Norfolk & Western Railway announced yesterday that it has acquired more than 8 percent of Piedmont Aviation Inc., a major regional air carrier, and that the Roanoke-based railroad is seeking a "significant common stock position" in the airline firm.

If N&W ultimately gains control of Piedmont, it would represent the first time since federal aviation regulation was established in the 1930s that U.S. rail and air operations would be under common ownership. Although Piedmont officially said yesterday that it is not interested in a combination with N&W, transportation analysts said such a merger makes sense.

Earlier this year, Piedmont thwarted a takeover bid from expansion-minded Air Florida Systems. But there was a great deal of hostility between managements of the two airlines at the time. In contrast, there was no evidence yesterday of similar bitterness between N&W and Piedmont.

The Roanoke rail line, consistently one of the most profitable U.S. transportation companies, already has reached an agreement to merge with Washington-based Southern Railway to form one of the nation's largest railroads. The Interstate Commerce Commission is studying the proposed rail combination.

N&W said it used company-generated cash to buy 650,000 shares of Piedmont through Aug. 27 for $18.28 million -- or $28.25 a share for 8.2 percent of the airline firm's 4.7 million common shares. In New York Stock Exchange trading yesterday, Piedmont was the fifth-biggest percentage gainer -- up $2.75 a share, or 10 1/2 percent, to $28.87 1/2. N&W fell 37 1/2 cents to $39.75.

The railroad revealed in a document filed at the Securities and Exchange Commission that in June it held discussions with Piedmont "regarding a possible combination of the two companies or the acquisition by N&W of a substantial equity position" in the air firm, which is based in Winston-Salem, N.C.

Piedmont responded in July that it was not interested in such discussions, N&W stated. And Piedmont said yesterday there had been just one brief discussion. "Piedmont feels it is in the best interests of our company to remain independent," a company spokesman said.

N&W stated yesterday that it currently does not intend to acquire Piedmont, to seek representation on the airline board, to make a tender offer for stock or to propose a merger. But the railroad also emphasized that, depending on business and market conditions, it may buy more stock in Piedmont.

An owner of 10 percent or more of an airline's stock is presumed under federal aviation laws to have a controlling interest, and that requires approval of the Civil Aeronautics Board.

However, under laws that opened up deregulation of the air industry in 1978, CAB controls over mergers and acquisitions were relaxed substantially. Previously, surface transportation firms effectively were prohibited from owning airlines; now the acquiring firm simply must demonstrate that an airline/surface-transport combine is in the public interest. Already, air carrier Tiger International has acquired trucking concerns, for example.

Piedmont has been flying high under deregulation despite initial misgivings by that company's managers. Piedmont Airlines, the major business of Piedmont Aviation, serves primarily the southeastern part of the United States with routes extending west in more recent years to Houston, Dallas-Ft. Worth and Denver and north to Chicago, Boston and New York. Piedmont is the third-largest user of National Airport here, with 62 daily flights.

At a time of general weakness in the airline industry, Piedmont posted record profits in both the first and second quarters of this year because of increased business from the company's new routes and connecting flights. Revenues have increased by one-third from last year. The company also is engaged in general commercial aviation sales and servicing, including the sale of private business aircraft.

N&W is one of the major rail systems in the East and Midwest, largely as a carrier of coal. It also has hoppers full of cash to spend -- $221.7 million as of June 30.

Analyst Andrew Kim, at the securities firm of F. Eberstadt & Co., said Wall Street is taking the N&W interest in Piedmont far more seriously than the Air Florida bid. Federal approval for N&W to control Piedmont probably would occur with little delay, he stated.

More important, "From a purely economic standpoint, a rapidly growing company such as Piedmont has cash needs that are very large . . . they need to invest to grow . . . and N&W has tremendous cash generation," Kim said. New tax laws probably will create even more cash for N&W, he added.

The major need of airlines currently is buying expensive, new planes. Proposed standards for National Airport would require Piedmont to buy a new generation of fuel-efficient, quiet planes over the next five years, for example. Piedmont earned $16 million last year, up 44 percent from 1979. N&W earnings rose 17 percent to a record $232 million.

Kim suggested that an N&W-Piedmont connection would be just one of many transportation industry combinations under relaxed federal regulations in the 1980s.