Atlanta's 20-month-old convention center is doing such terrific business the city wants to expand it. In New Orleans, building a similar facility became "a horror show" as costs jumped from an initial estimate of $63 million to a final price tag of $165 million when it opened. The roof of a center in Hartford, Conn., collapsed last winter under tons of snow.

So what will happen here if Washington finally builds a convention center complex of its own?

The experience of convention centers around the country can help in some ways to predict, and possibly to affect the success or failure of the project.

"If you can't have a successful convention in Washington, you might as well give up," said Jeter Walker, director of the Norfolk Convention Bureau. "But there's never going to be a clear answer before a center, any center, is built."

Norfolk's relatively inexpensive, $28 million convention hall and cultural center, SCOPE, is taking credit for bringing Elvis Presley, Frank Sinatra, Broadway plays and the Bee Gees to an entertainment-starved town. But the impressive complex still needs to book more conventions than wrestling matches into its facility.

So far, the Norfolk center has not generated a great deal of tax revenue. But that is not considered, a real problem. Built as a local urban renewal project that entitled the city to receive federal tax credits, the center is regarded as a bargain by almost everyone. In contrast, it will take New Orleans years to pay for its expensive complex, even though the center is attracting numerous bookings.

There are plenty of meetings and conventions for the booking - perhaps more than 7,000 nationwide - and the size of their attendance adrequired meeting space is growing annually, according to several convention industry sources.

Chicago, New York City and Washington rank one, two and three, respectively, in ability to capture the convention market, recent attendance records show.

Convention delegates spent $200 million here in 1976 and $215 million last year. Center advocates say Washington could take an additional $100 million if it had a facility to handle the larger convention meetings.

The sprawling McCormick Place in Chicago - with 800,000 square feet of display space - has long attracted the larger conventions and trade shows. Lately, however, soaring union costs and labor problems there, and at Detroit's Cobo Hall, are encouraging many past exhibitors to try newer facilities in the Southwest and West.

"If they come to Chicago, they're crazy," said Ann Harris, convention coordinator for the Chicago based International Association of Auditorium Managers.

Space resources, the labor situation, location and the facility management for any particular center are important considerations when an organization, association or exhibitor is choosing where to meet.

Availability of hotel rooms also is crucial, since the finest convention hall in the world will not attract eager conventioneers unless there also are sufficiant living accommodations.

Despite all these variables, convention center construction in the nation is booming as cities large and small seek new ways to compensate for sub-urban migration. They hope to offset a deteriorating tax base by bring more visitors - and their wallets - to town.

A convention center in Washington, according to a study by Gladstone Associates, would attract between 310,000 to 390,000 new convention delegates and exhibitors to the city each year. They would be drawn from an estimated some of the more than 100 largest national conventions that cannot now come here because of inadequate facilities.

The Gladstone report estimated that these new delegates would spend more than $100 million a year on city hotel rooms, restaurant meals, retail stores, transportation and entertainment.

These expenditures, in turn, are expected eventually to generate more than $12 million a year in tax profits for Washington even after the city has paid the estimated $10.1 million a year in debt service payments and operating expenses.

If these projections are realized, Washington's convention center - to be built south of Mount Vernon Square between 9th and 11th Streets NW - would be the most successful facility of its kind in the country.

But the project has its detractors, and the feasibility figures published in the Gladstone study are a major source of contention in the controversial dispute.

Opponents of the center have challenged the estimates for attendance, delegate spending and length of stay in the city. They question projections for revenue to be gained from so-called spinoff development around the center, and they say supporters of its construction have underestimated the competition from other cities for convention business and the competition that will come from some of the city's own hotels.

"If we increase the supply of convention centers, do we dilute their potential? The answer is yes," said J. Kevin Lawler, a senior associate for Gladstone Associates and the man who served as project director for the firm's study of the proposed complex.

But Lawler, like others questioned about Washington's competitiveness in the convention market, characterized the city as "special." He said its tourist attractions, status as they nation's capital and overall beauty give people "more of a reason to meet here than, say, Atlanta, which is getting the big rush now."

Austin Kenny, executive vice president of the Washington Area Convention and Visitors Association, concurred. He said Washington, which last year drew 720,000 delegates to 825 conventions and meetings, could have attracted more people if it had a suitable facilities.

The city's three biggest convention sites are the Sheraton Park Hotel, which has slightly more than 60,000 square feet of meeting space but is expanding to 110,000 square feet, and the Washington Hilton and Shoreham Americana hotels.

Some groups have met at the D.C. Armory, but that facility is considered inadequate for most gatherings and has the additional handicap of having no air conditioning.

Kenny, noting the continued expansion of the convention business, gave as an example the National Tire Dealers and Retreaders Association, which first met in Washington in the late 1950s.

At that time, Kenny said, the group "used the Shoreham garage, which had 30,000 square feet. Next time, in 1964, they used all 60,000 square feet of the expanded Sheraton Park. Then they told us they would be unable to return here because they had grown so much they would need 150,000 to 200,000 square feet."

When the National Association of Broadcasters met here in 1977, Kenny said, "they had to split their exhibits into three hotels. They were scheduled to return in 1983 but have rescheduled themselves into Las Vegas." He said the American Bankers Association is another group that has said it needs more space to meet in Washington.

Bob Lettwin, publisher of Sales Meetings Magazine, which keeps convention statistics on more than 25,000 associations and corporations, noted another big plus in Washington's favor as a convention choice.

"Washington is loaded with speakers, which means the association only has to pay limited fees for their transportation," he said.

But the city's lure as a convention meeting place is being challenged by opponents of the proposed center. One of the most outspoken of that group is Jack Phelan, a research economist for the bureau of economics at the Federal Trade Commission.

"The idea of Washington as special is all hypothetical," said Phelan, who questioned whether convention delegates would actually number as many, or stay in the city as long, as the Gladstone report suggests.

"The 44-day (in the study) estimate is rather high," he said. "They don't stay that long in New Orleans, San Francisco and New York, and surely there's lots to do and see in those cities."

Phelan, in a separate analysis he prepared for his testimony against the project before a congressional sub-committee, has estimated the convention center will attract only 100,000 new delegates to the city and actually may cost the city a net loss of $6 million to $9 million.

The government economist, who obtained some of his convention business estimates from an earlier draft report never published by Gladstone, also said that the expanded Sheraton Park will be able to handle most of the convention delegates who are not able to come here now.

Hotel officials there, however, estimate that as many as 48 convention groups will still be too large for the Sheraton park facility when it opens in October 1979.

"We certainly will be in competition for some of the same business," said Nord Schwiebert, the hotel's vice president and managing director.

He estimated the expanded Sheraton Park will be able to host 75 to 90 percent of the groups who cannot now come to Washington, but he said a convention center should be built because the growing convention and exhibit business could use both facilities fully.

Schwiebert's only concern is for the newly imposed 80-cent tax on occupied hotel rooms, which he said "has proved extremely counterproductive in other cities." The tax was enacted to help pay for some of the center's initial costs.

Phelan, summing up the basic objection to the center from numerous civic groups, some elected officials and a Senate subcommittee, said this: "The convention center will be paid for by 690,000 D.C. residents but is, basically, a subsidy to the private convention and tourist industry."

He said the cities of the proposal are not very comforted by the Gladstone Associates report and its estimates for the project's financial success.

"I don't think it was a true economic report," Phelan said. "I think it was a justification report since the city had already made up its mind to build the center."

One reason for this suspicion is an allegation that the Gladstone firm has an interlocking relationship with another subsidiary firm, Quadrangle Development Corp., that has made real estate investments in land not far from the proposed convention center site.

Gladstone's Lawler said he is "perturbed" at this suggestion of a conflict of interest and thinks the issues surrounding his firm's report "have been grossly distorted."

The Quadrangle firm, in existence since 1972, is a subsidiary of Gladstone but operates "completely autonomously" from it, Lawler said. Even though both firms share the same offices on M street, he said, they use separate staffs and have separate corporate officers.

Quadrangle does own property in the area of 13th and E streets NW, about five blocks away Lawler acknowledged , "but that can't conceivably be considered in the area of the convention center." Gladstone was also a central consultant for the Pennsylvania Avenue Development Corporation (PADC).

Lawler also angrily protests Phelan's suggestion that there were really two reports on the convention center and that an initially negative one - from which Phelan took some of his data - was revised to show a more optimistic view of the center.

"We did do an earlier (convention center) study for people associated with the Board of Trade," Lawler said. "But it was never meant to be a market study, only to look at the finanical perimeters" of the project.

Critics of the center remain unconvinced, however, arguing that Gladstone's connections with Quadrangle, which owns property in the downtown and near the West End, raises questions about the development studies the firm has done for PADC and for the city in the West End.

When the General Accounting Office tried to analyze the conflicting accounts for estimates of the center's success or failure, it judged the consultant's methodology to be "reasonable," but concluded there were "areas of vulnerability" in projections for construction costs and net financial benefits. GAO said the center could end up costing more and bringing in less than was estimated by Gladstone.

About the only thing proponents can agree on is that no one can really say for certain what will happen if Washington builds a convention center.