There could be 400 knot headwinds, in which case the plane could take off without needing any thrust at all

Actually, the real answer is that after a few seconds of thrust, the centifugal forces will cause the plane's wheel to violently explode, letting the entire plane down onto a belt moving at (probably) the speed of sound or higher, causing the plane to be violently shreded and shot backwards. Depending on your definition of plane, you could count some of the debris cutting through the air at 700 miles per hour as "part of the plane flying".

It is vital to understand the difference between airspeed and groundspeed if you actually want to fly.

The most sensible interpretation that makes it useful to think about IMO is "the treadmill does its best to keep the plane stationary". In which case, the ramp up to infinite speed happens, but not infinitely quickly because the wheels have some angular momentum. And then it becomes more a quality control question of whether the treadmill or the plane wheels explode first. If the treadmill explodes first, it will probably destroy the plane and its engines with shrapnel, and the plane won't be capable of flying after that, but it might get lucky and remain in a good shape to take off from the debris field!

I like how the question is implying that the plane's wheel speed is the sole reason why it takes off.

you could also consider that the wheels spinning faster and faster causes them to eventually approach the speed of light. In which case the plane would start gaining relativistic mass until it was too heavy to lift off.

This is effectively the same sort of rig used for testing plane landing gears. The plane is effectively 'tethered' in place, with only the wheels turning on the same spot. There is no airflow over the wings. No lift. For regular liftoff the wheels aren't what cause it to take off, the wheels move the plane in order to create airflow over the wing, which is what creates lift. Put simply, if there isn't enough airflow over the wings to lift the plane, it doesn't matter what the wheels are doing.

4:51 "We can say the value of the belt and the wheel are equal at infinity". As a mathematician, I am disgusted.

1:20 As a pilot I would say "IT DEPENDS", and kinda YES! If you imagine there is also head wind at speed around 160-180 mil/h it would fly easily, even without that belt with wheels totally standing still :D Most people forget, that only airspeed is important, and ground speed is irrelevant. EDIT: For people b1ching about: "did you ever saw 150KT wind?"! Its totally imaginary situation, did you ever saw moving belt under 747 at speed up to 300KT?

This is like the "I'm 14 and this is deep" equivalent of physics questions

It doesn't matter if the wheel bearings are frictionless. The wheels can transfer horizontal forces to the plane through the axels regardless of the rotational friction of the bearings. The engines provide some amount of thrust X on the plane. In order to maintain the problem constraint the belt has to provide an equal and opposite force X on the wheels. This introduced a moment on the wheels because the axels are pushing forward with X force at the center of the wheel and the belt is pushing backward with X force at the bottom of the wheel. Make reasonable assumptions for the radius and angular inertia of the wheels and you can solve for the wheels' angular acceleration. The problem constraint can hold (and the plane won't be able to accelerate or take off) as long as the wheels can continue to accelerate at this rate.

Another thing this question made me think was how the rotating belt would cause some air/wind to move backwards due to fluid dynamics. In general this is not a well formulated question.

that is exactly the same problem I have with these kinds of questions, they require disregarding some factors to work, but then you can have completely different answers depending on what factors you choose to ignore.

As a flight instructor, this was a pain to explain to my students.

It depends on the airspeed over the wings and the angle. There have been airplanes that have "taken off" due to high winds like a Cessna in a 60 knot winds but it's highly unlikely that the wind would be blowing hard enough in most circumstances to provide enough lift for a 747 (160 knots, almost 200 mph) to takeoff. And the fact that it's on a treadmill with it's engines blast would have zero effect on the takeoff itself, but would obviously matter if you wanted to keep said airplane aloft and not have it crash back into the ground.

The assumption is that the treadmill belt can move at infinite speed and that the all laws apply to the regular old jet plane, no skidded, sliding, frictionless wheels, no nothing! The wheels being powered or not has zero to do with anything, the result is the same; if the engine pulls the jet forward at 250mph and the airplanes weight on the wheels move the treadmill belt backwards at 250mph, then the plane is going nowhere. The wings only come into play if the plane can move fwd.

These questions are an example of memetic ideas. The ones that have proper context and detail die off. The ones that are ambiguous so people keep talking about them persist

You always know you're going to lose your mind when the question starts with: "Assuming there is air friction"

The wheels on a plane are free spinning so unless the conveyor belt is able to move so fast that the force of friction of the wheel shaft turning is enough to counteract the thrust of the jets, which almost certainly would destroy the landing gear through the heat produced by the friction, the plane is still going to move forward because it doesn't push against the ground: It pushes against the air and it will have no trouble taking off.

My guess, start of the video: Plane takes off as normal, but wheels spin twice as fast as they normally would. Added drag would just be from the rolling resistance of the tires on the belt and the bearings, which are minimal to the amount of drag an air frame needs to produce lift.

Honestly he deserves some kind of award for the dedication to pull out a treadmill and record his point on it. Bravo Mehdi.

I've heard this described as a language problem not so much a physics problem. I remember the "Mythbusters" episode years ago, and I got it wrong then, and it pissed me off to no end, trying to figure out where I went wrong. Then my wife explained it to me, and I had it in my mind. For a bit. But I lost it. And now revisiting it has lead me to the conclusion that I am going to plug my ears and hum and live in my world where if air isn't passing over the wings the fricken jet doesn't take off.

Medhi, I have a similar idea, in this condition the conveyor is rotating in the same direction of the plane’s nose and the constant speed of the plane’s take of speed. And instead of the wheels there are just rods touching the conveyor. The friction is non zero non infinite. The conveyor is as long as it needs to speed up the plane. Will the plane fly? Consider all other conditions that are not mentioned here like earth. I’ll like to watch a entire video about it.

Hello, which textbooks for electrical engineering undergraduates do you recommend every student should own? I am a big fan of your content.

as someone who grew up watching the Mythbusters it's fun the see that till this day this simple physics problem is still a mystery to a lot of people. Wait till you guys find out about the truck full of birds and the bridge problem.

This question has even messed with licensed pilots, but I like to look at it in this way: Stand on a treadmill in roller skates and with the treadmill having a rope tied to the front of it. Hold the rope (important!) and turn on the treadmill full blast. You’ll be stationary, but if you tug even SLIGHTLY on the rope, you will move forward on the treadmill. The forward thrust doesn’t care about the wheels because that’s not the force involved.

yes. The back force of the conveyor against the forward motion of the plane should not be capable of stopping the plane from taking off. The only caveat is if the wheels and bearings are not capable of handling the load of the plane at the speeds they would need to be turning in this scenario.

I needed this video, I'm an aerospace engineer, I had both professors and colleagues states that the plane wouldn't fly because of the speed matching it got me really mildly mad lol. On the third solution I actually think it can take off, if friction and thrust match it only means that it won't accelerate, but if the speed is high enough it could take off, also considering that lift is not an on/off thing, but it grows, the friction between the wheels and the conveyor belt is constantly dropping

Commercial pilot here. 5:27 would be correct - except the tires would explode from overspeed long before you reached that velocity. Even at twice the takeoff velocity, the tires would come apart from centrifugal force.

I guess you have to make at least one of these videos with no explosions to compensate for that capacitor alarm clock... But it's still funny as heck.

Absolutely love how you merged in that ad read.. hahaha

No wind over wings, no take off

"I hate it with a mild passion!" 🤣 ... very hard to stay focused with this recurring remark. Super-nicely done!

Your content helps me through some tough times that i've been going through while still learning new things. Thank you, Mehdi!

LOL, the belt will create additional headwinds and extra ground effect that will significantly reduce the take-off speed. However, as soon as the airplane exits that local wind, it could encounter some issues.

well in that case depending on the exact conditions of the experiment it is possible if it accellarates the air around it due to friction with the huge conveyor belt. thos could create a liw pressure zone below the plane sucking it down but also accellarating more air in front of the belt so that in theory it might be possible to create sufficient wind speed relative to the plane wings so that it takes off? would have to crunch some numbers for a precise andwer. i think it would be possible depending on wind condition and the exact plane and runway design

That was a weird one. One of the things I very much dislike about certain tests is multiple choice questions with 2 right answers but the question wants the "best" answer which is subjective. Here's looking at you A+ Cert Exam.

Hey Mehdi, this got me thinking: can you do an episode on how airplane power outlets work? Like, are they "grounded"? How much draw do they support? Thank you.

i love this plug so much😂😂

I'm impressed at the number of answers you came up with, lol. I wrote this before watching: Only if there's a lot of head wind rofl. That the conveyor belt starts moving at all implies some force is attempting to move the plane forward. We would call that thrust. With headwind in excess of the stall speed and thrust to match the headwind, it could basically hover in place. Whether or not a proper plane can fly is not determined by it's speed. It is determined by the speed of the air over the flight surfaces, the wings. Airspeed determines whether a plane can fly, not wheel speed. And I'm having a hard time believing that even a full thrust 747 is going to cause the magic conveyor belt to move fast enough to push enough air over and under the wings to achieve lift.

In the second case; wheels turning on frictionless bearings: the conveyor will start moving backwards at absurd speeds as soon as the plane starts inching forward, but if the conveyor belt is wide enough, there will be a boundary layer of air stuck to the conveyor belt, and the air's viscosity will induce a wind backwards. It's velocity will drop the further away from the belt, but eventually, it will be enough at the wings to induce lift, so the plane will fly without moving forward.

The question on twitter was phrased poorly I think. The version I know from the past stated that the belt would match the speed of the plane (instead of the wheels). That way it's much less confusing imo.

I think answer 4 is also a case of fishing for reasons that the reflexive "no, it can't" is right. The question isn't "does the plane take off while sitting still?", the question is "CAN the plane take off?", as in "does it have the capability?". Every plane, before taking off, spends some amount of time at the end of the runway NOT at takeoff thrust. If we interpret the question in the way that makes 4 correct, then NO plane EVER flies, under ANY conditions.

Here's a better question: A 747 is sitting on a runway. Its ground speed is zero, meaning the aircraft is stationary with respect to the ground. It is receiving a 250-mph headwind. The engines are running and their thrust is perfectly opposite the headwind. If the pilot pulls back on the yoke, will the aircraft take off? Answer: yes. It will take off, and it'll look really weird because its ground speed will remain zero. The only thing that matters to the aircraft is its airspeed.

Watching his video-which was released 5years ago- for the first time, made me wonder whether he's still alive. I am so happy that he is. Just subscribed.

No, because the plane takes off because of air pressure differential (under/over wings) while moving "THROUGH" the air. It's also why a stationary plane can take off if there's a lot of wind.

It won't lift off. Assuming a take off speed of 300kph, the wheels would be moving at 600kph at the point of liftoff. Since the 747 tires are only rated up to 380kph, the tires will explode before reaching liftoff speed, and the plane will crash and burn as its landing gear is destroyed.

Could you revisit this topic? If the conveyor belt is moving at the same speed as the wheels at all times, the airplane is stationary wrt the ground. Thus no lift can be generated.

Case 3 is definitely the most realistic, however if the belt is wide enough, the plane will likely take off due to boundary layer and ground effect :)

The wheels will slide over the conveyor belt and the plane will take off. This is like plane taking off from water. Or if you put sleds on a plane and start it from ice. However, if you include additional requirement that wheels cannot slide then the only possible solution is that plane stays in place.

The moment you add friction is the moment it becomes what fails first. If we have friction on the plane's wheels, we have to have friction on the conveyer belt. All the rollers in the conveyor belt need to spin at a higher RPM than the wheels of the plane and I would argue that the conveyer belt will fail before the plane's wheels and there for the plane is still able to take off.

Of course it would because whether or not it takes off has little to do with the ground it's on but rather the air it travels through. Since an airplane's thrust is generated by pushing air towards the back, it doesn't matter if the conveyor belt rolls in the opposite direction, the plane will still advance forwards through the air and eventually take off once enough air pressure is generated under its wing.

If engineers built planes with wheels that created enough friction to even compare to the force of lift from the powerful engines, no one would be flying today. Of course, I say this with a mild passion.❤

I saw that on twitter and my first thought was.. the plane is not driven from the wheels so..... im excited ElectroBOOM is covering this.

One thing not mentioned was the wheels’ inertia causing rolling resistance, which would push the plane backwards at an exponential rate. One way to use this to our advantage in this situation is to use the reverse thrusters just to get the plane rolling backwards, causing the conveyor to move forwards and the wheels to spin backwards faster and faster, and the inertia would speed the plane up forwards towards takeoff speed. There are caveats to this, for example; the main gear has the most inertia being far heavier than the nose gear, and it is closer to the centre of mass to enable the plane to rotate easily during takeoff. Most of the weight and acceleration force would go through the mains, risking a wheelie or even a tail strike. The planes wheels would also be moving way faster than the plane (in the opposite direction) which could cause them to break apart from excessive forces. Lastly the plane would be able to reach takeoff speed without engine thrust but would need throttle to maintain speed once it is no longer contacting the conveyor belt.

The conveyor belt moving would pull air with it, no? If the conveyor belt gets fast enough, this air it's pulling could be enough to let the plane lift off

Even in the situation where you have friction everywhere, as the speed of the conveyor belt increases it will be dragging a sizable boundary layer along with it, if the runway conveyor belt is long enough ahead of the plane it would eventually create enough headwind to takeoff from a "standstill" anyway.

Feel like I get an aneurysm every time someone implies a plane's wheels are powered

It will take off with the wheels not spinning... because the action/reaction produced by the engines is what makes the plan move relatively to air, not the spinning of the wheels (which are a consequence of the movement, not its cause). If the plane had no thrust but motors on the wheels, the plane would have stayed stationary.

The problem in this scenario is how the scenario states "the conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction." It FAILS to specify if the speed it's matching is the rate at which the wheel is spinning, or the rate at which the wheel's physical position is changing with respect to the ground that the conveyor belt is sitting on. In the latter case, it's pretty straightforward; if the wheel's position is changing at a rate of x, the conveyor belt's rate of travel will be -x. In the former case, when the wheel begins to move forward its angular velocity increases with respect to the conveyor belt, so the conveyor belt speeds up to match the wheel, which causes the wheel to spin faster again, and on up until the wheel flies apart due to the feedback loop. Or the wheel starts spinning at the speed of light, in the fantasy land where the wheel is indestructible. In any case, the wheels aren't what is moving the aircraft forward; they're essentially free-spinning bearings with a non-zero but negligible effect on the aircraft's ability to accelerate. A jet aircraft isn't a car. The engines work by throwing air and combustion gasses backwards, and that is what provides thrust thanks to newton's third law of motion. The only way the conveyor belt will slow down the aircraft enough to prevent it from taking off is if it's spinning so fast that it's able to act on the aircraft through what little force DOES make it through the wheel bearings. Though at that point, the conveyor may also be moving the nearby air fast enough that the wings are able to gain enough lift to take off anyway.

Thank you Mehdi! Every time this comes up I say "Yeah, I know the 'correct' answer but the question is silly". In a world with friction there is no way to know whether the plane would take off unless the speed of the belt is defined in a more meaningful way - otherwise it would be a case of testing it and seeing whether the plane could take off with burst tires due to the heat created in the wheel bearings due to ever increasing ramp speed.

Another aspect is: the conveyer has friction with the air above it. as it runs, it moves the air which increases the wing speed and lift.

There could be winds that could help the plane take off. Also putting on full power thrusters can help as well. I don’t know much about planes, but IMO, i think its possible for the plane to take off. I mean, the only problem I see here is that the plane is as long as conveyor belt. Again, just my opinion. Im probably wrong lol. The wheels moving fast might easily disrupt the plane from taking off.

If the plane speed is 0, doesnt matter if the wheels are at 1000 or 0 kmh, the plane wont take off. And since the wheels are stuck to the plane, and the wheels will not move in relation to the ground, because the conveyer belt will always have the same speed as the wheels, the plane will not move in relation to ground, therefore the plane will have no airspeed and no lift to take off. Simple.

Yes, because the speed of the wheels have nothing to do with the acceleration of the plane.

I think part of the problem is people seem to think airplanes operate on a time machine built out of a DeLorean principal. The wheels need to reach a certain speed, at which point, the plane takes off. Of course, the wheels on a plane are only there because it causes too much damage to the plane when you let to scrape down the runway. You could replace them with hovercrafts and it would work exactly the same.

To me it reads as the conveyer belt speed relative to the ground will match the speed of the wheel relative to the plane, speeding the conveyer belt up until they match. Which means the plane cannot move relative to the ground unless the thrust force overcomes the friction between the tyres and belt. Seems unlikely to me but here's some math. 747-8 weighs at least 220t Coefficient of static friction for rubber to rubber is 1.15 To overcome the static friction it would need 252t of thrust( essentially it would need to be able to accelerate going straight up). It produces a max of 120t so no luck. This is also assuming the engines point straight back and ignoring a few other hard to quantify things that might be going on.

It’s impossible to design the said conveyor belt because it assumes the speed of conveyor belt instantaneously matches the wheel in other direction. As mehdi noted, there is no conveyer belt / wheel speed where the required equation checks out when the plane is moving forward - which it will if three is thrust. You can’t just say the conveyor belt will do this - explain how and the we can show where it will fail. It will likely involve some feedback circuitry with delay and that can lead to a solution.

Absolutely, it will take off if the tires do not explode. It’s about airspeed vs ground (tire) speed. When the wings feel about 150 knots airspeed over the wing, it will fly. In this situation, the wheels will be turning 300 knots. Remember, the wheels do not drive the airplane forward. The wheels just spin. HOWEVER, the tires on a 747 are rated to about 225 knots and will likely disintegrate before the airspeed is suitable for takeoff. I wrote this before watching your explanation. I think we are close

The easiest way to think about this conceptually is wearing roller-blades on a treadmill, while being tied to a rope attached to a wall in front of you. You can grab onto the rope and pull yourself forward, the wheels on your feet while just rotate more. In the plane's case, replace the rope with air.

the humor is brilliant! ;'D

personally i'd say whichever runs out first, the planes fuel, or the electricity powering the conveyor belt, which only adds more variables and makes it even more of a pain to answer.

even before medhi says why the plane thing annoys him, I'm just going to say this: THE PLANE DOESN'T USE ITS WHEELS TO GO FORWARD, IT WILL STILL FLY edit: 5th scenario, the belt begins to move so fast that it generates enough wind for takeoff

Jet planes are powered by thrust, not traction. The only possible thing that might prevent the plane from taking off is the possility of the tires bursting from excessive speed. But after V1, that's academic anyway.

As someone who decided to take physics instead of chemistry in high school i immediately knew the awnser, all the kids in high school called me stupid for it WHOS LAUGHING NOW

My initial intuition is that the engines push the plane forward not the wheels, so the wheels would blow up because of over speed if the belt always matches them

My guess: You cannot answer the question without knowing how much angular momentum is transferred from the wheels onto their axes as backward momentum. Assuming that the thrust of the plane comes from the engine, and the axes are entirely frictionless the wheels will just spin aimlessly with twice the velocity of the plane in the opposite direction, supplying only upward force, as the plane accelerates as normal, and takes off.

I think questions like these are intended to get people talking and to get them to realize what assumptions they take for granted. I assumed no bearing friction when I saw the question. So I learned something from the discussion. I think that's at the heart of these kinds of problems

Wouldn't the belt accellerate the air through boundary layer friction under the plane thus giving the condition needed for lift, which is fast air under the wing? Or suck it down, depending on wing position, especially at infinite belt speed, that's why F1 cars are tested on a rolling road to test the venturi tunnels

The oversize conveyor belt unexpectedly tears, jams, stretches, slews off the pulleys, chews up an innocent bird, causes noise complaints from local residents, vibrates excessively until fracture, or otherwise mechanically fails. Resulting debris gets caught in engine intake, and explodes spectacularly.

Wheels are only there to be a reasonable bearing so that when the plane takes off (thanks to the engines), there's not too much friction with the ground. It might help to instead imagine the same problem with a seaplane -- a plane with no wheels. There the friction with the ground (water) is prety high, and yet the seaplane can still take off.

So glad somebody actually acknowledged the problem of the friction of the wheel bearing reaching infinity preventing the plane moving regardless of the fact that wings use lift, the amount of people i've tried to explain that answer to only for them to smugly not get it at all is so painful

well yes, because the wheels move freely from the thrust of the turbofan engines and so will still move the plane forward unlike a car that needs the wheels to push along the surface (in this case the moving conveyer belt)

In the test you showed at the end. Does the plane wheel goes twice faster? Because the wee are just there with no power

electro never ceases to amaze

I expect that if the belt exactly matches the wheels speed, then all of the engines thrust will be consumed by increasing rotation speed of the plane wheels (they will act like breaks to the thrust force). In reality this would require the wheels to speedup very quickly to insane speed ripping the tires apart, because the rotational inertia of those wheels is very small while the engines thrust is huge. Continuing on, let's assume that tires and wheels are indestructible, and the belt as well, in that case the belt would increase its speed untill the belt surface reaches almost the speed of light, and so would the tire surface, and at that point i guess that they would slowly increase their speed closer and closer to the speed of light with the rotational inertia of the wheels and tires approaching Infinity, so the finite engine thrust will never be enough to push the plane forward in that scenario so i reckon it can't take off in that situation.

As far as the wheels go, they said the belt only had to go backwards as fast as the plane was going forward so the wheels with only reach double the speed rather than go to infinity

remind me the problem of the sailboat with a fan (on the boat) pushing the sail... that result in the boat to not move... In this scenario you have to consider that the airplane is moving relatively to the earth and not to the conveyor belt... given a strong wind even a parked airplane will take off

2:17 - I usually kill people and run away easily in those dreams.

there could be a 4th option if you consider te friction between the belt and the air, which can be significant if the belt goes really fast : in this cas it creates a headwind that could provide enough airspeed to lift the plan, although it would be really turbulent

I think this is essentially a modern rehash of Zeno’s paradox. (Achilles races a tortoise. Tortoise has a head start. Race starts. Achilles covers the distance to where the tortoise is, but in the time that took, the tortoise has moved. Then he has to cover that distance, but the tortoise moves again. This, for infinity. ‘Achilles can’t overtake the tortoise’) In reality, that’s not how a race works. Similarly, this scenario tells you a thing is happening that can’t really happen. So of course it breaks a few brains. (I also think even though the ‘runway sized treadmill’ is often explained in the wording, this question is almost always accompanied by a diagram that makes it look like the treadmill is only the length of the plane, which straightaway primes the readers mind to imagine the question is saying ‘can the plane take off vertically on this treadmill by getting the treadmill up to the planes take off speed.’)

5:11 i love the vocalised motor noise you made here lol

(Related to 0:40) Yes, the plane can still take off. The speed of the conveyor belt matching the speed of the wheels will not affect the plane's ability to take off because the plane's propulsion comes from its engines, not from the wheels. The engines provide the necessary thrust to move the plane forward, and the wings generate lift that allows the plane to become airborne. The speed of the conveyor belt might make it more difficult for the plane to take off, but it won't prevent it from doing so. The plane's engines will still generate enough thrust to overcome the resistance from the conveyor belt, and the wings will still generate enough lift to lift the plane off the ground. Therefore, as long as the engines are functioning properly and the pilot applies the correct takeoff procedure, the plane can take off from the conveyor belt runway. - ChatGPT 2023

It's difficult because if the conveyor exactly matches the wheel's speeds the plane can not move. But yet the jet engine is pushing against the stationary air and not driving the wheels directly, so can move the plane forwards no matter how fast the belt turns (until the rolling resistance of the wheels is so high that it impedes the plane's motion, or perhaps surface air gets moving with the belt).

At least they defined which plane is on the belt. Most people ask the question without specifying the plane. The Harrier GR.1 will take of in all cases when the engine is on.

Hi, I'm a new member and I wanted to tell you to do an experiment. this experiment consists that the light can break due to too much light it makes?

3:09 is the common incorrect depiction of lift. If the lines return to where they started, no lift is produced. The correct image should have the trailing lines arching downward, which, thanks to equal and opposite forces makes the plane gain lift.

I remember Mythbusters did an episode on this, as a kid I understood that the plane wheels spin independently and are not driven like car wheels, so the plane can accelerate independently of the wheel speed

A stationary belt and a runway are identical. The engines provide thrust. The plane flies. The end.

This is the definition of overthinking, and I love it.