Engineers for the railroad industry have reinvented the wheel.

The principle remains the same, of course. The wheels on locomotives, boxcars, tank cars, passenger coaches and cabooses will still be round. They will still be made of steel and still roll on steel rails. The wheels will still go clickety-clack when they run over joints in the rails. Country singers probably will still write songs about rolling wheels between ditties about pickup trucks and jet engines taking "Baby" away.

To the casual observer of a passing freight, the wheel may even look the same. But it won't be. The wheel will roll smoother, last longer and be less likely to crack on account of heat buildup. According to the railroads' calculations, the new wheel will save the industry, and hence its customers, almost $700 million over the next 15 years.

On top of that will come another benefit -- fewer derailments. The Association of American Railroads estimates that wrecks caused by damaged wheels will drop from the 200-per-year level of the early 1980s to perhaps 10 per year after the wheels are phased into full service.

Many derailments are small -- but nevertheless costly -- affairs. However, from time to time, a wheel failure will bring about catastrophe, such as a 1969 derailment in Laurel, Miss., in which a broken wheel caused a chain reaction of exploding tank cars that destroyed 54 homes and damaged 1,350 others, killing two people and injuring 33 others.

So what's different about the new wheel?

Other than the roundness, just about everything. The main unchanged part is at the center, where the wheel fits on the axle. There is still a hole, called the bore, where the axle fits through the wheel's hub, and they're still shaped the same.

The differences are in the "plate," the formerly flat sheet of steel between the hub and the rim, the part that meets the rail.

One of the most important changes is in the plate. For a century and a half, it was believed that the plate should be straight -- flat as a pancake, flat as a phonograph record. Change Comes Slowly

But almost two decades ago, a wheel manufacturer, Griffin Wheel Co., decided to make a wheel with a curved, or parabolic, plate. The British were already experimenting with another version with an S shape, as opposed to Griffin's parabolic shape. A Griffin spokesman said the company's research showed that the parabolic plate would cut down on cracked wheels, but the curved plate did not catch on big for a number of years. Griffin continued to sell the wheel, and as the rail industry gained more and more experience with the wheel, it became obvious that the curved plate was, indeed, not breaking as often.

"The railroad industry is an old-line, established industry," said Griffin's president David Whitehurst. "They don't change quickly."

When a wheel breaks, it is almost always caused by excessive heat, which is usually the result of the failure of an individual rail car's braking system.

On trains, each car has an air brake system, controlled by the engineer through changes in pressure in an air line that runs the length of the train. There is a brake to slow each wheel, with a steel or cast iron shoe pressing directly on the outside of the wheel. When the engineer releases the air brakes on a long freight train, the brakes on one car sometimes stick, and the locomotive might drag that car for many miles. As the brakes rub, tremendous heat builds up in the wheel. This condition may lead to a cracked wheel, or the heat may alter the crystal structure of the metal, making it more brittle and leading to failure weeks or months later.

In the late 1980s, research carried out by the Association of American Railroads determined that curved plates -- either parabolic or S-shaped -- had superior resistance to failure.

Dan Stone, executive director of the association's Chicago Technical Center, said the curved shapes allow the plate to act like a spring, flexing when overheated, avoiding the buildup of excessive forces that are transmitted through rigid straight plates. Damage is often caused by the buildup of tremendous pressure that has no place to go, but the curved shapes give the plate resilience under pressure, sometimes returning to its original condition after the heat is removed and sometimes simply mitigating the damage to the point that the wheel can complete its full service life.

"It doesn't heal itself, but it prevents itself from getting any worse," Stone said of the new wheel shape. Fewer Replacements Needed

Until the new wheel came along, railroads assumed that when their wheels became discolored with a large, dark-brown area, they were heat-damaged and had to be replaced. Research showed, however, that most discolored wheels were not damaged, and the industry was wasting perhaps $135 million a year by throwing away good wheels. With the new shape, heat damage is all but eliminated, and the old replacement practices were ended.

As a part of this research, the railroads discovered that hardening the wheel rim by cooling it rapidly with water after casting -- called "rim-quenching" -- added even more time to its life.

As of last Jan. 1, all newly installed wheels must have the new shape.

The new wheel was a blow to many steel companies, which had made the old wheels through the so-called forge-and-roll method, called wrought steel. It costs so much more to make curved-plate wheels the old way that several major wheel makers -- U.S. Steel, Armco Steel and Bethlehem Steel -- dropped out of the business along with other smaller companies. The new wheels are made by casting.

The shape of the plate is only half the story of the new wheel. The wheel's tread -- the outer edge of the rim, which actually touches the rail -- also has a different shape and so does the flange, the part that hangs over the edge of the rail to keep the wheels from slipping off.

It turns out that for nearly 150 years, the railroad industry did not heed the messages the wheels were sending.

During the first 10 to 15 percent of a conventional wheel's expected service mileage of perhaps 200,000 miles, it was losing 30 to 40 percent of its tread and flange life. This "wear-in" process ended when the wheel reached what was considered a worn shape.

The new wheels have been given a new "worn" tread shape from the beginning. They are lasting many thousands of miles longer and rolling more smoothly. The saving in fuel costs alone in 1991 is expected to be $10.5 million, growing to $131 million a year in fuel and replacement savings by 2003.

"The problem is that Mother Nature wanted the worn profile," Stone said.