A further 19 people were injured, four of them seriously, the authorities said, as an investigation into the accident was launched.
The plane failed to take off, and ploughed into the crowd, hitting a candyfloss stall and killing the 45-year-old woman working there.
“As it started, it looked as if a tyre suddenly burst,” one eyewitness told local reporters. “It only took off a few metres from the ground but didn't gain height and then smashed, out of control, into the candyfloss stall.”
The air show, which was due to continue today, has been cancelled.
In a further unusual accident at the weekend, 23 people were hurt, three of them seriously, when an ICE train ran into a flock of sheep in a tunnel, and came off the tracks.
The accident occurred when the Saturday evening ICE from Hamburg to Munich entered the 10-kilometre-long Landrücken tunnel between Fulda and Würzburg.
A police spokesman said, “As the train entered the northern tunnel, a flock of sheep were on the rails, which were hit by the train.”
It seems the train continued for three kilometres before four carriages derailed. At least 20 sheep were killed.
The passengers were evacuated. One woman told a reporter, “there was unbelievable smoke and dust, I thought I was going to suffocate. First you could just see meat, then I saw dead sheep, half dead sheep and a couple which were still alive, looking at me. I am happy to be alive.”