ENERGY FROM the sun - rather than Arab oil - is now warming and bathing guest, and washing their laundry and their restaurant dishes at several U.S. resorts, inns and motels, both north and south. The sun is even heating water for a downtown restaurant in Washington, D.C., and in at least one southwestern resort it is heating the water than in winter makes the heat exchangers work and in summer helps cool the guest rooms.

All the technical problems have not yet been solved, especially when space-age-oriented engineers try to leap past tried and tested solar-energy hardware into complicated and unproven satellite-type installations. And cost-benefit ratios have not yet proved out because the payout time - the years it takes of savings from reduced use of gas, oil, electricity and coal to match the original cost of solar installations - is variously estimated at 7 to 10 years.

None of the major solar installations has been in use in this country anywhere near that length of time.

Two hotel management pioneers in solar energy - La Quinta Motor Inns Inc., which started a successful installation last year in one of its inns in Dallas, Tex., and RockResorts, the Rockefeller hotel chain, which also put in solar energy last year at Little Dix Bay in the British Virgin Islands - are both going ahead full speed with additional solar-energy installations. Both spent their own money on their first experiments, getting no funds from the U.S. Department of Energy or its predecessor, the Energy Research and Development Administration, and little help.

Despite a few setbacks, caused mostly by overengineering and sometimes superfluous technology, and with the help of nearly $4 million of taxpayer money in solar-energy installation grants, other hoteliers are now showing keen interest and making considerable progress in installing such systems.

La Quinta, fully satisfied with its test installation in Dallas, is spending $513,000 of its own money (plus a federal grant of $559,000) to put solar energy into 11 La Quinta Motor Inns now building or planned> including a 122 unit hotel in Salt Lake City, which is not exactly in the sunbelt. RockResorts, pleased with its test at Little Dix, is adding $79,000 to a federal grant of $72,000 to make solar hot water at Caneel Bay Plantation on St. John, Amer- ican Virgin Islands, and is matching a federal grant of $138,000 for solar hot water at its Woodstock Inn in Vermont.

Both RockResorts and La Quints resisted the temptation of fancy engineering and opted instead for comparitively simple solar-heat collecting panels. These are flat copper panels, 3 to 4 feet wide, 7 to 8 feet long, and 3 or 4 inches deep, with water tubes running through the copper sheeting. Mounted on hotel rooftops, parking garage tops or on the ground, the panels are painted black for maximum absorption of the sun's rays and are covered by clear glass or plastic to keep the heat in (just as the interior of an automobile left standing with windows closed in the sun gets hot). Water is pumped slowly through the tubes to pick up the heat form the sun. In temperate climates, from Texas north, a glycol solution similar to radiator antifreeze is substituted for water; the heat it accumulates warms potable water through a heat exchanger or radiator.

In such basic installations, the only moving parts are the pumps to move the water or glycol around and the flow valves. The panels are set facing south and tilted toward the sun at an angle that is generally the same as the latitude of the building; this provides maximum exposure to the sun. Even in the winter at northern latitudes - for example. Vermont - on a day that the sun shines, a solar system is supposed to provide water well within the 120-140 degree temperatures usually furnished to hotes guest rooms. Depending on the size of storage tanks and quality of insulation, such systems can store enough warm water to go two to four days without sunshine; but all hotel installations have back-up heating systems set to come on-line automatically when the water temperature drops.

Engineers experienced in solar-energy equipment are quick to note that solar energy is not free; it costs money to make the initial installation, and there are maintenance costs and cares. For example, in city installations dirt and grime collect on the glass covers and must be washed off every few weeks; at coastal and island installations, salt crystals settle on the glass between washings. Yet, once the system is set and operating, maintenance appears to be quite low; there are no monthly utility bills for the sun's rays, and these systems do not consume high-priced, finite fossil fuels - gas or coal.

The reasons American Motor Inns Inc. leaped at solar energy for its 325 room, eight-story Frenchman's Reef Holiday Inn beach resort on St. Thomas, in the U.S. Virgin Islands, was steadily soaring price of oil and electricity needed to air condition its guest rooms and public space. Last September, when the resort, in partnership with the Energy Department, finished the largest solar-energy cooling system in the world at a cost of $554,000 (75 percent paid by the federal government), they expected to save $100,000 a year on fuel-oil costs.

This was a very scientific installation with 13,000 square feet of collectors on two roofs of the hotel, with Fresnel-type lenses concentrating the sun's heat on copper tubing containing water. Air conditioning reauires much hotter water than that needed for guest rooms, kitchens and laundries, so the engineers went for advanced technology. For maximum solar heat, the collectors were set up in gangs of 24, each gang powered by cables and pulley systems driven by electric motors activated by silicon-cell electric eyes. The eyes were supposed to follow the sun and order the motors to keep the collector panels always turned directly to the sun.

In order to measure how well the complicated system was working and to measure its productivity, 62 sensors were wired into the apparatus and hooked to a control panel that reported electronically to the National Aeronautics and Space Administration offices in Huntsville, Ala. Original results were reported to be satisfactory and exceeding expectations, but then nature took a hand.

As any engineer who has ever been there or even looked at a map should know, St. Thomas is and island with the Atlantic Ocean on one side and the Caribbean Sea on the other; Frenchman's Reef stands at the water's edge, and sea water is very salty. It did not take long for the invigorating salty sea air to corrode much of the fancy machinery that was supposed to motivate the mobile collectors and put the whole works out of commission. Now a major overhaul and replacement project must be undertaken that may well cost as much as the half-million dollars the project cost originally.

Solar engineers not obsessed with Department of Energy and NASA space-technology thinking, wonder out loud why an installation in the Caribbean had to be monitored, like a space satellite, in Huntsville, Ala., and how come the prospect of sea-salt corrosion was not anticipated. They also argue that at this stage of the art of solar-energy use, the simplest installations using already proven hardware are advisable, especially for hotel plants.

Marvin Rubin, an executive engineer in La Quinta Motor Inns Inc., is more than satisfied with the demonstration solar-energy system tested in their Dallas motel, which he said has already cut the motel's use of natural gas for heating and cooling by 45 percent and electricity by 11 percent. He said he anticipates this system will pay for itself in about seven years, and he warns against use of sophisticated hardware with as yet no proven reliability on earth. In the 11 new La Quinta solar projects, Rubin plans to use existing hardware - collectors, pipes, pumps, storage tanks - that is proven by long use.

Rubin is more optimistic and has more faith in solar energy than do some hotel-industry "experts" in this field. He fears that some opponents, or doubters, of solar-energy development have - or represent - vested interests in other sources of energy, such as natural gas, oit and electric plants.

"If we spent one-tenth the money, energy and effort that this country did on space on the development of solar energy," Rubin said, "we could solve our energy problems."

Digby G. Brown, vice president of engineering for RockResorts, is happy with the installation now functioning well at Little Dix Bay and is pushing ahead, using contemporary, conventional hardware.

"Based on our experience with a research-and-development project at Little Dix Bay, where we established the economic viability of solar hot water," Brown said, "we are proceeding now with two large solar installations at Caneel Bay and Woodstock. For the future, we are closely watching the advancement of the solar-panel art, as we know it is only a matter of time before more efficient, less expensive means of collecting the sun's heat will be available. Based on our three programs, we will consider additional solar systems for air conditioning and space heating as well as hot water at any or all of our resorts as the systems can be economically designed."

At Caneel Bay, where the solar-energy installation should become operative in May, Brown anticipates that solar energy will pay back its initial costs in seven years, with annual electric-energy savings of $20,000. The need to go to solar energy in the resort-hotel business becomes evident from Brown's estimates that in a tropical resort such as Little Dix or Caneel a guest can use 200 gallons of water a day, taking hot showers or tub baths after tennis, swimming, golf or sailing and before dressing for dinner. Downtown commercial hotels consume less water per guest because businessmen and convention delegates leave their rooms in the morning, do not return until late afternoon or evening, and thus have less opportunity to use the plumbing and electricity. But such hotels need more energy than resorts to heat and air condition public space, ballrooms and meeting rooms.

While it is possible to retrofit many existing, horizontally laid out resort hotels and motels with solar energy, high-rise city hotels are difficult because they have so little flat-roof space compared to their energy needs. RockResorts studied one high-rise Hawaiian hotel and abandoned the idea because it would require about five acres of solar collectors.

Some high-rise hotels are solving the problem ingeniously by hanging solar collector panels on the south side of the buildings and incorporating them right into the wall, vertically or at a slight angle toward the sun. The new 16-story, 250-rrom Radisson Plaza Hotel now under construction in St. Paul, Minn., uses an 11-storey-high, trignagular, glass-covered battery of soalr collectors tilted back against the south side of the building from a second-floor setback. This is expected to provide 35 percent of the hot-water and hot-air ventilation needs of the hotel, which will open in 1980; on the roof 10 loop windmills are expeected to generate additional electricity. The Energy Department has promised a half-million-dollar grant toward the job.

Marriott Corporation ran into retrofit trouble installing 300 3-by 7-foot collectors on the roof of its Hogate's Restaurant in Washington, D.C. They had to shore up the roof because of the weight of panels and steelwork, adding $5,000 to the $300,000 cost, of which the Energy Department put up 90 percent. The system began working in January, but exactly how much energy and money it is saving awaits final installation of metering devices. It is now estimated that the sun will provide 55 percent of the restaurant's hot water.