The four crew members of the balloon DaVinci TransAmerica, battered by a violent thunderstorm that had been following them most of the day, rode their craft to earth just after midnight today in a field in northwest Ohio.

The balloon's pilot, Vera Simons of McLean, Va., suffered a leg injury and was being X-rayed early today at St. Rita's Hospital in Lima, Ohio. The three other crew members were reported uninjured.

The crew members landed in a field, then made their way a mile and a half to a farmhouse and were driven 15 miles to the hospital.

The forced landing was described by one of the meteorologists monitoring the flight as "as safe as could be expected at night, in a strange area, under hazardous conditions."

The last radio contact with the crew, which had sought to make the first nonstop balloon crossing of the United States in the 10-story-tall, helium-filled DaVinci, came at 11:56 last night.

A crew member, talking to meteorologists monitoring the flight from Bedford, Mass., said: "The ground is coming up fast. We are ballasting everything we can."

The term ballasting refers to jettisoning objects aboard the gondola to lighten it in an attempt to regain altitude.

The last radar fix on the DaVinci was at 6,000 feet over Van Wert, Ohio, according to the meteorologists. Shortly before the last radio message was received from the crew, the balloonists reported: "We just broke out next to a town and airport. We're at 6,000 feet and still in lightning. There's lots of thunder."

The thunderstorm, which had chased the balloon across Missouri, Illinois and Indiana, pulled the craft into its winds soon after 11 last night, battering it and dumping snow and heavy rains into the 10-foot-square fiberglass gondola.

The crew radioed that it wanted to abandon the attempt at a transcontinental flight. At that point, Tom Edmunds, one of the meteorologists, remarked, "They (the crew) sound like they might have had it."

But those monitoring the flight were reluctant to bring the balloon to the ground because a night landing is made extremely dangerous, by the possibility that the gondola might get caught in power lines or other obstructions.

The balloon ascended to as high as 22,000 feet last night in an effort to catch winds that would keep it ahead of the howling storm which was described by meteorologists as "of the worst magnitude."

The crew was low on oxygen and doing without it at altitudes up to 15,000 feet, although it normally is used at that height.

At midday yesterday, the balloon was running several miles ahead of the storm, which had violent up and down drafts starting at 4,000 feet above the ground and moving up to 60,000 feet.

The balloon was blown directly over the famous 630-foot Gateway Arch in St. Louis, and across the Mississippi River.

Earlier yesterday, when the DaVinci was slightly east of downtown St. Louis, pilot Simons suspended two Army surplus smoke grenades on fishing lines from the gondola and trailed red and green smoke streams behind her.

The smoke clouds, however, were a brief diversion for the balloon's four=member crew, which had to dump sand ballast over the city at 1 p.m. EDT to gain the altitude needed to outrun the thunderstorm.

The storm, kicking up strong gusts of wind and flashing lightning that was visible at midday, chased the DaVinci across Missouri yesterday morning. It followed the craft through the Missouri River Valley at a distance of about 40 miles.

By late yesterday the DaVinci, which lifted off last Wednesday from Tillamook, Ore., had traveled more than 1,800 miles.

The four members of the balloon crew, who last Friday broke a long distance mark for ballooning in the United States, would have broken the-all-time balloon endurance record at 4:23 a.m. today, surpassing the record of 137 hours and 6 minutes.

That record was set in August 1978 by the three-man crew of the Double Eagle II, which flew 3,150 miles from Maine to France in the first successful manned balloon crossing of the Atlantic Ocean.

As the DaVinci passed over St. Louis yesterday, Simons, a contemporary artist specializing in helium mobiles, said she didn't have time to display much of her "art" equipment packed aboard the balloon's cube-shaped, fiberglass gondola.

In addition to the smoke grenades, that equipment includes a 1,000-foot-long plastic mirror that can be suspended from the gondola, scores of strobe lights, and so-called "message units"-- postcards addressed to Simons' house in McLean. The cards request that the finder write down what he thinks about balloons and mail it in.

Simons was busy calculating the amount of sand she needed to dump overboard, to permit the balloon to climb quickly from 9,000 to 14,000 feet. A DaVinci spokesman in Bedford said yesterday that nobody here would notice the sand falling on them. "More junk comes from a smokestack in a half hour," the spokesman said.

Crewmember Hyde said the relaxed on-board mood of Sunday afternoon, when the cfel drank ine and ate a leisurely dinner over Kansas, ended yesterday in the scramble to get away from the thunderstorm.

"You bet the picnic is over," said Hyde, an eye surgeon who specializes in cornea transplants in nearby Kansas City.

The balloon's rapid ascent over St. Louis yesterday forced air traffic controllers at Lambert Field, the nation's eleventh busiest airport, to divert some airline flights over the city and warn all others to be careful of what was referred to over aircraft radio as "that slow-moving vehicle." the crew drank wine and ate a leisurely dinner over Kansas, ended of way over all other aircraft.

The balloon's path over St. Louis came as a surprise to officials of the Seven-Up soft drink company, which has its world headquarters there and is the balloon's major sponsor -- with five banners covering such of the craft's gondola. The balloon had been expected to fly 150 miles north of the city.