Principles of flight?

[AirNZ]

If anybody is still having trouble, just elaborate on pidge's rolling road dyno example. Imagine instead of being on a giant conveyer belt, the plane is on top of three rolling road dynos (one for each set of wheels assuming the plane has three sets of wheels).

Each one spins backwards as the planes engines create thrust. The wheels will spin forwads in reaction to the how fast the thrst should be pushing the plane forward.

Can the plane thrust itself forward off the dynos??? Of course it can.

To say that a dyno is a bad example in this case because the wheels sit inside the rollers is missing the point. If you need to, imagine a perfect dyno where you could perfectly balance the lane on top of a single perfect roller as in RomanV's drawing.

[RedMist]

Adamal, you really want to read those nine pages.

AirNZ, there is the rub. In order to get forward motion there must either be disparity between the wheelspeed and conveyor reverse. Or the wheels must skid.

Lets take dynos as an example. If wheelspeed matches dyno speed the vehicle will never ever climb out of the dynos. Because in order to do so wheelspeed has to be greater than dyno speed. So you accelerate using thrust the wheels attempt to move, the dyno reacts instantaneously and reverse rolls, you instanatly accelerate both wheels and dyno to have enough wheelspeed and friction on said spindles and bearings to counteract the thrust. To climb out of the dynos is to ignore the constraints of the question posed as the wheelspeed is greater than the dyno (conveyor) speed.

I think the magnitude of the thrust is possibly the issue. Lets think of a big fan, just enough to get a car rolling. If I apply thrust and I roll the road backwards what happens? the wheels accelerate more than is possible with the simple fan, but at some point the friction in either the road surface to tyre contact or bearing surfaces to counteract that small thrust.
What happens if we slightly increase the fan power. The speed at which the wheels move and consequently the dyno rollers move increases, and the frictional forces become greater to the point where we dont acclerate any more.
Lets strap a jet engine to it.... same thing... greater speed.
Okay solid fuel rocket.... same thing.... greater speed.

More thrust... greater wheelspeed.... greater conveyor speed... until the wheels slip.

[RedMist]

So if the plane is moving forward at all, the belt is not doing it's job. Which according to the question can't happen, because the speed always matches.

That's a problem right there, because we're working off a falsehood.

Dead right! But unfortunately about as realistic as a conveyor the length and width of a runway. Its the constraint of the proposed question, for wheelspeed / conveyor disparity the question needs to be worded differently... .but then it wouldnt be such a difficult task to answer and there wouldnt be 10 pages on it already.

[RedMist]

Treat the conveyor belt as one gear, the wheel as the other.

Meshed gears rotate in opposite directions, correct? If the wheel rotates anti-clockwise, the converyor belt will "rotate" clockwise, staying in mesh.

Beautiful example. If both cogs are turning, in opposing directions at exactly the same speed can one gear rotate around the other? Because thats what you are stating in the plane instance.


You have a set containing the numbers 1 to 9 {1,2,3,4,5,6,7,8,9)}
Which numbers in that set are divisible by 3?
Why?[/quote]
Simple. All of them. You didn't state you required a whole number.

[AirNZ]

Two further examples with the dyno, and why wheelspeed is irrelevant.

1. Imagine the plane is already in the air with the landing gear down. It's travelling at 100km/h and has a dyno strapped to each wheel. Will spinning the wheels on the plane backwards magically cause the plane to stop moving forward and drop out of the sky because the dynos spinning the wheels backwards cancel out the thrust provided by the engines?


I don't think it would fall, but feel free to correct me with good enough reason.

2. Imagine the plane is strapped to a solid enough set of dynos for each wheel on the ground before takeoff. Provided it could create enough thrust to overcome the friction caused by the dynos being flat on the ground, it could still take off, no matter how fast the dynos are spinning the wheels backwards right?

I still don't see how spinning the wheels backwards counteracts thrust, when the wheels spin freely and independently of the thrust provided by the engines.

In any case, I think it's been shown that so long as the wheels are in contact with the rolling belt, they must be travelling at the same speed as the belt, as can be shown by a freeze frame at any given moment.

As for the cogs example, if you're looking at one cog going around another cog, you see it that way because of your point of reference. In reality if you can detach yourself from the way we nomally view things with our eyes from any one given position, you would see that that one cog rotating around another is actually, two cogs rotating at identical speed around each other.

If you don't believe me, imagine instead of two cogs just two wheels with a sheet of paper between them. Each of the wheels has ink around it's circumference. Insert the paper between them and not only does the paper not rip itself up, but the lines drawn by the ink on opposite sides of the paper are exactly the same length, indicating that both wheels (or cogs) are in reality travelling at the exact same speed the whole time.

The revolutions per minute of the two wheels (if they were different sizes) will be different, but at their circumference they are still travelling at exactly the same speed. If we take that meaning of matching speed the belt always travelling in the opposite direction at the same speed as the wheels unless, as has been said before, there is slip.

If we take the meshed gears idea and apply it to RomanV's drawing with the two wheels, it helps show that at any given moment the belt and wheels can be shown to be perfectly [/b]meshed even while the plane is moving forward.

[V8MOFO]

Yea, I have just had an epiphany. Thinking of the toy car on the tredmill... Think about it, If you believe that pushing the car ( by hand, no power going to the wheels ) along, the only way it would actually move forward relative to the ground would be if the wheels were moving faster than the belt. If you add more thrust ( more push! ) and the car did move, the wheels would slip, do a burnout, do a skid!. Thus failing to match the conditions of the original setup.
If it were all possible, and the wheel did slip, the belt would have to 'slip' at the same time, and strange things would happen, which I dont know.
Like I said early, maybe the belt would accelerate to infinity? The only way to properly measure it would be to change speeds in the differences of a few metres per second ( for the plane ).
And as the original question said ''as wide and as long as a runway''. A place can't afford to lose any speed or momentum with the length it is given.

[EVOGTX]

I have the answer! Its a Harrier jump jet and takes off vertically! They never specify what sort of plane it is. So there.

Problem solved

[RomanV]

Yea, I have just had an epiphany. Thinking of the toy car on the tredmill... Think about it, If you believe that pushing the car ( by hand, no power going to the wheels ) along, the only way it would actually move forward relative to the ground would be if the wheels were moving faster than the belt. If you add more thrust ( more push! ) and the car did move, the wheels would slip, do a burnout, do a skid!. Thus failing to match the conditions of the original setup.

Unless.... The belt doesnt move at all.

eg. The speed of the car, relative to the (not moving) belt, is 10kph to the east.

The speed of the belt, (and the rest of the world for that matter) relative to the car, is 10kph to the west.
In other words, the belt has MATCHED the speed of the wheels, and in the opposite direction.... Criteria satisfied.

The speed of the wheels and the belt are matched.... 10kph relative to each other.

[RomanV]

Lets take dynos as an example. If wheelspeed matches dyno speed the vehicle will never ever climb out of the dynos. Because in order to do so wheelspeed has to be greater than dyno speed. So you accelerate using thrust the wheels attempt to move, the dyno reacts instantaneously and reverse rolls, you instanatly accelerate both wheels and dyno to have enough wheelspeed and friction on said spindles and bearings to counteract the thrust. To climb out of the dynos is to ignore the constraints of the question posed as the wheelspeed is greater than the dyno (conveyor) speed.

This is of course, unless the dyno doesnt roll about its centre.... What if it rolls on the tangent of the wheel? (The line on the pic)
It doesnt state that the conveyor rolls around a centre line, like you are implying.



eg... Imagine that the dyno is the 'imaginary' wheel, and both the 'real' and 'imaginary' wheels rotate along the line, as opposed to around their centres.

Foward motion is obtained, both of the wheels travel at exactly the same speed, one in the opposite direction of the other.

The 'line' doesnt move, which would be the equivilent of hard ground, or a conveyor that is stationary.

[pidge]

Beautiful example. If both cogs are turning, in opposing directions at exactly the same speed can one gear rotate around the other? Because thats what you are stating in the plane instance.

You are assuming speed of rotation of the wheel is directly linked to the speed of the wheel. The wheel is able to rotate freely, independant of the speed at which the wheel itself is moving.

Take a matchbox car and a sheet of paper. Roll the car over the sheet of paper. The speed of the wheels = speed of the car, relative to the ground and to the sheet of paper, and the rotational speed of the wheels is the same speed of the wheels and car.
Now hold the car car still and pull the sheet of paper. Relative to the ground, the speed of the wheels and the car are still the same (and zero), but the rotational speed of the wheels is the same as the paper.

Now push the car while pulling the sheet of paper (at the same speed - hey, this sounds familiar...). The speed of the car and wheels, relative to the ground are the same, and opposite to the speed of the sheet of paper. The rotational speed of the wheels is same as relative speed of the
sheet of paper and car, twice either speed.

The speed of the wheel is determined by the speed of the plane. The speed of rotation of the wheel is determined by the relative speed of the plane and the converyor belt surface.

Oh, and go look up planetary gears - where one gear rotates about another... found in automatic gearboxes.

You have a set containing the numbers 1 to 9 {1,2,3,4,5,6,7,8,9)}
Which numbers in that set are divisible by 3?
Why?

Simple. All of them. You didn't state you required a whole number.

Bravo! Now, that question was asked in a 5th form certificate exam some time ago, without the "why?" bit. How many people got it "wrong" by answering it correctly as you did? (at least one didn't - my brother was marking that guy's/gal's paper, and had an argument with the head marker about it...)

[snwtoy]

Here's another one:

You have a set containing the numbers 1 to 9 {1,2,3,4,5,6,7,8,9)}
Which numbers in that set are divisible by 3?
Why?

The correct answer is there are 2 answers:
The 5th form level, where it is implied the answer must be a whole number
and
The 6th and above form level, where such implications are swiftly discarded.

[Mr. Mainstream]

my brain hurts from reading that and i wont be able to sleep for day


bring back pervert

[pidge]

my brain hurts from reading that and i wont be able to sleep for day

Go read up on General Relativity and String Theory. Now THATS a real mind-scrambler.

e.g. read the article on de Sitter Universes at Wikipedia, and either feel your brain try to escape or your eyes roll up into your head...

[blitza]

*Skips 9 pages of stuff he can't be bothered reading*

Too many concerning factors if you ask me.

One of the biggest is the size of the leading edge of the wing. The larger the curve of the leading edge effects the amount of 'lift' that can be created by the wing. The down side is that this will reduce the planes top speed, but we're not concerned about this here.

One thing is that in this situation, the runway is only as long as it is wide. If we're assuming that the width of the runway in question is the same as say, Auckland International, then you're probably not going to be able to take off in ANY plane (Except my dad's Zennith Air STOL701 Microlite ) unless the rate of acceleration is increadible. (When you consider that a 747-400 is about as long as a runway is wide!)

WTF??

I always thought lift charistics were dictated by the chord/span/rib ratio, but then I wouldnt know..........




TOOT '06?

[V8MOFO]

*Skips 9 pages of stuff he can't be bothered reading*

Too many concerning factors if you ask me.

One of the biggest is the size of the leading edge of the wing. The larger the curve of the leading edge effects the amount of 'lift' that can be created by the wing. The down side is that this will reduce the planes top speed, but we're not concerned about this here.

One thing is that in this situation, the runway is only as long as it is wide. If we're assuming that the width of the runway in question is the same as say, Auckland International, then you're probably not going to be able to take off in ANY plane (Except my dad's Zennith Air STOL701 Microlite ) unless the rate of acceleration is increadible. (When you consider that a 747-400 is about as long as a runway is wide!)

WTF??

I always thought lift charistics were dictated by the chord/span/rib ratio, but then I wouldnt know..........




TOOT '06?

If you read the question again. It states that the belt is as wide and as long as the runway. So a normal runway with a travelator over it.

[RedMist]

Lets take dynos as an example. If wheelspeed matches dyno speed the vehicle will never ever climb out of the dynos. Because in order to do so wheelspeed has to be greater than dyno speed. So you accelerate using thrust the wheels attempt to move, the dyno reacts instantaneously and reverse rolls, you instanatly accelerate both wheels and dyno to have enough wheelspeed and friction on said spindles and bearings to counteract the thrust. To climb out of the dynos is to ignore the constraints of the question posed as the wheelspeed is greater than the dyno (conveyor) speed.

This is of course, unless the dyno doesnt roll about its centre.... What if it rolls on the tangent of the wheel? (The line on the pic)
It doesnt state that the conveyor rolls around a centre line, like you are implying.



eg... Imagine that the dyno is the 'imaginary' wheel, and both the 'real' and 'imaginary' wheels rotate along the line, as opposed to around their centres.

Foward motion is obtained, both of the wheels travel at exactly the same speed, one in the opposite direction of the other.

The 'line' doesnt move, which would be the equivilent of hard ground, or a conveyor that is stationary.

Great example.

Okay, now both wheels rotate at exactly the same speed. They remain perfectly vertical with one on top of the other, the top one will NEVER accelerate down the line without the other one directly below it.
However that relates that wheelspeed to another wheelspeed, not a conveyor. So wrap the line around the bottom wheel, and fix that wheel to the ground, and you now have a conveyor. And now the bottom wheel is fixed wheelspeed = - conveyor speed. So why now does the top wheel out accelerate the bottom wheel?

It simply doesnt. No acceleration, no forward movement.

[RedMist]

You are assuming speed of rotation of the wheel is directly linked to the speed of the wheel. The wheel is able to rotate freely, independant of the speed at which the wheel itself is moving.

Actually completely the opposite. I assume the speed of the rotation of the wheel or wheelspeed, is completely independant of the speed of the wheel in relation to ground, or groundspeed.

Take a matchbox car and a sheet of paper. Roll the car over the sheet of paper. The speed of the wheels = speed of the car, relative to the ground and to the sheet of paper, and the rotational speed of the wheels is the same speed of the wheels and car.

Agreed, however you seem to be changing the definition of terms with every example. In this example you relate wheelspeed, groundspeed and conveyor speed as three seperate quantifiable measures. Which they are.

Now hold the car car still and pull the sheet of paper. Relative to the ground, the speed of the wheels and the car are still the same (and zero), but the rotational speed of the wheels is the same as the paper.

In this instance wheelspeed no longer exists. Are you saying a spinning wheel has no speed? You just stated a spinning wheel = 0. Then you introduce a new variable, rotational speed. Now I gather you believe rotational speed to be only the rotational component of the speed of the wheel, the other being distance from a point? However if we already have wheelspeed, groundspeed and direction (which we have), given the proviso of no slip we can calculate rotational speed. ITS WHEELSPEED.

Now push the car while pulling the sheet of paper (at the same speed - hey, this sounds familiar...). The speed of the car and wheels, relative to the ground are the same, and opposite to the speed of the sheet of paper. The rotational speed of the wheels is same as relative speed of the
sheet of paper and car, twice either speed.

In this instance you ignore wheelspeed all together and take groundspeed as your point of reference. If groundspeed vs conveyor belt speed was the question asked, which it is not, then you are correct. But was NOT the question posed.

The speed of the wheel is determined by the speed of the plane. The speed of rotation of the wheel is determined by the relative speed of the plane and the converyor belt surface.

Again you state that a spinning wheel has no wheelspeed.

Oh, and go look up planetary gears - where one gear rotates about another... found in automatic gearboxes.

I know perfectly well what a planetary gear is, they are also found in some differentials. I fail to see your point, however I'll relate it to the example above. Are you stating that a spinning but stationary cog such as those in a gearbox has no cogspeed?

[RedMist]

Yea, I have just had an epiphany. Thinking of the toy car on the tredmill... Think about it, If you believe that pushing the car ( by hand, no power going to the wheels ) along, the only way it would actually move forward relative to the ground would be if the wheels were moving faster than the belt. If you add more thrust ( more push! ) and the car did move, the wheels would slip, do a burnout, do a skid!. Thus failing to match the conditions of the original setup.

Unless.... The belt doesnt move at all.

eg. The speed of the car, relative to the (not moving) belt, is 10kph to the east.

The speed of the belt, (and the rest of the world for that matter) relative to the car, is 10kph to the west.
In other words, the belt has MATCHED the speed of the wheels, and in the opposite direction.... Criteria satisfied.

The speed of the wheels and the belt are matched.... 10kph relative to each other.

Bloody good example and a good concept one I hadn't thought of ! If we run the aircraft at a tangent to the conveyor. Wheelspeed can match - conveyor speed but the aircraft will move (in reverse) until it slips off the side of the belt. Good old vector mathematics.
In your instance the conveyor speed would be 10kph in a southerly direction so the effective tangental direction would be south east.

However I still doubt the plane will take off, in reverse, for a short distance.

[Ako]

Here's how I see it, after pondering for waaay too many hours.





The dyno example can confuse you a bit... But look at it this way. The car on the dyno = the plane, the dyno = the conveyor, and the guy pushing the car from behind = the planes engines.

Even if random guy pushes the car, the dyno WILL SPEED UP TO MATCH THE NOW INCREASED SPEED OF THE CARS WHEELS. For it to get pushed off the dyno, then the rules of the conveyor are broken - its not matching the speed of the wheels.

Now, to put this into the right situation again.


The plane is sitting there. Not moving, at all. The plane goes full throttle - now what the hell happens? Damnit I've just confused myself. Okay, full throttle means the plane will move forwards. There is nothing stopping its progress, apart from friction through the wheels/ground. They aren't actually firmly holding it back though.

But, the wheels will just speed up to say, 300kph, normally. The conveyor will match this speed, in the other direction - so the wheels will be going 600kph all up, the conveyor doing 300kph in the other direction. It won't get any faster, because the plane will take off then.

There's nothing STOPPING the plane from moving forwards. Like has been said, the wheels could spin at 100,000,000rpm for all the rest of the plane cares, it will still move forward unless something actually forcibly stops it.



Hang on, thats way too straightforward.

[RedMist]

Indeed it is too straightforward.
You got it right for the dyno example, but broke the rules for the conveyor example

Wheelspeed does not match negitive conveyor speed.
At 600kph the conveyor will be doing -600kph.
at 10,000kph the conveyor will be doing -10,000kph IE 0 groundspeed.