On a typical Monday morning, about 30 representatives of Ohio State University board commerical airliners for Washington. They will spend the day here prowling the halls of Congress, the federal agencies and the grantsmanship ghetto near Dupont Circle seeking some of the $63 million in federal aid the school receives each year.

So heavy is the traffic between Columbus and the nation's capital that Edwin M. Crawford, Ohio State's vice president for public affairs -- and the school's chief lobbyist -- wants the school to buy its own airliner.

"We've got enough passengers for flights at least three days a week," Crawford said.

So vital have federal dollars become in the higher education industry that Ohio State is but one of at least 100 institutions to have opened offices in Washington or hired lobbyists in the last decade to represent their interests on Capitol Hill and with federal agencies.

"Our job is to make sure that the honey pots are there and that they are well filled," said Peter Goldschmidt, who heads the Washington office of the University of California, which receives more than $300 million in federal funds each year.

At Princeton, where 41 percent of the university's $100 million annual budget comes from the federal government and 45 percent of the students receive federal financial aid, lobbyist Nan Wells estimates she spends about one-third of her time in Washington.

Last year, when Congress was considering changes in the complex formula for distributing student aid, it was Wells who argued for language that would stretch eligibility as widely as possible. The result: an extra $1.5 million in grants and loans for Princeton students, money that eventually found its way into the university's coffers.

"At Princeton, our tuition will never cover costs, so we have to count on alumni, friends -- and the federal government," Wells said.

To press their points, most institutions rely on a combination of their state delegations and an 'old boy network' of graduates.

At the University of Tennessee, a vice president, Walter Lambert, keeps careful track of all students receiving any part of the $9 million in federal tuition grants or loans distributed over the school's five campuses.

When it comes time to vote on such measures, he has the list broken down by congressional district and he makes sure each Tennessee congressman knows exactly how many of his constituents are receiving the federal largess.

Harvard's Parker Coddington can count 17 senators, nearly one-fifth of that body's membership, as alumni, as well as 36 alumni in the House.

"We do talk to our alumni," said Coddington, who heads a staff of three of Harvard's office of government and community affairs. "Some of them are extremely helpful. Some seem to be on the other side."

Sen. Paul S. Sarbanes (D.-Md.), who is a graduate of both Princeton (B.A. 1954) and Harvard Law School, said he has maintained "a strong interest" in Princeton since his undergraduate days, but he recalls no direct lobbying from his alma mater. However, he frequently consults with Princeton's president, William G. Bowen, on economic matters.

As far as lobbying is concerned, Sarbanes said he gets "plenty" from his home state schools and the various educational associations that represent large numbers of schools.

Most Washington representatives of higher education no longer quarrel with use of the term "lobbyist," but they are not required to register as such. Most agree with the University of Missouri's Sandra Moody that the broader designation of "federal relations officer" better describes their work.

Moody spends more time tracking down grants in the federal bureaucracy than she does trying to influence legislation on the Hill. But, she said, "You can't have one without the other. It requires legislative effort to establish the grants."

Adds Harvard's Coddington, "Really, only a small part of what we do would be called lobbying. And I don't think there is anything wrong with lobbying. As we look at it, it's exercising our right to petition the government on matters of serious interest to ourselves."

Hill staffers who work on education bills mark 1972 as the turning point in the growth and sophistication of federal relations officers.

The issue that year was student loans and how they would be distributed. The college reps -- few of whom would answer to the name lobbyist in those days -- argued that the money should be distributed by their respective institutions, and the House, at the urging of longtime education activist Rep. Edith Green (D-Ore.), went along.

But Sen. Claiborne Pell (D-R.I.) and his colleagues on the Senate subcommittee on education balked, insisting that loans go directly to students, who then could apply them at the schools of their choice.

After a long, bitter conference with the House, and what Pell called "the fudge factory on Dupont Circle," the Senate won, establishing a method of distributing loans -- now amounting to nearly $15 billion a year -- that still prevails.

After that defeat, higher education spokesmen "came down out of their ivory towers and went to work finding out how the system works," one staffer said.

Now, eight years later, college and university lobbyists are so sophisticated that Pell said recently they probably could win the battle on how loans are distributed, although that no longer is an issue.

A House staffer said college lobbyists "are now aware of when we want to hear from them and when they are being a pain." But they still have a long way to go, he said, to match elementry and secondary school organizations, such as the National Education Association and the American Federation of Teachers, which put pressure on candidates and target opponents for defeat.

Higher education lobbyists are "almost wholly uninvolved in electoral politics," the staffer said. "They still are content to sell the idea that education is good, good for the economy, good for defense, good for us all, and they don't want to tarnish that perception by working in the trenches" at election time.

In other respects, the duties of a college lobbyist are not that different from those of a lobbyist for a giant corporation or a trade association. Princeton's Wells, for example, carefully cultivates relationships with members and staffs, follows bills through the legislative process and argues her case for deletions or additions. She also makes a point of being available for small favors.

"When somebody in our office wants Princeton football tickets, we call Nan," said Michael McCurry, press secretary to Sen. Harrison Williams (D-N.J.). "She always puts them in touch with the right person."

Not long ago, McCurry said, someone in their office was admiring Wells' orange and black Princeton umbrella. Within a few days, Wells had found one for him.

"What I don't do," said Wells, "is contribute to political campaigns or have a political action group."

Wells came to Princeton three years ago from the Washington office of the State University of New York, established during the mid-1960s when New York organized its state universities and colleges into a single unified system.

It costs SUNY $200,000 a year to maintain its Washington office, according to William Claire, who heads the five-member SUNY staff here. But for $100 million a year in federal grants, Claire figures it's worth the investment.

"This is big business," he said.

Contributions to the growing number of Washington based offices -- more than 50 at last count -- is the high cost of commuting.

"With the skyrocketing cost of air fare, $600 a round trip for me, a Washington office makes more and more sense," said Colette Seiple, assistant chancellor for university relations of the University of California at Santa Cruz.

But commuting has the advantage of allowing the lobbyist to keep his or her president personally informed of events in Washington. And, noted Lynne B. Clake of the University of Miami, a private institution that gets $60 million, or one-third of its $180 million annual budget from Uncle Sam, "the weather is better" in Coral Gables.

Even opening an office here would not eliminate most of the commuting by Ohio State professors and administators, Coleman said, because many of OSU's 3,684 faculty members have their own pet projects that are financed by Washington-based organizations.

"With our own plane," Coleman said, "I could leave Columbus at 8 a.m., put in a full day in Washington, and be home for dinner by 8 p.m."