The plane landed at Christchurch after failing to land at Invercargill
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Dense fog and two aborted landings have prevented Prince William from visiting a school during his New Zealand tour.
The prince and his aides were among 65 passengers on an Air New Zealand flight to the southern city of Invercargill when it hit bad weather.
The pilot told passengers that he "wouldn't have seen the runway until we were about to hit it" as he changed route northwards to Christchurch.
The prince was said to be "completely relaxed" and was never in danger.
Pilot Jeff Lynton told the passengers from the cockpit: "Ladies and gentlemen, boys and girls, sorry about that.
"We made two approaches. We did the best we could."
William was seated at the back of the plane with his friend Thomas van Straubezee.
Mr Lynton said afterwards: "I wanted to get the boy down.
"He's got things to do. I've only had this once before and I've been flying for five years. "
With fog and cloud at 300ft, Mr Lynton had descended to just over 400ft before deciding to ascend again.
The prince had to cancel plans to visit Arrowtown School, where more than 300 pupils had decorated the windows with union jack bunting and were waiting excitedly for him to start a rugby match.
The prince's spokesman said: "He's very sorry he couldn't be at the school.
"As far as the aircraft was concerned he was completely relaxed. He knew the plane was in good hands."