J. Lynn Helms, it is said on Capitol Hill, is the most technically brilliant, but politically naive, administrator the Federal Aviation Administration has had.

He is the first FAA chief in more than a decade who could design an airplane that would fly, and no one on the FAA career staff can smoke a technical fast ball past him. Senior members of that staff, who have served many administrators, speak of him in tones approaching awe.

Helms' unquestioned management skills were demonstrated when the air traffic control system worked, as he had said it would, after the Professional Air Traffic Controllers Organization (PATCO) struck in August, 1981. Drew Lewis, then the transportation secretary, depended on Helms' assurance that it could be done before he jumped aboard the White House bandwagon and vigorously supported firing 11,400 controllers.

Helms, 58, also has ended years of bickering between the FAA and competing aviation interests over development and installation of a new air traffic control computer/communications system that everyone agrees is needed. The report to Congress, outlining concepts, schedules and costs of at least $10 billion over 10 years, is regarded in the business as brilliant.

The Congressional Budget Office, which rarely embraces large expenditures, said the plan "appears to represent very good value" even if its assumptions about future aviation traffic levels are too optimistic.

"There are no significant national issues on which Helms has trouble up here at all," an experienced Senate observer said. On the other hand, "There are any number of little back-home political things--such as whether to close this or that underused tower--that he could have handled much more quietly," the observer said.

The heartburn level in the transportation secretary's office is known to rise quite high in coping with political problems Helms has kicked up.

One involved a General Accounting Office report that Helms used the FAA's Lockheed Jetstar, a snappy business jet based at National Airport, for many trips that could have been taken by commercial air. In typical GAO style, the costs of operating the Jetstar and other FAA airplanes were totaled and compared to the costs of commercial flights. Potential savings to the taxpayer: hundreds of thousands of dollars.

Transportation Secretary Elizabeth Hanford Dole, new to the job, found the GAO report on her desk almost on the day she arrived. She prepared a DOT statement on how responsibly DOT-owned aircraft will be used in the future. She flies commercially herself whenever she can, she noted pointedly.

Helms is preparing a point-by-point rebuttal of the report and plans to release it publicly. "The greatest experiment now is going to be to see if the news media will give equal certification or circulation to our analysis of the report that they did to all of the stories of misuse," Helms said in an interview.

The GAO was particularly outraged about a Jetstar flight taken by Helms from Phoenix to Scottsdale, a Phoenix suburb. That "famous flight," as Helms called it, was an emergency landing made because the Jetstar's hydraulic system failed on takeoff.

"Why didn't the GAO know all this?" Helms said. "They didn't ask . . . . And in each of those cases cited by the GAO , we're going to be able to show, very positively that there were errors."

At a recent hearing, Sen. Alfonse M. D'Amato (R-N.Y.) questioned Helms sharply about the GAO report. Helms did not blink. During the time of the GAO investigation, he said, he was personally checking on the recovery of the air traffic control system. He flies commercially when he can, he said.

"I've taken commercial this year more than I've taken the Jetstar," he said in the interview, "but only on the Jetstar" can he communicate instantly with FAA headquarters to find out how his traffic control system is doing. Is he going to have to pay a political price for all this?

"I don't know what it would be," he said. " . . . If I get fired tomorrow, it would take 20 minutes to pack and go back to retirement. So no, it's not a case of taking them on.

"I happen to believe that Mr. Bowsher [Comptroller General and GAO chief Charles A. Bowsher] is both an ethical and very credible person. I know Charlie. He's a fine gent, without any exception. He's truly dedicated. But in this case, his organization made major errors, and I'm going to point it out, to the Congress and to the public . . . ," Helms said."

Retired chairman of the Piper Aircraft Corp., Helms does not need the FAA job. He is a millionaire several times over, and Lewis persuaded him to come out of retirement because it was clear that someone with his record of achievement would be needed. Major labor problems with the controllers were on the horizon, and the agency faced several enormously technical electronic and computer issues.

Helms' most recent financial disclosure statement lists assets of at least $3.9 million, much of it in real estate and industrial holdings. His income in 1981 on dividends and interest, rent and capital gains alone exceeded $330,000, and he said he gives to charity all but $1 of his FAA salary of $69,800.

He seems to be having a wonderful time. He seasoned a recent interview with stories about receiving letters from controllers telling him what a good place to work the FAA has become and told how he explained the need for slowly rebuilding the air traffic system to a questioning airline executive.

When he came to the FAA, Helms said, labor-management relations were "so much worse than I had assumed." When a task force studied FAA's management after the PATCO strike and recommended a strong new emphasis on management training and human relations, Helms was ready, he said.

"I wasn't really concerned about solving what the [task force] came up with for air traffic; I was concerned about the entire FAA. So the program we laid out was to address the needs of the FAA, not just air traffic . . . ," he said.

Helms also seems to think he can make a difference, that he can impose enough change that an agency long known for management difficulties will not revert to habits that helped spawn the PATCO strike when political winds next bring in a new administrator.

"I can only do the best I can," Helms said. "Five times I took over companies and turned them into profitable enterprises, and every one of them, as far as I know, is still making a profit.

"In the case of this organization, I don't think it will stay 100 percent. The reason it won't is because it is a different institution . . . , the government . . . . There's all kinds of restrictions on what you can do with people, and the very nature of those prevents you then from being able to institutionalize to the extent that you can do it outside," he said.

Helms disagrees with the conclusion of the conservative Heritage Foundation that the FAA's problems are those inherent in government bureaucracies. The foundation used that argument to buttress its position that air traffic control should be a private-sector function.

For one thing, Helms noted, the FAA's air traffic service also controls military air traffic, and so has a major national defense mission that must remain under government control.

For another, he said, "I don't feel there's something inherent that makes the government a bad manager. People are bad managers, not organizations."