Airplane on a Conveyor Belt
December 8, 2005
11:54 am
A riddle was proposed on the Neal Boortz show today:
If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?
Astoundingly, Neal and the rest of his crew took the position that the plane would sit there stationary! Good God… this man is a pilot and has a law degree! I could understand a random high school dropout being fooled by this, but a pilot?
Then I googled the riddle, and found a thread on Airliners.net that has been raging on, with the vast majority of people taking Neal’s position… that the plane would not be able to take off.
Their argument is this, to quote one poster:
Thrust acts accordingly to Newtons Third Law of Motion - every action has an equal and opposite reaction. In the case of an aircraft, the reaction of the engines is that of forward motion, against whatever medium it is stationary. But the ground the aircraft is sitting on in this case is NOT stationary, its providing an exactly CANCELLING force pushing the aircraft back.
The problem here, of course, is that the poster (and Neal) cannot disengage themselves from seeing the airplane as a car. The difference between a car and a grounded airplane is that a car uses its wheels to propel itself forward, and an airplane moves itself forward by moving air. They assume that the runway moving backwards would move the plane backwards. This is what would happen with a car (that is in gear), so why not for an airplane? Well, because an airplane’s wheels are free rolling. There is obviously some friction, so there would be some small backwards force, but it would be infinitely small as compared to the forward thrust of the airplane.
You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control.
So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object. Next, we’ll see what happens when the object is trying to move forward. Attach a string to the matchbox car. Place the car at one end of the paper, and use the string to start pulling the car forward with a steady force. As the car moves forward, start pulling the paper out from under the car, backwards. Do you feel increased resistance as you pull the string? Of course not. The wheels are free rolling! Spinning the wheels does not make the object move!
When an airplane takes off, there is one major forward force… the forward thrust. The main rearward force is air resistance. The turning of the wheels provides a small frictional force, but because the wheels are free-rolling, this friction is very small. Unless the wheels are locked, the friction is always going to be less than the thrust, which means that the overall force is still forward, and the plane will still move.
Gah… people are freakin’ stupid.
Update: There is a variation on this riddle that says that the conveyor belt matches the speed of the plane. It doesn’t matter… the plane still takes off. The conveyor belt could be going 5 times as fast as the plane, and the plane would still take off. You’d get into issues about tires blowing out, but assuming that the wheels can take the strain, the airplane would still take off.
Update: Well here we are more than two years later. The show “Mythbusters” attempted the experiment. And yes, the plane took off. The laws of physics still apply. Back to life as usual.
That was my whole point previously. Assuming that it can eventually break free of the treadmill, AT THAT POINT it will NOT have sufficient speed or thrust to remain airborn.
As the plane moves forward…say 1 knot, the belt moves backward at 1 knot. The wheels will move at a speed equal to 2 knots. That’s all. The friction at the wheel bearings is pretty much negligible.
Kevin - that would be 2 knots in relation to the ground - not air speed. Air speed is still zip (which makes it kinda hard to fly).
No, that is still 1 knot of airspeed. The plane is moving in relation to a stationary observor…say the control tower. The plane moves 1 knot north, the conveyor 1 knot south and the wheels spin as if a plane on a conventional runway were doing 2 knots. This relation remains true as long as the conveyor matches the planes speed.
Harry, you are mistaking a proportionate increase in friction for an equivalent increase. Friction will increase with wheel rpms because a certain amount of energy is lost in every rotation, mainly due to a deformation of the tire at the contact patch, but the coefficient of rolling friction is low enough that it does not significantly counter engine thrust. When you roll something, friction does not increase so dramatically that it prevents you from rolling it faster.
No, I don’t think I’m mistaken. I don’t think the amount of friction that has to be overcome is the issue. The issue is that it can never be overcome because of the increasing speed of the belt.
Look at it this way: Plane on a runway that doesn’t move at all. Can it take off? Of course it can. All that has to happen is enough thrust be generated to overcome the friction.
Put the plane on a runway that’s moving backwards at a constant velocity of 10 mph. Can it take off? Yes, with the same principle, just generate enough thrust to overcome the friction. But does it require the same thrust to overcome the friction as the first example? No, it would require a slightly higher amount of thrust to overcome the slightly higher amount of friction.
Same plane, same runway, now it’s moving backwards at a constant velocity of 100 mph. Can the plane take off? Yes, same reason as above. Is the amount of thrust needed the same as the 10 mph runway or is it greater? Clearly, it’s greater. The difference may be small or even to use your word negligible, but it’s size is not relevant because until the friction is overcome the plane will not move forward.
With a runway that has a constant velocity (whether it’s zero or 1000 mph, doesn’t matter) the amount of thrust needed to overcome that friction is achievable. But in our instance the runway speed is not constant. It starts at a level, compared to the thrust of the airplane, that is great enough to keep the plane still and it always stays at that relative level by matching the speed of the wheels.
The parameters of the puzzle put the plane in a hole that it can never dig itself out of, namely it has to overcome a friction level that is increasing because of the efforts to overcome it.
Mathematically, I think if you could chart the relationship of thrust to the friction level that you were trying to overcome it would be an asymptote, that is it will approach the level infinitely, always getting closer but never crossing the level needed to achieve forward motion.
Here’s another way to look at it: Put your plane on a motionless runway and generate the exact amount of thrust needed to have the plane begin to move forward.
Now pick the plane up and place it, while still generating that same amount of thrust, onto a runway that has a higher co-efficient of friction (rougher runway surface for instance). Can the plane move forward? No, because the thrust generated is only enough to overcome the friction on the the first runway. Increase the thrust so that the new level of friction is overcome and the plane starts to roll forward. As soon as that happens pick it up and place it on a third runway with an even greater co-efficient of friction. Will the plane move? No, same reason as above, not enough thrust is being generated to overcome the new level of friction, even though it may be a very tiny amount, it still needs to be overcome.
Keep doing this infinitely and you’ll never be able to get the plane to move forward on these ever rougher runways for the same reason that the plane on the conveyor belt runway won’t move. Namely once it reaches the level of thrust necessary to achieve motion, the level of thrust necessary to reach motion has increased.
Here’s another illustration: The plane needs to generate (hypothetically) 100 pounds of thrust just to move forward on a stationary runway. If he generates 95 pounds can he move? No. How about 99 pounds. No movement. How about 99.99 pounds. Still no movement. How about 99.99999999999999999 pounds. Nope, not gonna do it.
So the pilot guns the engines to exactly 100 pounds of thrust. The plane starts to move forward, but suddenly the co-efficient of friction goes up slightly and he now needs to generate 101 pounds of thrust. Is he moving? No, because he hasn’t overcome the friction. He ups the output to 100.99999999999999999999999999999 pounds and the plane still won’t move. Once he crosses the magic threshold to 101 pounds the plane starts to roll forward, but you know what happens and now he needs 101.25 pounds of thrust. At 101.25 pounds of thrust he needs to overcome the new friction level and needs to have 101.255 pounds of thrust.
No matter how much this happens, he’ll never reach enough thrust to overcome the ever increasing friction levels.
(The puzzle presumes that the speed change of the belt is instantaneous. If it’s not, then there would be a time of forward motion before the belt speed changed. Could the plane take off in this scenario? That’s another thread.)
Sorry to be so wordy, but the plane is still as grounded as an Independence Air 737.
Still not a pilot or an engineer, just overcaffeinated
Yes, but this friction increases linearly. The formula for kinetic friction is U=Nμd N is the normal force (unchanging), μ is the friction coefficient (unchanging). The only thing that changes is d, the distance over which the friction is applied. d is proportional to twice the speed of the plane. The only way the plane can’t overcome that friction is if the friction force is equal to half of the engine force… and that’s simply not the case.
Not necessarily true. Remember that there are two friction coefficients… μ(static) and μ(kinetic). Kinetic friction is always less than static friction… which means that the force required to start an object moving is less than the force needed to keep it moving. Everyone has experienced this… moving furniture or some such thing. Once you overcome the static friction, the object lurches forward because you are providing much more force than is needed to overcome kinetic friction, so the object accelerates (sum of the forces does not equal zero). So it is quite possible that the plane, already rolling, would roll on the third runway, because while it doesn’t have enough force to overcome runway 3’s static friction, it is already rolling and only needs to overcome the kinetic friction, which is significantly less.
Couple of problems here: you’re applying μ(static) to a kinetic system. Once the plane starts rolling, if the force is constant, the plane will accelerate, because μ(static) is out the window and μ(kinetic), its much smaller brother, is now in play. Also, you said that the coefficient of friction goes up slightly… first of all, static friction is constant. It is a threshold that must be breached. Once you breach it, you are dealing with the kinetic coefficient of friction, which is also constant (and is lower). The only thing that changes is d… the distance traveled (by the wheels) which is equal to twice the speed of the plane relative to stationary ground (since the wheels are going twice as fast).
Think about it… if friction increased once something got moving, and kept increasing as you increased the force exerted… nothing would ever move!
I still have a very hard time seeing how the plane will take off. For everyone who believes the wheels simply rotate more quickly to compensate for the conveyor’s movement, explain this: why is more thrust needed to push a plane through snow or mud or standing water than is needed on a dry concrete runway? Under your premise, the wheels should simply rotate faster to keep up with the engine thrust. That is not what happens in the real world. 100 knots of engine thrust does not mean equal speed across those various mediums. The fact is that friction against the wheels acts directly on the plane. It pushes against the wheels’ forward motion. That force is translated from the wheels to the struts to the fuselage, and that’s how it acts against the force of the engines.
If the plane needs 100 knots of speed to take flight while the conveyor is moving backward at 100 knots, I still say it won’t take off. While it may not be stationary, the backward motion of the conveyor will transmit frictional force to the entire plane, and that will push against the engine thrust. You simply can’t negate that force. If you can, releasing the brakes with no engine thrust while the conveyor moves backward should leave the plane standing still — but that absolutely doesn’t happen. Instead, the plane is pushed backward and eventually thrown off the back of the conveyor. That same force is what acts against the engine thrust. The only way you can say that the wheels play no part in counterforce against the engines is if the plane would sit motionless on the conveyor with no engine thrust and no brakes (with the wheels spinning freely beneath it).
I won’t call anyone stupid for having a different opinion, and I won’t question their academic credentials. Honestly, that’s why so many have become disinterested in this debate. I’d just really like to hear a reasonable, mathematically and scientifically sound explanation for how the plane will take off under these circumstances. Thus far, no one has provided one. We know friction on the wheels acts directly on the plane when moving it over surfaces that aren’t just flat dry concrete. How is that force suddenly irrelevant on a surface that moves backward?
You’re right… it doesn’t stay still. But it doesn’t move backwards with very much force… μ is fairly small, in the scheme of things.
Also correct. But this friction will never exceed the thrust needed to create that friction, once the wheels are rolling. The frictional force is proportional to twice the forward speed… but is much, much less. If it weren’t, planes wouldn’t be able to take off under normal circumstances.
In mud, the frictional force would be greater… but would still be proportional to twice the forward speed.
The frictional force generated by the combo of the plane’s forward motion at X knots and the runway’s backwards motion at X knots is minute when compared to the force needed to propel the plane forward at X knots. And because of the proportionality relationship, it doesn’t matter how high X goes, the plane still moves forward.
Let me clarify with this. Unless the riddle is quantified with additional constraints, the plane won’t take off. Given what we know from the question, we assume that 100 knots of speed is needed for flight. If that’s the case, it absolutely won’t take flight.
Too many people who believe it will take off assume a 1-to-1 ration between engine thrust and fuselage movement. Everyone agrees the air and conveyor and wheels all create frictional forces, even if minimal, and this reduces the speed of the plane as related to engine thrust. Therefore, if engine thrust is equal to 100 knots and drag from the air, wheels and ground reduces that thrust slightly, the plane won’t take off given a 100 knot minimum speed. It’s simple math and science in this case. 100 knots of thrust is less than 100 knots of forward movement. Drag (parasitic and induced) from the air, ground and wheel rotation causes a small reduction in the translation of thrust to movement. Given that everyone is agreed on that, 100 knots of thrust and 100 knots of backward conveyor movement equals
Why are we restricting the engines power? Any airplane is likely more than capable of ataining liftoff speed under such conditions. The frictional forces imparted by the wheels is negligible and any drag that comes into place is present whether we have a conveyor or not.
What is interesting is that the answers here are all over the board. One group contends that the wheels have nothing to do with anything, another say the wheels are the key to break with the treadmill, and so on. I must say that it has at least gotten people thinking - albeit often on the wrong tangent.
The proverbial bottom line is this: I’m not necessarily advocating that this is possible, but IF it can take off it has to achieve sufficient ground speed to take off (like on a runway)…or NOT have enough speed when it finally leaves the end of the treadmill. And remember, all it says is that it is a LONG treadmill.
Can everyone at least agree on this?
Before you lecture us on “simple math and science,” you might want to review the difference between thrust and speed.
Thrust is type of force (measured in pounds or newtons), whereas the knot is a unit of speed (nautical miles per hour). In simple terms, force is a push or pull on an object, and speed is its change of position (distance traveled) over some time. It is therefore nonsensical to talk about “100 knots of thrust.”
I’m not just nitpicking, either; confusion about speed and force is central to the way people are misunderstanding this problem.
Recollect the old trick where you pull the tablecloth out from under the dishes without them falling on the floor. The cloth moves with high speed, but exerts very little force on the dishes. Speed is not the same as force. Just because a belt moves quickly under an airplane, doesn’t mean it is exerting tremendous force on that airplane.
Keep in mind, Harry, that engines can produce far more thrust than just what is necessary to initiate motion. Say you have a 100,000 lb. airplane with two turbofans generating 20,000 lbs. thrust each for a total of 40,000 lbs. thrust. Say the coefficient of rolling friction is .05 (just my guess). The force of friction is the coefficient of friction times the normal force (which is the force perpendicular to the surface, which in this case is directly upwards and equal to the weight of the airplane). This means you need 5,000 lbs. of force to move the airplane, only one eighth of the available thrust.
Again, don’t work from the assumption that available thrust is just barely enough to get the plane moving from a standstill. There is plenty of thrust in the budget. Explain how the belt’s moving backwards causes friction to skyrocket from 5,000 to 40,000 lbs.
It sounds like you are vastly overestimating the significance of rolling friction. We see wheels all over the place because wheels make it easy to push things without encountering massive resistive forces.
If you want to assume that we have just enough thrust to initiate motion, then you are right that a slight increase in rolling friction would prevent acceleration from occuring. But (1) this is an unrealistic assumption because planes have far more thrust available than needed to start motion; and (2), you haven’t explained the physics of how you think friction varies with speed. In fact, much of what I have read suggests the force of friction does not vary with speed. In other words, as you push something along a surface, it is not harder to keep it moving forward at 10 mph than it is at 5 mph.
(My statement ignores air resistance, which does increase with speed, but it is true as pertains to the wheel/belt interaction we are discussing).
So prove it.
You’re right! But I’ve shown the problems with this line of argument. Also, the coefficient of friction is a constant that depends on the material properties of the two surfaces in contact. It doesn’t vary with speed. Pour water or glue over the belt and then it would change.
Independence flew RJs and A319s. I think they were switching to A319s when they ran out of time. We’re still waiting on a refund.
Not sure about that, Mark. We’re talking about wheels, and rolling friction is a form of static friction, not kinetic, because the wheels are not slipping across the surface.
I was actually talking about the friction inside the wheel… but you’re right, there is also rolling friction between the ground and the wheel. Of course rolling friction is very low (the whole reason we use wheels!)
This puzzle is actually about one very simple question, namely, can the plane achieve any forward motion on the conveyor belt. If it can overcome friction and make any forward motion then it can achieve enough forward motion to generate lift and take off. Focusing on any other question or subject is chasing rabbits as they are irrelevant.
Contrary to the view expressed above, I am not underestimating the amount of thrust that can be generated by a plane. In fact, I’ll posit that the plane can generate an infinitely high level of thrust, just as the belt can travel at an infinitely fast speed. The plane will still not make any forward motion because the increasing thrust causes the belt to speed up which increases friction which increases the level of thrust needed to overcome the friction.
One of the examples I mentioned above has not been responded to. Put three planes on three runways. Runway 1 has a constant velocity of 0 mph, runway 2 has a constant velocity backwards of 10 mph and runway 3 a constant backwards velocity of 100 mph. All three planes can take off but each requires a different level of thrust to do so because the backwards velocity of the belt creates greater resistance.
I admitted that the level of friction increase may be small, negligible, or even minuscule, but it still has to be overcome to gain motion. If a plane needs 100 knots of speed to gain lift he cannot gain it with 99.9999999999999999999999999999999 knots. Even though the difference is negligible, the difference still has to be overcome.
You can increase the number of planes on runways with constant velocities, increasing the velocities and you’ll always get the same result, a greater runway speed means some additional level of thrust is needed. The amount of the additional thrust is only relevant because it exists and has to be overcome.
Nice to see we agree on something!
You are underestimating the amount of thrust available relative to rolling friction. Just about any powered vehicle can produce far more thrust than is needed to overcome friction, because it is desirable to accelerate a vehicle quickly. Your typical car engine can thrust forward a lot harder than what you could do if you got out and pushed.
You are fixated on this notion that thrust and friction are equal or almost equal, and that a vehicle moves by just marginally overcoming friction. But this is not true in reality.
I submit that all three runways require the same thrust. My understanding is that rolling friction does not vary with speed. The backwards moving belt contributes to the angular velocity of the wheels, but its friction does not increase as the wheels turn faster.
It is true that the wheels can only turn so fast before the tires burst (I imagine they would burst before the wheel bearings fail). This, however, is not due to increasing friction, but due to a constant frictional force applied over a greater distance (i.e., many circumferences) in a given time. It is the difference between force and energy. The frictional force is constant, but the energy loss to friction increases as it is applied over some distance. That’s why a rolling wheel will eventually come to a stop even without air resistance. At high speeds, the energy loss occurs more quickly because the distance traveled is compacted into a smaller time frame. Yet the materials of the wheels can shed heat only so fast. At some point, there will be too much internal heat build-up and the tire will burst. Yet the frictional force — the force resisting the plane’s forward movement — has not increased. Well, at least not until after the wheels have disintegrated and the plane is riding on its landing gear!
All of these thrust vs friction scenarios are meaningless, like apples and oranges, when compared in the context of a ground vehicle and an airplane. The car has to break road friction and a plane has to do this AND do it by also “manipulating” the pull of gravity via lift, etc.
I think we need to review the original word problem carefully and agree or disagree on an important point:
“The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind. Can the plane take off?”
The big question: The way this word problem is “worded”, are the wheels allowed to spin faster than the conveyor belt? I think the answer is no.
All of the thrust discussions above are trying to prove that the thrust can overcome the speed of the conveyor belt. For any “real” conveyor system that can be built, that would be absolutely true. But the word problem doesn’t allow for realism!
If it requires 150 mph for a certain plane to take off, the wheels will need to spin 150 mph faster than the conveyor belt, or else the plane is not moving forward fast enough to take off. The constraints on the word problem do not allow this, the speeds must be equal. The wheels and conveyor belt will quickly reach infinity (neglecting friction), but they will still be equal, and the plane won’t move. If the belt is spinning at an infinite speed, the wheels need to spin at infinity + 150 mph, which again isn’t allowed by the rules of the problem.
So no, the plane in this meaningless problem won’t take off.
For any conveyor system that can’t spin at an infinite speed (meaning anything that can be built) the plane would definitely take off, barring a blown tire or seized bearing.
This is another example of how physics questions can be so unpractical in the real world, because those with experience know that the plane will take off…so the problem is written to prevent any sense of realism from entering the answer.
That’s why you want engineering practices to be applied, when you design your airplanes and runways
Wanna be REAL picky about the wording?
It says above: “If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots…”
I kinda doubt that a normal plane would be capable of “exerting the thrust needed to move it forward at 100 knots” on ground (OK, a treadmill) that is moving in the opposite direction. The key word here (besides TRYING) is thrust NEEDED, folks.
Take a normal small airplane. When taking off in a normal situation, it is given full throttle and, while on the ground, can BARELY achieve sufficient speed (say 85 for sake or arguement) to lift off. If it had to get up to this speed on the treadmill, and do so in order to fly, it would have to in reality be moving fast enough to hit 85 knots PLUS the 100 knots that the treadmill provides in the opposite direction - something a normal plane is incapable of doing on the ground. The question states that it achieves this thrust…my contention is that it is incapable of achieving the needed thrust to go that fast - hense the question is an impossibility.
I think there may be one way for the plane to go lift off the conveyor belt. (Maybe someone already mentioned this…I didn’t read every post.) I have a feeling this technique would be getting more involved than the original problem intended…
Original problem again: (as stated in post #52)
“Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?”
So now it gets to definitions again, when it says “There is no wind.” does it mean that the conveyor belt won’t generate any wind?
From my previous post, I assumed that the conveyor belt and wheels would quickly reach infinity and since the wheels cannot move faster than the conveyor belt, the plane would be motionless.
The ride might be a little bumpy until the wheels lift off!
If that is the case, what does the airflow above a huge conveyor belt look like if the belt is moving extremely fast? Does the air across the wings move fast enough to lift the plane, as in a huge wind tunnel? (you can’t discount air resistance on a problem like this, can you?) Someone out there may know the answer. Some engineer might even be able to design a conveyor belt that would do it
If so, I would guess that the plane would lift just above the conveyor belt (Does that qualify for a “take off”?)
I’m not very sure what would happen after that…
I suppose the wheels will start slowing down, which will slow down the conveyor belt (by definition), slowing down the airflow. Since the air that isn’t impacted by the belt is still at 0 mph, the plane still needs to get up some speed before it can fly in the air not effected by the belt. Maybe if the belt slowed down very gradually it might make it, but otherwise I think it would drop again and start the whole process over…
No plane can “barely” achieve sufficient speed to lift off. That would be very poor design, and make for a very dangerous plane!
Consider the amount of thrust needed to make the plane go 100 knots on a regular runway. Now, consider it exerting that same thrust, but on a runway that is going backwards at 100 knots. How fast does the plane go in relation to a static observer? Probably between 90 and 99 knots, depending on the friction. The runway going backwards at 100 knots does not move the airplane backwards at 100 knots (which would give it an airspeed of zero). That part deserves to be bolded.
The runway going backwards at 100 knots does not move the airplane backwards at 100 knots.
It doesn’t even come close.
Sigh.
Mark, Mark, Mark:
Methinks thou art cruisin’ at too high of an altitude!
Until it applies any kind of a counter thrust in a different direction, an airplane or ANY currently non-powered gravity-bound object will, indeed, just SIT on the treadmill and move backwards with it at 100 knots or whatever speed the treadmill is moving. It will then need thrust to equalize this and even more to surpass it.
Db, that is simply incorrect. If what you’re saying is true, magicians the world over would have a hard time pulling your table cloth out from under your dinner.
Geeze - I never said the treadmill is suddenly YANKED out from under the plane like the tablecloth reference you made. Be reasonable.
I’m being completely reasonable. The only difference is increased acceleration, and don’t forget it was you who placed absolutes in your post.
Now, in this case the conveyor CANNOT move until the plane does, as they are synchronized. So the static friction of the wheel bearing is pretty much irrelevant.
And finally, for a question. Please name the specific force responsible for retarding the forward movement of the airplane.
So…you are saying that if you were on a “people mover” (a horizontal treadmill like you see at airports) you would not move along with it? Uh huh.
READ THE QUESTION: …and the conveyor belt STARTS moving -
The belt is originally at a standstill and then it starts moving. The plane wil move WITH it unless other forces act upon it otherwise.
You also ask: And finally, for a question. Please name the specific force responsible for retarding the forward movement of the airplane. Aside from the constant of gravity, I’m not aware of any active force that will retard the forward movement of the plane - assuming it is not powered up, naturally.
Of course people move forward on people movers! However, that doesn’t illustrate this example at all. Perhaps if the plane had no wheels and only bare struts. Or if those people were wearing rollerskates. You have to understand that the wheels are absolutely critical.
The question as it is traditionally worded states the conveyor matches the planes speed. In this case, they both start ate exactly the same time. But to be honest, it really makes no difference in the end.
How does gravity, an acceleration acting on the vertical, effect the horizontal movement of the plane?
I think we are both getting much too picky. However…
You ask: How does gravity, an acceleration acting on the vertical, effect the horizontal movement of the plane? Are you serious? Gravity affects everything! The entire time a plane is flying (or even on the ground) it is fighting gravity.
In flight the plane is fighting gravity with another force acting on the vertical…lift!
The request still stands. What specific force or mechanism is keeping the plane from moving forward? When we disregard friction, gravity ain’t gonna do it. Even considering friction, gravity still ain’t gonna do it.
?? Forces don’t inhibit things - they cause things.
So demonstrate how gravity doesn’t inhibit you and jump 1,000 feet into the air.
I think its clear you have nothing more to add.
Kev, you are starting to worry me.
Do you ever READ these? We already COVERED gravity!
Just above I already answered your question: You ask: How does gravity, an acceleration acting on the vertical, effect the horizontal movement of the plane? I replied: Are you serious? Gravity affects everything! The entire time a plane is flying (or even on the ground) it is fighting gravity.
Unless powered, gravity will hold it in place and keep it from moving forward (assuming the treadmill is level).
But why will it hold it in place? Even in the most basic of physics classes you learn to separate forces into components. Gravity, in this case acting on the vertical, does nothing without friction to hold the plane still. Nothing at all! Even with the force of friction, we still have way too much thrust for it to make any difference. So tell me, how to you propose gravity, acting in the wrong axis, will prevent this plane from moving forward?
Sigh.
It will hold it in place the same reason you are not rising out of your chair as you type this. Again, if there is no force pushing you in any direction, gravity will hold you right there. The same thing will apply if you are sitting on a moving treadmill - you will go with the flow, Kevin.
Rising happens in the vertical direction. We’re talking horizontal directions Db. And no, an object will simply be in equilibrium if no forces are applied or if all forces are equal. It can move at constant speed in any direction.
Again, gravity pulls things down. The normal force pushes things up. These forces are acting on the plane to keep it still when it’s sitting on a tarmac. They have absolutely no effect on the horizontal movement of the plane when we disregard friction. They don’t “keep it in place”.
i have no arguement with you saying that: Rising happens in the vertical direction. We’re talking horizontal directions Db. And no, an object will simply be in equilibrium if no forces are applied or if all forces are equal. It can move at constant speed in any direction.
However…PLEASE tell me you didn’t just say that gravity has no effect on a plane moving in a horizontal direction…
And what do you mean by normal force?
Gravity does not have an effect on the planes horizontal movement, when ignoring friction. Why would it? By what mechanism would gravity affect forward motion barring friction?
The normal force is basically the force that counteracts gravity. When you’re sitting in your chair, you’re essentially in equilibrium, so the force of gravity pulling you down must have an equal and opposite force balancing it. That’s the normal force.
To nitpick, it is actually normal force that pertains to friction, not gravity. It doesn’t matter here because we assume the belt is a flat surface, but if the belt were on a slope, we would need to use trig to calculate the normal force and, thereby, the force of friction acting on the airplane. On flat surfaces, of course, the normal force simply equals the weight.
Db: the reason the normal force exists is that atoms have electrons, which have a negative charge, and as you know like charges repel each other. So when the atoms in your feet approach the atoms in the floor, they repel each other, which prevents you from falling through the floor and all the way down into the earth’s molten core. Pretty helpful, that normal force.
This is wrong, wrong, wrong! (Well, 99% wrong.) Are you guys so lazy you won’t do a simple experiment to prove it to yourself? Just looking around you can probably find a half dozen ways to prove it. Here’s one:
A bottle of shaving cream on an empty cardboard UPS box.
Put the bottle on the box and slide the box under it, simulating the wheels of the plane on our conveyor belt. The bottle most certainly does NOT move with the box. It spins in place (spinning forwards, opposite the direction of the box) and after you run out of box the bottle falls down and jolts back a little bit. This is because there is friction that pushes it back, but not a whole lot. It therefore has a small amount of backwards momentum when it lands on the floor or table. The bottle clearly does not go hurling backwards equally as fast as the box.
But now try using your fingers to prevent the bottle from rolling. Better be careful! Unable to roll, the bottle will tend to move back equally with the box as you slide it backwards. So don’t let it get away from you. That is the equivalent of the belt moving backwards when the plane has its brakes on.
You can’t let the comparison with a person running on a treadmill seduce your brain so easily! It is not the same thing! A free-spinning wheel on a belt turns around a low friction bearing; your foot on the treadmill is connected to a complex internal structure that does not rotate on its own. Put on some roller skates and you will be able to stand in place with the treadmill moving at spreads high speeds. Holding on to the handles would be sufficient to brace yourself. Kick off the roller skates and your feet would go flying back, pulling you with them. It’s a big difference.
Matt, you’re absolutely right that the force of friction is proportional to the normal force, but since we were talking about the plane being on a flat surface, I just kinda cut out the middle man :).
OK, about that treadmill. Lets assume that the plane is sitting on it, unpowered, as the treadmill zooms along. The planes wheels are spinning madly and (for sake of arguement) it is basically staying in one place.
Now, to really confuse people, picture an old skiing towrope - the kind you have to grab hold of with your ski gloves in order to be pulled. You squeeze and squeeze until you finally find yourself being pulled by it until you finally have a good hold on it and you are being pulled along at the same speed as the rope (which is always a constant speed).
Back to the plane. I believe that, even if you could mimic the condition where the plane is basically in one place, wheels spinning, the wheels will eventualy slow down to the point where it will be going in the same direction as the treadmill - and at the same speed.
One last thing to Kevin, who said above that: “Gravity does not have an effect on the planes horizontal movement.” Ever been in a hot air balloon? It affects both in the same manner regardless of what direction. Horizontal is level - more or less. Gravity pulls one up or down (depending on the counter force) and, if you start at an altitude of a mile and end up on the ground the distance travelled is a lot more than if you went in a straight level line…
Of course you will not fall straight down…but that isn’t gravity’s fault! Take any object and evacuate all of the air and drop it straight down from a mile up. It’ll fall perfectly straight, all the way to the ground.
Remember drawing free body diagrams in high school physics? The force of gravity points downward and the normal force points in a direction perpendicular to the surface the object is on(or opposite the y component of the gravitational force). Since our plane is on a flat surface we don’t need to deal with any trig, and the normal force is exactly equal, and exactly oppposite, to the force of gravity. The vertical axis is in equilibrium! This is confirmed by a quick glance to show us that indeed the plane is not falling through the earth.
So all we need to worry about is horizontal. In our case, we have friction and thrust. Friction is proportional to the normal force(or gravity in this case, but not always) and thrust is generated by the engines. In our case thrust is much bigger than the frictional force going the opposite direction. So we go forward. And then we take off.
Simplified to a large extent, yes, but essentially all we need.
Here you’re on the right track. Let’s say we have this towrope near the belt and the pilot is able to hook his airplane onto it. The rope will pull the plane forward, relative to the ground on either side of the treadmill, because it is pulling directly on the mass of the airplane. The belt cannot directly touch the plane. The belt can just spin the wheels. Now suppose we have a really strong towrope connect to a powerful motor. It pulls the plane forward really fast, the wings generate lift, and the plane takes off (though it will glide back to the earth if it has no engine). Is an airplane’s engine any different from the towrope, though? The engine pushes against air, but it, too, exerts a direct force on the aircraft, which experiences a corresponding acceleration.
You don’t explain why. The reason the wheels spin is that the belt is exerting a frictional force on the tire. As long as the belt exerts this force, the wheel will continue spinning. It won’t slow down.
You seem really confused about gravity. The earth’s gravity pulls you down. Not up. Not left or right. Down. As in, towards the center of the earth. A hot air balloon moves horizontally because of air currents. It moves up because of buoyancy. Gravity always pulls down.
Now, you could argue that without gravity, there would be no atmosphere to have air currents, nor buoyancy, nor would we humans even exist to be having this discussion. So in a broad sense, most of our environment is a consequence of the earth’s gravity. But for purposes of analyzing forces acting on an object, we may safely say that gravity acts downward and any lateral or upward movements are due to forces acting in other directions.
Kevin I doubt this person has ever studied physics. He is not familiar with basic physics terms such as the normal force, and his thoughts on gravity are just plain strange. I don’t think he was ever taught a physics approach to looking at a problem, how to break down all the forces acting on something and figure out the net result. I’m not trying to brag; I only took a couple years of it in school and probably forgot most of it! But I know there is a systematic technique to physics that produces (usually) clear answers, which you just can’t get using your hazy intuition. A person familiar with physics would not say “gravity pulls one up or down depending on the counter force”!
How I phrase things has nothing to do with my knowledge of physics. Of course gravity pulls you down - but I said that if you were traveling in the air in a horizontal direction and were suddenly just under the control of gravity )as in non-powered flight) you would initially go in an arc and then, eventually, straight down or close to it.
And the reason I said: “Back to the plane. I believe that, even if you could mimic the condition where the plane is basically in one place, wheels spinning, the wheels will eventualy slow down to the point where it will be going in the same direction as the treadmill - and at the same speed.” is because friction, however minimal, will eventually kick in enough to slow it down BECAUSE THE WHEELS ARE NOT POWERED. Make sense? It would be different if something was also holding the plane in that position (a rope or whatever) but short of that it has to eventually slow down…and move at the same speed as the treadmill.
You have forgotten air resistance: it is only air resistance that slows your forward movement. Gravity only pulls you down. The reason you would fall in an arc, rather than straight down, is your inertia — that is, your tendency to keep moving with the same forward velocity until a backwards force acts on you. Gravity causes you to fall downwards, but doesn’t affect your horizontal speed, so you follow a trajectory that is forwards and down — a arc. Once you consider air resistance, however, you would see your forward speed continuously reduced. But you can’t confuse this with gravity. Gravity is only pulling down, and doesn’t affect your horizontal movement.
But the force you are talking about is insubstantial compared to the thrust available from the engines.
Apologies for splitting this into two posts.
AAAGH!
Matt, PLEASE read what you are commenting on BEFORE you write. I clearly said that, in this alternative scenario I suggested for the sake of arguement, “…OK, about that treadmill. Lets assume that the plane is sitting on it, unpowered, as the treadmill zooms along.”. THE ENGINES ARE OFF! You saying “But the force you are talking about is insubstantial compared to the thrust available from the engines. ” has nothing to do with this particular scenario - there is no engine thrust; they are off.
Geeze…
You also said that “Gravity causes you to fall downwards, but doesn’t affect your horizontal speed, so you follow a trajectory that is forwards and down — a arc.” No arguement here about the arc, but of course gravity affects your horizontal speed. It could be said that it even changes the horizontal speed to a vertical speed. If you are going, say, 100 knots in a straight horizontal line, then you cut your power so gravity can be more evident, your horizontal speed will immediately slow and your falling vertical speed will take over - all due to gravity.
Db, that is completely false. With no wind resistance your horizontal speed will never change. The only thing that stops you will be when you crash into whatever has created that gravitational field.
Wrongo. It will cease being horizontal and become vertical. The instant it starts to drop immediately reduces the speed in which it is going horizontal.
Db, I can offer you no other advice than to pick up a high school textbook on physics or visit a website and read for yourself. Gravity simply will not effect horizontal speed.
Geeze, Kevin. Lets go toss a frisbee and I’ll stand twice as far away from you as you can throw it. Are you saying that gravity won’t cause it to drop and that it will retain the same speed until it reaches me?
Or…perhaps…gravity will cause its HORIZONTAL speed towards me to slow and finally stop when it hits the ground… Ya think?
Yes I do think. Because we live on earth, where there’s air and hence, air resistance. That’s what causes a frisbee to slow down. Gravity causes it to hit the ground.
If we remove all of the air and throw a frisbee, it will move horizontally with the same speed it left my hand with until the moment it strikes the ground.
This is stuff you learn in the first month of an 11th grade class on physics.
Your original statement was: “Gravity simply will not effect horizontal speed.”.
Thanks for agreeing with me even though you probably didn’t realize it.
Your reasoning: “If we remove all of the air and throw a frisbee, it will move horizontally with the same speed it left my hand with until the moment it strikes the ground.”
No argument here that it will act like that in a vacuum. But that answer kinda bounces around the question.
And uh…WHY does it strike the ground? Gravity pulled it down - hense gravity absolutely does affect it. Otherwise it would continue in a straight horizontal line.
No, gravity didn’t effect the horizontal speed in any way. It pulled it toward the ground, but the friction with the ground is what slowed/stopped it.
If your point is to tell me gravity is responsible for the object striking the ground and hence gravity has effected the horizontal speed, you certainly haven’t made that connection overtly.
You said, and I qoute, “It could be said that it even changes the horizontal speed to a vertical speed. If you are going, say, 100 knots in a straight horizontal line, then you cut your power so gravity can be more evident, your horizontal speed will immediately slow and your falling vertical speed will take over - all due to gravity.”
Kevin, you misinterpreted what I said. Perhaps if I had substituted the word DIRECTION for SPEED that would clarify what I intended and not cause you confusion. I thought it was kinda clear (when I clarified that it went from horizontal to vertical) that I meant the direction of the speed of the object. Gravity affects the direction. Your wind resistance and similar factors only slow it down. Got it now?
No, I don’t. The speed in the horizontal direction is unchanged. The speed in the vertical is increasing because gravity causes an acceleration.
If, in a vacumm, I throw a frisbee at 10 MPH, it will go 10 MPH until it hits the ground. I can be standing on my own two feet or on top of the Empire State Building. Velocity in the X stays the same as the velocity in the Y increases, in the negative direction. If I were looking to predict where my frisbee will land, all I do is find the time it would take for it to fall from whatever height I happened to be throwing it from and multiply that by the speed at which I throw it.
Yikes. The only reason horizontal motion stops is because of horizontal forces like friction. Thus, gravity has no horizontal effect until an object hits the ground. On an planet with gravity 1000 times the strength of earth’s 9.8 m/(s)^2 … if you threw an object horizontally at 5mph, it would keep going 5mph horizontally until it hit the ground, minus wind resistance. That’s not to say that it wouldn’t fall, but the horizontal vector component of its speed would not be affected by gravity in the slightest. The axes operate completely independently of one another. Neglecting wind resistence, the answer to the question “what is the horizontal speed of a thrown object, right before it hits the ground?” is always “the same as its initial horizontal speed.”
If you threw two objects, one which was affected by gravity normally, and one that was not (that would never fall… just “float”)… as soon as the normal object hit the ground, both objects would have traveled the same horizontal distance (again, ignoring wind).
Yeah, Yeah, but bottom line is gravity does affect horizontal speed ’cause gravity is the primary cause for the speed to STOP when it is pulled down and hits the ground. Otherwise it won’t hit the ground.
Sir Isaac would roll over in his grave…
How can it possibly be the “primary” cause? Without the friction caused by the ground the object doesn’t stop at all.
Argh - the ground is the final resting place - gravity causes it to hit the ground. Therefore gravity causes it to stop at that point - therefore gravity does have an effect on horizontal force.
You are taking some elements from your Physics 110 class too literally - you have to look at the big picture.
Gravity causes it to hit the ground, but so what? If the ground were frictionless, what would happen? The object would keep going horizontally forever. Gravity has done nothing but introduce our object to the ground. It simply has not caused it to stop.
Db, generally when one finds himself in a hole he stops digging.
I’m not arguing laws of physics. I’m stating cause and effect - which you just validified above. If not for gravity, it would not hit the ground and cease its forward (horizontal) motion. Therefore gravity DID end up affecting it! How in the world can you continue to argue this obvious thing? Lets get beyond this, shall we?
My original contention waaay back before this branch was that any UNPOWERED object on a moving treadmill - regardless of whether it was on wheels, would (due to gravity and friction) eventually (if not already) come to a complete stop on the treadmill and just sit there moving, or riding, along with it. This whole fiasco started when someone commented that it would not some to a stop on the treadmill because gravity never affects horizontal movement.
If the wheel bearings were frictionless, an unpowered plane would stay in one spot as the wheels spun. If we consider friction, the forces involved are so relatively small that in the context of the problem with a powered aircraft they’re really not important.
If the wheel bearings were fricionless, the wheels would spin without ever stopping… if the plane depended on the friction of earth to move like a car, then if it was frictionless it wouldnt ever move. if the ground were frictionless for a plane the wheels would never spin and the plane would slide forward.
its not hard… if thrust is > than drag it will accelerate and continue to till liftoff. if drag is > than thrust it will accelerate in the opposite direction (of decelerate depend on viewpoint) if thrust is = to drag it will be at a constant velocity at whatever speed it was at when they became equal. Now.. the forces of drag are wind resistnace which would be the same as on a normal runway. bearing resistance, which with aeronautical grade bearings can virtually be ignored. and rolling resistance, which its equation would be coefficient of rolling friction which = about .001 * weight. *SPEED DOESNT FACTOR IN THE EQUATION. so on a 747, thrust = 50k lbs per engine * 4 engines so 200k lbs thrust. its weight is 847k lbs * .001 and drag is roughly 10k lbs…. 200k > 10k.. it accelerates and would continue to till take off,
If the question says: the conveyor matches the speed of the wheel at all time, the plan speed will be zero in relation to ground and will never take off! If you think that the thrust of the engine is pushing the plane forward…. THE SPEED OF THE WHEEL MUST BE FASTER THAN THE CONVEYOR BELT! This is basic physics.
Not true at all.
Imagine the conveyor matches the planes speed, and moves in the same direction. The wheels don’t spin at all and the plane takes off just fine.
Also, don’t get caught up with the conveyor matching the wheels thing. The question, as it’s usually presented, says the conveyor belt will match the speed of the plane. As, the plane moves 10 knots north and the belt 10 knots south. This doesn’t stop the plane from moving at all.
The question says:
If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots,
Ya know, if it is “exerting the thrust needed to move it forward at 100 knots”…then it is moving forward at 100 knots. The treadmill has nothing to do with it as the question ALREADY says it is applying sufficient thrust to move forward at 100 knots - not TRYING to move…IS moving!
… on a stationary runway. The question just deals with what effect (if any) the movement of the conveyor belt has on an airplane exerting that thrust. Answer: very little.
No, the question asks “will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?” And if part of the question states that it is “is trying to take off by exerting the thrust needed to move it forward at 100 knots”, then obviously the thrust needed to make it move forward at 100 knots ON A TREADMILL is MORE that that needed on a regular runway - but it is still applying enough to make it move that much regardless.
Yeah, I know that isn’t the intent of the problem - but (technically) with the way it is worded that is the answer. It states that the plane is applying enough thrust to move at that speed - so it IT moving at that speed - so yes, it will fly under this condition.
‘Nuff said.
Read again. It’s applying enough thrust to move it forward at 100 knots. Then the runway goes backwards at 100 knots. Before the runway moves backwards, there’s no way of knowing how much additional thrust is needed to counteract the runway’s backwards movement, so the 100 knots can’t take that into account. It hasn’t happened yet.
Regardless, this is a tangent. It’s probably better to focus on the “conveyor belt moves backwards matching plane’s (absolute) forward speed” variation.
What happens if the plane is landing on the conveyor belt at 100kts? When the wheels touch will it now be at o kts ground speed?
Now I’m wishing there was some way to track down old Boortz shows. I thought Neal had it right, at least by the end of the conversation (which is all I got to hear; since my local radio station shifted things around a bit, I don’t get to listen to Boortz as much as I’d like). I thought that when I started listening, he was trying to explain to Royal that if there’s a kid pulling a wagon, and the wagon is on a conveyor belt beside him (assuming the kid can somehow exert only forward force on the wagon and he’s not on the conveyor, too), the wagon still moves. Assuming he’s saying the plane’s propeller or whatnot is like the kid standing on the side of the conveyor belt, it seems like that argument would support the plane’s flying.
I could be wrong, though. I came into the conversation in the middle, and by the time I understood what they were talking about, I was almost out of range of the station.
Yeah, but I suspect that it would take more to pull the wagon on a moving treadmill than it would on a sidewalk.
Now…if you can make this wagon FLY, let us know…
it flies…. see my post on #167
Would the force required to pull the wagon be more if the conveyor belt was moving? Yes. Would it be significantly more? That depends on how well the wheels are oiled.
If the kid’s pulling a perfectly designed airplane instead of a wagon, and the kid can run fast enough sans conveyor belt to get the wagon-plane in the air, then he’s not going to need a lot more running power to get into the air with the conveyor belt. IF he’s pushing his limits getting it into the air originally, he may not make it. Otherwise, he’s still in good shape, I think.
I guess Sooks is the God of Air and knows all…? What an ego!
not really… how is it an ego? i just used physics did a free body diagram… looked up the numbers for a 747, input the numbers and analyzed the results. I have no problem if you cna show me where i made an error and ill be gladly open to debate… you just cant argue with physics.
Here is another example if you dont think its true. Tilt the conveyor belt so its vertical. now take a matchbox car and attach a magnet or something similar so that its wheels will stay attaced to the belt. now place the car on the belt and drop it.. do you think that the belt will keep the car hovered in air because it is matching its speed??
Db, not a whole lot more. If you are strong enough to pull the wagon, the additional frictional force due to the moving treadmill would only be a small fraction of your strength.
Sooks: I was kidding about the omnipotent way you made it sound that, since YOU said it, it is right.
As for the 747…why even bring it up? The question is for a plane, not a jet. Two different animals.
Another Matt: Granted, it isn’t a whole lot more…but it is more. That makes a big difference.
db.. ok, i guess looking at it..it could have came off that way. i just wrote it really fast. however.. whether or not i used a jet is irrelevant. according to the equations..the speed has nothing to do with the equations. i will admit.. being on the belt prob increases the drag slightly as the wheels will be spinning twice as fast and then creating more heat thus raising the coefficient of friction. but it isnt going to change it drastically. in my example for the drag to be equal.. the coefficient of friction would have to be somewhere between .35 and .3 which is like 300x greater than what it is now. it simply isnt going to increase that much from that little change
No problem, Sooks. Just having some fun with ya.
The entire question is like a mobius strip anyway and depends how you interpret the original question.
I was in the Miami airport last week and had the opportunity to ask our pilot the puzzle. He actually gave me what could best be described as a lopsided grin and said that he has been asked this a lot recently. His answer, simply, was to just say that regardless of a treadmill or landing strip it still has to achieve sufficient speed to take off.