First off, failure to follow flight crew instructions is a crime and you could could be charged with a felony depending on how bad the offense is. Does this mean that you will go to prison for not turning on airplane mode? No, but you might get a fine if they can prove it.
Back in the day when cellphones were rare and used analog signals, they could in fact mess with an aircraft’s navigational radios. However today cellular devices use digital signals and also use a lot less power because network towers are more prevalent and closer together. So if there is no need to worry about the airplane going wildly off course due to someone who cannot disconnect from the world for an hour or two.
But lets say that all 150 people on board choose not to place their devices in airplane mode. Well now we are going to have some problems. Now we have a very large number of radio transmitters and receivers in a very small space, which translates in to a lot of electrical energy inside a machine that uses sensitive electronics to navigate and communicate. Often the pilots will hear a clicking sound and transmissions might be distorted and or garbled.
The pilots heading indicator (pretty much an electric compass with gyroscopes) use a magna-meter for direction. This instrument uses the earths magnetic field in the same way that a compass is used in giving direction. If there is enough electrical energy near these magna-meters, then it could mess with instrumentation. This is also why powerful magnets are considered hazardous material in air cargo. It is also worth noting that electricity on its own can mess with standard magnetic compasses, and it is one of the ways that we can test to see if our windshield heat is working (in airplanes that are private jets and larger, the windshield is heated by running an electrical current trough a heating element that is laminated in to the windshield).
Turning on airplane mode on your cellular devices largely helps you battery life. When the device sees that it is getting farther away from towers or has little to no signal, then the device will use more power as it tries to pick up a signal.
Author – C Wellen (Pilot)