The "Aeroplane on treadmill" conundrum... [Archive]

FlyingForFun

6th Feb 2006, 17:32

This question came up a few months ago at work. After much discussion, everyone at work agreed that the question was flawed.tracks the plane speed and tunes the speed of the conveyer to be exactly the same.What speed are we talking about here? Are we talking about the speed of rotation of the aircraft's wheels? If the aircraft moves forwards at 5kt, the conveyor would then have to start moving backwards at 5kt. But this would of course increase the speed of the aircraft's wheels to 10kt, which would then cause the conveyor to speed up... and before long, the conveyor would be going infinitely fast. This is the answer that is given on the website.

Or are we talking about the airspeed of the aircraft? In which case, if the aircraft starts moving forwards through the air, the conveyor would start moving backwards. Now we need to know some more about the aircraft's wheels. If they are perfect, i.e. no friction, the wheels would be spun backwards, but this would not slow the aircraft's movement through the air, so it would take off at its normal rotate speed.

If the wheels have friction (as all real-world wheels do), then the action of the conveyor on the wheels would cause the aircraft to move backwards, whilst the propellor would continue to move the aircraft forwards. (If you don't believe me, think about an aircraft without its engine running sat stationary on the conveyor, and get the conveyor to move backwards - the aircraft moves with the conveyor. Having the prop running would not affect this.) Since most wheels only have a little friction in them the prop would probably overcome the conveyor, i.e. close to the no-friction case. The aircraft would still rotate at its normal rotate speed, but it might take a little longer to reach this speed than it would if the conveyor wasn't slowing it down. So your conveyor would have to be at least as long as a runway to avoid the aircraft going off the end of it.

FFF
-------------

TheKentishFledgling

6th Feb 2006, 21:02

distaff_beancounter

6th Feb 2006, 21:21

What about the other one I've seen doing the rounds:
If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird?
And If the aircraft is flying at, say, 500 kts and the bird has a max speed of 100 kts - will the bird manage to fly from the back to the front of the aircraft?

TheKentishFledgling

6th Feb 2006, 21:55

Makes me think of one my old physics master said to us...(sorry, diverging from the original thread somewhat..)

If you're in a space craft (theoretically) travelling JUST under the speed of light, and you run from the back to the front of the spacecraft (enough to make up the difference from space craft speed to the speed of light), are you then travelling at the speed of light? What then happens if, while you are still running, the rocket accelerates to a speed GREATER than the speed of light....?

tKF

QDMQDMQDM

6th Feb 2006, 22:49

If you're in a space craft (theoretically) travelling JUST under the speed of light, and you run from the back to the front of the spacecraft (enough to make up the difference from space craft speed to the speed of light),

Three things happen as you approach the speed of light:

1. You get heavier
2. Time slows down
3. You get foreshortened in the direction of travel

In other words, you won't have anywhere to run.

Also, of course, the speed of light is a constant for all observers, yadda, yadda, yadda...

QDM

AerocatS2A

7th Feb 2006, 01:41

If the aeroplane is not moving THROUGH THE AIR it cannot fly.

Correct, however the conveyor belt has no means of stopping the aircraft from moving through the air. The aircraft does move through the air, and it does take off.

SkyHawk-N

7th Feb 2006, 06:47

What about the other one I've seen doing the rounds:

If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird?

No

And If the aircraft is flying at, say, 500 kts and the bird has a max speed of 100 kts - will the bird manage to fly from the back to the front of the aircraft?

Yes

If you're in a space craft (theoretically) travelling JUST under the speed of light, and you run from the back to the front of the spacecraft (enough to make up the difference from space craft speed to the speed of light), are you then travelling at the speed of light? What then happens if, while you are still running, the rocket accelerates to a speed GREATER than the speed of light....?

Nothing. Prove me wrong!

TheKentishFledgling

7th Feb 2006, 07:52

Nothing. Prove me wrong!

Easy ;)

tKF

ThePirateKing

7th Feb 2006, 09:46

If the aeroplane is not moving THROUGH THE AIR it cannot fly. If it's on a conveyor belt, the belt doesn't care what speed the air is moving and the belt won't move the air to move (OK, it could be argued that the "boundry layer" of air to the belt has a velocity, but realistically it's enough to ignore in this case).
All the time the belt is moving "backwards" at the same speed the a/c wing is moving forwards, nothing will happpen.
Think of yourself running on a treadmill (unpleasent thought, I know...!)....when "running" at the same speed as the belt, you are stationary - your relative wind = 0, therefore no angle of attack, therefore no lift.
Good one though, has got me thinking about how to word an answer.
tKF

Well, yes. That was my original thought when I posted this thread. However, in reading some of the arguments on the original site, I am now convinced that the aircraft will fly.

The basic argument says that since the wheels of the aircraft are free to rotate (i.e. not powered like a car) the movement of the conveyor belt will do nothing except cause the wheels to rotate. Assuming no friction, the aircraft will remain stationary. Now... start its engine, and it will pull itself forward through the air until it gains sufficient speed to take off. The difference between this and a similar question involving a car is that a car powers itself by pushing against the ground, while an aeroplane powers itself by pushing against the air.

TPK:ok:

Ni Thomas

7th Feb 2006, 10:45

OH I see! It's a looooong treadmill, loooong enough to accelerate through the air to gain lift (with the tyres spinning like mad) sufficient to take off and climb over the ubiquitous 50ft barrier ...
Now.... what about the landingon aforesaid treadmill? :p

raisin

7th Feb 2006, 10:56

Assuming no friction, the aircraft will remain stationary. Now... start its engine, and it will pull itself forward through the air until it gains sufficient speed to take off.

It will gain sufficient speed to take off relevant to the conveyor belt. The ASI will read zero as the propeller is working to maintain the aircraft's position on the conveyor belt, not to move forward throught the air.

The whole "system", i.e. the conveyor belt AND the aircraft must be considered to see whether it will take off. As the conveyor belt is not moving through the air, the aircraft will remain on the ground/conveyor belt.

Yorks.ppl

7th Feb 2006, 11:41

This ran to 14 pages on jetblast, so to try and save everyone here is the proof that it will fly
http://videos.streetfire.net/player.aspx?fileid=35E964D9-38DB-4EFD-BE8D-D6BA1A43A06B

AerocatS2A

7th Feb 2006, 11:50

It will gain sufficient speed to take off relevant to the conveyor belt. The ASI will read zero as the propeller is working to maintain the aircraft's position on the conveyor belt, not to move forward throught the air.

What exactly does an aircraft's propulsion system do? It pulls the aircraft through the air not over the ground. The ASI will NOT read zero, it will read as per a normal take-off. The treadmill has no means by which it can slow the aircraft down. We are talking aeroplanes, not cars.

Here is an excellent tongue in cheek analogy from the Straight Dope thread:

OK, how about a different thought experiment? We have a plane on a perfectly normal runway, but next to the runway are a bunch of people whistling. The plane starts its engines, but the more the engines rev up, the louder the people whistle, so the plane can't move at all. If it did move, the people would just whistle even louder, to prevent it. Since the plane can't move, being prevented by all the whistling, there's no airflow over the wings, so the plane doesn't take off.

The treadmill has about as much affect on the take off performance of the aircraft as the people whistling do.

SkyHawk-N

7th Feb 2006, 12:24

If it did move, the people would just whistle even louder, to prevent it.

What if more people joined in the whistling but at the same volume as before? :rolleyes:

raisin

7th Feb 2006, 12:55

AerocatS2A

Yes, I see that now. Thank you.

chrisN

7th Feb 2006, 13:59

Quotes:
Originally Posted by High Wing Drifter
What about the other one I've seen doing the rounds:

If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird?

Sombebody's answer: No

CN- not necessarily, it all depends.

Quote:
Originally Posted by distaff_beancounter
And If the aircraft is flying at, say, 500 kts and the bird has a max speed of 100 kts - will the bird manage to fly from the back to the front of the aircraft?

Sombebody's answer: Yes

CN - again, not necessarily, it all depends. Like the truck driver with a load of birds in the back who had difficulty in climbing a hill, so banged on the back to get the birds to fly and reduce the effective weight. It all depends . . .

Chris N.

SkyHawk-N

7th Feb 2006, 14:28

CN- not necessarily, it all depends..

It all depends . . .Chris N.

It all depends? On what?

I'm sure you're right but it would be great if I could see proof of why I am wrong. :E

Skyhawk.

chrisN

7th Feb 2006, 14:41

S, see your pm's. Regards - Chris N.

FlyingForFun

7th Feb 2006, 14:48

It all depends? On what?Two scenarios.

First, imagine a totally enclosed cabin. The cabin contains the pilot, the bird, many billions of air molecules, amongst other things. The aircraft's wings have to carry the weight of everything in the cabin. Makes no difference whether the bird is on the floor of the cabin or not, it is still in the cabin, and so still needs to be carried.

Scenario number two: an open cockpit aeroplane, with the bird flying six inches above the top of the cockpit, at the same speed as the aeroplane. The bird is clearly carrying its own weight, and does not require the aeroplane to carry its weight.

The reason for the difference, I think, is that in the first case, the downwash from the bird's wings strikes the floor of the cabin and exerts a force on the floor of the cabin which is equivalent to the weight of the bird. Whereas in the second case, most of the downwash from the bird's wings escapes from the aeroplane. I've never actually seen proof of this explaination, though.

The interesting things is the in-between situation. For example, the open-cockpit aeroplane with a bird sitting on the seat. During the flight, the bird decides to take off and leave the aeroplane. At what point does the aeroplane stop carrying the bird's weight?

You can apply a very similar argument to the bird moving at 100kt and the aircraft moving at 500kt.

FFF
---------------

chrisN

7th Feb 2006, 15:01

FFF - quite so.

And now for something that really happened, as I read it years ago.

During WWII, some PoW's passed their time building tiny paper gliders from the paper lining of cigarette packets.

Then they progressed to a powered aircraft, by capturing a fly, and gluing it to the tiny model. It worked.

Then they tried aerotowing, but found a 1-fly powered aircraft was too weak.

So they built a twin, one fly each side. There were assymmetry problems, as the flies were reluctant to synchronise their efforts, but eventually they managed to effect an aerotow takeoff successfully.

So the flying creature's efforts, if not totally enclosed, have an effect on drag by overcoming it with thrust, and perhaps on lift too, depending on the circumstances.

Chris N.

High Wing Drifter

7th Feb 2006, 15:14

HWD, dont, just please for all man kind, dont!
Sorry Stue!

Hmmm. I've gone from one view to the other.

I think the the bird in flight, or a model aeroplane or whatever would not be sensed by the enclosing aeroplane because lift is, as I understand it, the result of pressure differentials in the area immediately around the wing. I think this is regardless of wether you consider Bernoulli, Newton or both responsible for lift. However, if the bird or model aeroplane or whatever were in ground effect, then I think at least some of the weight would be sensed. But then again, if the enclosing aeroplane's cabin is pressurised it must sense the weight of the bird, but that negates the pressure differential lift argument. I'm missing something, I'm sure!

Would I be squidged to a pulp if I lay down on the runway with a 747's wing (attached to 747) flying a few feet above me (assuming I was suitably secured to prevent my otherwise imminent demise in its wake!)?

stue

7th Feb 2006, 16:05

Would I be squidged to a pulp if I lay down on the runway with a 747's wing (attached to 747) flying a few feet above me
Dunno? anyone want to volunteer to find out??:p
As yorks.ppl said, this went on for ages on JB, every one decided that it could fly. (well, most people)
You have started summat now HWD, i hope you are proud!:rolleyes: :p

dublinpilot

7th Feb 2006, 16:24

Coming back to the conveyor belt one.

One thing that we haven't considered is friction.

I accept that under normal circumstances the aircraft should accelerate through that air and take off.

However, lets follow this through a bit.

If the aircraft has its engine turned off, and the conveyor belt is turned off, and we have zero wind, then everything remains stationary.

Now the conveyor belt is turned on, due to the effects of friction the aircraft will stay stationary relative to the conveyor belt, and move back wards relative to the ground (which the conveyor sits on) and back wards relative to the air.

Now the aircraft starts its engine and runs at idle speed. We all know from experience, that at idle power most aircraft don't produce enough trust to over come friction. So the aircraft will still remain stationary relative to the conveyor belt, and move back wards relative to the ground and the air.

Add a little power to the aircraft engine, and it will start to slowly creep forward on the conveyor belt, as it overcomes the friction. However due to the effects of the friction and the small amount of power added, the aircraft will slowly move forward relative to the conveyor belt, but still hasn't over come all the friction, so it will still move slowly back wards relative to ground, and the air, just not as fast back wards as before.

Now add a little more power, and the power of the engine finally matches the effect of the wheel friction. Now the aircraft will move forward relative to the conveyor belt, at the same speed as the conveyor belt moves back wards. Relative to the ground and the air, the aircraft is now stationary.

I think so far we all agree. What happens next is where the discrepancy arises, and is due to the badly worded question.

Scenario 1: At this point the aircraft adds its remaining engine power, and uses this to accelerate forward relative to the airflow, and generates lift, and takes off.

Scenario 2: The conveyor belt starts to move a little faster. This generates extra friction on the wheels. The aircraft still moves at the same speed relative to the conveyor belt, but once again starts to move back wards relative to the ground and airflow.

The aircraft now adds a little extra engine power to over come the extra friction, and now moves forward a little faster relative to the conveyor belt, and once again its engine output matches the friction and its movement relative to the ground and airflow becomes nil.

If the above keeps being repeated (adding friction by increasing the conveyor belt speed, and adding engine power to compensate for the friction only) until the engine is at full power, then the aircraft will eventually be moving incredibly fast relative to the conveyor belt, but will have a nil speed relative to the ground and to the airflow.

Admittedly the conveyor belt would be running at a speed many multiples of the aircrafts normal take off speed, and in practise the tyres are likely to explode, and the the wheels fall off due to the heat from the friction, and the aircraft is likely to be thrown off the conveyor belt by the minor bumps being turned into huge bumps by the speed, but if we are only asking about the theory, then it is possible.

So I guess it all comes down to how we interpret the original question.

The only correct answer is a question back to the questioner. What is the airplane's speed relative to the air?

:}

dp

Send Clowns

7th Feb 2006, 16:29

dublinpilot

You have made an incorrect assumption that invalidates your case.

Friction of movement between two solid objects does not have a simple relationship with speed. Friction is greatest when they are stationary in relation to each other, but drops immediately when they start to move and thereafter remains low - it doesn't rise quickly with speed. Bearing friction is a small fraction of total drag for an aircraft taking off; parasite drag and induced drag make up a much greater force.

The case you suggest cannot happen - until the aircraft moves (through the air) the conveyor would have no speed, so the conveyor cannot match the speed - it must always lag the aircraft, and the aircraft would have an airspeed.

mad_jock

7th Feb 2006, 17:26

Has anyone got ?

1. a remote controlled airplane.

2. a electrical running machine that goes faster than the remote controlled aircraft can fly striaght and level at with max power.

The experiment would be simple.

1 tie the aircraft with 2 bits of string in a V out the front secured by 2 hooks which would unhook when the aircraft goes past.

2. Start the aircraft

3. Start running machine and get it going faster than the aircraft flys at.

4. Open throttle and take a video as it farks off the end of the running machine.

Then we can put this ****e to bed.

TheKentishFledgling

7th Feb 2006, 17:42

:D :D :D :ok:

Like the idea!

tKF

Gingerbread Man

7th Feb 2006, 19:03

Can I drift onto something that i've wondered about since A-level physics? Let's say you're in space standing on the inside wall of a cylinder that rotates. The cylinder rotates at such a speed that when you are standing on the wall, you experience 1G. If you now jump up, what happens? :confused:

mad_jock

7th Feb 2006, 19:43

After you have left the cylinder you will still have the side velocity at the point of jumping. Then add what ever downwards compent by using the velocity triangle to work out the resultant.

The point were you will hit the wall again will be determined by that.

For very small jumps it will appear that you just go in and out relative to the wall. For larger jumps you will see the slight angle.

You used to be able to do it on fair ground rides. They spin you up and put it vertical and you stick to the wall. If you stand horizontal and skip you can feel the slight sideways force on your ankle when you land.

You also feel a great sideways force round your ear afterwards when your mum gets her hands on you after watching said physics experiment.

Penguina

7th Feb 2006, 21:36

Mind you, if the treadmill were running in the other direction - ie, in the direction of take off - that would be a simply _marvellous_ asset for short field ops. Especially if you had an enormous hairdryer at the end of the runway. :hmm:

Don't try the above at the gym though. On second thoughts, if they have CCTV there... :D

SkyHawk-N

8th Feb 2006, 06:36

the downwash from the bird's wings strikes the floor of the cabin and exerts a force on the floor of the cabin which is equivalent to the weight of the bird---------------

Surely displacement of air has an affect to all this?

This is real interesting! can't think of anything I'd rather be doing on a still, cloudless morning......hang on a minute!!!

Skyhawk.

LowNSlow

8th Feb 2006, 08:02

[B]dublinpilot[B]you're talking shoite me auld son. := If there was the relationship between wheel bearing friction and speed that you describe then your car would never move away from the kerb as friction would increase in proportion to the speed! :{

Fortunately, after overcoming the initial "sticktion" of a stationary bearing, bearing friction remains realtively constant as long as the bearing in question is properly lubricated appropriate to the speed it is rotating / sliding at.
:ok:

dublinpilot

8th Feb 2006, 10:40

You have made an incorrect assumption that invalidates your case.
Friction of movement between two solid objects does not have a simple relationship with speed. Friction is greatest when they are stationary in relation to each other, but drops immediately when they start to move and thereafter remains low - it doesn't rise quickly with speed.
I don't think I have.
If I remember my leaving certificate physics correctly the law was "The co-efficient of static friction is greater than the co-efficient of dynamic friction."
Once the aircraft starts to move forwards relative to the conveyor belt, the level of friction immediately drops. However it does not disappear. If I remeber correctly, it increases thereafter with speed, albeit slowly.
I'll readily admit that the velocity that the converyor belt would have to be traveling would likely rip the wheels off before it gave enough friction to hold up the engine, but none the less, in theory it seems possible.

[b]dublinpilot[b]you're talking shoite me auld son. If there was the relationship between wheel bearing friction and speed that you describe then your car would never move away from the kerb as friction would increase in proportion to the speed!

Low & Slow, the difference between the airplane example and a car is quite profound. In the airplane situation the conveyor belt can move at unlimited speed (in theory). The ground can't move at all under a car ;)

dp

dp

mad_jock

8th Feb 2006, 10:47

Penguina

They already have this and have it in production.

The belt is running at about 15-20 knts and the fan is anywhere between 0 and 50knts of wind.

Its called an aircraft carrier :D

Actually it doesn't matter what speed the threadmill is doing the only thing the aircraft carrier is doing is steaming into wind to get the intial airspeed up. The relative speed of the ground under the aircraft wheels will have no relation at all on take off distance presuming no friction.

PS it really is quite amusing seeing how none engineers think the world works. How effects which engineers instictively ignore are given huge weighting and how complicated very simple engineering systems become.

J.A.F.O.

8th Feb 2006, 11:27

I am a bear of little brain so please only use short words when trying to explain to me how stupid I am; surely if every time the prop bites at more air to move the aeroplane forwards along our moving runway the runway moves backwards then the aircraft never moves in space, therefore has no airspeed, therefore sits on the conveyor belt revving itself to death.

I know some of you will find it difficult to believe that someone this stupid has access to a computer but it makes my head hurt so please explain.

High Wing Drifter

8th Feb 2006, 11:48

JAFO,

Just think of it as a tailwind simulator. Your groundspeed is more than your airspeed (twice as much to be precise)

dublinpilot

8th Feb 2006, 11:55

Jafo,

Ignore my arguments above, because they are really more theory than practice.

Try to think of it the other way around; an airplane landing on a conveyor belt.

The airplane is in a 60kt headwind, and the pilot leaves some power on......enought to maintain level flight with a nose up attitude.

Just as the airplane is about to touch down the pilot flares a little more so that the wheels barlely touch down, and the weight of the aircraft is partly supported by the wheels and partly by the conveyor belt.

All that happens is that the wheels are spun by the conveyor belt, but the engine still pulls the plane forwards though the air, and the airflow over the wings support it weight.

The pilot then lets the angle of attack fall so that all the weight is now supported by the wheels, but leaves the engine running. The airplane still stays stationary on the conveyor belt.

If the pilot now applies full power, the aircraft accellerates forward and climbs away.

All the conveyor belt is dowing is spinning the wheels. The airplane is pulling against the air, not the belt (ignoreing friction).

I hope that helps!

dp

mad_jock

8th Feb 2006, 12:20

The air isn't as such stuck to the moving ground.

the confusion here is because you making it very complicated.

The propellers job is to transfer power to the air which results in a force towards the rear of the aircraft. The air is not attached to the belt so it is free to be accelerated by the prop producing the force.

The wheels on the ground are just there to stop the prop hitting the ground.

While taking off they have minimal resistance to forward motion but in the engineers brain all it is, is a force resisting the plane going forward in the oppersite direction to the force produced by the prop.

Now the wheel/ belt is treated as a system in it self. The sum total of all the proccesses going on will produce a resisting force. And usually in the grand scale of things it will be forgotten about by engineers because its less than 1% of all the other forces.

Now you add all the forces up resisting the forward motion of the aircraft so thats the forces due to the wheels, forces due to aero drag and you subtract them from the force produced by the propeller. If the resultant force is positive the plane will accelerate forward relative to the airflow if it is negative it will go backwards if it is zero it will stay stationary.

Its a bit like all the stuff to do with the difference between Ground speed and airspeed when your doing nav.

With any system engineers are taught to simplify first down to just the basic forces involved and not really care how they are produced. Then form whats called a free body diagram which graphically shows you whats going on. Some get by with just sticking numbers next to the arrows and some preffer to draw the arrows to scale. In this case you would have. Where x is the plane.

T<---------------------------------X->D

Now the problem is that experence allows the engineer to forget about some things because they know that it won't matter for that problem. We tend to work to 3 significant figures any thing less than that just gets forgotten about because of all the other presumtions and arse covering with materials means you will be very lucky to get an answer that will be correct to anything more than that anyway. You can see from the diagram that the force forward is way more than the force the other way. This would be at the start while the aircraft isn't moving relative to the air flow.

As it speeds up the aero drag increases so it becomes.

T<---------------------------------X------------->D

Then once it becomes airborne the drag produced by the wheels is removed. Thats why some times you feel a little bust of acceleration as the wheels lift.

And the plane continues to accelerate until.

T<---------------------------------X--------------------------------->D

Then the plane is at a constant speed relative to the airflow.

So whats happening at the ground is really irrelavent to whats happening to the airflow around the wings and prop. The wheels ground produce a force and the propeller produces a force. If the force from the propeller is greater than the force from the drag from the ground it will move forward. Which will then make airflow over the wings which will produce lift for flight.

MJ

Penguina

8th Feb 2006, 13:46

Mad Jock:

Oh yeah! :D

Damn this thread. I took ages getting to sleep last night because I just couldn't stop my brain from drafting a checklist for short-field-conveyor-belt take off technique to best use the residual airspeed in the initial stages of the climb-out before drag decayed it back to what your prop could supply! :8 :{ :zzz:

dublinpilot

8th Feb 2006, 14:05

:D :D :D :D :D

High Wing Drifter

8th Feb 2006, 14:34

I just couldn't stop my brain from drafting a checklist for short-field-conveyor-belt take off technique
Careful, or you'll get DFC all excited again :D

Aeronut

8th Feb 2006, 15:23

Well if this were true (which it is not!)

we could solve the need for huge big aerodromes all over the country (for take off at least)- no need to demolish ancient woodland or entire villages to site a new runway - just install a small treadmill under the wheels of an airliner - whizz it up and away you go, according to those without a grasp of how an aircraft flies. - AIRSPEED:ok:

We could then sell of half of Heathrow for housing (to accommodate treadmill technicians?), since you no longer need the take off runway!:p

stue

8th Feb 2006, 20:57

Guys and Gals, GET OUT MORE!!!!:}

distaff_beancounter

8th Feb 2006, 21:57

They already have this and have it in production.
The belt is running at about 15-20 knts and the fan is anywhere between 0 and 50knts of wind. Its called an aircraft carrier :D
Actually it doesn't matter what speed the threadmill is doing the only thing the aircraft carrier is doing is steaming into wind to get the intial airspeed up. The relative speed of the ground under the aircraft wheels will have no relation at all on take off distance presuming no friction.
Surely if an aircraft carrier works the same as the conveyor belt under discussion, then the carrier should steam OUT of wind and the aircraft should take off into wind, by flying off the STERN of the carrier???
This is all tooooo much for my poor little brain - I am planning to fly a REAL aircraft off a REAL stationary runway, tomorrow! :)

J.A.F.O.

9th Feb 2006, 02:54

Well, thank you all for trying, anyway.

I think I'll stick to real aeroplanes and static runways but, before I do, I need a very long lie down in a darkened room after reading all the posts.

Penguina

9th Feb 2006, 18:29

GET OUT MORE!!!!

Stue:

A man who has had occasion to post on pprune 256 times is on very shaky ground, very shaky indeed! ;)

Why do I keep coming back to this thread? :hmm:

FlyingForFun

9th Feb 2006, 19:31

A man who has had occasion to post on pprune 256 times is on very shaky ground, very shaky indeed!Penguina

Join Date: Dec 2001
Location: London
Age: 27
Posts: 303Pot... kettle... black???

Hmm, I'll get my hat now I think...... :D

FFF
---------------

distaff_beancounter

9th Feb 2006, 22:05

Right Kiddies - today I took stue's advice to "GET OUT MORE" and spent the day flying, but I still can't get this puzzle out of my mind!
.
I am no physicist, but I have to agree with J.A.F.O. above. My very simple thinking is as follows:-
Flying an SEP off a short runway today:-
I lined up, held it on the toe brakes, and applied full power - RPM read 2800, ASI nil and the aircraft remained stationary.
Only after a roll of about 200m, with the ASI increasing towards 65kts, did it show any inclination to fly.
.
If I then put the same aircraft on your mythical conveyor belt:-
I use no brakes and apply full power - RPM reads 2800, ASI nil and the aircraft remains stationary, albeit with madly spinning wheels.
.
So, the only differences between the two scenarios are:-
- Stationary wheels -v- madly spinning wheels
- Travelling through a 200m long parcel of air -v- staying in the same bit of air
.
So, I still do not understand what forces there are, acting on the aircraft, to make it fly off the conveyor belt, that are not present at the moment just after the brakes were released on the runway.
.
PLEASE, PLEASE would someone explain this to me in very short simple words, otherwise I will spend another sleepless night trying to understand it! :{

TheKentishFledgling

9th Feb 2006, 22:09

I've not read the last few pages of this thread, but I still don't believe the aeroplane would fly!

IF it was in a wind tunnel in this scenario, yes, but just in a gym or whatever, it wouldn't.

Imagine that (god forbid ;)) you're at the gym running on the treadmill - you have no "relative" wind, therefore if you were a wing, no angle of a attack, therefore no lift!

tKF

Tex37

9th Feb 2006, 22:39

Unless I have completely missed the point here (which is not impossible due to the amount of posts) then the said aircraft would be effectively stationary with respect to both the ground and the air as it is actually not moving - just overcoming the speed of the conveyor and the drag of the gear?

I thought that one of the basic principles we all knew was that for an aircraft to fly we need lift, which is created by airflow moving over wings i.e you need airspeed.

No movement through the air = no airspeed = no air moving over wings = NO FLIGHT

I'll grab another beer!

stue

10th Feb 2006, 07:35

Stue:
A man who has had occasion to post on pprune 256 times is on very shaky ground, very shaky indeed!
My god, is it really that many?? I DO need to get out more!!:p Good call, i think ill go flying today then!;)
and as for how many times you have posted FFF........??:} :p

FlyingForFun

10th Feb 2006, 07:45

Ok, I've decided not to follow my own advice, and I've not yet got my hat.

For those who don't get the idea that the prop moves the aircraft through the air, and not through the ground, here's an analagy:

Thing of the prop like a screw, and the air like a nut. Now you have an aeroplane with a screw on the front of it, with its wheels on a conveyor belt. The first two or three threads of the screw are already inserted into the nut.

As the screw turns, it will move forwards into the nut. This will cause the wheels to start turning, but the conveyor will move in the oposite direction, in an attempt to hold the aeroplane back. But no matter how fast the conveyor moves, the screw, if it continues turning, will continue to pull the aircraft forwards into the nut, and there's nothing the conveyor can do to stop it.

So yes, the aircraft will move.

FFF
-------------

J.A.F.O.

10th Feb 2006, 08:09

Long lie down over.

Tex, TKF and Distaff - thank you for saying that you too cannot see the emperor's new suit - I thought I was alone.

I'm never going to understand how the aircraft ever moves through the air if it can never move over the gound at all so I've made a decision.

DON'T CARE DON'T CARE DON'T CARE

Yorks.ppl

10th Feb 2006, 08:39

Has anyone actually watched the video which proves that the plane will move forward?
Here it is again for any that missed it.
watch it carefully. The plane will fly.
http://videos.streetfire.net/player....D-D6BA1A43A06B

dublinpilot

10th Feb 2006, 10:11

Yorks,

That link is abbreviated. Have you got the full link?

dp

Yorks.ppl

10th Feb 2006, 10:26

http://videos.streetfire.net/player.aspx?fileid=35E964D9-38DB-4EFD-BE8D-D6BA1A43A06B

Hope this works.

distaff_beancounter

10th Feb 2006, 10:40

Has anyone actually watched the video which proves that the plane will move forward?
Here it is again for any that missed it.
watch it carefully. The plane will fly.

Thanks for that. I have now watched the video several times carefully.

It appears to show that the fan on wheels moves forward, due to the conveyor belt not moving as fast in the opposite direction.

Then AFTER it runs off the end of the conveyor, it continues to move forward.

So, it DOES show that something on non-driven wheels, propelled by a fan, will move forward. (Just like an SEP on its take-off roll, really).

It DOES NOT show that it will fly!

D-B
As puzzled as before, but now a fully paid up member of the "Emperer's New Clothes Society" and the "Flat Earth Society" :)

Yorks.ppl

10th Feb 2006, 11:51

"due to the conveyor belt not moving as fast in the opposite direction."

I rather thought it looked to me like the belt was moving faster in the opposite direction so the non flyers will think it should move backwards.

Of course, it doesn't matter a jot either way, you can pull the paper as fast as you like, the fan will still move forward .

FunkyMunky

10th Feb 2006, 14:07

Anyone got a treadmill and a small toy car at home?

Treadmill = our fancy conveyor belt runway.
Small toy car = pretend that's our aircraft.
Your Hand = pretend that's the result of the force between the aircrafts engines and the air.

Place the little car on your conveyor belt, hold it so it doesn't move relative to a fixed point off the treadmill, and turn the treadmill on. The wheels will spin, but the car shouldn't "move" because you're holding it in place. This is akin to the force of the aircrafts engines overcoming the relatively tiny amount of friction within the wheels that would cause it to be moved backwards by the treadmill runway.

Now try to push the car up the treadmill...lo' and behold, it IS possible :zzz: The force applied by your hand is similiar to the force caused by the aircraft engines. The air has no relation to the treadmill because they are not attached, just like your hand is not attached to the treadmill. If the aircraft engines cause a greater force to be applied via the air, than the conveyor belt can due to the tiny amount of friction in the wheels, the aircraft WILL move forward relative to the air, or any fixed point off the conveyor belt.

With the engines off, the only thing which would cause the aircraft to move back on this conveyor belt runway, is friction within the wheel bearings. To move relative to the air on the conveyor belt runway, the aircraft must be able to overcome this frictional force - if it couldn't, how could any aircraft taxi on normal ground?

The misconception here is that the motive force and the "backwards" force by the conveyor belt are being applied through the same medium - the wheels. This is true in the case of a CAR, where the car engine may not be able to keep up with the conveyor belt. In an aircraft, where the motive force is applied via the air, the wheels can spin as fast as they like - the frictional force in the wheels will be so small that the force applied to the air by the engines will easily overcome it and the aircraft will move forwards. It will fly!:eek: :D

J.A.F.O.

10th Feb 2006, 15:29

But surely the original question stated that the conveyor belt tracked the aircraft's speed and adjusted the speed of the belt to match. Therefore the aircraft would never move forwards, therefore it would have no airspeed, therefore the emperor is naked.

Something like that, anyway.

chrisN

10th Feb 2006, 16:19

Why I am bothering I do not really know but for heaven's sake, read the question - quoted below:

"An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?"

(a) Nowhere does it say the conveyor goes at the same speed as the plane. (b) It says the plane taxies - which most of us interpret to mean that it moves relative to the air it sits in and so also relative to the ground/earth upon which the conveyor's base and mechanism stand, because with low friction wheels that is just what it will do when acted upon by the force of its propellor pushing air backwards.

Chris N.

FunkyMunky

10th Feb 2006, 18:25

the conveyor belt tracked the aircraft's speed and adjusted the speed of the belt to match. Therefore the aircraft would never move forwards, therefore it would have no airspeed, therefore the emperor is naked.

If the aircraft is taxying along on stationary ground, its wheels spin as a component of the aircrafts forwards movement. The motive force is NOT applied via the wheels...it is applied via the air!!. If the ground suddenly starts moving backwards at the same speed as the aircraft moving forwards relative to the air, the net effect is that the wheels simply spin at double the speed! The aircraft still moves forwards relative to the air.

It doesn't matter how fast the conveyor belt moves beneath the aircraft, as the only way the conveyor belt can move the aircraft backwards is due to the small amount of friction within the wheel axles. If the engines provide enough force in the opposite direction (remember the force is being applied via the air!! not the wheels) to overcome this tiny amount of friction (which they do so whilst beginning to taxi on normal ground every day!) then the plane can move relative to the air.

If you watch the video above, it is easy to see...the fan is applying the force via the air. It doesn't matter what speed the paper "conveyor belt" is moving at, as long as the force on the air by the fan is enough to overcome the friction within the wheels (it MUST be enough else aircraft would never be able to taxi!).

Try the thing with the toy car and the treadmill again. It doesn't matter how fast you set the treadmill - it is still possible to apply great enough force with your hand to move the car opposite to the direction of the treadmill belt. The net effect of this movement is simply that the wheels spin faster than they would if the car wasn't moving - the spinning becomes a component of the cars forward motion, and the belts rearward motion. This force from your hand is exactly the same as the force applied by the engines of a plane, in that it is a force on an object outwith the treadmill (the air or your hand).

Cool_Hand

10th Feb 2006, 20:02

I am completely amazed how long this discussion goes on, in this forum and Jet blast and all of the other places. It amazes me even more that on a site for aviators that the idea of how an aeroplane works can confuse them. There have been some excellent explainations as to why the aircraft will fly and it WILL take off and fly. To debate it this far down the line beggars belief.

The conveyor belt acting on the wheels is a completely different system to the jet engines acting on the air. The conveyor belt will stop the aircraft moving forward as much as it will slow down a low flying aircraft that flies over it. Actually, why a low flying aircraft? just make it an aircraft.
It has essentially no effect on it.

Why the problem?

If you're flying at 60 knots into a 60 knot headwind what is your ground speed? ZERO. Why has the plane not crashed? Because ground speed has nothing to do with how an aircraft flies.

If an aircraft gained it's speed through driving it's wheels, as soon as it lifts off it would lose speed and land/crash. It pushes air not ground.

FunkyMunky

10th Feb 2006, 20:42

If an aircraft gained it's speed through driving it's wheels, as soon as it lifts off it would lose speed and land/crash. It pushes air not ground.
Sums it up really :p It will fly (in my humblest of opinions...I am not a professional physicist or anything :p ).

Jo Cover

10th Feb 2006, 20:47

Is this for real?

Unless there is movement of air over and under the leading edges of the flying surfaces at a speed in excess of the aircrafts stall speed the aircraft will not fly.

The conveyor belt can be moving at 1000 kts and the aircrafts wheels can be turning at 1000 kts but, if there isn't sufficient airflow over and under the wings, the aircraft will not fly. (unless its a Harrier, JSF etc)

Try taking a small model a/c to LGW or similar and try it on a travelator! If the aeroplane has sufficient airflow over the relevant surfaces, in excess of its stall speed, it will fly, if it dosen't, it wont get off the ground (travelator).

Someone give it a go on the early shift!

FunkyMunky

10th Feb 2006, 21:06

The conveyor belt can be moving at 1000 kts and the aircrafts wheels can be turning at 1000 kts but, if there isn't sufficient airflow over and under the wings, the aircraft will not fly. (unless its a Harrier, JSF etc)
The aircrafts wheels are free-spinning!! As long as the engines provide enough power to overcome friction within the wheels, the aircraft WILL move forwards relative to the air! There will be relative airflow, and the aircraft will fly!

What you say above is technically correct, because for the wheels to be spinning at the exact same speed as the conveyor belt, the aircraft must be stationary relative to the ground/air. You must realise that once the aircraft moves forwards relative to the ground/air, the wheels will spin FASTER than 1000kts, if the belt is going at 1000kts.
Try taking a small model a/c to LGW or similar and try it on a travelator! If the aeroplane has sufficient airflow over the relevant surfaces, in excess of its stall speed, it will fly, if it dosen't, it wont get off the ground (travelator).

I'll bet money on it flying. The motive force will be applied to the AIR, not to the travelator surface! There are only a few possibilities here :-

1. The engine is left off/idling and the travelator builds up speed slowly enough that the friction within the wheels is not overcome. The model a/c moves backwards with the travelator.

2. The engine is powered up JUST ENOUGH that the frictional force within the wheels is overcome and the aircraft remains stationary relative to the air/any fixed point. This is exactly what would happen when the aircraft taxis on normal ground, except in this case, the wheels don't spin because of the aircraft going forwards - they spin because of the travelator belt going backwards underneath.

3. The engine is throttled up to full power, or any power setting beyond that used in outcome 2, above. The force applied between the propellor and the AIR is great enough to overcome the frictional force within the wheels, AND propel the aircraft itself forwards through the air. The wheels spin at the speed of the conveyor belt, PLUS the speed of the aircraft moving forwards. The aircraft easily takes off.

The ONLY thing allowing the conveyor belt to move the aircraft backwards is the friction within the aircrafts wheels and axles. As soon as this friction is overcome, the aircraft is able to move forwards just like any other taxying aircraft on normal, stationary ground! The only difference would be the wheels spinning at a greater speed -which DOES NOT MATTER because the motive force is applied via the air. The wheels only spin at this speed because they are free-spinning, and able to - NOT because an engine is making them (Not directly anyways...the increased speed is of course a component of the engine moving the rest of the aircraft forward).

The aircraft will fly!

Jo Cover

10th Feb 2006, 22:34

Funny thing that, thats what I just said....

FunkyMunky

10th Feb 2006, 22:44

Funny thing that, thats what I just said....

I apologise if I misinterpreted your post, but it seemed like you were of the opinion that the aircraft would not fly :)

My mistake :)

Tarq57

11th Feb 2006, 07:33

UNBELIEVEABLE!

Yet strangely irresistable.
Friction on axles/bearings is a tiny percentage of the net force trying to prevent an aircraft accelerating. (Which is, mainly, mass)
True, on many light singles, you need a burst of power to start moving, then ground idle will usually suffice. This is due more to the tyres, which are slightly flat at the bottoms, and is called rolling resistance. Once they've started turning, rolling resistance rapidly decreases. A lot.
For the conveyer to respond to the aircraft movement (which of course, it will, at pretty much normal acceleration) it would have to rapidly spin up to close to infinity. Some conveyor! I suggest most structures wouldn't be up to the challenge. But, hypothetically (gee, you think?) if one could, tyre resistance might just be caused to increase sufficiently to prevent the engine thrust from accelerating the aircraft to takeoff speed. This would be accompanied by startling noises of tyres blowing out in overspeed, and chunks of rubber scattering like missiles. Best viewed from afar.

distaff_beancounter

11th Feb 2006, 12:45

Hi Folks

I am still not convinced either way on this one, so I have just looked at the video again.

It appears that the strip of paper being used as the 'conveyor belt' is being moved right to left, thus moving in the same direction as the skate-board wheels' rotation.

If so, wouldn't this help the skate-board 'aeroplane' move left to right, instead of opposing it?

D.B. - now terminally puzzled! :confused:

J.A.F.O.

11th Feb 2006, 14:57

DB

I'm confused, too. To contradict my previous post it seems that, sadly, I do care.

Before anybody thinks they have to point it out I know that an aircraft pulls or pushes itself through the air, not along the ground. I know that the thing that makes aeroplanes fly is relative airflow over the wings but my, probably somewhat befuddled, thinking went thus:

1. Aircraft in contact with conveyor belt.

2. Aircraft pulls (or pushes) itself forwards through the air

3. Coveyor belt moves backwards therefore opposing this forward motion

4. Return to 2.

So, the aircraft never has any motion through the air because every time it moves forwards the belt moves it back. It never has enough airspeed to leave its contact with the belt, it never flies. I don't give a stuff about wheel friction or any other nebulous nonsense, it just doesn't move itself through the air because each time it tries it's moved backwards.

Probably a load of rubbish, though.

Can't understand any more than that - might just have to go rotary then I don't care what the bloody conveyor belt does.

distaff_beancounter

11th Feb 2006, 18:07

J.A.F.O.

Thanks - I now entirely agree with you - even though I am not sure what it is that we agree about! ;)

Tarq57

11th Feb 2006, 22:13

J.A.F.O
How does the conveyor belt move the aircraft backwards?

FunkyMunky

11th Feb 2006, 22:51

3. Coveyor belt moves backwards therefore opposing this forward motion

J.A.F.O., The conveyor belt does not oppose the forward motion, apart from the negligible effect of friction within the wheel bearings easily overcome by the power of the engines, as seen every day when aircraft taxi on stable ground!

Hold a toy car in the air then press it onto a moving treadmill such that the wheels spin up, but the car does not move relative to the air or the fixed ground outwith the treadmill. You are holding the toy car in a fixed place, with the only effect being that the treadmill causes the wheels to spin.

Now use your hands to move the toy car "up" the treadmill, in the opposite direction to that at which the belt is moving.

What are your hands doing? They are applying an external force to the car, NOT RELATED to the moving belt system, in order to move it relative to the air. In this case, the reaction is between your hands and the surfaces of the toy car. This is the EXACT SAME FORCE the engines on an aircraft would provide, with the reaction in that case being between the air (every bit as "external" to the system as your hands), the engines and their exhaust.

Does anyone HONESTLY believe that they will not be able to push a simple toy car up a moving supermarket checkout belt, or exercise machine? The principle is almost exactly the same as that of the aircraft on the conveyor belt runway as far as I can see, and it works fine! The aircraft would fly.

Tex37

11th Feb 2006, 23:01

After a non-alcohol induced think I have to say that what I posted earlier was Bo**ocks!

With the exception of the nominal friction of the gear - of course it would move forward - unless the conveyor was capable of infinitive speed which would of course set the gear on fire!

The prop is biting the air and the air is not conneted to the ground - so apart from spinning the wheels, nothing would change!

Coat is on - left the building!

J.A.F.O.

12th Feb 2006, 11:42

J.A.F.O
How does the conveyor belt move the aircraft backwards?

Because the aeroplane is sat on the conveyor belt.

If your aeroplane is only ever stationary or moving relative to air and not ground you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.

Or, is that what tie downs are for?

:hmm:

FunkyMunky

12th Feb 2006, 14:43

you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.

That's a perfectly fair point - but becomes irrelevant once the engines have started pushing against the air!

If you sit the toy car/plane/whatever on the treadmill/conveyor belt/whatever,
and turn it on, the vehicle will move back with the treadmill, like you say.

Why? Because friction within the wheel bearings inhibits them from spinning up and allows the force on the wheel by the conveyor belt to be "transferred" to the entire aircraft.

This frictional force is very, very small, but clearly evident - on normal ground it may take more power to get an aircraft moving initially than just to taxi along once already moving. The engines, in providing slightly more power, have overcame the small force of friction within the wheel system, and allowed them to spin!

This is exactly what happens when the conveyor belt is moving and the engines are applying force in the opposite direction. The conveyor belt "tries" to move the aircraft backwards, but the only way it can do this is through the small amount of friction in the wheel bearings. The engines have already overcame this friction, as they would when taxying on normal ground, so the net effect is that the engines push the aircraft forwards relative to the air, whilst the conveyor belt simply spins the wheels faster than they normally would (as a component of both the forwards motion of the aircraft and the rotational point of the wheels, and the backwards motion of the conveyor belt).

J.A.F.O.

12th Feb 2006, 15:04

Funky

You've been very patient but if you don't stop explaining it I might be forced to admit that I was wrong and that - given a long enough conveyor belt for the aircraft to gain sufficient airspeed - the aeroplane may just fly, perhaps.

I won't be on Pprune for a little while so I'll leave you all debating the length of conveyor belt needed for the average light aircraft and working out effective groundspeed on take-off.

I might then admit that the emperor has on a pair of socks at least.

mad_jock

12th Feb 2006, 15:30

J.A.F.O

The belt length would be virtually the same as the normal takeoff run on a runway.

I am considering emailing the production company that does the telly programs on weird science experiments suggesting it.

Unfortunatly i don't think it would take up much air time though for the setup costs.

You could have a a conveyer at an open air mine and a remote controlled aircraft. With the belt turned off do a take off measure it. Then turn the belt on. These things run at way more than Vr for a remote controlled aircraft. And then do it again and compare the TO distance.

And if it helps imagine that the aircraft doesn't have any gear at all. Its held on 3 skids with no wheels. The skids would be equivalent to wheel speed of zero so the belt speed would be zero. Would you expect a skid under carrage plane to take off?

This would be equivalent to a snow kitted plane like the antartic survey twin otters.

And i also have read a story about a high performance fighter who's throttles stuck on a high powed ground run. With the hand brake on and the full pressure of a 16 stone bloke who doesn't want to go flying on the toe brakes. It still managed to build up enough speed that take off was going to happen so he took the brakes off so the tyres wouldn't blow and became airbourne. Because the aircraft was in maint the bang seat was US with rockets removed. I believe he managed to get the aircraft back safely and got an award for getting it back in one peice

ThePirateKing

13th Feb 2006, 12:00

J.A.F.O
you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.

Isn't that why we're all taught to park facing north or south? :suspect:

TPK:ok:

CBLong

13th Feb 2006, 15:42

Excellent thread. I too found the question misleading and originally jumped to the wrong conclusion. I agree that, as described, the aircraft would take off normally. However, it's interesting to wonder where the question came from, and whether it was deliberately worded to be a trick question, or is it more likely the person who wrote didn't know what they were on about.

I guess it's similar to how setting a crossword is harder than solving one.

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

The bit about the conveyer going at exactly the same speed in the other direction is clearly meant to mislead the reader into thinking that the two speeds cancel out in some way - if not, why "exactly" the same speed?

The question setter seems to be deliberately trying to make you visualise a situation analagous to a runner running on a treadmill, though this could never happen in practice.

Another point which may not have come across clearly enough in all the previous posts is this - imagine the aircraft sitting on the conveyor, engines off, brakes off, conveyor off. Now, the conveyor starts moving at, say, 20mph backwards. The aircraft will *not* suddenly accelerate backwards to keep pace with the conveyor - assuming frictionless wheels, it wouldn't move at all; in practice, it will sit still, the wheels will spin up to the normal 20mph rpms, and there will be a small frictional force from the tyres which will slowly accelerate the aircraft backwards.

Now then - downwind turn, anybody?

:eek:

TheKentishFledgling

13th Feb 2006, 16:12

Just to remind some of the original question...

This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)

So we are assuming the treadmill CAN keep up with the speed of the a/c.

It won't fly!

tKF

CBLong

13th Feb 2006, 16:48

tKF,

Agreed, if there were anything acting in the system to prevent the aircraft moving forward, it could never fly. The problem with the question is that there's nothing in the described system that will prevent the aircraft moving forward. The 'trick' in the question is that the reader is tempted to assume that the conveyor moving backwards will stop the aircraft moving forward - but the question doesn't actually say that explicitly, and it couldn't happen in practice.

This is all assuming low / zero friction at the wheels / tyres, of course - if the pilot is lazily resting his feet on the toe brakes then, of course, the aircraft will be dragged backwards with the conveyor.

TheKentishFledgling

13th Feb 2006, 16:53

Again, looking at my quote from the original question.

If the speed acting against the motion of the aeroplane (ie the treadmill) is the same as the speed of the a/c (as the question states), then the forces are equal - therefore it has no forward speed - therefore it can't fly!

tKF

OVC002

13th Feb 2006, 16:58

You are sitting in Tipsy Nipper, situated on the aforementioned conveyor. The conveyor starts to move. The aircraft will move with it because its wheel bearings are not frictionless. An observer at the end of the conveyor tosses you a slightly elastic rope which is secured to the ground. If you hold on, as you reach the end of the slack in the rope you will slow down relative to the conveyor. You start to pull yourself towards the end of the belt. The conveyor speeds up to oppose you. This is irrelevant, you will reach the end of the conveyor very shortly, because the thrust system is entirely unconnected to the conveyor and the only opposing force other than the normal weight/inertia of the aircraft is the friction of the wheel bearings. The force of pulling on the rope is equivalent to the thrust of the engine/prop.
If a man can overcome the conveyor slowly, the engine will have no problem in doing so quickly.

IMHO the aircraft will fly.

Unless, of course, the question really requires us to consider a real world physical property i.e. friction in bearings, together with a physical impossibility i.e. a conveyor belt capable of almost instant acceleration and practically infinite speed. In which case the conveyor will simply accelerate to the point where the drag from the bearings will equal the thrust from the power unit.

CBLong

13th Feb 2006, 17:06

From my point of view, you're mixing up the terms 'speed' and 'force' a bit too loosely. The speed of the treadmill doesn't 'act on' the aircraft - speeds don't act on anything. It isn't valid to say that, as the speeds are equal, the forces are equal.

I guess it all comes down to how each reader visualises the friction component. From my A-level maths and physics, I automatically discount friction when considering this sort of problem. In theory, you're 100% correct - if the aircraft's wheel bearings produced loads of friction, or if the brakes were dragging, then you could have a situation where all the thrust of the engines was required to overcome the drag of the brakes, just to hold the aricraft at zero airspeed. That's definitely an assumption too far, based on the question, though.

FunkyMunky

13th Feb 2006, 22:43

Bear with me I'm drunk, and have been for most of my postings on this thread

Kentish,

If the speed acting against the motion of the aeroplane (ie the treadmill) is the same as the speed of the a/c (as the question states), then the forces are equal - therefore it has no forward speed - therefore it can't fly!

The speeds may be the same (opposite in direction but equal in magnitude velocity) but the forces are NOT equal and are not balanced!

Why? Because the forces are not being applied in the same way.

The "force" from the conveyor belt is only one of two things.

If the aircraft is stationary on the belt (i.e. the engines are off/idling), then :-

1. A force occurs between the surface of the tyre and the surface of the belt, due to friction. When the belt moves, this force will always attempt to spin the wheel, assuming the wheel is parallel to the belt. If the belt is moving slowly enough, without any abrupt acceleration, and without any force from the engines, then :-

2. The force between the belt and the tyre is "transferred" as a result of the very small amount of friction within the wheel bearings to the whole of the aircraft. This results in the aircraft moving slowly backwards with the belt. This will only happen if the belt accelerates slowly enough as not to overcome the friction present within the wheels and their axles.

As soon as the engines are throttled up:-

1. The friction within the wheel bearings/axles is overcome when the force between the engines and the air is sufficient. This MUST happen, otherwise aircraft all over the world wouldn't be moving around on the ground under their own power and rolling on their own wheels!

2. Because the friction within the wheels has been "overcome" by the force of the engines acting forwards (the friction still exists, but it is small enough compared to the force applied by the engines to be irrelevant now), there is no way for the frictionary force between the belt and the tyre to be "transferred" to the rest of the aircraft. The conveyor belt now exists solely to spin the wheels of the aircraft, as the engine force has "kick started" the spinning motion of the wheels.

I havn't quite completed Physics A-Level (Advanced Higher up here, way up yonder cold Scotland) and I'm quite intoxicated so I'm probably wrong and some all-empowering might of higher wisdom will come to disprove me later :ok: But...I think it will fly! :rolleyes: :O :O :D

By the way, Yorks.PPL posted a relatively simple demonstration of why the plane probably will fly earlier!! It can be seen at http://videos.streetfire.net/player.aspx?fileid=35E964D9-38DB-4EFD-BE8D-D6BA1A43A06B

For those not convinced by the simplicity of a sheet of paper, an electric fan and a skateboard, you could always try the toy car + treadmill idea, or stick a working model aircraft on a travelator...if you care such! :8 :ok: