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Let's simplify things a bit.

We we have a stock Boeing 747, no modifications.
It is on a magical runway sized conveyer belt that matches exactly the speed of the wheels on said 747 in the opposite direction. Magic. No exceptions or anything like that.
Can the Boeing 747 take off from the magical conveyer belt?

What are the rest of the conditions? Are the wheels constrained, prevented from rotating about their hubs?
If not, then it can take off.
If the wheels are constrained, but the conveyor belt surface is not constrained from moving in reaction to the lateral forward motion of the plane, then the plane can take off even though its wheels never rotate. The static friction between the wheels and the belt surface will ensure that the relative linear velocity between the plane's wheel tread and the rubber belt on the conveyor is zero, but the belt will roll on its bearings, thus moving with respect to the bearings and the earth.
As long as no force prevents forward motion of the plane, it can take off.
 
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What are the rest of the conditions? Are the wheels constrained, prevented from rotating about their hubs?
If not, then it can take off.
If they are constrained but the conveyor belt surface is not constrained from moving in reaction to the lateral forward motion of the plane, then the plane can take off even though its wheels never rotate.
As long as no force prevents forward motion of the plane, it can take off.

No the wheels are not constrained. Stock 747. Though, how are you certain that the plane will be able to take off with the conveyer belt blazing by underneath it (a force possibly preventing forward motion through various means)?*

The conveyer belt can not move except at the exact speed of the wheels in reverse.


*Ok, so I think the discrepancy here is not in the physics or math, it's in whether the speed of the wheel refers to the speed of the hub of the wheel or the circumference of the wheel. If it refers to the hub: yes, I agree that the plane can take off, but can it take off if it refers to the circumference?
 
No the wheels are not constrained. Stock 747. Though, how are you certain that the plane will be able to take off with the conveyer belt blazing by underneath it (a force possibly preventing forward motion through various means)?*

The conveyer belt can not move except at the exact speed of the wheels in reverse.


*Ok, so I think the discrepancy here is not in the physics or math, it's in whether the speed of the wheel refers to the speed of the hub of the wheel or the circumference of the wheel. If it refers to the hub: yes, I agree that the plane can take off, but can it take off if it refers to the circumference?

Yes. A wheel allows a linear velocity of its hub and an angular velocity of its circumference, but if it's allowed to freely rotate, the tangent point touching the surface of the conveyor belt (or a runway) has no linear velocity. Therefore the linear velocity of the conveyor (or runway) would also be zero. As long as they are not sliding against each other their relative velocity is zero.
 
The conveyor belt is "designed" to "match" their "speed", which is not possible within the limits of current engineering.

Meanwhile IRL the plane takes off and someone gets yelled at for the destruction of a comically large conveyor.
 
Interesting. Do you know which ones?

.....I was wrong.....

Went down that rabbit hole, discussions, studies, PDF's, why they should and why they can't. I did learn that a 747 loses about a kilo of rubber at every landing. The PDF was a study and they discovered a significant reduction in loss by pre-spinning the tire.

Now, it was on a YV show like 60 Minutes or something that I saw this. It's been too many years...I haven't really watched TV for 14 years :p

Wanted to add; this was discussed in the Boing in-house magazine to some depth. They really went at it ;)
 
No worries. I assume they have experimented with spinning the wheels up, but never followed through for whatever reason. Need to look at the aircraft in its totality for the reason I think.

The braking system on the 787 is an engineering masterpiece and an absolute work of art! If you haven't seen it, see what you can find on the web.


How's that conveyor going?
 
The conveyor belt is "designed" to "match" their "speed", which is not possible within the limits of current engineering.

Meanwhile IRL the plane takes off and someone gets yelled at for the destruction of a comically large conveyor.

What about "magic conveyer belt" do you not understand?
 
What about "magic conveyer belt" do you not understand?
The part where it's not in the original problem "definition". If a person gets to add magic to one side of the equation, the jet on the other side has substantially enhanced wish-granting properties.
 
Maybe someone could put on some skates and stand on a treadmill. That will answer the question. Bottom line, there needs to be enough airflow over the wings to generate lift before the plane can take off.
 
The part where it's not in the original problem "definition". If a person gets to add magic to one side of the equation, the jet on the other side has substantially enhanced wish-granting properties.

No magic added. It was just ignored earlier. Stock 747 means no modifications.
 
Only on TRF do we get a 4 page argument about planes on imaginary treadmills.
 
The belt is a black color, made of 100% responsibly sourced poached alligator skin leather reinforced with Kevlar and covered in asphalt slats, then barfed and deficated on by magic rainbow unicorns and well trampled by an army of infuriated garden gnomes, why do you ask?

No particular reason, just a need to know. It did answer my next question--what kind of magic? Unicorn poo make a great lubricant !!! That takes care of the friction problem. I assumed the gnomes are union employed, those guys are always pissed at something and might be a source of inconsistency in any direct observations anyone makes. I'll stick with my previous answer-the plane doesn't fly. But, it does hop as the union boss gets thrown under the rotating tires!
 
Gimme a helicopter.

Of course, that could open up a debate over whether or not a postage stamp on a blade can put it out of balance and cause a crash:facepalm:

Bill McCullough
15T2FN1
Skids are for kids
 
Gimme a helicopter.

Of course, that could open up a debate over whether or not a postage stamp on a blade can put it out of balance and cause a crash:facepalm:

Bill McCullough
15T2FN1
Skids are for kids

No it won't !! But a stamp sized square placed on a blade will quiet it to near silence. No wop, wop, wop. Even the really fast movers that go BRRRRRRR will sound like--ssssssssss
 
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