They are men and women justifiably proud of their wonderful flying machine. Their unique airplane is the world's only flying, teaching eye hospital. The doctors, nurses and flight crew of Project Orbis flew their refitted DC8 jetliner into the capital last week.

Between a hangar and a runway at the north end of National Airport, Orbis was inspected by a gathering of 200 people that included the Surgeon General, a senator, a White House official and an assistant secretary of state. Officialdom's flyby was public confirmation of what has been known privately in the 15 months that the hospital has been traveling to all parts of the world: in the fight against blindness and eye diseases, Orbis has been a winged blessing.

Inside the plane, part of the story is told by the array of modern medical equipment. An ophthalmological operating suite in which 800 surgeries and 400 laser procedures have been performed is the centerpiece. A few feet away is a treatment room for corneal transplants and advanced technologies like ocutone. A scrub area, a conference room, ophthalmological cameras and lamps, a sterilizer, refrigeration, a recovery area and a library are some of the other facilities.

The medical team of Orbis went to 15 cities in 10 countries in its first eight months. These included Ecuador, Jamaica, Colombia, Peru, Indonesia, Malaysia, Thailand and Pakistan. It recently returned from Jordan, Tunisia and Morocco, and leaves in a few days for several Latin American countries.

Organizationally, the nonprofit Orbis is similar to the Hope ship and the Peace Corps. It treats the immediate needs of patients on the plane, as well as inviting in host-country doctors for on-board training to learn more about the art. When the plane leaves, the expertise stays.

One flying eye hospital is no more than a small beginning when compared with the immensity of the suffering. Doctors working on Orbis report that globally 42 million people are blind. A half-billion people have eye diseases and disorders that, if untreated, can lead to blindness. The rate of illness is increasing faster than that of population growth.

Until a hundred eye hospitals are airborne, Orbis doctors talk about "the multiplier effect" of the project's teaching. In a year's time, about 1,000 host- country doctors come to the plane for its surgical programs and to observe the operations. If those doctors in turn help only one new patient a day for 250 working days a year, in 10 years nearly 14 million patients will be helped.

The record of Orbis since March 1982 and its projections for the future, represent a soaring of compassion. Much of America's other relations with the world's sick and poor appear to be either permanently grounded or about to crash-land. In 1970, according to the House Foreign Relations Committee, 0.32 percent of our gross national product went to developmental assistance. In 1982, it was down to 0.2 percent. That ranks us 16th among 17 major Western countries. Only Italy is behind the United States, and that may be changing. Italy is increasing its contributions.

In a few years, America, the Earth's richest and most comfort-laden nation, is likely to be the stingiest Western country.

At the same time that we are pulling back economic aid, one of the most rapidly growing parts of the federal budget is military assistance. Moral blindness, unlike corneal blindness, isn't treatable by surgery.

Among those at National Airport were L. F. McCollum, the former chief of Continental Oil, who in the 1950s served as the chairman of Project Hope. Going from a ship to a jet, McCollum is now chairman of Orbis. He is a link to the corporations and foundations that donate equipment and money to the project. Financially, Orbis, with headquarters at 330 West 42nd St., New York 10016, is about as cost-effective as any health-care facility in America. The low overhead in its $3.5 million budget means that eye operations, which might cost between $2,000 and $3,000 in the United States, are done at an average cost of $10 in the plane. To date, more than 60 American ophthalmologists have donated their time and expenses to work on the plane in all parts of the world.

In Washington, the strongest political supporter of Orbis is Sen. Charles Mathias (R-Md.). While showing his wife through the plane last week, he voiced sentiments similar to those he expressed last December in Congress about Orbis: "Amid all the bad news these days, it is a joy to have something pleasant to contemplate." And take off with.