I doubt whether this will help, but I’m still in the “no airspeed - no lift” camp.
Rather than having a treadmill that matches its speed to the plane, let’s just consider a treadmill that moves at a constant speed. Let’s also use the example plane that takes off at 60 kt and has a maximum speed of 150 kt, and assume no wind, and no, or a minimal, interaction between the movement of the treadmill and the movement of the air above it. I’m deliberately not including the wheels in the discussion.
If the treadmill is moving at 30 kt, the plane will need to travel forward at 90 kt, relative to the surface of the treadmill, in order to take off.
If the treadmill is moving at 60 kt, the plane will need to travel forward at 120 kt to take off.
If the treadmill is moving at 100 kt, the plane will need to travel forward at 160 kt to take off - which it can’t do. We’ve prevented the plane from taking off without needing a treadmill capable of infinite speed, frictionless wheel bearings, or anything else physically impossible.
A plane’s maximum speed is airspeed, not how fast the wheels are capable of turning. What are you imagining would keep the plane from going fast enough to take off?
23 years of flying jets must make me backward and clueless.
As long as a wing has airflow and it does not exceed the critical angle of attack, it produces lift – it is flying.
If the air moves with the conveyor belt and therefore relative to the wings, call up Indy Center, we are in business.
If the air is not moving relative to the wings on the aircraft, you have the following situation: No airflow, no airpeed. No airspeed, no aoa. No aoa, no lifties. No lifties, no fly. Captain goes back to the hotel and declares another 12 hours of crew rest.
Let’s put a little different spin (pun intended) on this. Assume that you are walking along a conveyor belt which is matching your speed. You take out your trusty bow and arrow and shoot the arrow at a target in front of you. The conveyor belt suddenly speeds up to match the speed of the arrow, but in the reverse direction. Does the arrow reach the target?
Other than the fact that you will probably get knocked flat on your face by the sudden change in speed, the conveyor belt will have no effect on the arrow.
Now, if you want, you can dangle a string from the arrow with a little axle and wheels on it which will touch the conveyor belt. Will the arrow reach the target? This is the same thing that will happen with the airplane.
Depends on how you interpret the wording of the problem, and that is the source of the confusion, not any misunderstanding of the physics.
The problem in Cecil’s column says “The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).” What it doesn’t say is whether the plane is moving forward with respect to the Earth or with respect to the conveyor belt. And that is the basis of the disagreement.
The treadmill is providing it with a 100kt tailwind. Indeed, what’s the difference between keeping the air still and moving the ground at 100kt, and keeping the ground still and moving the air at 100kt?
Another thought experiment.
Let’s put the treadmill at the edge of a cliff, so that the surface of the treadmill moves towards the cliff, and run it at 60 kt.
Now, let’s put the plane at the other end of the treadmill, facing towards the cliff, without starting the engine.
When it reaches the end, will it be flying at 60kt, or will it just drop straight down?
What Tevildo just described is a catapult.
It’s used to gain a maximum amount of airspeed in a little amount of wheel roll.
Like shooting an F-18 off an aircraft carrier!
Everyone agrees, with no air flowing over the wings the plane won’t take off. That’s not the issue at all.
For those who think the plane will remain stationary wrt the air: **WHAT FORCE IS COUNTERACTING THE THRUST OF THE JET ENGINES? ** The converyor belt has no way of applying force to the plane no matter how fast it spins. The plane cannot remain still, it has a huge friggen force vector from the jets and nothing to counteract it. The plane is moving forward, it will take off.
The question doesn’t state that the plane remains motionless wrt the ground. It just talks about how the conveyor belt will react which is a red herring since it has no effect on the plane. There’s nothing in the question that forces the plane to stay still. It’s poorly worded and people infer that the plane must stay still, but that’s not the case.
A similar situation would be a ski plane taking off from an unexpectedly fast moving glacier. Aside from a tiny bit of initial friction, the skis and the snow have no way of stopping the plane, no matter how fast the glacier decides to move.
As people are coming to realize, it all boils down to whether or not the plane moves forward WITH RESPECT TO A STATIONARY FRAME OF REFERENCE NOT ON THE TREADMILL. This is the key. Unfortunately, the wording of the question is ambiguous on this point.
However, it seems that by stressing the fact that the reverse motion of the runway is always exactly matching the forward motion of the plane, the question strongly implies that the plane’s net motion relative to the Earth is zero.
If the plane does have forward motion relative to the Earth, then, as someone earlier stated, the question really is, “does spinning the plane’s wheels at a faster rate have any effect on the plane’s takeoff?” If this was the intent of the question then that’s pretty lame!
Not even close!! If you put an accelerometer in the jet launched from the carrier it would register several G’s. In Televido’s example there would be very little acceleration to measure.
Forget about Mr. Newton and Mr. Einstein. Someone call Stephen Hawkins. Whenever this subject comes up in a thread there is a black hole briefly formed on Earth into which all rational thought goes and cannot escape.
I will avoid the event horizon by ducking into some pacific trench for a few minutes looking for a ray gun.
As I understand you, the treadmill is propelling the plane at 60kts, relative to the earth, and the plane itself will be travelling at 60kts at the end of the treadmill. Assuming 60kts is the plane’s takeoff speed, then yes, it flies. Briefly. (It soon stalls due to lack of an engine adding additional speed and lift). Your scenario (if I understand it) is somewhat like a catapult on an aircraft carrier. But I think maybe I’m not following you somehow?
A plane (or any vehicle with idealized, free-moving wheels) will not be conveyed down towards the cliff. It will stay in place.
If you were to stand on such a treadmill, the friction in your sneakers would drag you to the cliff. If you were to park a car on the treadmill, the parking brake would hold the wheels from spinning, and the friction would drag it towards the cliff.
A freely spinning wheel will just spin in place, car or plane.
Guys, the “it’ll never fly” group is postulating a conveyor belt that will hold an airplane stationary with respect to the ground. The “of course it’ll fly” group, including Cecil, is pointing out, rightly, that such a device can’t possibly exist – an airplane’s wheels just can’t generate enough rolling drag to prevent an airplane from moving.
It’s not G forces that cause the jet to fly off the carrier!!! It’s airspeed.
G forces are just the result of the acceleration to the required airspeed in the short period of time.
Those who say that the plane won’t take off if there is no airspeed are correct in that assertion. However, the conveyer belt does not prevent the plane from gaining airspeed: the plane accelerates relative to the conveyor belt, and takes off, no matter how fast the belt spins, because the plane’s thrust is not coming from its wheels.
Consider it this way: Imagine that instead of a plane, it’s a car with wings. Imagine further that in the absence of a conveyor belt, this car with wings achieves liftoff once it hits 300 mph. (Liftoff will be momentary, since once the wheels leave the ground it loses its propulsion, slows down, and descends). If this car with wings is now put on a conveyor belt that matches its speed, it will never take off, because it will remain stationary with respect to a fixed observer off the conveyor belt.
Now, replace the winged car with a plane. Unlike the winged car, the plane’s forward motion is not a result of its wheels pushing against the ground (or the conveyor), but of its engines pushing air from front to rear. The fact that it’s on a conveyor doesn’t make any difference as to the thrust its engines generate, it accelerates normally (and moves forward with respect to the conveyor). Its wheels, which are not connected to any sort of drive shaft, spin freely as the conveyor spins the opposite way, and have no impact on the plane’s acceleration.
If the spinning conveyor could prevent the plane from taking off, what in the world would keep it in the air once its wheels left the ground?
The reason this is confusing is that if you imagine the plane remaining stationary with respect to a fixed observer, it’s obvious it will never take off. However, the plane would NOT remain stationary with respect to a fixed observer as a result of being on a conveyor belt.
[QUOTE=Telemark]
“Everyone agrees, with no air flowing over the wings the plane won’t take off. That’s not the issue at all.”
“For those who think the plane will remain stationary wrt the air: **WHAT FORCE IS COUNTERACTING THE THRUST OF THE JET ENGINES? ** The converyor belt has no way of applying force to the plane no matter how fast it spins. The plane cannot remain still, it has a huge friggen force vector from the jets and nothing to counteract it. The plane is moving forward, it will take off.”
OK, I think I see your objection to the plane won’t move forward arguments. What you are saying is that the moving treadmill, wheels, etc. are irrelevant. What matters is the forward thrust from the jet, and none of these factors will counter the forward thrust generated by the jet engine. This sounds reasonable to me, so it seems that, yes, a jet plane would gain forward motion with respect to the Earth (and surrounding air), and therefore would eventually be able to take off.
Imagine a similar scenario to the one in the question, where you have a jet plane with no wheels at all. Instead, we’ll add a maglev track to the treadmill runway that perfectly levitates the plane 3 feet off the ground against the force of gravity. Now you turn the engines on - ZOOM the plane obviously moves forward no matter how fast the treadmill turns in the opposite direction. This is similar to the “shoot the arrow while running on a treadmill” example.
It does seem that the plane must move forward!
So why don’t I move forward while I’m running on a treadmill, or my car move forward while running on those rollers at the garage during my vehicle emissions test? Because both I and my car depend upon applying force via the friction between either my shoes or the car’s tires to get forward movement. Planes are indeed different, all the wheels do is keep the fuselage from scraping across the ground, their forward motion is generated by the jet or prop.
It seems I’ve fallen into the “Will take off” camp!!
I too am in the “no airspeed - no lift” camp. Which is precisely why the plane DOES take off.
Imagine you hold in your hands a toy airplane, complete with unpowered landing gear that can freely spin. In front of you is a conveyor belt that is going at a pretty good rate.
Now, slowly lower the toy airplane so the wheels touch. What happens? The wheels start to spin, but the plane, relative to your feet, does not move - right? The force of your hand is pushing forward while the conveyor is trying to pull the plane backwards.
But remember, the freely spinning wheel causes the effect that your hand is disconnected from the conveyor belt. Is there anything stopping you from moving the plane forward? Even if the conveyor speeds up, can it possibly stop your hand - even slow it down? No.
So what can the conveyor do to stop the engines/props of the plane from thrusting the real plane forward? The same thing: nothing.
It’s not specific about what the plane’s speed is relative to. Obviously, lots of people have interpreted it as meaning that the belt turns fast enough to keep the plane stationary wrt the Earth.
Well, if the glacier were moving at thousands of miles per hour, so that the friction on the skis exactly offset the thrust of the propeller, then it would. It would be quite a trick to engineer a conveyor belt that could turn that fast, but it’s a thought experiment, so practicalities aren’t germane. The confusion about the answer is directly related to confusion about what the question is asking.
