This is the time when Robert S. Jacobsen can look out the door of his spacious office east of Luray, Va., and see the first blush of fire red on the dogwoods, the first tinge of yellow on the tupil poplars.

It is not a comforting sight.

Jacobsen, superintendent of Shenandoah Natioanl Park, turns to his new toy, a slim electronic calculator. On it he attempts to plot the future of his crowded, 193,000-acre purview.

"Let's see," he muses, "we've had as many as 52,000 visitors in a single day. At an average of 3 1/2-people per car, that's more is a car, 16 feet? Fourteen feet? Alright, let's say 14 feet per car. We've got 14,000 cars times 14 feet apiece." He multiples and a figure pops up on the calculator screen.

"Now divide that by 5,280 feet, which is a mile, and what do we get? That's 39.39 miles of steel, if you put them bumper to bumper along the highway. And the whole Skyline Drive is only 105 miles long.

"This gives you a feel for the magnitude of this operation. We're at a point now on busy where the overlooks are all filled, the campgrounds are filled, the lodges are filled, all with this 39 miles of steel."

Where to put the mases of steel and humanity that soon will stream to the mountains, demanding peace, quiet and spectacular scenery?

Three years ago Jacobsen and the Shenandoah staff came up with a plan that's relieved some of the burden and opened the wilderness to the masses: back-country camping.

The idea was to let the folks who were willing to rough it get off the beaten path, away from the overused campsites and trails. The response has been astounding.

Today, in the third year of the program, Shenandoah has far more back-country campers per acre than any other national park. This year Jacobsen expects 100,000 people to spend the night under the stars without running water, bathrooms, rangers to protect them or first-aid stations to run to if they stub their toes.

By comparison, mighty Yellowstone had only 42,000 back-country campers in its 2.2 million acres last year; the closest rival to Shenandoah's record was Sequoia, where 128,000 camped out in twice the space of Washington's woodsy backyard.

The reason: Shenandoah has perhaps the most liberal back-country camping regulations of any national park. Campers are required only to sign in at any ranger station for a free permit. After that, anyplace in a 150,000-acre area is open to them.

The basic requirement is to stay "out of sight," according to the Park Service brochure. "Pitch your camp at least 250 yards away from any paved road and half a mile from any developed camping area," it advises. "Fade into the wilderness by camping out of sight of any hiking trail, out of sight of any other camping party and at least 25 yards from any stream."

There are other stipulations: No open fires, no stopping in shelters except for emergencies, two-day maximum stay, no pets, no digging.

The effect of all this has been to disperse the impact of people at a time when, in Jacobsen's words, "We're beginning to wonder just how many people we can serve and still protect the natural resource."

It's also risky business, putting 100,000 people out in the woods unsupervised. So far disaster has not struck.

The biggest worry Jacobsen has is over the campers who wake up in the morning and say, "Let's go over to the park today."

These folks tend to end up together, and the effect is that they cluster along the most popular trails, which is exactly what Jacobsen is trying to avoid.

"Plan your trip," Jacobsen pleads. He recommends a specific library of inexpensive maps and books that provide a complete picture of the park and accurate information on where to go.

The library: "Guide to the Appalachian Trial and Side Trails in the SNP:" "Circuit Hikes in the SNP," and three maps - SNP Northern, Central and Southern sections. All five are drawn up by and available from the Potomac Appalachian Trail Club 1700 N St. NW. Washington, D.C., or from Shenandoah Natural History Assn., Luray, Va. 22835.

The idea is to find your own out-of-the-way site where you will never hear the snap of a pop-top or the mutterings of the 11 o'clock news from a Winnebago next door.

It's worth the effort.