Narrative:

My student was flying the pattern at ZZZ; landing runway xx. Student had controls on short final and was going a little fast (70kts) on short final; he noticed and pulled the power to idle and verified full (30degrees) of flaps. I was shadowing the controls and helped get him into ground effect. Upon touchdown; the mains didn't fully touch down and the airplane was still flying. ZZZ's runway is [fairly short]; and my company doesn't allow touch and go's. Upon the mains fully coming down; I began to fully brake. I didn't retract flaps because I knew at any moment I might need to add full power and didn't want the loss of lift (associated with retracting flaps) to cause a sink or unusual attitude right over the runway. With approximately 400 feet of runway remaining I was still applying full brakes. With approximately 300 ft of runway remaining; we were not reading an airspeed but I estimate it around 40 knots; too fast to make a complete stop but not fast enough to take back off. Right before the threshold numbers (xy) I decided that I would continue to brake (fearing any attempt to try and take back off would lead to a potential stall...I did not know if we were above or below stall speed and the thought of stalling upon take off was something I wanted to avoid. Realizing we didn't have enough usable runway to make a complete stop; I continued to apply full brakes but I'm not sure if one of the brakes locked up or if the brakes were applying uneven braking; but the airplane veered to the right and off the end of the runway and down a slope. I immediately cut the mixture (right about passing rw xy numbers). We went down the hill to the right. Both myself; the instructor; and my student were not injured at all. The airplane came to a stop in the grass and the nose wheel deflated after rolling over a rock; resulting in the propeller to lightly strike the ground (there were small marks on the prop and grass marks). Once going down the hill we both braced and the airplane came to a complete stop at which time I removed the keys; turned the master battery off and assured the fuel cut off valve was pulled.

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Original NASA ASRS Text

Title: C172 instructor reported aircraft departed runway during landing roll out.

Narrative: My student was flying the pattern at ZZZ; landing RWY XX. Student had controls on short final and was going a little fast (70kts) on short final; he noticed and pulled the power to idle and verified full (30degrees) of flaps. I was shadowing the controls and helped get him into ground effect. Upon touchdown; the mains didn't fully touch down and the airplane was still flying. ZZZ's runway is [fairly short]; and my company doesn't allow touch and go's. Upon the mains fully coming down; I began to fully brake. I didn't retract flaps because I knew at any moment I might need to add full power and didn't want the loss of lift (associated with retracting flaps) to cause a sink or unusual attitude right over the runway. With approximately 400 feet of runway remaining I was still applying full brakes. With approximately 300 ft of runway remaining; we were not reading an airspeed but I estimate it around 40 knots; too fast to make a complete stop but not fast enough to take back off. Right before the threshold numbers (XY) I decided that I would continue to brake (fearing any attempt to try and take back off would lead to a potential stall...I did not know if we were above or below stall speed and the thought of stalling upon take off was something I wanted to avoid. Realizing we didn't have enough usable runway to make a complete stop; I continued to apply full brakes but I'm not sure if one of the brakes locked up or if the brakes were applying uneven braking; but the airplane veered to the right and off the end of the runway and down a slope. I immediately cut the mixture (right about passing RW XY numbers). We went down the hill to the right. Both myself; the instructor; and my student were not injured at all. The airplane came to a stop in the grass and the nose wheel deflated after rolling over a rock; resulting in the propeller to lightly strike the ground (there were small marks on the prop and grass marks). Once going down the hill we both braced and the airplane came to a complete stop at which time I removed the keys; turned the master battery off and assured the fuel cut off valve was pulled.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.