I have a 4x6x16 to use for the header of a swing set. I was going to span 12 ft between supports and cantilever 4 ft but I now would prefer to put the supports at each end. I would hang 4 swings over the 16-ft span. Assuming 200 pounds per swing, would this be safe. I plan to use 12-ft splayed legs.
Looking at span charts, such as http://www.southernpine.com/app/uploads/AL_33-38L.pdf I see the Total Load for a plywood covered angled roof from SYP is as low as 34 lb/ft for a 2x6, and doesn’t simply double for a 4x6.
You are talking about a clear span of nearly 16’ with a total weight up to 400lbs swinging back and forth exerting greater than your listed weights when swinging hard — I think you’d want much closer supports and a lot of extra bracing. You might not immediately break the beam, but I can see it flexing a lot, and possibly pulling down the sides, especially if they are not attached to rigid anchors at the ground. From wood, for that type and use of span, I think you should look at a laminated, engineered beam.