THE COAL STRIKE is likely to be a long one, bringing great hardship to the miners and their families. It has been a mismanaged affair from the beginning - a terribly sad display of foredoomed hope among people who do hard and dangerous work, and who are now rebelling as much against their own union's inept leadership as against the companies. The winter is going to be a harsh one in the mining towns. It is hard to conceive of less promising circumstances in which a union could call a strike.

The largest customers, the utilities and the stell mills, have accumulated stockpiles to carry them literally to the end of the winter. Some of the coal-burning generating plants can be easily converted to oil. The strike will not halt coal production. At the beginning of this decade more than two-thirds of the country's coal was produced by miners who belonged to the United Mine Workers, but today they produce barely half of it. Weeks and months will pass before the nation as a whole begins to feel any serious effects of the strike.

The reasons for this strike do not readily lend themselves to the conventional kind of bargaining across a table. One of the reasons is the continuing chaos within the union itself. Another is the long history of harsh and violent relations between the union and the companies. Another is the isolation in which most miners live in small settlements with poor schools, weak political leadership and few amenities of any sort.

The daily friction between labor and management seems to be far higher in the coal mines than in most industries and, whatever the cause, no effective way to resolve these recurring disputes has evolved. The number of grievances is wildly out of line with other industries' experience. A great many of the miners consider that grievance procedures useless, with the result that wildcat strikes are endemic and absenteeism is high. That hurts production and reduces the flow of royalites into the union's health and retirement funds. Because depletion of the funds has forced the union to cut back health benefits, the miners' sense of grievance has increased, and they have found no way to express it but by striking. The strike has now cut off all health benefits - a desperately serious matter in Appalachian communites with no healt services but the union's clinics.

The turmoil goes back to the transformation that has overtaken the coal industry within the past decade.Well into the 1960s it was considered a dying industry, with declining production and steadily dropping employment. Dying industries are rarely known for enlightened labor relations. Then the utilities' use of coal began to climb and, when oil prices began to shoot upward in 1973, coal prices followed them. The coal that sold for $6 a ton in the 1960s now goes for $20. Employment is up for the first time in half a century. Wages are rising, but not so fast as profits. Now President Carter is pursuing a national energy plan that crucially depends upon a tremendous increase in coal production.

Both the Carter administration and Congress have been reluctant to take a hand in matters customarily left to labor-management negotiation. But in the coal industry, in recent years, the process of negotiation has not brought much satisfaction to either side. The companies have not achieved the stable production that they want and the miners have not gotten grievance procedures that they consider adequate or stable welfare benefits. The principal product of this strike will very probably turn out to be only more hostility, more suspicious and greater deprivation among the people of the coal fields.