It really depends on the material you are turning, depth of cut, tooling, etc. I mostly get a big hairball of long curly spring like strings from aluminum and steel. Aluminum strings can be a few feet in length, steel tends to be sub inch to a few inches those probably travel the farthest. Brass and cast iron create tiny chips that don't go far at all. Spindle speed also a factor of course. I would say you are fine with 3 feet out front with the occasional escapee flinging itself outside that zone. The lathe is well behaved, its the mill that will fling chips in a 10 foot radius and make a big mess.
That said do consider safety, I would not want to be boxed into a small area without an escape route if something goes horribly wrong on a lathe.