On October 27, 2021, at 1750 eastern daylight time, a Beech BE-23 airplane, N2353Z, was substantially damaged when it was involved in an accident near Ballston Spa, New York. The flight instructor and student pilot were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The student pilot checked the fuel levels during the preflight inspection, measuring 1 inch of fuel in the right tank and 3 inches of fuel in the left tank with a ruler. Based on his calculations of the airplane’s fuel consumption during the 3-day, multi-leg flight home from Texas after purchasing the airplane, he determined that each inch represented 1 hour and 15 minutes of flying, and therefore they had 5 hours of flying time. The student and instructor departed Saratoga County Airport (5B2), Saratoga Springs, Florida, around 1530. They flew in the practice area then around a nearby lake before returning to 5B2, where they completed eight touch-and-go takeoffs and landings. About 2 hours and 20 minutes into their flight, after turning to final approach on the ninth landing, the engine sputtered, stopped producing power, and the propeller continued to windmill. The instructor took control of the airplane, established the best glide speed, and performed a quick check of the mixture, carburetor heat, ignition, and master switches, but was unable to restore engine power. He selected an area for a forced landing and as the airplane descended, he noted power lines in their flightpath. He pitched the airplane up to avoid power lines and heard the stall horn sound. The airplane missed the power lines, descended to the ground, and landed hard, fracturing the nose landing gear. The airplane then nosed over and slid to a stop. Examination of the wreckage by a Federal Aviation Administration (FAA) inspector revealed that the airplane came to rest upright in a nose-down attitude. The right wing was substantially damaged where the right main landing gear pushed up into the wing. There was no evidence of fuel in the left-wing tank and the right-wing tank was about 1/8 full. The flight instructor stated that they used fuel solely from the left tank, did not switch fuel tanks during the flight, and leaned the mixture during the cruise portions of the flight. Postaccident examination of the airplane revealed that the left fuel tank gauge needle indicated “E” and the right fuel tank gauge needle indicated just above “E” when the airplane’s electrical master switch was selected ON. Both right and left fuel caps were secure and the fuel vents were unobstructed. No fuel was present in the left tank, and about 1 inch of fuel was present in the right tank. All fuel lines from the left and right fuel tanks to the fuel selector, gascolator, both fuel pumps and the carburetor were intact and devoid of fuel. No fuel was found in the gascolator bowl or the electric fuel pump. The examination revealed no other preimpact anomalies or malfunctions that would have precluded normal operation. The airplane’s pilot’s operating handbook (POH) stated, “do not take off when the Fuel Quantity Gages indicate in the yellow band or with less than 11 gallons in each main tank.” A cockpit placard specified a capacity of 26 gallons for the left fuel tank and 26 gallons for the right fuel tank; however, the student reported that the airplane’s tanks held 60 total gallons of fuel. In follow-up interviews with the flight instructor and student about fuel planning, the student indicated that they were leaning the fuel mixture and had a tailwind when returning home from Texas and calculating the airplane’s fuel consumption rate. Both indicated that the fuel measured 9 inches when full. When asked about the fuel planning performed before the accident flight, the instructor responded, “Neither of us did and that's the problem.”