Riddle me this batman

[IlPadrino]

To me, its a relatively simple dynamics problem. The sum of the forces acting on the plane is nonzero, therefore there is an acceleration. I don't see why its so hard.

I think some might consider the moving conveyor providing a force exactly counteracting the thrust... or else moving the airplane back an inch every time it moves forward an inch. I'm sure both are wrong and the explanation is fairly simple, but it gets confounded by a lot of ancillary (and useless) information (e.g. how long is the conveyor? - it doesn't matter!)

 

[benbo]

I think some might consider the moving conveyor proving a force exactly counteracting the thrust... or else moving the airplane back an inch every time it moves forward an inch. I'm sure both are wrong and the explanation is fairly simple, but it gets confounded by a lot of ancillary (and useless) information (e.g. how long is the conveyor? - it doesn't matter!)

The reason we don't discuss the rolling resistance is because it wasn't given in the problem. If it is not given we either have to assume that it is zero or neglible, or we can't solve the problem. Because it is possible for rolling friction or static friction to be so great the plane doesn't move. It is caled a "brake" I believe. Since it isn't given we have to neglect it. Any number we put in is just an assumption on our part. What friction force would you put in the problem?

As far as the length of the conveyor, I never thought about it but rdbse did. And he is right in that there is no drawing given for the problem. He pictured a short conveyor that ended in a cliff or a wall or something. I think the point he was trying to make was that even though the conveyor made no real difference in the motion of the plane, it didn't help it take off either. I assume you don't think the plane can take off from a ten foot conveyor? Because that would sure make airport design a lot simpler, at least it would require a lot less real estate. Again, I didn't think of this, but I don't think you can just declare perfunctorily that it doesn't matter.

Sorry folks, I just can't help myself form arguing about this. Maybe it's because I was wrong at first. I'm like a person who has a religious conversion and can't stop talking about it. I need to go to conveyor anonymous. I promise this is my last post,

 

[benbo]

Hey Sapper,I did not force you to look at this thread again, so no reason to get ill. You contradict yourself by saying it does not matter how short the conveyor is, but add that it needs to be long enough to obtain critical velocity. If we can agree that the length does matter, I will agree that the plane will fly and let it rest.

Sounds like an argument my wife was making. You mean length does matter?! So PE-Ness was right. Now I'm really done reading this thread. I'm too depressed.

 

[IlPadrino]

The reason we don't discuss the rolling resistance is because it wasn't given in the problem. If it is not given we either have to assume that it is zero or neglible, or we can't solve the problem. Because it is possible for rolling friction or static friction to be so great the plane doesn't move. It is caled a "brake" I believe. Since it isn't given we have to neglect it. Any number we put in is just an assumption on our part. What friction force would you put in the problem?

Fact 1: Any flying (not falling!) airplane requires sufficient air velocity over its wings to generate enough upward lift which counteracts the airplanes mass (which given gravity creates a downward force).

Fact 2: An airplane creates thrust independent of its wheels.

Fact 3: Given an airplane sitting freely on any movable surface (e.g. a conveyor belt, a trailer, etc.), a force equal but opposite to the rolling resistance (i.e. rolling friction) and axle friction of the airplane wheels will keep the airplane stationary despite the moving surface.

Fact 4: Rolling resistance is a function of [what?] and axle friction is a function of [what]?

Just because it wasn't given doesn't mean we have to neglect it... we live in the real world so we can assume real-world conditions. If you want to jump to

"Fact 5: The rolling resistance and axle friction of an airplane is orders and orders of magnitude less than the thrust provided."

then we're done...

Fact 6: The conveyor makes no difference in the ability of the airplane to take off.

As far as the length of the conveyor, I never thought about it but rdbse did. And he is right in that there is no drawing given for the problem. He pictured a short conveyor that ended in a cliff or a wall or something. I think the point he was trying to make was that even though the conveyor made no real difference in the motion of the plane, it didn't help it take off either. I assume you don't think the plane can take off from a ten foot conveyor? Because that would sure make airport design a lot simpler, at least it would require a lot less real estate. Again, I didn't think of this, but I don't think you can just declare perfunctorily that it doesn't matter.

If the conveyor is on a runway (as specified in the problem), it doesn't matter how short it is... after the conveyor ends, the runway continues and the airplane is just fine making the transition from the conveyor to the runway. Nor can the conveyor be too long... the airplane will take off at the normal distance. If there's a cliff or a wall, it's not like any runway in the world except an Aircraft Carrier.

Sorry folks, I just can't help myself form arguing about this. Maybe it's because I was wrong at first. I'm like a person who has a religious conversion and can't stop talking about it. I need to go to conveyor anonymous. I promise this is my last post,

Spoil sport.

 

[FLBuff PE]

What friction force would you put in the problem?

f = 64/Re from my Environmental Engineering Reference Manual for Laminar Flow, which I would consider a smootly rolling airplane on a conveyor belt. If we assume that the Reynold's # is the maximum for Laminar flow, 2099, then f = 0.0305

On a seprate note, what if the conveyor runs across the runway? Will the plane cartwheel (as my RC plane did once when a particularly nasty crosswind caught the wings during takeoff)? Let the debate begin! opcorn:

 

[Dleg]

^^Now THAT would probably derail the takeoff, and could easily lead to cartwheeling.

 

[IlPadrino]

f = 64/Re from my Environmental Engineering Reference Manual for Laminar Flow, which I would consider a smootly rolling airplane on a conveyor belt. If we assume that the Reynold's # is the maximum for Laminar flow, 2099, then f = 0.0305

I was talking about rolling friction and axle friction... the whole world isn't about Environmental Engineering (despite what you guys would have me believe) - every now and again the mechanical nature of the world makes them MechEs useful. But, hey, if you don't know the answer, don't worry - I'll just find the local Boy Scout troop and ask the 9-year-old Pine Car Derby expert. Yeah, they're not PEs, but they do have practical experience on their side.

 

[FLBuff PE]

Yeah, they're not PEs, but they do have practical experience on their side.

I have neither, so I shall bow out of this discussion...

 

[cement]

f = 64/Re from my Environmental Engineering Reference Manual for Laminar Flow, which I would consider a smootly rolling airplane on a conveyor belt. If we assume that the Reynold's # is the maximum for Laminar flow, 2099, then f = 0.0305On a seprate note, what if the conveyor runs across the runway? Will the plane cartwheel (as my RC plane did once when a particularly nasty crosswind caught the wings during takeoff)? Let the debate begin! opcorn:

I visited an old B-52 base and the the landing gear would turn about 15 degrees or so to help compensate for partial crosswind. The potential calculations are making my head spin! :blink:

 

[Dleg]

Having no references readily available, all I will say (and I think, all that we need to know) is that the rolling resistance of a rubber aircraft tire on a ball-bearing axle is very small compared with the other horizontal forces involved in the problem (thrust and aerodynamic drag).

 

[IlPadrino]

Having no references readily available, all I will say (and I think, all that we need to know) is that the rolling resistance of a rubber aircraft tire on a ball-bearing axle is very small compared with the other horizontal forces involved in the problem (thrust and aerodynamic drag).

I sure wouldn't disagree with that. So even though we don't have the answer to Fact 4, we can accept Fact 5 and move to the end:

Fact 1: Any flying (not falling!) airplane requires sufficient air velocity over its wings to generate enough upward lift which counteracts the airplanes mass (which given gravity creates a downward force).

Fact 2: An airplane creates thrust independent of its wheels.

Fact 3: Given an airplane sitting freely on any movable surface (e.g. a conveyor belt, a trailer, etc.), a force equal but opposite to the rolling resistance (i.e. rolling friction) and axle friction of the airplane wheels will keep the airplane stationary despite the moving surface.

Fact 4: Rolling resistance is a function of [what?] and axle friction is a function of [what]?"

Fact 5: The rolling resistance and axle friction of an airplane is orders and orders of magnitude less than the thrust provided.

Fact 6: The conveyor makes no difference in the ability of the airplane to take off.

I'm sure an aeronautical engineer could fine-tune the facts to make it more precise, but I don't think there's anything here that they'd disagree with. If anyone disagreed with Fact 6, I'd just ask them to point out which previous fact is wrong or which fact is missing.

 

[Dleg]

I don't disagree, but, much like I am Legend, I think you jumped to the ending too quickly. Try this:

Fact 6: Given the problem statement, the speed of the conveyor belt will be constantly and instantly changed to match the speed of the aircraft, but in an opposite direction. This means that if at any given instant the aircraft is moving forward (in a positive direction) at speed x, the conveyor will be moving backward (a negative direction) at speed -x. The wheels of the aircraft, therefore, will always be rotating at a speed of (x - -x) = 2x, or twice the speed they would rotate if rolling across a stationary surface.

Fact 7: The difference in the rolling resistance experienced by a free-spinning airplane wheel between speeds x and 2x is very small at ordinary takeoff velocities, and remains several orders of magnitude less than the thrust provided by the airplane's engine(s).

Fact 8: The other important horizontal force that opposes thrust is aerodynamic drag. If the airplane is an ordinary airplane that is capable flying under non-conveyor belt conditions, we can assume that the aircraft designers have taken aerodynamic drag into consideration and provided the aircraft with an engine(s) capable of overcoming this force and accelerating the aircraft to necessary takeoff and flying speeds.

Fact 9: Because the thrust generated by the engines is a horizontal force that greatly exceeds the opposing horizontal forces of aerodynamic drag and the rolling resistance caused by the conveyor acting against the free-spinning wheels, the superior force of thrust will cause the airplane to accelerate forward.

Fact 10: Because the airplane accelerates forward under the influence of the thrust from its engines, it will reach the forward velocity necessary for takeof.

Fact 11 (or perhaps this only belongs as a comment) Due to the small increase in rolling resistance caused by the airplane's wheels spinning at twice their normal rotational velocity, the distance required to achieve liftoff speed will be slightly longer than ordinary.

 

[IlPadrino]

I don't disagree, but, much like I am Legend, I think you jumped to the ending too quickly. Try this:
Fact 6: Given the problem statement, the speed of the conveyor belt will be constantly and instantly changed to match the speed of the aircraft, but in an opposite direction. This means that if at any given instant the aircraft is moving forward (in a positive direction) at speed x, the conveyor will be moving backward (a negative direction) at speed -x. The wheels of the aircraft, therefore, will always be rotating at a speed of (x - -x) = 2x, or twice the speed they would rotate if rolling across a stationary surface.

Fact 7: The difference in the rolling resistance experienced by a free-spinning airplane wheel between speeds x and 2x is very small at ordinary takeoff velocities, and remains several orders of magnitude less than the thrust provided by the airplane's engine(s).

Fact 8: The other important horizontal force that opposes thrust is aerodynamic drag. If the airplane is an ordinary airplane that is capable flying under non-conveyor belt conditions, we can assume that the aircraft designers have taken aerodynamic drag into consideration and provided the aircraft with an engine(s) capable of overcoming this force and accelerating the aircraft to necessary takeoff and flying speeds.

Fact 9: Because the thrust generated by the engines is a horizontal force that greatly exceeds the opposing horizontal forces of aerodynamic drag and the rolling resistance caused by the conveyor acting against the free-spinning wheels, the superior force of thrust will cause the airplane to accelerate forward.

Fact 10: Because the airplane accelerates forward under the influence of the thrust from its engines, it will reach the forward velocity necessary for takeof.

Fact 11 (or perhaps this only belongs as a comment) Due to the small increase in rolling resistance caused by the airplane's wheels spinning at twice their normal rotational velocity, the distance required to achieve liftoff speed will be slightly longer than ordinary.

Holy Shit, Batman!

Fact 6 and 7 are unimportant given Fact 5: If the rolling resistance and axle friction are orders and orders less than the thrust provided, it doesn't matter if the wheels are spinning at 1x or 2x normal (i.e. non-conveyored) speed.

I thought Fact 1 covered Fact 8, but I guess I forgot that different airplanes of the same weight can require different take-off speeds. But, still, we could rewrite Fact 1 to account for that.

Facts 9, 10, and 11 seem unneeded, given airplanes NORMALLY take-off and Fact 5 tells us the conveyor doesn't significantly change normal.

So... if you agree with the conclusion, what are the minimum facts needed? I'm sure we can do less than 11 and maybe 6 wasn't enough.

 

[DVINNY]

You can do 347 facts.

some people still will not believe it.

 

[IlPadrino]

You can do 347 facts.some people still will not believe it.

Less is more. With 347 facts, non-believers are sure to ground themselves on a bunch of unnecessary facts (that although perhaps correct still cloud the picture).

I've made a few changes based on Dleg's input but still haven't included a fact about aerodynamic drag. I challenge any non-believer to address Fact 5 by pointing out which previous fact is wrong or which fact is missing. I promise it will be a short discussion.

Fact 1: Any flying (not falling!) airplane requires sufficient air velocity over its wings to generate enough upward lift which counteracts the airplanes mass (which given gravity creates a downward force); air velocity is created by thrust.

Fact 2: An airplane creates thrust independent of its wheels.

Fact 3: Given an airplane sitting freely on any movable surface (e.g. a conveyor belt, a trailer, etc.), a force equal but opposite to the rolling resistance (i.e. rolling friction) and axle friction of the airplane wheels will keep the airplane stationary despite the moving surface; any force greater will move the airplane in the direction opposite of the movable surface.

Fact 4: Rolling resistance is a function of [what?] and axle friction is a function of [what]?"; the rolling resistance and axle friction of an airplane is orders and orders of magnitude less than the thrust provided.

Fact 5: The conveyor makes no difference in the ability of the airplane to take off.

 

[Guest]

I think there is something missing and in fact I will re-iterate what I believe it is at the crux of the problem.

What is the interaction of the air (fluid) medium?

If we remove the treadmill, everyone will agree that the lift that produces flight is due to the differential pressure across the span of the wing. Right? That pressure differential is a result of the plane air flowing over the wing from forward propulsion (thrust) resulting in the so-called Bernoulli Effect. I think we can all agree upon that scenario.

Going back to the treadmill, in my mind, the interceding fact between #4 and #5 to be confirmed/disputed:

Fact #4.5: "The flow of the air over the wing span and its' effect on the lift of the plane is INDEPENDENT of the treadmill"

:2cents:

JR

 

[Dark Knight]

:deadhorse: :deadhorse: :deadhorse:

 

[Guest]

Whatever happened to Sappers' FBD ?? :dunno:

JR

 

[IlPadrino]

I think there is something missing and in fact I will re-iterate what I believe it is at the crux of the problem.
What is the interaction of the air (fluid) medium?

If we remove the treadmill, everyone will agree that the lift that produces flight is due to the differential pressure across the span of the wing. Right? That pressure differential is a result of the plane air flowing over the wing from forward propulsion (thrust) resulting in the so-called Bernoulli Effect. I think we can all agree upon that scenario.

Going back to the treadmill, in my mind, the interceding fact between #4 and #5 to be confirmed/disputed:

Fact #4.5: "The flow of the air over the wing span and its' effect on the lift of the plane is INDEPENDENT of the treadmill"

:2cents:

JR

OK, but why not include Fact 4.5 in Fact 1 (which I had wanted to use to set the stage for "normal" but then had to add Fact 2)? I'd also pedantically point out that the flow of air is not INDEPENDENT of the treadmill; Fact 4 tells us the friction is small (orders and orders less than the thrust) but it will still slightly slow down the relative airspeed of the airplane (and therefor the flow of the air over the wings.)

Sapper's free-body diagram won't win any artistic awards, but it's certainly complete and demonstrates Facts 3 and 4. I'd only nitpick that "no new forces" overlooks the fact that the magnitude of the friction forces will certainly change with the doubled rotational speed of the tires.

 

[IlPadrino]

:deadhorse: :deadhorse: :deadhorse:

What, and you're against increasing the post-count of the board? If nothing else, we're a few posts further ahead of "the other board".