On September 2, 2023, about 0806 mountain standard time, a Piper PA-28-140, N6834W, was substantially damaged when it was involved in an accident near Prescott, Arizona. The private pilot, student pilot, and two passengers were not injured. The airplane was operated as a Title 14 Code of Federal Regulations (CFR) Part 91 personal flight. The private pilot, who was pilot-in-command (PIC), and the student pilot, who owned the airplane, both reported that they had flown the airplane with the two passengers earlier that morning from Falcon Field Airport (FFZ), Mesa, Arizona, to Prescott Regional/Ernest A Love Field Airport (PRC), Prescott, Arizona. The private pilot, who was seated in the left seat, stated that he flew the airplane until the flight approached PRC, at which time the student pilot, who was seated in the right seat, took the controls for the approach and landing. Both the private pilot and the student pilot reported that the flight from FFZ to PRC was uneventful. The student pilot stated that while at PRC, the airplane was partially refueled, and he verified that the tanks were filled only to the tabs, as requested. The private pilot estimated that they were on the ground for about 20 minutes before boarding for departure. According to the private pilot’s calculations, the airplane’s ramp weight was about 2,112 lbs (38 lbs under the maximum gross weight) and within the center of gravity envelope. The student pilot stated that “our calculated rollout” for the airplane’s weight, density altitude, and planned short-field takeoff configuration “was around 2,700 ft.” According to the private pilot, the student pilot assumed control of the airplane for the departure, taxied the airplane to runway 21L, and performed the run-up checklist uneventfully. The student pilot reported that, while conducting the “run-up checklist and leaning checklist…all instruments were on the green.” Both the private pilot and the student pilot reported requesting a “short delay” from the air traffic controller before takeoff; according to the student pilot, he used that time to review the short-field takeoff checklist with the private pilot, including verifying the flap setting, rotation airspeed, and climb airspeed. The student pilot stated that he set the flaps at 25° and planned for a rotation speed of “55 knots” (about 64 mph) and a climb speed of “64 knots” (about 74 mph). The student pilot stated that he taxied the airplane onto runway 21L, applied brake pressure, advanced the throttle to full power, checked the instruments, then released the brakes. He stated that the airplane “went airborne” about 3,000 ft down the runway, and that, for the first few seconds, “everything look[ed] and sounded perfectly normal.” He stated that, once the airplane ascended to about 200 ft agl, it “stopped climbing.” Around the same time, he noticed the stall warning light illuminate with “every intent of us on pulling on the yoke to maintain the rate of climb.” The private pilot stated that he observed that the airplane “was not achieving the expected rate of ascent” and that the student pilot “subsequently reported a drop in rpm.” The student pilot stated that, “after a few seconds…trying to gain airspeed by leveling the nose,” he noted that the airplane was not able to maintain altitude or airspeed, and he realized that they needed to conduct an emergency landing. The private pilot stated that he took control of the airplane to attempt to maximize airspeed and pitch for glide distance while the student pilot notified the air traffic controller that they were going down. The student pilot stated that the private pilot performed the “power off” landing from memory because there was no time to retrieve the checklist. The private pilot stated that, “due to the elevated nose attitude,” his forward visibility was limited, but the student pilot saw a road off the right side of the airplane. The student pilot stated that he took the controls and descended the airplane toward the road. The private pilot stated that, as the airplane descended, “the loss of power was accompanied by a pronounced noise and vibration” from the airplane and that, shortly thereafter, the airplane’s left wingtip made contact with a tree. The student pilot stated that the airplane struck “the top of trees on our path, and, right after, a tree branch to the left of the airplane made contact with the left wing.” Both the private pilot and the student pilot reported that the airplane then spun around; the student pilot estimated that it turned about 270° before it came to rest upright next to the road on which they were trying to land. All occupants exited the airplane, and first responders arrived within minutes. Photographs from the accident site showed the airplane resting on its nose on the side of a road with the nose landing gear displaced upward and to the left against the bottom of the fuselage. The fuselage was buckled at the firewall, the empennage was buckled aft of the cabin and displaced to the left, and the left wing showed leading edge crush damage near the tip. The flaps were in an extended position. Small branches and leafy tree or shrub material were at the top front of the engine cowling behind one propeller blade, which showed some chordwise scratching and paint loss on the leading edge near the blade tip. The other propeller blade was bent aft about midspan and underneath the nose of the airplane in contact with the road. POSTACCIDENT EXAMINATION A postaccident examination of the airframe revealed continuity throughout the fuel system. The fuel selector valve appeared undamaged and rotated normally, and each detent was noticeable. Throttle and mixture control cable continuity was established from the cockpit controls to the carburetor, and all levers moved freely from stop to stop when actuated by hand. An external fuel source was attached to the engine and the engine was started. The engine throttle was advanced to about 1700 rpm. The engine ran throughout various power settings uneventfully for about 5 minutes. A functional check was conducted of the magnetos with a change of about 75 rpm between magnetos. The throttle was advanced to the full forward position, and a static rpm of about 2700 was observed. The engine ran smoothly during the operational check and exhibited no unusual indications before it was shut down using the mixture control. AIRPLANE PERFORMANCE INFORMATION The OH for the airplane specified a maximum gross weight of 2,150 lbs. Section IV, Performance Charts, provided performance charts for Take-off Distance vs. Density Altitude and Rate of Climb vs. Density Altitude. Based upon a calculated density altitude of 6,357 ft (see “Meteorological Information” below), the calculated takeoff distance ground run for the airplane at maximum gross weight was about 1,700 ft, with a distance of about 3,500 ft to clear a 50 ft obstacle. The calculated rate of climb was about 400 ft per minute at maximum gross weight. Section III of the OH specified that the takeoff technique involves “allow[ing] the airplane to accelerate,” then easing “back on the wheel enough to let the airplane fly itself off the ground. Premature raising of the nose, or raising it to an excessive angle, will result in a delayed takeoff. After takeoff, let the aircraft accelerate to the desired climb speed by lowering the nose slightly.” The Short Field, Obstacle Clearance takeoff procedures in the OH specified lowering the flaps to 25°, accelerating to 55-60 mph (about 48 to 52 kts) to begin rotation, and, after breaking ground, accelerating to the best angle of climb speed of 74 mph (about 64 kts). The procedure stated, “slowly retract the flaps when the obstacle has been cleared and continue to climb at 85 mph” (about 74 kts). The Short Field, No Obstacle takeoff procedures were similar but specified accelerating to the best rate of climb speed of 85 mph (about 74 kts) after rotation. The Ground Check procedures in the OH stated, “carburetor heat should also be checked prior to takeoff to be sure that the control is operating properly and to clear any ice which may have formed during taxiing.” METEOROLOGICAL INFORMATION At 0753, the weather reported at PRC included temperature 19° C (66.2° F), dew point 16° C (60.8 °F), and altimeter setting of 30.27 inches of mercury. For these conditions and airport’s field elevation of 5,045 ft msl, the calculated density altitude was 6,375 feet. The calculated relative humidity at this temperature and dewpoint was 83%. Review of the carburetor icing probability chart contained within FAA Special Airworthiness Information Bulletin CE-09-35 revealed the atmospheric conditions at the time of the accident were “conducive to serious icing at glide [idle] power.” ADDITIONAL INFORMATION FAA Advisory Circular 20-113, “Pilot Precautions and Procedures to be Taken in Preventing Aircraft Reciprocating Engine Induction System and Fuel System Icing Problems,” stated that, “to prevent accidents due to induction system icing, the pilot should regularly use [carburetor] heat under conditions known to be conducive to atmospheric icing and be alert at all times for indications of icing in the fuel system." The advisory circular recommended that, when operating in conditions where the relative humidity is greater than 50%, “…apply carburetor heat briefly immediately before takeoff, particularly with float type carburetors, to remove any ice which may have been accumulated during taxi and runup.” It also stated, “remain alert for indications of induction system icing during takeoff and climb-out, especially when the relative humidity is above 50%, or when visible moisture is present in the atmosphere.” According to 14 CFR 91.3, the PIC of an aircraft “is directly responsible for, and the final authority as to, the operation of that aircraft.” Title 14 CFR 61.89 stated that a student pilot may not act as PIC of an aircraft that is carrying passengers.