In this post, I want to address an interesting thought experiment that I “found on the internet”™.  The problem is usually phrased in a few different ways but here is the version I have chosen to attack.

The Problem

It was a calm, sunny day at Horsehead Airport.  An aircraft, ready to fly to a foreign country lines up on the airport runway, carrying out final preparations for takeoff.  On this calmest of days, the evil Dr. Horrible has decided to discombobulate the pilot of our aircraft by swapping out the runway for a long conveyor belt.  This belt is powered by a very powerful motor that can drive the conveyor belt and anything on it at  enormous speeds.  As the pilot throttles up for takeoff, he powers up his conveyor belt to move backwards.  His aim is to move the conveyor belt backwards just fast enough to cancel the aircraft’s forward motion, hence preventing the aircraft from achieving takeoff velocity.  Does he succeed in doing so?  Can the pilot still takeoff his aircraft or is he at the mercy of the evil Dr. Horrible?

What do you think would happen?  Take an intuitive guess.  Part of being a good scientist is getting good at making defensible guesses.  Also part of being a good scientist is realizing when your common sense and gut feeling are going to fail and training to guess more systematically.  When I first ran into this problem many years ago, my gut feeling was “Hmm..  if the conveyor belt moves as fast as the aircraft but in the other direction, then the two would cancel each other out and the aircraft would be at rest, unable to take off!”.  My second thought was “Wait a minute.. maybe the engines can produce enough airflow over the wings that the plane can lift off even if stationary!”.  The Mythbusters investigated a similar question a while back (here is a sneak peek).