When the Defense Department went to Congress this spring for permission to recruit more troops, the Army asked for 2,600 more soldiers.

The Air Force, despite its image as the technological companion to the proletarian Army, asked for 21,000 more active-duty forces, about eight times what the Army wanted and more than double the requests of all three other military branches combined.

That contrast reflects a pattern the services have followed for several years and are projecting into the future.

The Army may conjure up images of thousands of soldiers slogging through the mud; the Air Force, of a few pilots and technicians in crisp blue uniforms managing weapons worth billions of dollars.

But it takes thousands of people to maintain, operate and--especially in the case of nuclear weapons--guard the technological wizardry the Air Force controls.

During the next five years, the Air Force estimates that its 593,000-person active force will have to rise by 91,000 people, few of whom would ever see combat in the event of war.

And if the country deploys 1,000 of the now-fashionable "Midgetman" nuclear missiles, which would be small enough to haul around on trucks, the Air Force would need 50,000 people more, according to a Congressional Budget Office estimate.

"The Army equips the man," one Air Force colonel said. "The Air Force mans the equipment."

The House Armed Services Committee recently shocked Defense officials by voting against any active-duty force increases, a vote the full House is considered likely to endorse. But Air Force officials seem unconcerned, apparently convinced that Congress will have to provide in 1984 or 1985 whatever it rejects this year.

Behind that conviction are the weapons Congress already has approved for the Air Force.

Next year alone, Air Force officials said, the Reagan administration's build-up will give them 66 more F16 jets, 36 more F15s, 6 KC10 cargo jets, 390 air-launched cruise missiles and 48 ground-launched cruise missiles, among other weapons. During a five-year period Air Force officials expect their bailiwick to encompass 100 MX missiles, 90 B1 bombers, almost 300 new fighter jets and, barring an arms control agreement, 464 ground-launched nuclear cruise missiles in Europe.

Between 700 and 750 people--pilots, maintenance experts, security guards and others--are assigned to each wing of 24 jets, and they in turn require training, medical and other support personnel. For the controversial cruise missiles, which like the proposed Midgetman are small and movable, the demands for security and other personnel are even greater.

"It's not like money, where if you lose it it's insured," one official said. "These things are going to be taken out into the field, and you need whole crews of cooks and drivers and security people to go with them."

The Air Force told Congress it will need about 9,000 people altogether to manage the cruise missiles, which are scheduled to be deployed at specially constructed bases in Europe beginning this December.

The House Armed Services Committee did not question those figures when it rejected the manpower requests.

"It was just a way to grab their attention on an issue the committee has raised for years without much success--better use of their reserves," said Rep. Les Aspin (D-Wis.), chairman of the subcommittee on military personnel.

The Senate Armed Services Committee, in a preliminary closed-door vote, cut the Defense personnel request in half, allowing an increase of about 8,200 for the Air Force, according to aides. The issue still must be addressed again in Senate committee, on the floors of both chambers and finally in conference.

While Navy officials "reacted violently" to the House committee vote on personnel, according to Aspin, the Air Force surprised committee members by taking the action in stride. Tidal W. McCoy, Air Force assistant secretary for manpower, said, "We feel pretty strongly that we need" the 20,100 increase. "But it's like anything else; the world won't fall apart if we don't get them."

The Air Force grew by 4.4 percent between 1980 and 1982, slightly less than the Navy's 4.9 percent active-duty increase but considerably more than the Army's 0.5 percent growth to 780,000. Of 24,800 new Air Force positions, about 600 were pilots, according to Defense Secretary Caspar W. Weinberger's annual report to Congress.

One administration official said the Air Force has kept a low profile in defending its manpower requests because it already has the richest concentration of skilled and experienced officers.

Although the Air Force can justify personnel increases by the new weapons coming on line, it is more vulnerable to congressional scrutiny, the official said, since even during the worst days of military recruiting in the late 1970s the Air Force--with its commercially useful skills and lack of arduous combat duties--had far less trouble attracting and keeping skilled officers.