A college student's chicken-egg experiment scheduled to be carried aboard the Challenger space shuttle Jan. 22 could help to determine the feasibility of colonies in space.

John Vellinger, 20, of Lafayette, Ind., is developing a special incubator to hold 32 chicken eggs during the space mission. The eggs will be one day old when the shuttle lifts off, and they will be back on earth before they hatch. Meanwhile, another 32 eggs will remain on earth and will be subjected to the same conditions except weightlessness. The chicks that hatch from both batches will be compared.

A chick hatches 21 days after an egg is laid, and the embryo forms during the first 11 or 12 days -- when the eggs will be in space -- and then grows during the remaining time, Vellinger said. The goal of the experiment is to study embryonic development in a weightless environment to determine whether chickens can be raised in space as a food source. His hypothesis is that growth will not be impeded by weightlessness and might be improved because, in space, yolks will not be pulled toward the bottom of the eggs as they are on earth.

Beyond the questions about chickens are others about whether other animals can be raised in space to feed space colonists and whether human embryos can develop normally and be born under weightless conditions.

Vellinger's experiment was chosen for inclusion on the mission because in 1983 it was one of 10 winners in nationwide competition sponsored by the National Aeronautics and Space Administration's shuttle student involvement project. NASA designed the project to counter flagging student interest in science and engineering, according to John T. Jackson, the Johnson Space Center's manager for student experiments. Companies sponsor student experiments as part of President Reagan's effort to encourage corporate volunteerism, he said.

Kentucky Fried Chicken is sponsoring Vellinger. The company will spend about $50,000 for his salary and living expenses this summer as he works on his experiment at the company's research and development laboratories, for materials for the experiment, for his travel to Houston and for some publicity costs.

The incubator will contain 32 eggs because that's the maximum number that will fit into the 17-by-20-by-10-inch space and 60 pounds of mass that NASA has alloted Vellinger for his experiment.

The astronauts will have to open the airtight, clear plastic incubator lid once or twice during the seven-day mission to permit more oxygen to enter. Opening the lid also will reduce the humidity, however, so the astronauts will need to check the incubator's temperature and humidity recorder a couple times a day to determine when to increase the humidity by adding water to sponges inside the incubator.

As Vellinger developed the incubator, he had to make trips to the Johnson Space Center in Houston to consult with scientists there and to conduct tests.

He tested chicken eggs on a centrifuge there to see if they could withstand 3.3 times normal gravity, the force that is generated during the launch, and discovered they will withstand 5.9 Gs. He decided to protect the eggs from G forces, shock and vibration by resting them on foam pads and had to test seven kinds of foam to find the kind that allowed the most oxygen to pass through. Like all materials used in the experiment, the foam had to be NASA-approved.

His prototype incubator also was tested for vibration and shock on a special vibration table in Houston. No ill effects were discovered when chicks hatched from the fertile eggs that were tested, but Vellinger decided to increase the number of air-filled shock absorbers from four to 12 and to use springs that have more play in the coils.

Kentucky Fried Chicken engineers are helping Vellinger solve design problems, but he says he is going to them for help only after he takes his plans as far as he can. "That's what's really been the learning experience for me," he said. Because their usual work is far removed from the problems of astronauts, the KFC engineers' reaction has been one "of excitement," Vellinger said. He also is being helped by personnel at the Johnson Space Center, who "keep me in tune to that space environment, because you don't always think about it."

Kentucky Fried Chicken spokesman Gregg Reynolds said the company became interested in sponsoring Vellinger after a group of regional KFC franchisees heard a talk on space travel and then started to look for other such programs. Johnson Engineering Corp. of Boulder, Colo., which acts as a NASA consultant on the experiments program, heard of the franchisees' interest and called KFC, Reynolds said.

Reynolds' background was a factor, too: He had worked in the space program for Boeing Corp. at Cape Canaveral in public information and describes himself as a space buff. He is connected with KFC's corporate contributions program, which has been focusing on aid to education and improvements in education.

This fall, Vellinger will enter his sophomore year at Purdue University, where he is majoring in chemical engineering. He said that he doesn't know what he will do after he graduates, although the project has given him a "great fascination with design, [and] the space environment really fascinates me."

He will observe a launch at the Kennedy Space Center in October to see how the student experimenters work with the technicians there.