Arlington, facing more students than it had expected, will need to spend an additional $4.1 million on its schools next year, Superintendent Charles E. Nunley said last night.

Nunley asked the School Board for $74 million to operate the county's 27 schools and its special education center during the 1985-86 school year, an increase of 5.9 percent over the current school year.

The proposed budget calls for no new programs, but it does fund 67 new teaching and administrative positions amd follows the board's previously announced guidelines for pupil-teacher ratios and numbers of library books and textbooks.

At the School Board's request, Nunley submitted two budgets, the $74 million "management tier" that he supports and a $71.9 million "tentative tier" that he described as a "bare bones" proposal.

Neither budget contains money for salary increases, which will be set for all county employes under a "gentlemen's agreement" between the County Board and the School Board later this year, said School Board Chairman Gail H. Nuckols.

Nunley said he believed he had "an obligation" to suggest a 4.3 percent across-the-board increase.

The School Board wanted the "tentative" budget to require no more than $53.9 million in local funds, a guideline set by the County Board, which must approve the final budget. Nunley said he could not stick to that figure because of staffing and other changes adopted by the School Board and because the projected enrollment is 14,895, which would be 423 more than originally anticipated.

The tentative budget requires $54.6 million in county funds, 1.2 percent more than the local funding last year. It includes all the School Board's requests for textbooks, supplies and replacement equipment. It does not contain any money for new equipment and freezes the funds for library books at this year's level of $6,000.

The management budget, which Nunley described as "easy for me to support," requires $56.7 million from the county, a 5.1 percent increase over last year's local funding. Other funding comes from state and federal sources.

This budget would fully fund all the proposals adopted by the board, including such changes as lowering the student-teacher ratio in first-grade classes from 22 to 20.

Neither budget total includes funds for capital improvement, which were placed in a separate account for the first time. Nunley recommended $1.5 million in capital funds to remove asbestos , repave bus lanes and renovate roofs throughout the school system.

The School Board will hold five public sessions on the budget proposals, as well as a public hearing Feb. 21. It is scheduled to adopt a budget Feb. 28 and send it to the County Board.

In other action, the school board asked staff to come up with a specific model showing starting and ending times and the length of class periods, as well as the total cost, for implementing a seven-period day in the county's three high schools.

Nunley had recommended extending the current six-period day to seven periods in the senior high schools starting this fall, estimating the plan would cost $1.2 million in salaries for 44 additional teachers.

Board members criticized Nunley's proposal, saying they needed more specifics about how the school schedule would change and additional costs such as transportation and textbooks. "I want to know the bottom line," said Nuckols.