China's national airline is spreading its wings. Fasten your seat belts.

CAAC, China's only airline, does not fly in friendly skies. It is a company travelers love to hate -- the abacus airline. Everybody has his favorite horror story.

American tourist: "Our flight to Tibet was delayed by weather for four days."

Australian diplomat: "I've ridden the Canton-Peking flight 20 times and never been on time once."

American businessman: "We left right on time at noon. Lunch was a chocolate bar."

Chinese traveler Xi Wan: "Whoever wants to book a seat on a CAAC plane must take the risk of suffering from hunger and thirst or sleeping in the street."

"CAAC's bad service has become such a scandal that it gravely damages China's prestige," snarled the People's Daily in a front-page editorial.

The last observation is the one that counts, for that is the Chinese Communist Party speaking. Things will get better.

Which is just as well, for Americans will soon get a firsthand look at CAAC. An air agreement signed at the White House in September provides for the first direct U.S.-China air service in more than 30 years. CAAC's new 747s are tentatively scheduled to make two weekly round trips linking Peking and Shanghai with San Francisco and New York, via Tokyo, starting Dec. 1.

The American connection is part of rapid growth in both routes and passengers. CAAC carred a third more passengers last year than it did in 1978, and may increase by as much again this year. There is expanded service within China and new routes within Asia and to Europe. A direct Peking-Hong Kong flight -- the long-sought goal of professional China travelers -- will begin in November. So will direct service to London, joining already established routes to West Europe.

CAAC's 747 inaugural nonstop to Paris left Peking last April, commanded by a 69-year-old pilot who spoke only Chinese. On such international flights a translator rides as the fourth man in the cockpit.

CAAC's safety record is excellent, and the caution with which the airline operates is one reason its planes seldom leave when they are scheduled and sometimes do not fly where they are supposed to go. The caution is imposed not only by Chinese tradition but also by a relative absence of land-based flight aids in a gigantic and backward country that is still stitching itself together with new railroads.

CAAC -- which stands for Civil Aviation Administration of China but is often called other things -- is a good example of the travail that accompanies rapid change. Like every other enterprise in China it is trying to modernize overnight, to catch up with the rest of the world. In that, its growing pains are probably no worse than those of any other Chinese industry today. What distinguishes CAAC is that its shortcomings are highly visible to foreigners.

"Be fair to them," urged the Peking manager of a European airline. "They have a long way to go, sure. But they are trying hard, and every day is a little better."

A flight kitchen, as part of a joint venture with a Hong Kong company, recently opened in Peking. It's offerings -- most cold meats -- are available on some flights, although not always at mealtime. No longer does the CAAC stewardness, in pigtails and a shapeless blue jacket, wander through the aisle with a kettle of boiling water with which to replenish tea. On one recent 747 flight a cabin crew in prime but attractive new uniforms even managed a cup of instant coffee.

Food apart, once the plane is moving, CAAC is tolerable, if not relaxing.

It can be reassuring to know that CAAC will not fly at all if the weather is bad, and not at night if it can be avoided. More irksome is the realization that flights are sometimes delayed so the captain can have his lunch and a siesta.

And for purgatory there is nothing to match the CAAC reservation system, if that is the word. Tourists are immune to its horrors because their reservations are made by other people; if not, no tourist would ever come. CAAC has no reservation computers. All of its reservations are "processed" on old-fashioned file cards.

At the CAAC main office in Peking there reservations clerks, opaque as the glass that surrounds them, naysay like grim survivors of a burning pillbox. tIn Hong Kong it is usually possible to reserve a seat to Canton, but almost always impossible to get onward confirmation to Peking -- except sometimes on flights that do not exist.

Still, there are some CAAC charms that it will be sad to lose once modernization hits its stride. Where else in the world can a bemused American teach impromptu in-flight English to four stewardesses who have nothing else to do and be rewarded at journey's end with four beaming smiles and 31 sticks of CAAC chewing gum?