plane question

[bmc]

indeed. What makes you think that this means the conveyer will impart any force to the plane whatsoever?

The wording in the original post.

 

[Geoff St. Germaine]

If you're on a jogging machine and it's set to go at the speed you run at, how much distance will you cover in an hour, relative to the stationary floor around you? Not much. You will not have left the building while standing on the jogging machine, correct?

You're arguing quite vehemently that the plane won't take off, yet the jogging example is in no way analagous to the aircraft. In the jogging example the acceleration is relative to the treadmill (conveyor) in the aircraft example, it is relative to the air and the wheels aren't rigid, they can rotate freely. I can hold a skateboard in place on a treadmill with very little effort, because the wheel bearing have very low friction and there is very little force transfered to the skateboard itself from the treadmill.

It just seems that you don't understand what is going on in the situation. If you can provide me with a free body diagram showing what force is causing the plane to be held back against the thrust of the engines, then if will make sense.

 

[Geoff St. Germaine]

I don't even get how this is a trick question. No acceleration through the air, no lift. BMC's treadmill comparison is a good one.

Unfortunately it's not.

 

[Geoff St. Germaine]

Read the original post. The conveyor:

1. moves opposite to the direction the plane is headed.
2. it moves at the same speed as the plane.

Yes it does. Can you tell me how much force is being imparted to the aircraft from the conveyor? That is the key. Force balance. The plane has large engines pushing the plane forward and a little bit of friction in the wheels holding it back. The wheels would have to be terrible if they were to be able to hold the aircraft in place. One might say that they wouldn't be wheels at all.

 

[Davidoc]

Unfortunately it's not.

Right, because of the lack of connection between force on the wheels and force on the plane. I stand corrected. (If the wheels were locked, it would be a different story.)

 

[Dan1099]

The wording in the original post.

It says the conveyer will move the other way. How does this translate to force on the plane?

 

[Bassic83]

"What is the average wingspeed velocity of a swallow, migrating?"

"Is that the African, or the European variety?"

"What? I don't know that! AAAAaaaaaaaagh!"

 

[bmc]

Yes it does. Can you tell me how much force is being imparted to the aircraft from the conveyor? That is the key. Force balance. The plane has large engines pushing the plane forward and a little bit of friction in the wheels holding it back. The wheels would have to be terrible if they were to be able to hold the aircraft in place. One might say that they wouldn't be wheels at all.

I really don't think this was intended as a complex problem.

 

[LarryM317]

Ahhh Dan1099. I'm with you now, it's kinda confusing the way they word it. That's a pretty clever question.

I understand what you are saying.

 

[bmc]

"What is the average wingspeed velocity of a swallow, migrating?"

"Is that the African, or the European variety?"

"What? I don't know that! AAAAaaaaaaaagh!"

" He's pining for the fjords."

" PINING FOR FJORDS?

 

[bmc]

JUST SAY NO TO DRUGS.

 

[Bassic83]

" He's pining for the fjords."

" PINING FOR FJORDS?

 

[Dan1099]

I really don't think this was intended as a complex problem.

The problem is not complex at all. Forces from the props push one way. The conveyer moves the other direction. The wheels spin. Force balancing is physics 1.

The trick of the question is that even though the conveyer moves, it does not apply any force to the plane. It just spins the wheels.

 

[Geoff St. Germaine]

Alright, now I have to use a little physics and math.

A 747 has a maximum takeoff mass of 375 000 kg. I'm going to use model that is fairly simple and assume that the coefficient of friction is a constant (that is, independent of velocity).

A 747's 4 engines produce a total thrust (T) of 1.184 million newtons (MN).

The normal force (N) (weight) is 375 000 kg * 9.81 m/s = 3.678 MN.

Anyone who's taken basic high school physics (at least from where I've lived) knows that the force due to friction is mu*N where mu is the coefficient of friction. In order for the aircraft to be held in place the net force on the 747 must be zero.

So, we have T > mu*N in order to have an acceleration and a takeoff of the 747.

When we plug in the numbers we get that in order for the takeoff to happen, mu < 0.322.

Looking at a table of friction coefficients, the coefficient of friction for rubber and asphault, the coefficient of friction with dry asphault is 0.5 and for wet asphault it is around 0.25. So with the brakes locked on an asphault conveyor, the aircraft couldn't take off.

The coefficient of friction in the free spinning wheels is going to obviously be lower than when the brakes are applied. I can't find an exact number, but I wouldn't be surprised if the coefficient of friction was considerably less than 0.1. For steel and teflon the coefficient of friction is about 0.04. That would mean that the friction force would only supply 0.147 MN of force, so that there would be a net force of 1.037 MN of force acting to accelerate the aircraft. I wouldn't be surprise if the aircraft wheels had even lower friction than that due to lubricants and what not.

 

[Geoff St. Germaine]

I really don't think this was intended as a complex problem.

It only requires high school physics at best. It isn't a complicated problem. My problem is, how much current is collected out of a fully ionized, magnetized plasma by a TZM (titanium zirconium molybdenum) electrode inserted into it with a -100 V potential applied to it with respect to the vacuum chamber. I need the answer as a function of the poloidal and toroidal mach numbers and for arbitrary orientation of the probe with respect to the magnetic field lines.

Here's my probe:

That's a complicated problem.

 

[bmc]

It only requires high school physics at best. It isn't a complicated problem. My problem is, how much current is collected out of a fully ionized, magnetized plasma by a TZM (titanium zirconium molybdenum) electrode inserted into it with a -100 V potential applied to it with respect to the vacuum chamber. I need the answer as a function of the poloidal and toroidal mach numbers and for arbitrary orientation of the probe with respect to the magnetic field lines.

Here's my probe:

That's a complicated problem.

Go shovel your driveway or something.

 

[Dkerwood]

Wow. This has gotten really quite complicated.

Essentially, we have a primary force acting as a primary means of propulsion (ie the wheels and engines therein) and we have a secondary force designed to supplement the primary force (ie the jet engines).

The question now becomes one of acceleration. Given that the plane accelerates at rate R, regardless of where the force comes from, if the conveyor call accelerate the plane at exactly R in the opposite direction, all things being equal, the relative speed of the plane will not change.

Of course, according to the original wording of the question, the conveyor's sensors would then read the "speed" of the aircraft at zero, and reset itself to zero, at which point the plane would start to accelerate again.

However, assuming that this spaceage conveyor is capable of instantly recalibrating its speed relative to the plane, it's relatively safe to assume that the instant that the plane began to accelerate in any fashion, the conveyor would accelerate to match. The equal and opposite accelerations would cancel each other out, and the relative speed would remain at zero, given that the wheels remain in constant contact with the ground.

If the plane began to bounce, as it almost certainly would, however, the conveyor would produce no drag on the plane, and it would begin to accelerate. This acceleration would then be matched by the conveyor when the plane lands, and at this point, the plane would stop until it bounced again (unless the conveyor drags it back to its original position, which might happen, considering that the conveyor would be going the speed at which the BOUNCING plane was traveling, and thus would be traveling faster than the maximum speed allowed on the ground). At this point, we must consider these variables:

1. Maximum speed of the conveyor versus the maximum "bouncing" speed of the jet.

2. Maximum rate of acceleration of the jet given that it is accelerating from rest versus maximum rate of acceleration of the conveyor given that it is already in motion and simply must defeat the relative acceleration of the jet.

3. Length of the conveyor belt and whether or not the belt's purpose is simply to defeat acceleration or to confine the plane to one location. If it is the former, the plane will simply bounce forward until it is free of the conveyor.

4. Any other variables that may affect the situation (wind speed, durability of the belt versus that of the plane, any incline on the plane, weather conditions, etc).

All in all, if the conveyor's purpose is to defeat acceleration and its mechanical limitations are not to be considered, I do not believe that the plane would be able to take off without substantial vertical force.

Forthermore, once it made its way off of this conveyor traveling hundreds of miles per hour and transferred to the stationary ground, the plane would almost certainly lose control and crash, thus making it very difficult to take off.

 

[Bob Lee (QSC)]

Essentially, we have a primary force acting as a primary means of propulsion (ie the wheels and engines therein) and we have a secondary force designed to supplement the primary force (ie the jet engines).

No, there is only a primary means of propulsion: the jet engines. The wheels no not have motors. Even when the plane taxis, it uses the jet engines to push it along. That's why when you're on a plane you can hear the pilot briefly spool its engines up to start it moving along the taxiway.

 

[Geoff St. Germaine]

Wow. This has gotten really quite complicated.

Essentially, we have a primary force acting as a primary means of propulsion (ie the wheels and engines therein) and we have a secondary force designed to supplement the primary force (ie the jet engines).

Well, like Bob said, there's no engines for the wheels on an airplane.

The question now becomes one of acceleration. Given that the plane accelerates at rate R, regardless of where the force comes from, if the conveyor call accelerate the plane at exactly R in the opposite direction, all things being equal, the relative speed of the plane will not change.

Accelerations are due to forces. The force supplied by the conveyor comes through the friction in the wheels. If you look above there's a calculation pertaining to this.

Of course, according to the original wording of the question, the conveyor's sensors would then read the "speed" of the aircraft at zero, and reset itself to zero, at which point the plane would start to accelerate again.

In order to set the aircraft's speed back to zero, the conveyor would first have to supply more force than the engines in the opposite direction to stop the aircraft and then once it was at a stop it would have to provide an equal and opposite force to the aircraft. There's no way that it can do this through friction (and hence there's no way it can do it).

However, assuming that this spaceage conveyor is capable of instantly recalibrating its speed relative to the plane, it's relatively safe to assume that the instant that the plane began to accelerate in any fashion, the conveyor would accelerate to match. The equal and opposite accelerations would cancel each other out, and the relative speed would remain at zero, given that the wheels remain in constant contact with the ground.

Again, equal accelerations require equal forces when they're acting on the same mass. There is no way for the conveyor to impart a sufficient amount of force through the wheels. The friction is too small.

If the plane began to bounce, as it almost certainly would, however, the conveyor would produce no drag on the plane, and it would begin to accelerate. This acceleration would then be matched by the conveyor when the plane lands, and at this point, the plane would stop until it bounced again (unless the conveyor drags it back to its original position, which might happen, considering that the conveyor would be going the speed at which the BOUNCING plane was traveling, and thus would be traveling faster than the maximum speed allowed on the ground). At this point, we must consider these variables:

1. Maximum speed of the conveyor versus the maximum "bouncing" speed of the jet.

2. Maximum rate of acceleration of the jet given that it is accelerating from rest versus maximum rate of acceleration of the conveyor given that it is already in motion and simply must defeat the relative acceleration of the jet.

3. Length of the conveyor belt and whether or not the belt's purpose is simply to defeat acceleration or to confine the plane to one location. If it is the former, the plane will simply bounce forward until it is free of the conveyor.

4. Any other variables that may affect the situation (wind speed, durability of the belt versus that of the plane, any incline on the plane, weather conditions, etc).

We don't have to consider this because the conveyor is unable to hold the plane at rest in the first place.

All in all, if the conveyor's purpose is to defeat acceleration and its mechanical limitations are not to be considered, I do not believe that the plane would be able to take off without substantial vertical force.

The plane doesn't require a vertical force to take off. The thrust from the engines is more than sufficient. Unless the friction in the wheels is a very strong function of velocity (which it isn't for the speeds we're talking about) the friction force would about the same whether there is a conveyor or the plane is just on a normal stationary runway.

Forthermore, once it made its way off of this conveyor traveling hundreds of miles per hour and transferred to the stationary ground, the plane would almost certainly lose control and crash, thus making it very difficult to take off.

I doubt that. Have you ever seen a plane land? 747 wheels go from 0 to more than a hundred miles perhour at the instant of landing and it doesn't crash. They leave nice rubber marks and make some smoke, but unless they are in very bad shape and explode, there's no danger to the aircraft.

 

[Dkerwood]

No, there is only a primary means of propulsion: the jet engines. The wheels no not have motors. Even when the plane taxis, it uses the jet engines to push it along. That's why when you're on a plane you can hear the pilot briefly spool its engines up to start it moving along the taxiway.

Ah, then there goes my whole argument. The wheels are free spinning, then?