Will the plane take off?

[Bigglesworth]

For you Biggles because you're slow to agree with me, it's now $150. I'm considering offering you money if you'll finally realise that the aircraft WILL take off. I'm fresh out of ways to explain it, other than to get you to watch the youtube video posted earlier which explains it all.Try thinking about my earlier posts. You have a treadmill in a house with an engine stand on it and a 6 Cylinder Jabiru engine with prop. Do you REALLY think that the engine and prop won't move if they are at full power and the beefed-up treadmill is running flat out?

I follow all the physics easily (I got 90 something in HSC physics only a couple of years ago).

 

The fact is that it will take off if:

 

The speed of the conveyor is linked to the speed of the plane past the scenery which most people think it is, but that is a waste of time.

 

0r, if the conveyor belt is a practical one which isn't fast enough to destroy the wheels (such as in the video)

 

My point is that the conveyor belt DOES have an effect on the aircraft. But only if it is fast enough to destroy the wheel bearings, which, as w3stie points out, only needs to be about 200kts.

 

The video should show the plane at rest on the belt, then engine is on, plane rolls forwards and the belt speeds up until the wheels die and it brings the plane to a stop.

 

Then it can't take off.

 

<hand over the cash>

 

 

[Timm427]

This is the funniest argument ever - even funnier that myth busters had to disprove it.

 

1. Planes move by grabing air

 

2. Wheels spin as a result of that (infact the friction at the bearings in this scenario would be exactly the same as if you replaced the wheels with some that had half the circumference) (yes I know friction at the ground would increase with a smaller wheel I was just talking about the bearings)

 

3. If you want to stop a plane from moving forward you need to either

 

A. Lock it to the ground with the brakes or teather it to the hanger or

 

B. Sit it in a long tube and move air through the tube at the same relative speed that the Thrust less the drag would otherwise have propelled it forward.

 

If you choose to use option B dont forget to take the wings off because it will still fly and hit the top of the tube (also narrower tubes are cheaper).

 

 

[Guest brentc]

The video should show the plane at rest on the belt, then engine is on, plane rolls forwards and the belt speeds up until the wheels die and it brings the plane to a stop.

Then it can't take off.

It won't happen like that, because once the belt reaches 2mph as in the video, the aircraft will not be affected because the maximum friction provided by the wheel bearings has been reached! No conveyor in the world could go fast enough to overcome some quality bearings and a solid wheel.

 

It will fly NO MATTER WHAT!

 

You are suggesting that the aircraft will sit there with a conveyor belt running under it at 200 knots. Correct, it will, BUT the aircraft engine will only be idling. Once power is applied to the engine it will take off and take to the skies leaving you on the ground wondering what happened The conveyor could be moving at 1,000 knots, however the plane will still accelerate off and fly.

 

 

[Guest airsick]

I think what Biggles is saying is that the wheels would fly apart when they hit 200kts and thus leave the plane stranded on the runway.

 

It is probably true but I haven't flown an aircraft that requires 100kts (200/2) takeoff speed so it is a bit of a moot point (and clearly not in the spirit of the question).

 

He just wants to come up with a half baked reason as to why you should give him the cash. :)

 

 

[Bigglesworth]

Short question:

 

Have all of you who disagree with me, studied the equations I gave earlier to back up my claims?

 

Of course, in a real world situation the plane will take off. Thought about it for 2 seconds to realise that. Then wondered where the catch was.

 

But we don't live in the real world. This is the internet where Geeks rule supreme.

 

So: we have a convyor belt trying to halt any thing on it. Capische?

 

If anything moves, the belt speeds up to try to stop it. Catfish?

 

If the belt can't stop it (such as an aeroplane) it continues speeding up until it reaches infinity. THIS HAPPENS. we are online now.:big_grin:

 

Now, can your plane handle a runway moving under it at infinite knots?

 

Staying in the field of pure mathematics,

 

To take off from a runway moving at infinite knots, the plane must move over the runway at infinity plus about 60kts. Which is not mathematically possible.

 

So until someone starts fooling around with time dilation for when the speed reaches 3x10`8m/s (speed of light) that is the scenario.

 

I really wanted to find a way that I could solve it using integral calculus, but that doesn't fit .

 

 

[DrDexter1975]

Ummm...Bigglesworth

 

The conveyer simply matches the speed of the wheels - it simply won't be going fast enough to do any damage once the aircraft rotates and leaves the belt at 60ish kts!!!????

 

Sorry Mate - the theory doesn't beat this puzzle.

 

 

[ab0767]

The plane will actually fly.

 

The clue is that the conveyer belt will travel at the same SPEED as the plane, therefore the plane must be moving creating airflow over the wings.

 

If the plane in fact stayed stationary it's speed would be zero, and the conveyer would stop.

 

The plane accelerates - as it moves FORWARD at 1kn the belt starts and goes 1kn in the opposite direction and the wheels go 2 kn. The plane is still going forward at 1kn.

 

When the forward speed of the plane reaches take off speed, the plane takes off. The conveyerbelt is only affecting the speed of the wheels.

 

It took a while to get it

 

 

[Bigglesworth]

The plane will actually fly.The clue is that the conveyer belt will travel at the same SPEED as the plane, therefore the plane must be moving creating airflow over the wings.

 

If the plane in fact stayed stationary it's speed would be zero, and the conveyer would stop.

 

The plane accelerates - as it moves FORWARD at 1kn the belt starts and goes 1kn in the opposite direction and the wheels go 2 kn. The plane is still going forward at 1kn.

 

When the forward speed of the plane reaches take off speed, the plane takes off. The conveyerbelt is only affecting the speed of the wheels.

 

It took a while to get it

Thats what I thought at first.

 

But what is the plane's SPEED?

 

If the wheels turn at 2kts, then its speed is 2kts over the belt, then the belt must also turn at 2kts, causing the wheels to turn at 3kts, belt speeds up........ etc.

 

Next time you are taxiing, and the wheels turn at 2kts, would you say your speed is 2kts? If you are on a conveyor belt and wheels at 2kts, whats the difference?

 

 

[ab0767]

The speed of the plane is relative to the airmass, which is stationary (hence the need for ASI). The belt speed and the wheel speed have nothing to do with the Planes speed. The thrust is applied to the airmass via the propellor, not via the wheels on the belt

 

 

[Admin]

Ok, I will get in on this and say as a true and unaquivable fact that the aircraft:

 

WILL TAKE OFF

 

now the fine print:

 

1. That the wheel bearings can take the speed of the conveyor belt

 

2. The aircraft is a Harrier Jump Jet

 

 

[Bigglesworth]

The speed of the plane is relative to the airmass, which is stationary (hence the need for ASI).

SAYS WHO??????????

 

where does it say that speed is relative to airmass?

 

And where does it say that the air is stationary for that matter?

 

The plane is still on the 'ground', and since when do you taxi on airspeed???

 

The velocity of the plane could be measured against the scenery/still air, BUT if that is the case, the conveyor belt is as useless as tits on a bull. It won't stop anything, whether it is wheel driven, or propellor driven or magnetic attraction or whatever.

 

FOR THE QUESTION TO BE OF ANY SIGNIFICANCE, 'SPEED' MUST BE MEASURED AT THE WHEELS. I.E. RELATIVE TO THE SURFACE THAT THE PLANE TRAVELS OVER.

 

And in that case, things go funny.

 

 

[hihosland]

Bigglewsworth did say

 

"""The velocity of the plane could be measured against the scenery/still air, BUT if that is the case, the conveyor belt is as useless as tits on a bull. It won't stop anything, whether it is wheel driven, or propellor driven or magnetic attraction or whatever."""

 

exactement !!!!

 

 

[Captain]

My head hurts.

 

 

[Admin]

My head hurts.

Well quick Capt...get it off the conveyor belt, cause there's a plane coming

 

 

[Yenn]

If the belt is going at infinity wouldn't the wheels be going faster, and if so infinity is not infinite, or is it?

 

 

[jordy]

what happens if the conveyer is sitting on the equator facing east?????

 

.........its already doing 1000mph towards ya >.......................

 

 

[eastmeg2]

Intersting point Jordy.

 

Then all you need to do is face west and face west and apply some brakes, assuming they don't melt, or just wait for your wheels to disintegrate and the resulting skid will accelerate you up to flying speed in a westerly direction, up to 500kts gauranteed.

 

Cheers,

 

Glen (Who also got 90 something % for HSC physics, first for physics in the school, then went and got an Engineering Degree).

 

 

[jordy]

Compounding the equation is the fact that we all are hurtling through space at approximately 66,638.2mph... maybe our IAS should stand for Indicated Atmosphere Speed... The conveyor seems rather insignificant now doesn't it.

 

Oh yeah the plane does fly. The only thing the afore mentioned insignifcant conveyor changes is ground speed and I've yet to meet a pilot who upon takeoff rotates at a certain ground speed.....

 

Just a few thoughts rattling around............

 

 

[jordy]

[ will accelerate you up to flying speed in a westerly direction, up to 500kts gauranteed.

 

Cheers,

 

Glen (Who also got 90 something % for HSC physics, first for physics in the school, then went and got an Engineering Degree).

 

That messes with the Drifters VNE of 80kts a bit

 

 

[Guest airsick]

If the belt is going at infinity wouldn't the wheels be going faster, and if so infinity is not infinite, or is it?

So we have a question about a conveyor belt that no one seems to be able to agree on despite the fact that there is a correct answer and now you want to add another degree of difficulty by discussing something that is still debated in mathematics circles today - infinity.

 

What is

 

:infinity: + 1?

 

Still infinity.

 

What is :infinity:* :infinity:?

 

Still infinity.

 

What is :infinity:^ :infinity:?

 

Ahh, now this is interesting. We have the concept of 'degrees' of infinity. Countable sets, uncountable sets, :aleph:0, :aleph:1, and so on.

 

But we digress. Cantor, a famous mathematician went insane (;)) trying to get his head around the concepts of infinity so let's not get too tangled up trying to think about it. ;)

 

The simple answer? Yes, the wheels, even if they are going faster than the belt which is travelling at infinite speed, are travelling at infinite speed as well.

 

Oh, did I mention that the plane will take off?

 

 

[eastmeg2]

Come on Biggles! There are a few Convergence & Divergence theorems in calculus that you can use to give answers for that last post, provided you can scribble a formula for it.

 

 

[Bigglesworth]

OK, you asked for it.

 

How about we slightly change this thread to a competition for best/most confusing mathematical proof?

 

I will pay the winner $100 provided I can use their equations to get the $150 off brentc ;).

 

I'll start thinking soon, I have gotten rusty on calculus actually.

 

 

[Bigglesworth]

Calculus

 

As I said, I am a bit rusty, and tired so this is a basic starter:

 

Take the formula for a/c speed past the scenery to be

 

f(x)

 

Now, for the a/c to speed up, it must accelerate, i.e:

 

f'(x)= z

 

Where z is the acceleration.

 

Thus

 

f(x)=zx +c

 

the constant can be disregarded since the movement of the plane is analysed from a rest.

 

So the speed of the a/c over the conveyor is given by

 

Vconv= zx+N

 

Where N is the speed of the conveyor in the opposite direction.

 

Thus, from the information in the question, the speed of the conveyor, N, can be found by:

 

N=zx+N

 

Solving for N

 

N-N=zx

 

0=zx

 

Hence z=0.

 

Thus the a/c starts at a rest situation, and undergoes NO acceleration, since that would violate the conditions of the question, or the laws of mathematics.

 

Thus the aircraft will not take off.

 

Catfish?

 

PS standing on the runway is fine, since the laws of math stop everything from moving. We'll write it on your headstone.

 

 

[Timm427]

What if the wheels were skis and the conveyer was ice:confused:

 

 

[eastmeg2]

Setting N=zx+N is artificial restraint of the equation, you won't slip that one past me. I was hoping you'd come up with limit f(x) as x approaches infinity = f'(x) with x=infinity. Or was it 0?

 

With ski's on ice there's no wheel distruction, then we can dispnse with the calculus and revert to z=f/m, sorry Biggles.