they leaned wearily against their luggage.

Many of the airplanes they had expected to leave on could not reach Washington. The few planes parked at the airport could not leave.

Airport officials said that flight operations for most passenger aircraft generally are suspended when forward visibility falls below one-quarter of a mile.

The National weather Service said the fog, produced as warm moist air from the south swept over ground chilled by recent snows, cut visibility to less than one-sixteenth of a mile.

The Washington monument could not be seen from the Lincoln Memorial. At times the railway bridge over the Potomac River could not be seen from the highway bridges. And the almost constant daytime roar of jets flying into and out of NationalAirport was not heard.

Driving was still possible, but many motorists found it prudent to turn on their headlights and reduce speed.

At the airports, people were going nowhere -- or almost nowhere. A few tired travelers had been perched on a baggage carousel when it suddenly started up. They rode it for a few feet before being spilled off.

Elsewhere in the airport, Florence Kudlak, who had come here for a Saturday wedding moaned, "I want to go home."

Along with 14 others she was trying to return to Erie, Pa.

"We've been sitting like bumps on logs here," she said, from her make-shift seat atop a pile of crumpling luggage. "Doesn't it look ridiculous?"

Behind her a bank of telephones was in constant use. Callers at each phone gave an almost identical message. It was this: "We're stuck here in Washington."