Houston — Ambitious NASA plans for five space-shuttle launches and 18 unmanned flights this year have veered sharply off course. One result: Current relations between National Aeronautics and Space Administration (NASA) and Uncle Sam resemble what happens when a teen-ager gets his first car - and suddenly needs a larger allowance to keep the car roadworthy. In such cases both parties can dig their heels in, with parent claiming inability to pay and child warning that underfunding increases the risk of accidents.
NASA had counted on an extra $1 billion for a fifth shuttle to add to the two orbiters already delivered and the two under construction. NASA planners also requested $60 million to speed up an $8 billion program to orbit a permanent manned space platform by 1990. The fifth shuttle would provide more flexibility, allowing on-time launches for the 234 flights scheduled through 1994 even if one shuttle is put out of action for extended repairs. Similarly, NASA argues that adding a manned space station would help the shuttle program pay for itself by providing factory and warehouse facilities for the first commercial manufacturing operations in space.
NASA officials hoped President Reagan would use the space shuttle Columbia's July 4th landing last year to announce his support for both the fifth shuttle and the space station. He attended the carefully timed California landing, but issued only general approval for NASA achievements, not specific endorsements for future programs.
NASA hopes were further dashed by the 1984 budget. Despite paring its requests to what it considered absolute minimums, NASA found its budget trimmed by another $615 million to $7.1 billion for 1984. This 4 percent increase over 1983 spending, NASA spokesmen explain, doesn't even keep up with inflation.
To NASA officials, past years of budget cuts are to blame for the current two-month delay in launching the first flight of space shuttle Challenger. The liftoff of Space Transportation System Mission 6 (STS-6) was set for Jan. 24. Now the earliest possible date has probably slipped into April.
In what has turned into an embarrassing series of repeat performances, NASA briefings have discussed first one minor fuel leak and then a series of leaks and engine manifold cracks that have temporarily disqualified and discredited all of Challenger's three engines and one replacement engine.
Lt. Gen. James A. Abrahamson, who heads NASA's shuttle program, explained recently that Challenger's engine problems relate directly to ''reduced funding levels'' affecting shuttle assembly work. An initial manifold crack was traced to tubing that had been damaged during machining. One NASA official explained that instead of replacing the $3 million damaged unit totally, ''To save cost, we cut out a section and welded a new section in.''
Underfunding led to problems, General Abrahamson explained, because ''we just didn't have much hardware, and therefore we were reworking components.''
Looking on the bright side of the Challenger delays, Abrahamson says that NASA is developing new techniques for maintaining quality during manufacture and for testing units after final assembly.
NASA still hopes to launch a giant European-built Spacelab with STS-9 in October. This launch must take place by Oct. 15 or wait until February 1984 to obtain the right sun and moon alignments for planned experiments. But Spacelab's effectiveness will be limited unless a new pair of communications relay satellites is put in place beforehand by STS-6 and STS-8.
There is a darker side to Challenger's engine problems. To catch up, NASA employees and private contractors are working around the clock to make Challenger flightworthy. One shuttle official says overtime hours and tight budgets increase the risk of serious problems developing.
Abrahamson says despite the STS-6 delays, ''none of our customers has deserted us.'' But each delay adds to the appeal of the European Space Agency's competing unmanned Ariane rocket, now advertised in aerospace publications as ''Your place in space with an operational launch vehicle . . . the first commercial space carrier.''