First it was the airplane, which made Arizona as accessible to northerners as Florida. Then it was air conditioning, which saved people from sprinkling sheets on baking August nights. Cheap land attracted developers, the automobile defined the city's sprawl.

It happened almost overnight: in the middle of a desert, a 20th-century city.

But even with a 30 percent growth rate, booming Phoenix is not bustling.

"We were accused by an eastern writer of being the biggest small town in America," says Mayor Margaret Hance. "To me that's an accolade. It means the openness and friendliness has not disappeared."

Unlike other big cities, Phoenix has the feel and flavor of a small town. Its downtown is quiet by day, desolate by night. Its pace is noticeably slower than in many other large cities. Even its country music stations seem weeks behind those elsewhere.

Phoenix is built not around commerce but recreation, with acres and acres of parks and an outdoor life-style that is the principal attraction even for its best and brightest. But the focus of local political power is different.

For an increasing number of people here the small-town facade is giving way to the reality of urban life. They feel powerless and alienated from the city's decision-making. They especially object to the business establishment's degree of control and are fighting to create a new political balance here.

So far they have not been successful, but it appears their time is coming. City elections Nov. 3 could give a clue to how soon.

Most people say Phoenix, three times an All-American city, is attractive, enjoyable and efficiently run by the mayor, a six-member city council, and a strong city manager.

But as with many small towns, real power is exercised by the business and professional establishment, and Phoenix has raised this practice to a high--and increasingly controversial--art.

A few decades ago, this establishment was small. It included Eugene Pulliam, who published the extremely conservative local papers, and a handful of bankers and lawyers. In the late 1940s, they created an organization called Charter Government to help clean up the gambling and prostitution that then existed, and for almost 30 years, Charter Government hand-picked the mayor and the city council. To prevent the city government from having too much power, candidates generally served just two two-years terms.

In the middle 1970s, this informal power elite decided to annoint a new establishment. "Several of us got together and said, 'Why don't we form an organization of younger men with clout?' " says Frank Snell, 81, who came to Phoenix in 1927 and became one of its most powerful citizens.

The group is Phoenix 40, a Who's Who of the business establishment. Out of the Phoenix 40 has come a young leadership group, which each year picks about 45 men and women between the ages of 25 and 45, offers them training in leadership skills and grooms them for power. Phoenix 40 and its subsidiaries have contributed much to the city, but there is growing dissatisfaction with their ideas and their exclusionary approach to city government.

"They are the self-proclaimed group of city leaders," says Terry Goddard, a young lawyer who helped found Urban Focus, which is often at odds with Phoenix 40 over issues. "They have economic muscle and political muscle, and they keep the lid on."

The rapid increase in population is creating pressure for a new governing structure, possibly to expand the council and elect half of its members from districts. A petition drive is under way to put the question before the voters next spring, but the organizer is not confident of victory. "There's an irrational fear of Chicago-style ward politics taking over our clean city," says David C. Tierney.

But there are signs that the city establishment is less opposed to the idea than it has been in the past, and Mayor Hance believes it is inevitable. Changes in the council structure would likely guarantee representation for Hispanics, almost 20 percent of the population with no members on the council.

The nonpartisan city elections in November are also seen as a test. Mayor Hance is running without serious opposition for her fourth two-year term, but an interesting council race is under way. Charter Government has endorsed four of the six incumbents, but not the one black member and the one female, although its slate includes a woman and a wealthy Hispanic businessman.

One outsider trying to get in is Rick DeGraw, a professor at Arizona State University.

"The biggest issue here is that folks don't feel the city council represents them," DeGraw says. "There is an incredible vitality in this city, but it's slowly being eroded because people don't feel secure in their neighborhoods and the city has not done anything to make them feel secure."

But by the standards of older, industrialized cities, local politics here are bland and quiet. "You can argue apathy versus contentment from here to kingdom come," Hance says, admitting the lack of serious opposition concerns her. "Apparently our citizens are content with how things are going."

And how things are going.

Thirty years ago, there wasn't a square foot of shopping center space in the area. Today there are almost 9 million. Phoenix has gone from small town to the top 10 in America in little more than a generation.

It grew from 17 square miles and 107,000 people in 1950 to 329 square miles and 790,000 people in 1980. Its metropolitan area today is home to 1.5 million people. In the last decade alone, the city grew by 30 percent and the metropolitan area by more than 50 percent.

Yet, for a city of 800,000, Phoenix appears remarkably tension-free. Its economy is booming, fueled by the high-technology electronics industry; unemployment in August was 5.3 percent.

Housing is relatively inexpensive and plentiful, with open space for both leisure and future growth. Phoenix is one of the lowest-density big cities in the world, and 35 to 40 percent of its area is undeveloped.

"There aren't any flash points here," said George Britton, an aide to Arizona Gov. Bruce Babbitt and former city official in one of the Phoenix suburbs.

Phoenix is not without its share of big-city problems. Crime is on the minds of many people here, although Mayor Hance says crime decreased 11 percent in the first eight months of 1981.

Traffic is a growing irritant, because Phoenix is one of the few big cities in America without a freeway system. It hopes to have one someday, but without the help of the federal government, the cost may be prohibitive, despite recent approval of a sharp increase in the state gasoline tax.

Water was once thought to be the most serious threat to the city's future, but no longer, thanks to the Central Arizona Project, which will divert water from the Colorado River here beginning in 1985, and to a tough state groundwater policy that will reduce usage in the Phoenix area from about 220 gallons a day per person to about 100 gallons.

"Phoenix looks like it has been watered by Niagara Falls," says Babbitt. "But in wealthy suburbs, it's finally fashionable to have cacti."

The city prides itself on citizen involvement in government, on self-help and efficiency. After the tax-cutting Proposition 13 was approved in California in 1978, several hundred citizens were put to work on Phoenix's capital needs.

They decided the city should raise $253 million through the sale of revenue bonds, went out and raised the money necessary for a campaign and got the bond issue approved in 1979.

This spring, when the Reagan administration's budget cuts began to take shape, a local builder called the mayor's office, Hance said, and offered to repair 550 miles of city streets free.

Then an anonymous donor gave $20,000 to keep open three city swimming pools. A service group donated $10,000 to the city's silent-witness program, which encourages people to help solve crimes. Another group of citizens took responsibility for putting lights up at a new park. And a Boy Scout troop adopted a city park and now providing regular maintenance.

"Arizona still has the western can-do attitude, the feeling that when times are bad, we can take care of ourselves," Hance says.