Floating helicopter

In the video below, Matt gets to fly in a helicopter in the name of maths. For particular propellor rotation speeds and video camera frame rates, it can look like the propellors of a helicopter are not moving at all and the helicopter is floating in mid-air. Explore the maths behind this by watching Matt’s video and trying our activity.

Watch Matt’s video to understand the maths behind this phenomenon.

There are loads of other fun videos on the internet about this. Here is one about a ‘stationary’ boomerang: https://www.youtube.com/watch?v=HMZotSOi9vk 

And one about a fidget spinner: https://www.youtube.com/watch?v=w7BeEzKGTOA – 

And we’ve even made a worksheet to justify showing your students these videos!

In the worksheet students need to match up the helicopter propellors with the video camera frame rate that would make them appear stationary.

Some frame rates match up to multiple sets of propellors, and visa versa. But there is only one way to match them so they are all matched up. Be careful, the rotation frequency is in ‘rotations per minute’, and the frame rate is in ‘frames per second’. 

There are a number of different mathematical approaches. The students could put the numbers in to the formula developed by Matt in the video. Or they could consider how often (as a fraction of a second) each set of propellors will look identical, and then see which of the frame lengths are a multiple of that fraction.