President Carter has set himself on another collision course with his old mentor, Adm. H. G. Rickover, in trying to build smaller and cheaper attack submarines.

Carter for the first time has ear-marked money in his fiscal 1981 defense budget for an alternative to the $450 million-a-copy 688 class of nuclear-powdered attack submarines championed by Rickover.

The administration's basic argument is that there will never be enough money to build the fleet of 90 attacks subs the Navy seeks if the admirals insist that only the expensive 688 will do.

Therefore, administration leaders contend, it behooves the Navy specifically and the national defence generally to build a mix of 688 class subs and cheaper but slower ones of a new class nicknamed "Fat Albert."

Each Fat Albert -- so named because of the bulbouse shape -- would cost about $300 million. It would carry Tomahawk cruise missiles for hitting distant targets on shore, as well as the full array of antisubmarine missiles. The design of Fat Albert would be refined over the next few years out of appropriations ranging from $30 million to $50 million annually.

Although Fat Albert would be a little slower than the 688 class killer sub, its backers maintain that survival of a submarine in the deep depends more on quietness -- hearing the enemy before he hears you -- than on speed.

Also, proponents of the alternative sub assert, the effectiveness of an attack sub depends more heavily on the weapons it fires than on the undersea platform they are fired from -- the submarine.

Rickover and his allies are countering those arguments in meetings with friendly lawmakers. The House Armed Services seapower subcommittee, which has been the leading congressional champion of such Rickover causes as the Nimitz nuclear aircraft carrier, is mobilizing for the 688 versus Fat Albert battle.

The main line of attack against Fat Albert is that, given the Soviet threat, the United States cannot accept anything but the best in major weapons such as submarines.

These submariners are emphasizing that a few knots of speed in the depths might mean the difference between life and death, either to escape a pursuer or to use the extra power to pull out of a deep dive when something goes wrong.

In short, the extra performance is worth the extra cost, according to Rickover and his allies.

That was also the heart of this year's argument over whether the Navy should build another $2 billion nuclear-powered Nimitz aircraft carrier or switch to a smaller, cheaper ship that burned oil.

Although Carter favored the latter course, and vetoed a defense money bill last year to stop construction of another Nimitz, Rickover and his allies prevailed this year. Congress earlier this month approved another Nimitz, with the shortage and high price of oil undercutting the president's effort to sell Congress on the smaller, conventionally powered carrier.

However, important differences give Carter a better chance of winning the submarine battle:

Both the 688 and the Fat Albert would be built for several more years. There would be no immediate switch, as would have been the case if the president had gotten his way on the smaller aircraft carrrier to replace the Nimitz.

Both the 688 and the Fat Albert would be nuclear powered. The energy crisis, which helped save the Nimitz, would not apply.

There is a growing realization, in the Pentagon and in Congress, that costs of individual weapons must be reduced to enable the nation to buy enough of them to cover trouble spots all around the world. "The timing is right," one Pentagon executive said.

The Soviets have provided a rallying point for both sides of the argument by building six Alpha class highspeed attack submarines. The United States has clocked one of the Alpha subs at about 40 knots, compared to the top speed of about 33 knots for Rickover's 688 class attack sub. The Alpha, built of titanium, also can dive deeper than the heavier 688 can.

Backers of the smaller but slower Fat Albert are thus in a position to argue that a few knots difference between the sub and the 688 are irrelevant because the Alpha can outrace either U.S. sub.

Opponents of moving away from the 688 to the Fat Albert can counter that the Soviet Alpha dictates development of a faster U.S. attack subs, not a slower one.

Carter, who formerly was one of Rickover's submarine officers and is an outspoken admirer of the 80-year-old admiral, said in March that "I am not sure even a slightly smaller or different design" than the Trident missile submarine or 688 class attack sub "would give us in the long run more submarines or more effective submarines."

His new defense budget going to Congress next month indicates he has had second thoughts about sticking with 688s indefinitely. Nine 688 class attack subs are in commission and 23 more are under contract.