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Netherthorpe aerodrome is the home of the Sheffield Aero Club. Light aircraft and tiger moths, flying lessons, etc. It has two grass runways 553m and 382m long (the smaller being the shortest in England I was told). It's off the road between Thorpe Salvin and Nether Thorpe, and due to the proximity of the roads running around the airfield, planes have to be at an altitude of at least 20ft when they cross the perimeter, so the landing on the short runway must present a challenge to novice fliers.
Incidentally, if you want to get your private pilots licence (PPL) it'll take about 50 hours and #5 - 6k. A less stringent UK only version takes 30 odd flying hours (NPPL).
These people offer trial flying lessons from Netherthorpe for about 85-100 (Oct 2011):
Phoenix Flying.
I had a trial lesson a couple of years ago and it was great fun - we flex to Stannage Edge in the peak district and back.
takeoff
Netherthorpe control
hangars
approaching runway 06/24
In world war II (1939-1945) my elder relatives could recall Spitfires and Hurricanes taking off from here as they were being ferried about the country.
Below - the satellite view of the airstrip from Google maps: