Skyhawk 172/Cutlass 172
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 50; Flight Crew Total 7000; Flight Crew Type 500
Workload; Troubleshooting; Distraction; Human-Machine Interface; Confusion
Aircraft Equipment Problem Critical; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Aircraft
IFR Instructional flight for a new IFR student (his third IFR training flight) in [a] Cessna 172. We departed normally IFR on the departure procedure (Gongs 1) [but the] student was having difficulty maintaining the radial outbound; which I initially attributed to a case of vertigo. Coaching him to correct his course; I soon realized that the directional gyro (DG) was acting erratic. The heading bug was frozen and the DG I perceived to be lagging. Taking control of the aircraft I leveled the wings. Cross reference with the GPS track indicated that the DG was more than 40 degrees off. The heading bug wouldn't follow the DG card but would stay frozen where it was placed. I reset the DG to the wet compass and decided to return to our departure airport (Our evening flight was to be an IFR [round trip]). I then asked center for vectors back to the airport. He indicated that I should [have] ask[ed] for the vectors before turning towards the airport since he had an aircraft on the approach. I indicated I was having an equipment malfunction and difficulty in that arena. I leveled off at the assigned altitude; and Center asked if I needed a no gyro approach. The gyro seemed stable for the moment; so I reset it and indicated that we should be able to take vectors. I asked him what my heading was while being vectored onto the approach to ensure that I was flying the vectors he was assigning. He indicated I was off by 20 degrees. I checked the compass and set the gyro again and corrected. As we were vectored onto the ILS 13L approach; the gyro seemed stable. As the approach progressed; the gyro became erratic again. We weaved down the ILS and popped out VFR around 2000 feet. We then cancelled IFR with Center and landed without incident. In retrospect; I should have accepted the controller's offer of no gyro approach. Funny how you want to trust the instruments; and tough it is to ignore one; even one that is acting up. Machines don't heal themselves; so once it began acting up; I should have abandoned its information and relied on the controller. I did alert him to our problem as soon as I recognized it; however I could have handled the situation better; I feel.
An instructor pilot and his instrument rating student were on a training flight in IMC when the directional gyro failed.  ATC provided assistance to return them to their departure airport where they combined resources to exit IMC descending through approximately 2000 feet on approach.