Date: 202010
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: Small Aircraft; High Wing; 1 Eng; Fixed Gear
Operator: FBO
Operating under: Part 91
Mission: Training
Flight phase: Takeoff / Launch
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: Small Aircraft; High Wing; 1 Eng; Fixed Gear
Reporter organization: FBO
Reporter function: Pilot Not Flying; Instructor
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial; Flight Crew Multiengine
Human factors: Training / Qualification; Situational Awareness; Distraction; Confusion; Communication Breakdown; Workload
Second reporter function: Local
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Detector: Person Air Traffic Control
When detected: In-flight; Taxi
Result: Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Contributing factors: Environment - Non Weather Related; Human Factors; Procedure
Primary problem: Human Factors

Narrative: I was conducting a flight training event with my student pilot. We just returned to the airport to practice performance takeoff and landings. We had just made a full stop - taxi back. We called holding short that we were ready for touch and goes. We were told to hold short for landing traffic. Several planes land and depart. Both my student and I hear what we believe to be our abbreviated tail number being cleared for takeoff. We read back cleared for takeoff instructions; finish final items on the checklist; and take the runway. On our takeoff roll we hear Tower ask who is on the runway and I respond with our tail number. Tower then advises to either exit the runway or begin our roll. We were already on the roll; so we continued the takeoff. After our lap in the pattern we terminate the training flight and contact the ATC number. I believe I heard our tail number and believed it was a takeoff clearance. However; due to a high volume of traffic the morning of the event due to a lengthy TFR that lasted most of the day; there was a lot of training and jet traffic. I could have heard a similar call sign and my student could have stepped on the intended recipient of the ATC instruction. I know when there is a high volume of traffic waiting to arrive and depart it could be best to use my full tail number to lessen confusion; and take extra measures to ensure all radio communications are properly received and copied.


Second narrative: Aircraft X called up requesting pattern work during a high traffic volume session and was given hold short instructions; due to the fact that there was an IFR arrival jet on about a 3 or 4 mile final. Aircraft X subsequently read back his hold short instructions. I talk to 3 different aircraft before I cleared Aircraft Y for a touch and go. Apparently Aircraft X read back 'Aircraft X cleared touch and go' and then subsequently got onto the runway without me catching it. Aircraft Y clarifies their touch and go clearance and I canceled the touch and go clearance and gave them a left 360. During this time inside the cab my CIC/GC/FD was trying to clarify information about a TFR that was supposed to be going into effect shortly and we had received no prior information on. This resulted in several phones ringing during this already busy time. After scanning the runway I saw an aircraft who appeared to be holding on the runway with my jet traffic now within 2 miles of the runway; since I had multiple aircraft holding short of the runway I tried to quickly identify the aircraft; so I could taxi them off the runway in a timely manner. However Aircraft X didn't identify himself by name until about the 3rd time I reached out to them. With minimum time to react I told the aircraft to taxi clear of the runway or depart immediately. Aircraft X started their departure roll and as soon as airborne I told them to offset the runway so I had sufficient spacing with my IFR aircraft on final. Immediately following my Jet traffic landing the OM entered the cab and started trying to have the CIC help him find our local weather form; so our new trainee could fill it out. We started the day short staffed with no prior knowledge that someone would be coming in to cover for a couple hours; so the rotation wasn't going to happen as expected. When there are less people in the cab we have enough space to work without our masks and due to the fact that there were extra nonessential people in the cab I had to replace my mask; while I firmly believe mask should be required; they do interfere with the side tone which affected my ability to catch Aircraft X's incorrect readback. No one in the facility had received any information on the TFR that was supposed to be going into effect. This resulted in several miscommunications and confusion.


Synopsis: Flight Instructor and Local Controller reported the instructor's flight departed without clearance with traffic on very short final after mistakenly taking another aircraft's clearance for takeoff.