Date: 202111
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: Windshear; 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Takeoff / Launch
Airspace: Class G ZZZ
ATC / advisory: CTAF ZZZ
Reporter organization: FBO
Reporter function: Instructor; Pilot Flying
Reporter qualification: Flight Crew Flight Instructor; Flight Crew Commercial; Flight Crew Multiengine
Human factors: Situational Awareness
Second reporter function: Pilot Not Flying; Trainee; Student
Anomaly: Deviation - Speed All Types; Ground Event / Encounter Loss Of Aircraft Control; Ground Excursion Runway; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Landed As Precaution; General Physical Injury / Incapacitation
Contributing factors: Human Factors; Weather
Primary problem: Weather

Narrative: Weather conditions on the morning of the flight were clear with gusty winds out of the south. Winds were forecasted to increase later in the day as a cold front approached the region. Student was intending to go to basic training next week. The goal was to complete a 1.4 hour flight so the student could be signed out for the student's private pilot check ride. The instructor began a conversation with [a staff member] who flew the airplane the previous night on a cross country. The [staff member] indicated that there were no issues with the airplane when they flew. The student and instructor discussed what the goal of the flight was. The student and instructor discussed the weather conditions and how much time needed to be flown. A discussion about forecasted wind shear and turbulence took place. AIRMET's for those conditions were noted. The instructor talked to the supervisor and provided a briefing on the goal of the flight. The supervisor briefed the instructor on the conditions that were experienced when coming into the airport within the last hour. Airspeed was +/-10 KTS.; winds were out of the south at pattern altitude according to the PIREP provided by the supervisor.The student began the necessary checklists and started the engine. The student didn't notice any issues with the airplane during preflight. The fuel tanks were full at 40 gallons. The student and instructor briefed the flight once more and established roles. The instructor indicated he would be PIC for the takeoff and landing and controls would be given to the student after takeoff when appropriate. The instructor then began the taxi as the student completed the rest of the checklist items. The instructor stayed on the controls for the taxi until the airplane came to a stop for the run up. The run up was initiated by the student. As the run up and before takeoff checklist were completed; the student and instructor had another discussion about the wind speed and direction. The instructor directed the student to bug the wind direction and note the speed. The student bugged 180 degrees. Wind speed was 9 KTS.; gusting 19 KTS.; variable between 180 and 230 degrees. The instructor called back taxi on the CTAF and rolled out to the runway to use the full length of the runway for takeoff. The instructor then completed the 180 degree turn to depart. Takeoff power was applied and set. Static RPMs were above 2300 RPM and oil pressure was around 85-90 PSI. Airspeed came alive; and rotation was initiated around 55 KTS. and main wheels were off at 60 KTS. Airspeed began to build as the airplane crabbed into the wind. No issues with the engine were noted. As the airplane was trying to accelerate to Vy; airspeed was not building at a normal rate. The airspeed could not accelerate past 70 KTS. The airplane climbed to about halfway up the height of the surrounding trees before the aborted takeoff was initiated. It appeared that the wind had shifted to a tailwind and the aircraft was not going to gain sufficient airspeed. [The rejected takeoff] was initiated about halfway down the runway. An attempt was made to land on the remaining runway. Airspeed was not decreasing sufficiently to descend back towards the runway. Ground effect was experienced; and the airplane began to float. At that point; the instructor realized they may not be able to land on the remaining pavement. Flaps 40deg were put in about 3/4 of the way down the runway to help increase drag. The instructor realized this would momentarily increase lift and cause the aircraft to balloon. But the goal was to get the airplane as slow as possible to help with the impact. The airplane contacted the ground and ballooned up before settling back down on the remaining runway pavement. The instructor tried to brake using the toe brakes and aerodynamic braking by pulling full aft on the yoke. The airplane departed the end of the runway pavement and began rolling in the grass. As it rolled; it slowed down to roughly 20 KTS. ground speed and came to a rest in a ditch. At that point; the engine was secured; and the student and instructor were okay. The instructor made a phone call to the supervisor who came to the scene. The student and instructor exited the airplane with no issue and waited for help. The student had one injury on the knee from hitting the primer on the left side of the panel. The instructor got a cut on the hand from the carburetor heat. No other injuries were reported.  Contributing factors to the incident were the wind conditions. AIRMETs for wind shear and turbulence were active at the time of the flight; but the wind speed and direction were within limits of the aircraft. External pressure to complete the flight before a deadline contributed to the decision to go on the flight. Once power was applied and the airplane was airborne; the decision to abort the takeoff was initiated as soon as possible with the given indications. Other decisions once the aborted takeoff was initiated were done with careful consideration to reduce aircraft damage and personal harm.


Second narrative: [Report narrative contained no additional information.]


Synopsis: C172 Instructor and student pilot reported poor aircraft performance shortly after takeoff led to the decision to land on the remaining runway. The aircraft ran off the runway after landing; resulting in minor injuries to the student pilot.