The contrails left behind by airplanes, also known as white grooves or defractory trails, are a result of a complex polynomial that involves several factors. Firstly, clouds form when the humidity of air reaches 100%, which requires extremely low temperatures. Commercial airplanes fly in the highest layer of the troposphere, where temperatures can drop to -56°C.

The second factor is the engines used by airplanes. These engines generate thrust and burn fuel and oxygen to produce combustion gases and water vapor. The hot water vapor condenses and forms the snowy groove that we see on airplanes. Additionally, as the gas expands when it leaves the plane, it contributes to the formation of these contrails.

Contrails are often referred to as “contrail” in Anglo-Saxon countries, which is a contraction of “condensation” and “trail.” One question that arises from this phenomenon is why not all airplanes leave a trail behind them. The efficiency of an aircraft’s turbojet engine is determined by its coefficient between the work done by the engine and the chemical energy produced. Interestingly, studying the nature and persistence of contrails can be used to predict weather conditions.

During air shows, you may notice that some contrails are colored rather than white. These “polychrome grooves” are created by mixing dyes and releasing them at just the right time, so they do not actually form true condensation trails. Finally, there is a very interesting type of contrail called Prandtl-Glauert condensation clouds that form when an aircraft exceeds the speed of sound. These clouds take on a disk or cone shape due to a sudden drop in air pressure caused by supersonic flight.

In conclusion, contrails are formed through complex processes involving temperature, humidity, engine combustion gases and expansion effects during takeoff or landing procedures. While most commercial planes leave trails behind them due to their high efficiency engines running at supersonic speeds for long periods; however studying their nature can provide valuable insights into weather patterns making them quite fascinating for both scientists and aviation enthusiasts alike!