Date: 202009
Local time of day: 1201-1800
Location: ZZZ.TRACON, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Personal
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Cruise
ATC / advisory: TRACON ZZZ
Aircraft component: Engine
Component problem: Failed; Malfunctioning
Reporter organization: Personal
Reporter function: Trainee; Pilot Flying
Reporter qualification: Flight Crew Private
Second reporter function: Trainee; Pilot Flying
Anomaly: Aircraft Equipment Problem Critical; Ground Event / Encounter Other / Unknown
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Inflight Shutdown; Flight Crew Landed in Emergency Condition
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: A Instructor and myself were 1.5 hours into the flight portion of a Biennial Flight Review practicing steep turns between 3;700 feet and 4;000 feet MSL. Near the completion of a steep turn the aircraft began an intermittent low frequency vibration felt through the cabin floor. I asked the Instructor if he knew what that vibration was. He did not but suggested that we return to [base]. I released control of the aircraft to the Instructor and set the GPS. The Instructor trimmed the aircraft to Maximum Glide of 65 knots IAS with no flaps and turned on course. Carb heat was applied but further exacerbated the situation and was removed. We were at 3;500 feet MSL heading approximately 330 degrees and [the airport] was 16 NM in front of us. The vibrations were becoming more frequent and more intense. I tuned the comm 1 radio as instructed and we continued to descend with no power.It quickly became obvious that we would not be able to stay aloft long enough to reach [our home airport] at this rate of descent. I pressed NRST in the GPS and received [a nearby airport] at a heading of 290 degrees and 7.7 NM. The Instructor turned on course; but we could not get a visual. The vibration was now constant as was the descent and we agreed that we could not reach [that airport]. I entered the squawk code given to us by [ATC]and they located our position as we were descending through 2;100 feet MSL. TRACON advised of [the nearby airport]. The Instructor acknowledged and stated that we could not reach [that airport]. We turned west to the more rural area and began to look for suitable off field sites.We descended below 1;000 feet MSL and were unable to communicate with TRACON directly. A jump plane circling overhead relayed messages between our aircraft and TRACON. At 400 feet MSL; the Instructor and I agreed on a site to land. The Instructor performed S-turns to 100 feet MSL. I turned the fuel valve to the OFF position as we crossed over a levee and canal that bordered the east side of the landing site. The aircraft touched down 500 feet into a pasture and ground rolled an additional 500 feet to a complete stop. The aircraft came to rest with no power. There were no injuries to the two souls on board and no damage to the aircraft.


Second narrative: [Report Narrative contained no additional information.] Duplicate report.


Synopsis: C172 pilot reported a safe off-field landing resulted following loss of engine power.