Airplane physics question

Wax is just stirring the pot.

The question is irrelevant. Nothing that happens to free-spinning wheels can affect whether the plane flies or not.

You can't change the laws of physics

[ame]http://www.youtube.com/watch?v=SKD1spZSG-E[/ame]

 

Nope.

I still have not voted.

I want to be firmly convinced that the challenge within the question itself can be overcome.

 

Pilot's called Dirty Harry then.

 

Wax, I think you are being serious so I will try to explain differently.

Think about a people mover in an airport. A person standing on the surface is not moving relative to the conveyor below, yet without moving his feet the person is moving relative to his spacial surroundings. So instead of a the conveyor being powered from below, imagine it spins freely and is not powered. If you put a jet pack on the person's back, the conveyor with the move with the person on top of it will move forward even though he never takes a step.

Does that help?

 

I enjoy the responses by those much more knowledgeable than myself but I am bewildered by those completely ignoring the premise of the statement itself.

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation".

No mention of slips,drag or friction. As in many test questions written by high school physics teachers ( whom I assume wrote this question) many of these factors are not mentioned and thus not pertinent to the question.

For example:
What is the speed of sound?
As the question is written, the correct answer is approximately 786 mph.


BUT if you bring in other factors ( not mentioned in the original question) - such as altitude and temperature- the speed changes.


Again,
"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation".

If the above statement, AS WRITTEN, can produce forward motion of a car or plane on the ground,please explain.
The speed of the wheels must EXCEED the speed of the conveyor belt for forward motion to occur.

 

it pretty simple really

the images (like seen on myth busters for example) show one thing the ^^ above mistakes, which is that the planes wheels are NOT driven, the tread mill is the powering factor, and not the propeller of the plane

other fact as well known now is the wings are the sole lift mechanism, and to lift there MUST be some degree of airflow over them present

what we don't see in the images is the airflow the tread mill belt surface induces, in a rearward direction, thus affecting the wings, which are in a close enough proximity & parallel to the belt surface

the result is the plane lifts vertically, and as it moves up away from the belt surface, and out of the induced airflow effect, then looses lift and starts to fall rearward direction

the wheels spinning are just a result of the belt, and don't contribute in anyway to the lift of the airplane, and offer no forward power at all (remember they are NOT driven)

 

Hey Dr.,
I don't think anyone ignored (I didn't) the speed of the conveyor, but I think you might be mistakenly assuming that the conveyor rotating on its own axis is the same as the conveyor matching the rotational speed of the tires.

Thus my example of the brakes holding the tires still when the jet power is applied. The wheels won't rotate, the conveyor speed relative to the tire is also zero, yet the conveyor belt along witht the plane on top of it will move forward (and create lift as it moves through the air). At takeoff speed, the wheels are not turning even though the plane has reached enought aerodynamic force to lift off the ground.

Maybe I am wrong, but that is how I understand the question.

 

Very good point. It is all relative.
With the brakes holding-wheel is not rotating ( rotational speed is zero)
"yet the conveyor belt along witht the plane on top of it will move forward "
Directly violates the initial statement that the conveyor belt is designed to match the speed of the wheels ( which you say is zero), at any given time. "

 

What is not stated in the problem is the coefficient of friction. A conceptual treadmill that is able to match the wheel speed could have a coefficient of friction of 1 or 0 or something in between.

Most of the "it flys" are implicitly assuming that the coefficient of friction is low or 0, the airplane skids across the surface of the treadmill and it takes off.

Most of the "it doesn't fly" are implicitly assuming that the coefficient of friction is near or greater than 1. In which case, the friction is high enough that treadmill is able to hold the airplane back from any skidding and it doesn't take off.

An example of low friction would be teflon skis on ice, in which case the airplane skids across the ice easily and takes off. This is similar to the Mythbusters experiment with a plastic sheet being pulled rearward at a speed approximating the takeoff speed.

An example of high friction would be chocks or wheel brakes on a concrete runway, in which case the airplane doesn't move or scrubs the tires badly and doesn't take off.

 

It is stated because it is not stated.

=> No friction at the wheels.

 

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation".

It is not mentioned explicitly, but it is mentioned implicitly here: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, ..."

=> No slip, because the speed of the conveyor belt's surface = the speed of the wheels' surface at any given point of time.

I would have said 786 mph is wrong, because you don`t know the parameters. But I don't know about general agreement at high school physics.

No, this is not the case. Why? Because out of "the above statement, AS WRITTEN," cannot be followed whether it is steady-state or non-steady-state and even in case of an acceleration, which is non-steady-state, the speeds match.

You have to look at it instantaneously!

At every single point of time of an acceleration the speeds of belt and wheels match! It does not matter what speed wheel or belt had at the very point before or after the point of time we are looking at.

I give you an example:

Three points of time t1, t2, t3.

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, ..."

=> v_belt = v_ wheel

Acceleration:

v(t1) < v(t2) < v(t3)

=> v_belt(t1) = v_wheel(t1) < v_belt(t2) = v_wheel(t2) < v_belt(t3) = v_wheel(t3)


It is not this:

=> v_belt(t1) < v_wheel(t1) ; v_belt(t2) < v_wheel(t2) ; v_belt(t3) < v_wheel(t3)

 

exactly.

 

I see implicitly by the fact that the conveyor is moving that there are external forces, but when I just reread the question I don't see where explicitly there is a statement that the plane is applying power to its engines.

Unless there is a force that will propel the plane through the air at takeoff speed, it sits firmly on the ground at zero windspeed

 

It says:

Of course anything that isn't powered sits on the ground.

 

Bazinga

 

The conveyor belt isn't running in this case. As long as the plane does not move, because it is not propelled, the belt does not as well. Trivial solution: 0 = 0 ! And certainly it does not intend to take off in this case. But it says: "..., and intends to take off." Therefore it has to be propelled.

No one wonders that a glider sitting on the runway (= conveyor belt at zero speed) isn't taking off itself. It needs a towing plane, a winch or any kind of an engine. Pretty senseless otherwise.

 

If belt speed increases at the same rate as wheel speed, and the wheels are not powered, for the conveyor belt to move AT ALL the plane MUST first move forward at different speed. This would not comply with given conditions.

If conveyor belt speed and wheel speed HAVE to be ALLWAYS equal, then the plane HAS to stand still regardless of wheel/conveyor speed. (be it 0 mph or 1000 mph)

AND If the plane stands still and there is no wind it cannot take off.

 

http://youtu.be/bdGBQEY1vzo


via rubber ducky

 

This has been answered correctly before and by Myth Busters, let it go. Wheels don't matter.

Pete
Image Unavailable, Please Login

 

Wheels don't matter, yes, but wheel speed relative to conveyor belt speed does have to differ if the plane is moving over the conveyor, as it must to experience airflow over wings, incur lift, and take off. This breaks the condition of the question, which says the speeds of belt and wheel are matched.

Stupid question that states two conditions are occurring simultaneously, even though they cannot coexist. The two mutually exclusive conditions are:
1. Wheel and belt speeds match, meaning the plane is stationary (plane does not take off)
2. Jets are producing thrust, meaning, plane moves forward as belt cannot hold it (if plane moves, it takes off).

 

No.

Amphibious planes take off, proving that the wheel speed and belt speed make no difference to the plane moving forward. Yes wheels might go ridiculously fast but the plane will move forward.

But you guys keep going at it ...
Pete

 

I don't recall amphibious planes being mentioned in the original question.

Okay- let's try it this way.

The wheel has a diameter. With every single rotation on a stationary surface, the plane will move forward the length of the diameter of the wheel. Pretty simple.

Again,
"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation".

To simplify and satisfy the condition of the question as presented, the conveyer belt is designed to travel EXACTLY the length of the diameter of these wheels "in the opposite direction at any given time" .
Diameter of wheel=Speed of conveyer in opposite direction means no forward motion.

Forward motion as the question is written is impossible, thus no lift.

If you consider slip,drag and friction- which negates the words "exactly at any given time" ( and is not mentioned in original question) then forward motion is possible

 

If the airport conveyor belt moved in the opposite direction of the plane, your luggage would never make it into the terminal....it would get dumped at the front of the runway.

Let's say the conveyor is reverse-drive. So with the jet engines off and the fuselage tethered at the nose with a chain, you power the conveyor in reverse velocity. Now the wheels are spinning because of the chain. No wind yet. But turn on the jets, the turbines push air and keep the plane stationary on the belt without the chain. Further increase thrust it increments forward.

The wheels could be zinging along at a billion RPM's, makes no difference with unlimited jet propulsion, even if the tires were sprockets guaranteeing matched speed.

 

Here's the summary from mythbusters.


"The MythBusters first performed a small scale test with a model airplane and a small conveyor belt and were not able to get the model plane to take off from the belt, it merely fell off the front of the conveyor belt. They then tested a model remote-controlled plane on a moving length of paper. The plane moved forward from its starting position and took off. Finally they upgraded to full scale using an actual manned plane and a runway-sized tarp as a makeshift conveyor belt. Like the small scale test, the plane moved forward from its starting position and was able to take off from the conveyor belt. The MythBusters explained that this was possible because unlike cars, an airplane's means of propulsion is through its propeller or jet engine, not its wheels; a car's engine mechanically moves its wheels, which use their contact with the road and the traction it provides to generate forward movement, while the plane's wheels are free-moving and independent of the propeller, which uses air displacement for forward thrust. Therefore, the conveyor belt has no bearing on the forward momentum of the plane."


/thread

 

Nobody is claiming that the wheel speed and belt speed make a difference. They can't, as the thrust of the jet/propellor is not being opposed. Duh.

It's a condition of the question. Nothing to do with amphibious aircraft, but in order for an amphibious aircraft to move forward against an opposing current, it has to go faster than the current in the opposite direction. If it matches the current speed, it sits still on the water. If it has less forward velocity, it will get carried backwards.

The wheels will go at the speed of the plane forward plus the speed of the belt backwards. That's all. Not ridiculously fast, unless either of the above two components is high.