Skyhawk 172/Cutlass 172
Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial; Flight Crew Multiengine
Flight Crew Last 90 Days 150; Flight Crew Total 450; Flight Crew Type 250
Confusion; Situational Awareness
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
I have recording of our transmissions and Towers'. My student (student pilot) and I departed from Traverse City to the northwest and were gone for an hour. My student radioed Tower 11 NM out to the northwest and received our clearance to enter the Delta Airspace to return for touch and goes. Tower instructed to continue inbound for a right base for Runway 10 and report 3 NM to the northwest. My student continued inbound and 7 NM out; Tower instructed us to turn south and set up for a 3 NM final and to expect Tower to call our turn to final for a straight-in approach to Runway 10. Tower instructed us to turn a 3 NM final and as we turned inbound; Tower told us that we were following a company Cessna on a 1 mile right base and to report traffic in sight. We told Tower we were looking for traffic. A few seconds later we were a mile and a half from the runway. My student called Tower and inquired where the traffic was that following. Tower told us the traffic was on a mile and half final for Runway 10. My student replied we were on a mile and a half final as well. Tower then cleared us to land Runway 10. Then Tower inquired about the position of the other aircraft we were supposed to follow and they reported they were on a mile and a half final in our exact position. I instructed my student to execute a go around. At this point I looked out the window and saw them below us by about 50 FT and under our right wing. My student informed Tower that we are going around. Tower told us the company aircraft was below us and gave us directions to avoid a collision; adding that we were instructed to follow that aircraft. The other plane landed. We clear the airspace and came back in for a full stop landing. Tower clearly should have given our aircraft more separation earlier in the process of landing to avoid the situation. Tower instructed our every move as we approached the airport and entered the Class Delta and most importantly instructed us when to turn inbound on final 3 NM from the field when the other aircraft was clearly not on a 1 NM base but more like a 3 or 4 NM base.  I believe it was at this point that Tower should have seen an impending collision and instructed us to do a right 360 or some other delaying action to create more separation. However; I believe that partially I am to blame because I feel that I as an instructor was not paying close enough attention to the radio calls of what was going on in the traffic pattern as we approached the airport (because I was looking for traffic out the window and talking to my student) and I relied too much on false ATC reports to get my sight picture of where all the aircraft in the pattern were. I started to hear conflicting reports and knew something wasn't right and luckily nothing came of it. I am happy to be alive today.
Instructor pilot experienced a NMAC in the pattern when instructions from the Tower resulted in two aircraft being at the same place at the same time.