How fast does the plane need to go to take off? Because it would need to do that plus 150 to be at takeoff speed with respect to the air.
How fast does the plane need to go to take off? Because it would need to do that plus 150 to be at takeoff speed with respect to the air.
You are an asshole.
Welldone
Like a lot of people have said, the plane must have an airspeed of 150mph. Think of this: Imagine that on a normal runway, the plane's throttle allows a max thrust of 300mph. So halfway would exert 150mph. If you stuck the plane on the treadmill going -150mph, and set the throttle half way, the 150mph thrust would not move the plane forward, you'd have to set it full throttle to 300mph to generate the 150mph airspeed. But I'm an accountant, so I'd be more concerned with fuel cost and depreciation method.
Except that the treadmill exerts nearly zero force on the plane itself!
The treadmill is in the problem just to trip up silly accountants.
No, the plane will not take off. And here is the reason why.
When a plane is on a runway, it is on a hypothetical "stationary" surface. (hypothetical because the earth is moving)...
Yes the wheels are free spinning, but when you start the treadmill at 150 miles per hour, and set the plane down on the treadmill, the wheels begin spinning as fast as the treadmill. Yet the plane stays in place, (ie...when you run on a treadmill your leg turnover is as fast as the treadmill belt, or you get thrown off the back or run up the front)
Even if you were to turn on the "boosters" and equal out the treadmill speed, the free spinning of the wheels will not allow the plane to "move forward" because the spinning wheels keeps the plane "in place."
When a plane takes off from the runway, the speed of the planes force into the air causes the air to move around the wings at the needed speed to create lift. The plane (with spinning wheels) has no air moving over or under its wings. So the lift is not created to thus cause the plane to LIFT off the ground.
If you were to either, turn the plane around on the treadmill, with the plane moving at the same speed of 150 mph as the treadmill creating a net speed of 300 miles per hour, or to have some sort of equipment to creat wind speeds of 150 miles per hour to send into the front of the plane then the plane will NOT take off. Because there is not air moving over the wings.
If you can explain HOW the air is moving over the wings, THEN and only then will you be able to prove how the plane will take off.
okay, 'yeah..'
picture this: a jet is attached to a skate board on the ground. When the jet is turned on, it takes off pretty dang fast won't it?
No picture this: right beside that skate board, a jet is attached to a wooden crate on the ground. If this jet is turned on at the same time and is pointed in the same direction, will it go just as fast, or not as fast? Why or why not?
Answer this question right and you will find the answer to yours.
one more thing, 'yeah..'
yeah... wrote:
... the free spinning of the wheels will not allow the plane to "move forward" because the spinning wheels keeps the plane "in place."
Exactly how does "free spinning of the wheels . . . keep the plane in place"?
Remember planes do not accelerate by driving the wheels like a car or anything else which relys on traction for propulsion.
yeah... wrote:No, the plane will not take off. And here is the reason why.
Yes the wheels are free spinning, but when you start the treadmill at 150 miles per hour, and set the plane down on the treadmill, the wheels begin spinning as fast as the treadmill.
Even if you were to turn on the "boosters" and equal out the treadmill speed, the free spinning of the wheels will not allow the plane to "move forward" because the spinning wheels keeps the plane "in place."
If you can explain HOW the air is moving over the wings, THEN and only then will you be able to prove how the plane will take off.
You have answered you own question but you obviously cannot see why!
Remember the riddle
the riddler… wrote:As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving.
The plane is moving at the same speed as the treadmill. Therefore the plane is not stationary on the treadmill. When the plane reaches its normal take-off speed, it will start to fly.
The speed of the treadmill is irrelevant and is added to the riddle to confuse people.
I didn't say anything about landing gear. Big passenger jets are wheel-driven when maneuvering on the runway at low speeds.
Are you guys seriously this lousy? So how come when you run on a treadmill you don't run up the front of it? Because you allow your turnover to keep you in the middle of it. Just like not being thrown off the back. I'm not saying it is wheel driven I am saying that there has to be air speed over the wings. Say the tarmac is converted into a giant treadmill. The treadmill will be spinning in reverse direction that the plane is "pointed/headed" the plane is then brought up to the same speed as the treadmill that is going the opposite direction. To keep from being thrown off the treadmill the plane has to maintain a certain speed with its engines. That speed=the speed of the treadmill. Thus creating a moot plane that stays in one place as the treadmill goes the opposite direction it is pointed. IF and ONLY IF the plane is turned on to a HIGHER speed than the treadmill is going, THEN it would be able to eventually take off once airspeed over the wings is greater. IE-Running off the front of a treadmill by running faster than the speed of the belt.
Gravitation Gertie wrote:
I didn't say anything about landing gear. Big passenger jets are wheel-driven when maneuvering on the runway at low speeds.
Uh, no they aren't, they use their engines for power - even at low speeds, or tugs on the ground pull/push them along.
There is a company out there right now developing a "drive wheel" for big passenger jets so won't have to use as much fuel to drive around on the ground in the future (not certified yet).
Also, will some please explain to me how an airplane on a treadmill is supposed to generate lift?
Even if the plane's wheels attain a speed of 150mph, there is no airflow to generate the necessary lift to maintain flight.
The airplane might be able to get it's front wheel off the ground, but would crash horribly trying to get off the treadmill.
You need to remember, there is a difference between ground speed and air speed.
Which is why airplanes take off into the wind and not with the wind. If an airplane attempts to take off with a 150 knot tailwind, it will NOT be able to sustain flight. It will crash. But it can (theoretically) take off in a 150 knot headwind. Wouldn't be allowed to though...outside the certified limits of the airframe.
Look no further than wind shear events to see what can happen when airspeed gets reduced to 0. Happened in Dallas a number of years ago with fatal results.
Bernouilli's principle states that as the velocity of air over an object INCREASES its atmospheric pressure DECREASES. It's what allows a planes wings to create lift. So wouldn't the air speed of the treadmill belt, UNDER the wings create a LOW pressure UNDER the wings, THUS pushing the plane down TOWARDS the belt? Now on a runway, the air can move ALL around the wings, but when the plane is on the treadmill the only airspeed produced is that of the treadmill belt. So no the plane will not take off, it will be pulled down towards the belt.
Wrong, wrong and wrong again!
The airplane is moving forward, so the treadmill belt is not generating the only source of moving air. The planes wings are cutting through the air.
Also, a plane can still take off if there is no wind- the speed of the plane moving forward is enough to force air over the wings quickly enough to create lift.
the riddler wrote:
An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?
Went back to the original riddle for a little dissection.
If you make the assumption that the airplane is staying in relatively the same position while the treadmill gets up to 150mph or so, it cannot take off. This assumes the wheels are free-spinning. This is why I said the airplane wouldn't take off.
Now, if you make the assumption that the airplane switches on it's jets, and the treadmill is of necessary length, and you give the engines enough thrust to get the speed of the airplane up to V1 (enough airspeed to rotate), then yes indeed the airplane will take off.
First and foremost, we need to go back to the airspeed question.
If and when the airplane's engines begin to spool up, they will move the airplane - treadmill or no treadmill. The engines are working against the air, not the friction of the treadmill. Once those engines generate enough thrust to move the airplane at 150 knots (airspeed), the airplane will take off....however, the wheels spinning on the treadmill will be moving at 300 miles per hour (ground speed).
Speed of the treadmill is irrelevant, while the length is the most important thing. The treadmill will still need to be the same length as a normal runway for the airplane to have enough time to generate 150knots of airspeed required for rotation.
The riddle requires you to make some assumptions, and because we make different assumptions, we get different answers. I made the assumption that the planes airspeed would be 0, which is why I said it wouldn't fly.
I was able to see the other answer by revising my assumption on the length of the treadmill, and whether or not the airplane was moving forward on that treadmill.
. wrote:
Wrong, wrong and wrong again!
The airplane is moving forward, so the treadmill belt is not generating the only source of moving air. The planes wings are cutting through the air.
Also, a plane can still take off if there is no wind- the speed of the plane moving forward is enough to force air over the wings quickly enough to create lift.
No where in the riddle does it say the airplane is moving forward. Just because the engines are started, doesn't mean they are generating thrust.
That's an assumption that some people made, while others assumed it wasn't moving forward in relation to the air.
PDX Track wrote:
airplane up to V1 (enough airspeed to rotate)
V1 is "decision speed", i.e. the point at which the decision to take off or not is made. Vr is "rotation speed".
The plane will clearly take off.
The wheels (ideally) exert no force on the body of the plane. Assuming this is true (which it very nearly is), if the engines of the plane were not used, but the treadmill was run at 150 mph (from the front of the plane to the back) would the plane move backwards? No, it clearly would not. It would remain stationary as the wheels exert no force on the body of the plane. The treadmill (which only exerts force on the wheels) is powerless to influence the motion of the plane since it cannot apply a force to the planes body. No force equals no acceleration, equals no motion.
This problem has nothing at all to do with the relative motion of the plane to the ground or air. It is a conservation of momentum problem. Air will be forced through the engines (or pushed by the propeller) at an exceedly high rate. In order to conserve momentum the plane must move foward regardless of its coincidental location on a large treadmill. If it does not it will violate the laws of physics.
The problem could be restated: Can a plane at rest on a frictionless surface (the treadmill) still takeoff using its engines? Of course the answer is yes. As long as the plane is not in a vacuum it will propel itself by forcing air through its engines.
PDX Track wrote:
No where in the riddle does it say the airplane is moving forward. Just because the engines are started, doesn't mean they are generating thrust.
Once the engines are started they generate thrust. How can they not? Even a feathered prop will generate a small bit of thrust.
I love all the people that come on here without reading the thread thinking that they're really smart talking about bernoulli's principle and atmospheric pressure when they don't even understand the riddle.
No where in the riddle does it say the airplane is moving forward.
YES IT DOES!
Try reading it again. It says that the treadmill is moving backwards at the SAME SPEED THE AIRPLANE IS MOVING.
The airplane starts motionless (relative to the ground). From the riddle we know that the treadmill is also motionless. If the treadmill belt were moving backward while the airplane stayed in the same position relative to the ground, that would VIOLATE THE RULES OF THE RIDDLE. The airplane's speed relative to the ground and the treadmill belt's speed would not be equal as the riddle states clearly.
So the airplane turns on its engines and starts to move forward relative to the ground. By definition of the riddle the treadmill must now be turned on and moving backward at the same speed that the airplane is moving forward.
Read carefully. THIS DOES NOT MEAN THAT THE AIRPLANE STOPS MOVING FORWARD. If it did while the treadmill was on, that would violate the riddle. It does mean that the airplane must be moving twice as fast relative to the treadmill belt as it is moving relative to the ground.
This continues until the airplane reaches a forward velocity of 150 mph (relative to the ground and 300 mph relative to the treadmill), which is fast enough for it to take off according to the riddle.
Go back and read all of the posts made by "roger penrose". Then you all will understand that THE AIRPLANE WILL TAKE OFF. People have tried to sound smart by talking about free spinning wheels, jet thrust and negligible friction, all of which are irrelevant to the riddle and just complicate things.