On May 19, 2014, about 0930 mountain daylight time, a Piper model PA-28-180 airplane, N9631C, was substantially damaged when it departed the runway during takeoff at Yuma Municipal Airport (2V6), Yuma, Colorado. The student pilot was not injured. The airplane was registered to and operated by Heartland Aviation Incorporated under the provisions of 14 Code of Federal Regulations Part 91 without a flight plan. Day visual meteorological conditions prevailed for the student solo cross-country flight that was destined for Alliance Municipal Airport (AIA), Alliance, Nebraska.The student pilot reported that after referencing the airport windsock, which indicated a variable and gusty wind condition, he decided to takeoff on runway 16 (4,200 feet by 75 feet, concrete). He stated that before achieving liftoff, the airplane encountered a wind gust that raised the right wing. He was unable to correct for the wind gust before the airplane departed the left side of the runway and descended into a drainage ditch. The airplane lower forward fuselage and engine mount sustained substantial damage when the nose gear collapsed. He reported no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. At 0932, a local weather station, located in Yuma, Colorado, reported the wind direction was from 001 degrees at 18 knots, with 26 knot wind gusts. A review of wind data readings, taken during the hour before the accident, established that the wind direction and speed had been from the north at 13-15 knots with recorded wind gusts between 20-26 knots. Additionally, the wind speed had increased throughout the same time period. The nearest aviation weather reporting station was at the Wray Municipal Airport (2V5), located about 25 miles east of the accident site. At 0935, the 2V5 weather observing system reported: wind from 340 degrees at 18 knots, gusting 24 knots; 10 miles visibility; clear sky conditions; temperature 23 degrees Celsius; dew point 10 degrees Celsius; and an altimeter setting of 29.70 inches-of-mercury.