conveyor belt plane
I didn’t want to do it, honest, but I have really had enough of the “plane on a conveyor belt” myth, so I’m posting my take on the problem here. I’m using the kind of title that search engines will like, and I can point other people, on other forums, to this response.
The basic question goes something like this: if you could put a plane, of any size, on a conveyor belt, will it take off? The conveyor belt speeds up to match the plane’s exact speed, keeping it stationary, so it can’t move forward, right?
The question is framed badly – a bit like an “irresistible force vs. immovable object”. The first key point, which most people get, is that the engines are pushing against the air, not driving the wheels, which spin freely with a small amount of friction. This should make the answer easy, if you think in terms of Forces: the plane is trying to move forward, what would hold it back? Not friction – far too small a force. The plane moves forward, and eventually takes off, regardless of whatever the belt is doing.
Not enough? Well, what can the belt do, anyway? Another fundamental problem lies in the idea of the conveyor matching the plane’s speed. How would such a control system work?
- measure the plane’s speed
- speed up the belt to match the speed of the plane
- GOTO 1
Steps 1 and 2 both take time.
- All forms of speed measurement mechanism have an inherent time delay. If you doubt this, go back to the fundamental definition of what speed is: distance over time. This is even true of high-frequency speed measurement systems such as Doppler Radar or Lidar, as used by law enforcement.
Another way of looking at it: if you could take a zero-time snapshot of any object at any speed, it would always appear to be standing still (velocity=0), making that useless for velocity measurement: you need time to measure the distance travelled.
- If the conveyor has any mass, it can not change speed instantaneously. That would require infinite acceleration of its mass, meaning an infinite force would be needed (since force = mass x acceleration). Anything less, there’s a time delay. Don’t believe me? Try putting the figures in to the basic Newtonian acceleration formula, A = ΔV / T , where A = acceleration, ΔV = the change in velocity, and T = time = 0. Oh, and before you invoke Einstein, be aware that his Relativity formulae do not contradict Newton’s at these non-relativistic velocities.
- With these inherent time delays in the control system: by the time the conveyor reaches its intended speed, the plane has accelerated to a new speed, so the conveyor is slower than the plane, which is thus moving forward! Repeat until V0, V1, and Vr (takeoff).
Can I go now? 8)