The pilot reported that, he departed with 28 gallons of fuel onboard for a cross-country flight and he used 100% power during the flight. The flight was uneventful for a little over four hours, until the pilot was approaching his destination and the engine began to run rough and sputter. The pilot was unable to reach a nearby airport and force-landed the airplane in an open field where the nose landing gear collapsed, which resulted in substantial damage to the lower fuselage. The pilot and a law enforcement examined the fuel tank and discovered that the fuel tank was empty. Fuel usage computations indicated the engine likely consumed all the fuel onboard while operating at 100% power. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.