Hang gliding, paragliding, and mini-wing flights in the United States are governed by FAR part 103, Federal Aviation Regulation, Ultralight Vehicles (except for flights by FAA licensed pilots in FAA registered aircraft which are governed by FAR Part 61 and FAR Part 91) and may be governed in addition by other civil laws and regulations. Persons participating in hang gliding, paragliding, and mini-wing operations under FAR Part 103 are required by law to fly in accordance with FAR Part 103, and in accordance with any other applicable civil laws.
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FAA Documents - General
Federal Aviation Regulation 14 CFR Part 103 - Ultralight Vehicles (aka "FAR Part 103")
Additional resources for members are available in the Members Only Area: Flight Operations - Members Only