Can the plane take off?

Jaybeaux said:
For those that jog on treadmills, how much apparent wind do "you" create while running, irrespective of speed?

Answer: Zero
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The question should be - For those that wear jet packs and roller skates on treadmills, how much apparent Sheetrock do "you" destroy?;)
 
Blueone said:
Can’t believe you got sucked into this
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Haa...I almost did too!

But for the record, it will absolutely take-off, possibly even if the tires get blown off, and even without considering ground-effect factors of a very quickly moving treadmill below the wings, which would likely cause a take-off at a lower speed relative to the non-treadmill-moving ground.

Only airspeed matters and the frictional drag in the rotating parts of the landing gear is a small part of the force an aircraft has to overcome to take off. The engines push against the air, not the ground.

Wait...DOH!!
 
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jmauld said:
The thrust from the engines doesnt care about the speed of the tires. Nothing on the plane cares about the speed of the tires. That number is meaningless to it taking off. Only speed over ground matters.
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It's a frame of reference problem.

Aircraft speed relative to the non-moving ground: ground speed
Aircraft speed relative to the surrounding air: air speed
Aircraft speed relative to the treadmill: invent this one... tread speed
And one more: treadmill belt speed relative to non-moving ground: call this one belt speed

Tread speed impacts the wheel rotation speed and related friction and tire friction only.

There wouldn't be enough friction through the tires and wheels induced by the moving treadmill by the time the aircraft reaches the required airspeed to overcome the thrust available from the engines.

belt speed would be equal and opposite to ground speed
tread speed would be 2x ground speed
air speed would be ground speed + wind speed (which would include ground effect)
 
tc410 said:
Exactly. Only speed over ground matters. The plane has no speed over ground if the conveyor is maintaining exactly the speed of any forward momentum created by the thrust of the engines.

How many MPH is a car traveling on a dyno with the engine running 3,000 RPMs? ZERO. The car never moves but the wheels/tires are rotating like crazy.
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No, speed through the air matters. Think about the aircraft speed relative to the airport, regardless of the treadmill that starts moving below the wheels.
 
ttmott said:
The treadmill spins the aircraft's wheels. If the wheel bearings were frictionless the aircraft would not move regardless what the treadmill and wheels are doing. Agree? The "equal and opposite force" as you point out is isolated between the wheels and treadmill; nothing else have forces imposed (sans friction and inertial forces due to the mass of the wheels).

So from the "Brainless" Technical Contributor -

If the aircraft moves forward at 10 miles per hour using it's engines the wheels rotate (say) at 50 RPM without the treadmill moving. Then the treadmill counters that wheel rotation the wheels now rotate at 0 RPM. But, the aircraft still moves forward at 10 miles per hour. At this point the aircraft and treadmill are both moving forward at 10 miles per hour and the wheels are not turning at all.

So the aircraft is now at 120 miles per hour (forward speed = air speed) powered by it's engines and creating enough lift at the wings to take off and the wheels would spin at 500 RPM without a treadmill. With a treadmill countering the wheel RPM the wheels are now spinning at 0 (zero) RPM but the aircraft is still traveling at 120 miles per hour creating enough lift at the wings and taking off.

Now let's look as if the treadmill is spinning the wheels the same direction rather than counter - the aircraft is moving forward and wheels are spinning at 50 RPM then the tread mill adds 50 RPM resulting in wheel speed of 100 RPM but, lo and behold, the aircraft is still moving forward.....
Class is dismissed....
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And it's that last paragraph where the "wheels fall off" this argument. Once the plane starts moving AT ALL, then the wheels are going faster than the treadmill, thus violating the initial conditions set out in the story problem. The instant that happens the experiment is over and the plane doesn't take off.

Again, as noted earlier, physically it can take off for the reasons mentioned. But if you read the problem verbatim, then it can't.
 
km1125 said:
Again, as noted earlier, physically it can take off for the reasons mentioned. But if you read the problem verbatim, then it can't.
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That's simply not true, because the speed of the wheels means nothing. The only thing that matter is the speed of the plane, which is vastly dictated by the force of the engines. The friction in the wheel bearings will slow it down, marginally at best.

The plane will take off.
 
jmauld said:
That's simply not true, because the speed of the wheels means nothing. The only thing that matter is the speed of the plane, which is vastly dictated by the force of the engines. The friction in the wheel bearings will slow it down, marginally at best.

The plane will take off.
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The key to understand why the plane will take off is that the engines do not power the wheels. This is why the person running on a treadmill or the car on a dyno analogies cause confusion. In those scenarios, propulsion comes from contact with the ground. If engine in the car on a dyno was powering a propeller instead of the wheels, would the dyno spin? No. Would the restraints holding the car experience force? Yes.

It's a pretty fun engineering relative motion question.

I think to get it, you need to understand that the rolling resistance of the landing gear does not govern forward motion. Inertia then wind drag are the critical forces.
 
I don’t understand how people can’t see the disconnect between the wheels and the thrust on the plane.
 
Sorry, late to the game. It wasn’t a science question, it was an English question. “Can” the plane take off, Yes. It still has that capability. If they had asked “Will” it take off then all of your dialog applies. For my ten cents, unless that treadmill is as long as a run way its gonna crash because the thrust is going to move it forward no matter what.
 
For the wheel speed to match the conveyor the airplane would not be fully power up as it normally would during takeoff.

The weight of the aircraft along with jet blast would likely cause excessive buffeting of the conveyor belt.

For the plane to take off the wheels would spin twice the speed of the conveyor belt. The limitation of the wheel speed in the scenario is not realistic when my first point is considered.

The answer therefore is yes and no. This is a trick question.
 
Tie it all together...

bikini-airline3.jpg
 
jmauld said:
That's simply not true, because the speed of the wheels means nothing. The only thing that matter is the speed of the plane, which is vastly dictated by the force of the engines. The friction in the wheel bearings will slow it down, marginally at best.

The plane will take off.
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Yes, the speed of the wheels matter because it's specified in the wording of the problem, and those are the kinds of "words that matter". It doesn't matter how you try and move the plane... using its own engines, JATOs strapped to the wings, a winch, or another plane towing it, once the plane on the treadmill moves relative to the treadmill then you've violated the initial conditions set forth in the problem and the plane cannot and will not take off.
 
If the wheels dont matter...what if they were cemented into the ground, and wouldnt break off...could the plane take off?
 
km1125 said:
Yes, the speed of the wheels matter because it's specified in the wording of the problem, and those are the kinds of "words that matter". It doesn't matter how you try and move the plane... using its own engines, JATOs strapped to the wings, a winch, or another plane towing it, once the plane on the treadmill moves relative to the treadmill then you've violated the initial conditions set forth in the problem and the plane cannot and will not take off.
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"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction..."

I suppose interpretation of that statement could vary.

Sitting statically, the wheels are at rest, the treadmill is at rest. Forces on the plane fore and aft are zero.

Say the engines have available thrust of 50,000lbs. It has been shown a pickup truck can pull a large aircraft. Let's say a pickup truck has a pulling force of about 5,000lbs (approx 80% of drive axle weight is typically a good estimate, so this is generous), so we know the aircraft engines easily overcome rolling resistance (it would take less than 5,000lb thrust to get the plane moving). We also know this because aircraft accelerate under power on take off!

Power-up a little and the aircraft moves forward, causing the wheels to turn, which in turn, causes the treadmill to start. Modulate the throttle to keep the aircraft stationary relative to the ground (not relative to the moving treadmill). It would be a low throttle setting since the rolling resistance is fairly low (and decreases once not in a static state), less than 10% in this example.

Now, if you applied the other 90% thrust, the plane will accelerate forward relative to the ground, the wheel speed relative to the treadmill will increase, and the treadmill will speed-up such that its speed relative to the ground matches the wheel speed relative to the treadmill. The plane, however, is now moving relative to the ground and has airspeed.

The throttle could again be modulated to stop accelerating and maintain a new equilibrium with the plane moving forward relative to the ground and with airspeed.

Now interpretation is required or it becomes a control feedback problem.

What speed does the treadmill match? Since the plane has accelerated relative to the ground, the wheel speed must be the ground speed plus the treadmill speed in the opposite direction. However, the treadmill is trying to match the wheel speed. This would produce an endless loop and an impossible treadmill design. The treadmill would speed up indefinitely on its own and everything would self-destruct. Sure, the plane would not take off, but not for the reason I believe most are thinking.

However, if the interpretation is the treadmill is matching the equivalent wheel speed given the ground speed, then treadmill speed = -ground speed and wheel speed = 2 x ground speed. This would be a possible treadmill design and the plane would simply take off with the treadmill running at the same speed as take-off velocity (in the opposite direction) and the wheels spinning at twice their normal speed.

At twice their normal speed the wheels/tires would not likely produce enough resistance to prevent take-off, even if they self-destructed. It would depend on how loaded the aircraft was and how long the imaginary treadmill runway was.

Fun distraction this morning!
 
Some of you guys are over thinking this. Regardless of the speed of the conveyor or the landing gear, if there isn't enough air moving across the wing surface to generate enough lift to overcome the weight of the aircraft (gravity) and drag on the aircraft, that plane, any plane, will not fly. And that speed. where lift is generated, is different for every type of aircraft from a Cessna 152 to a 747.

Without the generation of lift from the wing a plane will not fly. You can run the conveyor at 3 times the speed of sound with the plane on it but if that wing is not moving through the air to generate lift it ain't going anywhere. The engine of a plane is used to create increased air speed over the wing surface. Does a wing need an engine to generate lift....no. Think of a glider.

For another example, think about a stall in an aircraft and why it happens. A stall occurs when there is no longer enough air moving across the wing surface to generate lift. That condition can happen as a result of air speed, angle of attack (the angle the wing meets the air moving across the wing) or a change to the shape of the wing surface.

Its all simple aerodynamics.
Shawn
 
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