On June 6, 1999, approximately 1110 mountain daylight time, a Cessna 177RG, N2637V, was substantially damaged during a forced landing near Cheyenne, Wyoming. The private pilot and his two passengers were not injured. The airplane was being operated by the pilot under Title 14 CFR Part 91. Visual meteorological conditions prevailed for the cross-country personal flight which originated from Waxahachie, Texas, approximately 5 hours and 25 minutes before the accident. No flight plan had been filed. The pilot reported to the Investigator-In-Charge that he topped-off the airplane's fuel tanks on Friday, June 4, 1999. On Saturday, June 5, he flew for approximately 20 minutes. After landing, he taxied back to parking. The total engine run time and fuel used was not determined. On the day of the accident, the pilot performed a preflight inspection of the airplane, but did not remove the fuel caps and look into the fuel tanks. He departed at 0545, and flew directly to Cheyenne (645 nautical miles). He said that they experienced strong head winds all the way: 20 knots increasing to 35 to 40 knots over eastern Colorado. The pilot said "fuel was a concern the entire trip," and "numerous fuel calculations were done enroute [sic] using GPS and Loran ground speed." The pilot stated he last calculated the fuel remaining over Fort Morgan, Colorado. These figures indicated that they had been airborne 4.4 hours, and that they had 1 hour of flight to reach Cheyenne. The pilot calculated that they would have 0.6 hours of fuel remaining (for a total of 6 hours of flight [not including the unknown fuel burned the day before the accident]) after landing at Cheyenne. FAA records indicate that the pilot radioed the Cheyenne Airport tower that he was on "short final to runway 26, was low on fuel, and was not going to make it." The engine lost power approximately 1.5 nm from the approach end of runway 26. The pilot performed a forced landing on a motor cross track. During the landing roll, the airplane struck several dirt embankments collapsing the right main landing-gear with subsequent damage to the right wing and fuselage. Postaccident examination of the airplane by FAA inspectors found the fuel tanks empty. A representative of Cessna stated that a 177RG II would consume approximately 4 gallons of fuel for starting its engine, taxiing to takeoff, engine run-up, takeoff, and climb to an estimated 7,000 feet. A lower altitude would probably use 3 gallons of fuel. Due to the lack of information on the first flight, accurate flight endurance could not be determined.