Skywagon 185
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor
Flight Crew Last 90 Days 55; Flight Crew Total 13280; Flight Crew Type 660
Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors
I was providing instruction to my instrument student.  He was in the left seat; flying the plane on autopilot; having been cleared by me (simulating ATC) to proceed via direct to the ZZZ VORTAC at 9;500 MSL; there to commence the RNAV XX approach; expecting a circle-to-land.  I obtained approval from the ZZZ tower for this practice approach; with the usual caveats about maintaining VFR; no traffic separation provided; etc.  That approval was granted while we were still about 10 miles west of the VORTAC; inbound to it at 9;500 MSL and perhaps 130 mph indicated. The top of ZZZ Class D is XX00 MSL; and we had no need to enter the Class D until we were final approach fix inbound.Soon after getting approval from the tower for the practice approach; the tower informed us that there was traffic at about our 10 o'clock; southeast bound.  I saw it immediately both visually and on our GPS nav screen.  It appeared to be a white high-wing LSA (Light Sport Aircraft); either a Remos or a Flight Design.  I can't recall if the tower was talking to that plane; but I'd guess not; as the traffic advisory was issued only to our own tail number; as I recall.I watched the LSA carefully as my student (via our A/P (Autopilot); in NAV mode) took us towards the VORTAC.  We seemed to be converging slowly; with only a 20 or 30 degree difference in our headings; and exactly the same altitude.  The LSA was rock-steady in maintaining its heading and altitude; and seemed to be on A/P; also heading for the local VORTAC.We were slowly closing on the LSA; holding a constant bearing about 30 or 40 degrees behind its right wing.  As the distance between us decreased to about a mile; I instructed my student to make a serious power reduction; which he would have done anyway over the VORTAC.  I thought that this would change the equation enough that we would fall behind the LSA.  After half a minute (or less); I realized that we were not slowing enough to make an appreciable difference in our closure; so I told my student to put his heading bug about 45 degrees off to the left of our heading; and punch the HEADING button on the A/P; which he did.  Our 185 then made a nice standard-rate turn to the left; and we passed directly behind the LSA; exactly at its altitude and about 500 feet away.  The LSA never wavered - as if he never saw us.After about a minute on our new heading; I 'cleared' my student from present position direct to the VORTAC to commence the approach.  We heard nothing from the LSA; nor did we see it again.  The practice approach and landing were without incident.As I recall; we were always behind the wing of the LSA; so we were the overtaking aircraft.  I fault myself for waiting too long before starting the turn to break the slow-motion convergence with the other airplane.  There was no chance that we were going to collide with it - I never stopped watching it; and I am an experienced formation pilot; good at judging closure rates and angles; etc. But I did not allow for the possibility that the LSA might make a sudden sharp turn towards us; or that its pilot might look out to his right rear and be unpleasantly surprised to see us there. If such a situation were to arise again; I would make an earlier turn or altitude change to get a good resolution; and try to keep a mile away from the converging traffic.  It makes more sense; doesn't cost any more; and sets a better example for my student pilot.
Flight Instructor on training flight reported a NMAC with another aircraft in cruise.