didn’t know we were talking about take offs. Doesn’t matter though. lets say that by some chance air temp at some particular airfield at 14000 is 40 deg below zero celsius. (below 40 something fahrenheit) air density would be around 0.9 kg/m3.
Now if we take some arfield at 0 feet at 50 degrees celsius (around 120 F), air density would be around 1.1 kg/m3. Still higher.
In conclusion, it would be almost impossible to have weather conditions that would make a high and cold take off better than low and hot. If by some miracle temperatures do drop to more-than-arctic values that’d provide you with nice air density, i doubt one could even start the plane in the first place.
Which actually happens. You don´t have runways there, but you do have snow for skis.
The South Pole is slightly over 9000 feet above sea level. It is said to be 50 years ago that a first ski-equipped plane landed there – in summer. There has never been over -15 Celsius or so observed on the South Pole – typical polar summer day temperatures are -20, -30 Celsius range.
In winter, the absolute minimum is -78,9 Celsius.
Vostok camp is not on South Pole, but it is higher on the ice dome at about 11 500 feet and farther from sea, so it is colder year-round. Summer maximum -22 Celsius. Winter minimum observed -89,2: the minimum ever observed anywhere on surface of Earth. This does not mean it is the coldest place on Earth… for example, the summit of the ice dome is just over 13 000 feet, but there is no camp there and the camps in Antarctic interior are not very many, so not sure what exactly is the coldest place.
Anyway, -89,2 is record, but -70-s and low -80s are common polar night weather. And an important point is that it is impossible to reach Vostok by air in winter. The reason is said to be not that engines would not start, but that the snow is too soft and thick in winter and would not allow ski planes to reach takeoff speeds.
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