Coal miner B.L. (Big Chew) Addair stuck a pack of Redman Chewing Tobacco into his left jaw, and, as he waited for the builge to mature for spitting, preticted that the major issue in the United Mine Workers' national election Tuesday will be to pick a leader who can unite the strike-torn union.

What 37-year-old mine mechanic Adair and others like him think matters a lot to the three men vying for the presidency of the 277,000 member union. It mattere even more to the Carter administration, which wants the unruly coal diggers to double the nation's black diamond output in 10 years to meet the energy crisis.

The election pits union president Arnold Miller, 54, against secretary-treasurer Harry Patrick, 46.Both were part of the team elected in 1972 to reform the UMW but the cleanup created problems that forced the two former allies into bitter opposition.

The lack of peace at the top is reflected in the coal fields, where rank-and-file miners have defied their leadership with wildcat strikes. Those walkouts have plagued coal production and cut into the union's health and pension system, which is sponsored from production royalties.

Miller's second challenger is Lee Roy Patterson, a 42-year-old western kentucky district union official who hopes to capitalize on the dissension. He frequently invokes the name of revered UMW leader John L. Lewis as he brands Patrick and Miller as an indistinguishable pair who have created the disunity that "destroyed the love and respect for each other that we once enjoyed."

Miller and Patrick point out that they democratized the union and won a 1974 bargaining agreement providing the largest single wage and benefits increase in its history. They also agree, in Patrick's words, "that Lee Roy is a Tony Boyle appointee who represents the darkest elements in this union." But they agree on little else.

Patterson concedes that he supported W.A. (Tony) Boyle, but not after the former union chief was convicted of ordering the murder of his rival, Joseph A. (Jock) Yablonski, (A Pennsylvania appeals court has thrown out the 1974 conviction and ordered a new trial.)

Patrick accuses Miller of "hiding in a Charleston motel every time this union has a problem. He's incompetent." Miller calls Patrick "an opportunist who supported me until he saw a chance to try to claim credit for what I've done - a lot of the time without his help - for the membership."

All three candidates claim to be leading in the race, but union observers predict the outcome will hinge on the number of votes. Incumbency could elect Miller if the turnout falls below the 65 per cent who voted in 1972, observers say. Miller is predicting a turnout of 150,000, with Patterson and Patrick getting a total of 50,000 votes.

Patterson, who has campaigned on equalizing pension benefits between retired and working miners, is hoping the union's 99,000 voting pensioners will turn out in force.

Patrick, whose poll several weeks ago showed him in third place, is believed by some mine leaders and independent observers to have moved up to a neck-and-neck finish with Miller, with Patrick winning if younger miners vote in large numbers.

All three candidates are doing some last-minute courting of the 14,000 an thracite (hard) coalfield pensioners, who draw only a $30-a-month pension. Patterson's campaign manager points out that Miller, who pledged a large anthracite pension, defeated Boyle by 14,000 votes in 1972.

A random survey of miners during a shift change at U.S. Steels's No. 9 mine at Gary, W.Va., indicated that more than half are undecided.

Roger Patterson, a veteran of 17 years of mining, said he was so disguested with the union dissension "I'd vote for Tony Boyle today if he was running."

Joe Pinter, a 34-year-old mine mechanic, reflecting the opinion of several miners, said he will vote for Miller because "I'm staying with a known factor."

Strike-weary jack setter Jim Carr, 29, was impressed that Patrick was pledging to win a contract provision that would allow wildcat walkouts only when authorized by a majority vote of the union local. "We're killing the golden goose right now," Carr said. "We need a union to protect us from the company and another one to protect us from the union."

Addair and other miners indicated they would not vote for Patterson because he was a strip-miner; others criticized Patterson for accepting contributions from leaders of the United Steel Workers Union.

Another touchy issue is the UMW's health fund. Patrick has charged that the fund plans to cut back on free medical care payments after the election. Miller strongly contests the charge, saying the health fund is independent of the union. Yet several local union leaders in southern West Virginia said they believe the charge is eroding Miller's support and ensuring a large turnout.

'I'm predicting that the man who gets 34 per cent of the vote, about a 2 per cent margin, will win," said the president of an 800-member local in southern West Virginia.

The winner will head bargaining with the industry for a new contract to replace the one expiring in December. Union and industry leaders predict a lengthy strike that could be a major setback to the economy.