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“It suddenly struck me that that tiny pea, pretty and blue, was the Earth. I put up my thumb and shut one eye, and my thumb blotted out the planet Earth. I didn't feel like a giant. I felt very, very small.” – Neil Armstrong (1930-2012)

Fresh Reads from the Science 'o sphere!

Saturday, December 22, 2007

Aeroplane On A Treadmill

Sometimes, we are so obsessed in our quest to find out all the answers in life that we neglect to examine the questions. This is parodied in Doug Adam's Hitchhiker's Guide to the Galaxy.

The problem is: even if a question is unclear or meaningless, someone can still find many answers to it.

Unfortunately, these answers do not advance our knowledge. Instead, they generate constant debates where nobody seems to get any closer to the truth.

Asking the right question is very important.

A superb example of this is the "Aeroplane on a treadmill" (aka "Airplane on the conveyor belt") puzzle, which has befuddled thousands of people for many years. This topic has sparked unending arguments in numerous Physics forums all over the world.

Here is the original question:

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?

Hmm... looks like a simple "Yes" or "No" question.

Except nobody seems to agree which is the correct answer.

The reason for this is because, well... both answers are correct, depending on how you understood the question.

How can this be?!??

Let me explain what I mean by reformulating the above question into two alternative questions:

1. An aeroplane is standing on a huge, computer-controlled treadmill. The treadmill tries to negate the forward speed of the vehicle by rolling in the opposite direction. The treadmill is long enough to accomodate the normal take off distance of the aircraft.

Will the plane take off?

The answer: Yes (with some exceptions).

The aeroplane will take off, because its airspeed depends on its engines, not on its wheels. Unlike a car, aeroplane wheels are unpowered and essentially free-wheeling. As a result, they do not produce much friction and the speed of the treadmill is not transmitted to the aircraft itself. Thus, the speed and direction of the treadmill is largely irrelevant.

In this scenario, when the pilot applies full throttle, the aircraft starts to move forward relative to the ground (or lamp post in above picture). The computer-controlled treadmill tries to slow the vehicle by rolling in the opposite direction at heroic speeds, but to no avail, since it only slows down the vehicle by a tiny percentage.

The wheels may be spinning at insane speeds, but the whole vehicle is accelerating normally (relative to fixed ground objects), eventually reaching take off velocity and then flying upwards into the skies.

Exceptions will occur if the wheels do produce significant friction, for example rusty old wheels or if partial brakes are applied. In addition, if the wheels are structurally limited to certain maximum spin speeds, then the tyres might burst during the take off run.

2. A computer-controlled aeroplane is standing on a huge, computer-controlled treadmill. The treadmill rolls in the opposite direction of the vehicle. The entire system is set up in such a way that the no matter how much engine power is applied and how fast the treadmill is rolling, the aeroplane remains stationary relative to the ground (or lamp post in the above picture). The treadmill is too short to accomodate the normal take off distance of the aircraft.

Will the plane take off?


The reason why the aeroplane will never take off no matter how much engine power is used is because aeroplanes take off primarily because of lift, not thrust.

If an aeroplane is forced to remain stationary, then its ground speed is zero and corresponding airspeed (on windless days) is also zero. No air is moving over its wings to generate the required lift to raise the vehicle into the skies.

The only way that thrust alone can make the aeroplane fly is when the vehicle has vertical take off engines, like in Harrier jets, which has a thrust-to-weight ratio of more than 1.

Of course, this exception is not in the spirit of the original puzzle.


So you can see that the correct answer to the puzzle depends on how the question is asked and hinges on one crucial point - does the treadmill succeed in keeping the aircraft stationary? If this part of the question is not agreed upon, then nobody will be satisfied with the answers.

There are other horrible questions that have triggered endless debate and conflict.

One of them has plagued humankind since the dawn of civilization.

Does God exist?



angry doc said...

My take is that the plane will take off if it is a propeller plane, but not if it is a jet-engine plane.

If it is a propeller plane with the propeller placed in front of the wings, the propeller will generate an airflow over the wings, and when the airflow passes over the wings a lift will be produced. However, the power required to produce a lift in this case may be higher than that required when the plane is moving.

If the plane is a jet engine plane, airflow is only produced when the plane moves relative to its surrounding, and so when the plane is stationary relative to its surrounding now lift is produced.

The Key Question said...

To Angry Doc:

Yes, that sounds plausible but as you've observed correctly to generate lift by propwash alone would require higher power rating than a normal take off, since the effective area of both the main wing and tail control surfaces is reduced.

A vehicle like the V-22 Osprey might be able to take off in this manner.

Anonymous said...

I would argue that a Jet plane could also take off, as the thrust from the expanding gases pressing on the nozzle would generate an opposing force on the aircraft engine... as with scenario 1, the plane would move forward relative to the ground, while the wheels moved at double the velocity.

The Key Question said...

To Anon 8:50,

Yes, that is described in scenario 1.

Anonymous said...

Is there any special system built in conveyer that controls the speed or tunes the speed? How it does all this?