Even if not very much force is required to deploy slats, in an airliner the hydraulics give control of all positions and ensure symetrical operation of each wing. To be sure to get this result, I guess a fairly large force is used.

Not forgetting, of course, a 'controlled' retraction which requires a motive force.

There's a reference to the Sabreliner's slats being sprung in this thread (post #8):

http://www.pprune.org/tech-log/9511-...tic-slots.html

so presumably the same applies to the F-86 variants that had slats (not all did).

The Triumph Gear Systems website gives maximum operating torque and rpm for their B767 leading edge actuator as:

Inboard 18,800 in.lb @ 2.2216 rpm
Outboard 12,000 in lb @ 2.345 rpm

If the actuator arm is six to ten inches long, then Owain's answer can be converted to a force in the range 1,000 to 3,000 lbf for that particular aircraft. This is the capability, ie the force available to meet all eventualities. The actual force required under normal operating conditions may be much smaller.

Every design will differ and I suspect assessment of the required force is very much a wind tunnel issue.

The use of slats and their effect in extending the Cd curves are well described here:
Anatomy of a STOL Aircraft

On the 727 there are 7 actuators in each wing moving the LEDs. No torque tube drives.

The DC-8 had slots which opened when flaps were selected.They were located inboard of the engine nacelles. Their function was to improve the airflow around the nacelle.If one or more failed to open a extra 10-15 kts was added to Vref if my memory serves me correctly.Failure to open on the ground was a no go item.