Airplane physics question

In your engineering office, why don't you grab a desk reference and look up the CF/F for rubber free rolling on asphault. Not the maximum available friction (traction) but the free rolling CF. That slight miscalculation you made is a HUGE one.

Might not want to let your other "engineer friends" read this, won't be the best for your career.

 

Short Answer: Of course the plane can take off.

This is a hypothetical question, like those used by physics professors to help with understanding the laws of physics. You don't need to take into account friction, wheel bearings, the rotation of the earth or the color of the flight attendants uniform.....not even the pilot's blood alchohol content is relevant in this scenario.

Jets take off because of engine thrust, they aren't wheel driven. Apply that thrust to the plane and it accelerates through the air mass. When it reaches flying speed it takes off. The plane doesn't care which way or how fast the wheels are spinning, or whether there is a conveyor belt under them.

Here is the part no one is reading correctly "THE OPPOSITE DIRECTION OF ROTATION"

Read it again. What it is saying is this: as the engines apply thrust and the plane begins to accelerate, the plane moves forward and the wheels want to begin to rotate, however....immediately the conveyor belt begins moving IN THE SAME DIRECTION AS THE PLANE. Which is opposite the direction of rotation of the wheels. Therefore the wheels NEVER actually rotate, the conveyor belt simply accelerates equal to the planes acceleration until the plane lifts off.

Now, if someone says "NO NO, THE CONVEYOR BELT IS GOING IN THE OPPOSITE DIRECTION".
Well, so what. The wheels DO NOT DRIVE THE PLANE. Jet thrust drives the plane.

So, to restate: Relative wheel rotation speed, and even direction of rotation is irrelevant in the hypothetical question posed. Therefore conveyor speed, and even direction is irrelevant.

To whomever said he wouldn't want to fly with anyone who thought the plane could fly, I say I wouldn't want to fly
any plane you designed.

 

Yes, I get it. You don't.

I hope nobody is getting mad about this, because hey, it ain't worth it. It's all for fun.

The wheels spin faster, which means the belt spins faster. The belt is not a passive belt, it is POWERED. It has to be, to match the speed of the wheels. Whatever speed the wheels go, the motors driving the belt spin it just as fast. If the friction between teh belt and wheels was infinite, and the power of the belt motors and the plane motors were infinite, the belt and the wheels would spin infinitely fast, and the plane would not move. But the frictio is not infinite, and that is the limiting factor as defined by the question.

So: those who think a Piper Cub could take off, you don't understand the question. those who think no plane could ever take off regardless of how powerful it is, you don't understand the answer.

 

hwyengr,

if you lie on your back on a skateboard under a truck, if you want to move yourself in relation to the truck, you could grab onto something on the underside of said truck and pull yourself forwards.

Now, if you hold on to the truck and your buddy drives it down the road, would you still be able to hold on to the underside of the truck, and even pull yourself forward in relation to it? You betcha you would, because the only extra force you are overcoming is the tiny bit of friction from the skateboard wheels' bearings as they buzz over the road.

If you started to pull yourself in relation to the truck 1 mph (so slowly clambering along towards the front, and your buddy added 1mph to the truck speed, what would be the difference as percieved by you?

You'd have the 1mph extra worth of (extremely low) wheel bearing drag to overcome and that'd be it.

The problem with the plane is the same - its pulling against the air that is in front of it/getting sucked in thru the engines, its not driving backwards against the belt.

I hope this makes sense to you - hope you have a good session with your engineer buddies.

Regards,

Rich.

 

Well, I have to go shovel the driveway. Thanks Alan for posting this, it was a fun and interesting discussion (which probably has a bit of life in it). I will take this one ot work Monday.

Thanks for the good debate, guys. Made me think, changed my original postion, and learned some stuff. Mark this one for "post of the year", Rob.

Anyone know how to put a MiG engine in a Cessna Caravan float plane....

 

But the maximum wheel speed is not infinite, it's only as fast as the plane is traveling. It's not an exponential equation, It's very very simple, the belt can only travel in the opposite direction as fast as the plane is traveling. What is so difficult about that? So that proves that the only additional force required for flight would be what is needed to spin JUST THE WHEELS at double the speed of the plane. Sigh.. I think Rich was right, some people will never get it.

 

Wow this was a great thread - thanks for posting it!!! My first 2 second guess was that it could not fly... but after thinking about it, changed my mind. I think we're all too used to cars which use the wheels for forward motion, and don't consider that a plane does not! VERY very cool thread - thanks again!

 

Excellent example, it's always been said that MOST engineers drastically overthink things and can't grasp some of the most simple real world issues... and this COMPLETELY proves how CORRECT that assumption is.

BTW I asked my 11yr old cousin what he thought, after giving it 2 seconds thought he said of course it would fly, the engines move the air not the ground.

Just for ****s and giggles I emailed the question and a link to this thread to Mythbusters

 

teak360 has a good point.

If you read the problem that way, then the conveyer 'goes with' the plane and the wheels never need to rotate.

However, as that statement would make for a pretty short conversation, even though the problem was worded like that, lets stick to the plane goes forwards/conveyor goes backwards version that everyone is so, er, enjoying.

What I don't get is that for the conveyor belt to be moving backwards AT ALL, the plane simply has to be moving forwards, yet some folk just doggedly insist that it isn't going anywhere.

mxblue: I think *everyone* who is an engineer should discuss this with their engineering colleagues. We could hand out 'Newton Awards' (in the style of Darwin Awards) to those who don't get it. These would consist of nothing more sinister than an apple, released from a height of about twenty feet above the award winners' heads, accelerated by the force of gravity, you know the rest!!!

I'm off for a beer, will be back to catch up later...

Regards,

Rich.

 

Hey Rich, thanks for the question. Yeah, I think we are together most of the way here. The plane engine tries to push the plane forward, the belt tries to push the plane backwardmayv=be easier to imagine the plane on a roller. the roller spins backward at the same speed as the wheel (say they are the same diameter and then they spin at the same rpm.) so no matter how fast the wheel spins the roller spins at the same speed. Plane engine pushes forward harder, the roller spins faster to push the wheel backward harder and maintain the same speed. As I said above, the roller has to be powered to do this, or else masless and frictionless (I think). Take your pick, but I don't much care for the massless frictionless assumption. Assuming a roller that can go infinitely fast is silly enough until you realise it doesn't need to because at some point it cant push any harder backwards on the plane wheel, becasue it runs out of friction.

If we go back to the pic, you see the plane trying to push forward and the roller trying to push backward. Imagine for the moment that the plane was wheel driven. At some point the traction would be exceeded and the wheels would spin. That would be the limiting point of the plane's acceleration. It could spin its wheels faster but it wouldn't generate any more force. the same appluies in reverse. If the roller is spinning backwards, trying to keep up with the speed of the plane wheel, at some point, the roller can't generate enough friction force to accelerate the plane wheel any more and they just spin against each other.

I see a lot of people confusing static, rolling, and sliding (dynamic) friction here. That's understandable, it's a confusing subject, especially when you are talking about rolling tires.

Rolling friction is a measure of how hard it is to push a wheel. Steel on steel is very low rolling friction, like on rail road cars. But when you have to stop the railroad car, you need to know how much grip steel has on steel, how much force that interface will generate when you put on the brakes. That is also low, which is why we don't use steel wheels on steel roads for cars. As long as you don't lock the wheels, the stopping force is determined by the STATIC friction coefficient. What? They're not static, they are rolling! Yes, but relative to each other the surface of the wheel and the surface of the road are not moving. That's right, the bit of your car tire touching the ground at any given moment is traveling at zero miles per hour. Think about it. But to make up for that, the bit of tire at the top of the wheel is traveling at 160mph, if you drive 80mph like me.

So when you slam on your brakes, if you do it right, you actually get to use the static coefficient of friction to stop, because the relevant bit of your tire is going zero mph relative to the road. If you are stupid and don't have ABS then you lock your brakes and only get the sliding (dynamic) coefficient of friction, and you take twice as long to stop. Threshold braking, anyone? Anyone?

To sum up, it's late (2AM), I have to work in the morning, and I have spent a LOT more time on this than I should have. Still happy to answer questions, but keep in mind, it's a silly thought experiment, and we should all be having fun with it, not getting mad about it.

And good night all, I really mean it this time!

 

I think what we've really discovered is the old divide between experimental and theoretical scientists.

 

Sleep tight Dubai/Scot, best to rest up rather than end up ragged out because of this thread.

Thanks for your illuminations - I still don't agree with you though!!

What you've said about the different types of friction is true, and the examples credible. I just don't think they are relevant to this problem - the centre of the wheel goes forward (say) 50, the conveyor backwards at 50. If it was a car, it'd stay put, but planes pull against the air, which isn't being manipulated to stop the movement of the plane.

As simple as that..? Anyone..? Bueller..? Bueller..?

Cheers!

Rich.

 

so in the end i'm still right. 9 pages later we come to the inevitable, the divide of those who believe and those who don't. it is interesting to see the sides, however in this case there really is a right/wrong answer. i do think though that if someone accutually built a contraption to prove the plane lifts off there will be those that just will not accept it. kinda like the old earth is flat/round debate.

look at another way, take a rocket that is ready to launch into space and strap some wheels to it and tilt up treadmill. will the rocket fail to leave the ground becouse the wheels have now entered the picture? ofcourse not it's silly to think it would. the thrust of the escaping gasses push the rocket skyword, same for the plane in question. the wheels are along for the ride.

 

Maybe it ain't over until we've convinced our friend in Dubai.

To be fair, he needs his rest right now, but I look forward to jousting with him again soon.

Alan - nice problem, thanks for posting it.

SMG - LOL - the '90 degree solution' nice! But why didn't you say that 9 pages ago!!

Going for a beer,

Rich.

 

i thought it was clear then, guess not. speaking of beer, i just got back from jack russel brewery with 4 cases of beer. ummmm good, think i'll go have a blueberry ale.

 

i think that the group here is little more respectfull of the others stand to avoid that kind of conflict. now nobody go prove me wrong here, this is entertaining and a good cerebral workout.

 

I nominate this for the "Mountain out of a Molehill" thread of the year.

Friction, rolling resitance, et al. were never meant to be part of the hypothetical here. People are obscuring the simplicity of the problem
with minutia and obsfucation. Reminds me of the government.

This problem also reminds me of the story of the old time mail pilots that thought if your course from point A to point B had a constant crosswind component, you would have to fly the entire course with rudder applied to counteract the crosswind (instead of simply crabbing).

 

20 pages and then shut down?? Now you tell us!! You dirty, rotten, no good £$%^&*!!

[I jest... ]

I now what you mean about the fighting, there was one about the game show where the contestant chooses one of three choices to find a prize then after some manipulation occurs they are asked if they want to change their mind (should they/shouldn't they?).

This too nearly brought people to murder their forum buddies, and the amazingly complex edifices of completely wasted thought that people built were quite staggering. Ultimately it was simple puzzle but I won't post it, at least not till everyone's calmed down over this one...

I keep trying to go get a beer - but there's this conveyor belt between me and the fridge!! I run and run and get nowhere, aaargh!

Rich.

teak360 - I agree, but all the while people have spent arguing about this Jodie Foster has had LOADS of extra time to find her kid... (sorry)

 

No...I don't think anyone got nasty or obnoxious about this thread at all. I found it quite humorous, entertaining and the whole insanity handled in a very gentlmen-like manner. The real challenge was in conveying our thoughts & information to another party who (albeit were ignorant fools ) saw things from a different perspective.

That's a brilliance in life, having a thought, being able to express & convey the information so that someone else understands it too. And it's even more challenging when that other person disagrees with you. It's like a puzzle...mentally stimulating and what makes us human.

I'm nominating SMG2 for "outstanding achievement in the field of arguing aeronautical physics"

 

thanks i'm flattered, does this mean i need to get out more?

 

so i tried to tell my wife about this amusing puzzle and when i finished, she looked at me as though i sprouted a second head. her reply "Who cares!!" and this from a women who holds a masters degree in science. so i guess only the nerdy ones get excited about these puzzles.

maybe thats why people don't talk to me at parties

 

Ah yes, I know what you're talking about. The odds after opening one door are split 66-33 instead of 50-50. I've seen big debates over that one, LOL! That would easily lock a thread down after a few pages.

 

I think the word you're looking for is "conversation".