The contrails left behind by airplanes, also known as white grooves, are a result of a complex polynomial that takes into account several factors. Firstly, clouds form when the humidity in the air reaches 100%, which only occurs at extremely low temperatures. Commercial airplanes fly at altitudes where the temperature is around -56°C.

The second factor is the engines used by airplanes to generate thrust force. During this process, fuel and oxygen are burned, creating combustion gases and water vapor. The water vapor then condenses and creates the white groove that we see in the sky. The last component of this polynomial is the expansion of gas when it leaves the plane’s engine, where molecules are compressed inside.

Contrails are called “contrails” because they were originally referred to as “condensation trails.” These terms were combined to create a unique name for this physical phenomenon. However, not all airplanes leave contrails. The efficiency of an airplane’s engine is measured by its coefficient between work done and chemical energy produced.

Contrails can be used to predict weather conditions due to their nature and persistence. Sometimes during air shows, we see colored contrails or “polychrome grooves.” These colors are achieved by mixing dyes and releasing them at just the right time, so they’re not true condensation trails. There is also a striking type of contrail known as Prandtl-Glauert condensation clouds that occur when an airplane exceeds the speed of sound and forms a cloud shaped like a disk or cone.