An Instructor Pilot and his Student reacted to a failing engine when in the traffic pattern and cleared for a touch and go landing. The Instructor opted to go around and then landed on a crosswind runway. The engine failed completely after landing.

Narrative

While practicing traffic pattern operations at a towered airport with a student pilot; the engine would not react fully to the student's power input. Once the situation was established; I took the controls. At this point in time we were cleared touch and go from a left hand traffic pattern. I advised the tower that the aircraft would be going around. This bought more time for us to decide as to a course of action. Because multiple traffic were in the pattern for the active runway; I decided to make a full stop landing on the cross wind runway. Tower advised of traffic to follow and how to enter the pattern for the cross wind runway. Once established; carb heat was applied and flaps were used to slow the aircraft. Once on final the power was reduced to idle and the aircraft made a normal landing. Once on the ground; I attempted to keep the aircraft on the runway and exit on a taxiway. Power could not be kept so the aircraft was shut down once off the runway on a high speed taxiway. Tower gave us taxi instructions to which I asked for a tow back into the ramp. When asked for information on why a tow was necessary I advised of troubleshooting currently going on. The situation was over within ten minutes and; while an emergency was not initiated; I had complete control of the situation the entire time from the start of the situation until the tow of the aircraft was complete. Some lessons learned: Declaring an emergency would have gotten us on the ground sooner; but was not necessary due to the power we had. Once in the pattern landing was assured.