Hammond, 36, was trying to break a land speed record in the car when it overturned several times.
It is understood that the 5000hp Vampire jet car was travelling at 450km/h when the crash occured.
Witnesses say that Hammond was taking his last run of the day when the car veered off the track in a cloud of smoke, turned over several times before finally landing upside down.
A North Yorkshire Fire and Rescue Service spokesman said that the car ? powered by a Red Arrows engine ? veered off the track onto grass before flipping over.
The vehicle's roll cage had saved Hammond's life.
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The parachute had deployed, and ambulance crews, with the help of Top Gear's film crew, managed to right the vehicle.