Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 140; Flight Crew Total 6800; Flight Crew Type 1500
Communication Breakdown; Distraction; Situational Awareness; Time Pressure
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors
I pulled out for takeoff in front of a solo student on Final in another 172. I was conducting a first flight introductory ride in a Cessna 172.  After joining two other 172s in the pattern and landing; my student asked 'Can we take off again?  I want to do it!'  I checked my watch; aware I had another lesson soon. Time permitted one quick trip around the patch so we taxied back to the runway. Our airport has a 1500 ft. displaced threshold; so we can't see traffic on base when at the end of the threshold: a C172 will typically turn Final just inside the end of the Threshold. As we reached the hold line another company 172 was just climbing out from a Touch and Go; and I heard the competition's 172 call Base. I had been sharing the sky all day with that airplane and my counterpart; a solid airman and good friend. I queried '... do we have room to skoot out in front of you?'  I knew [my friend] would be able to handle such a request like the gentleman he is.  I heard a response I understood to be in the affirmative; but my student spoke up over him. I announced and rolled.  Immediately after liftoff I saw the shadow of [an aircraft] just to my right; and heard the pilot announce a go-around. As I followed him up the Departure Leg I apologized. We landed behind him; and immediately upon parking I went over apologize again. Discovered [my friend] was in the office; that was his student pilot; flying solo; whom I had cut off. I knew the spacing was tight; my schedule was tight; and I knew [my friend] could handle it.  I did NOT know [my friend] had already left the airplane. My actions would've been considerably different had I known that was a student pilot solo.
Due to time pressure and a communication error; an experienced flight instructor entered the active runway and took off while a soloing student pilot was on final approach.