Okay, let’s put some sums to it:

Say the treadmill is running at 1m/s. You bowl a 3kg ball at 2m/s. so the bowling ball has kinetic energy of 6J.

But if the ball becomes stationary on the treadmill, what happens to that energy? It’s not gone into the treadmill – the treadmill is still going at the same speed. What’s happened to it?

But your model does not have the ball rotating, the 6J is sliding

Okay, imagine you roll the ball instead of bowling it – like those ramps they use for kids. Now it’s rolling – same difference.

Sure, but the energy is not 6J, you have rotational kinetic energy too

You do. So you go from 6J of angular kinetic energy and x rotational kinetic energy to zero angular kinetic energy and still x rotational kinetic energy. You’ve still lost the energy somewhere.

The same place you lose it when you roll a ball along a flat surface.

Are you aying that if you roll a ball down a slope and another down a sloed conveyor, the would both follow the same time- path?

you could in theory make it take off by putting a huge fan in front of it and blowing air over the wings, it would then take off from a standstill regardless of whether or not it was on a treadmill.

You could almost do that with a Feiseler Storch, 30m take-off with no head-wind:
https://en.wikipedia.org/wiki/Fieseler_Fi_156

Sorry, you can’t see the treadmill it’s just taken off from…

Are you aying that if you roll a ball down a slope and another down a sloed conveyor, the would both follow the same time- path?

No, because they’d have a different angular momentum.

But actually that’s a really good example – if you have the treadmill at an angle, will the bowling ball roll off the end?

It will eventaully, in fact you would need to continue to increase the speed of the onveyor just to keep the ball in place

Okay, now do the same thought experiment with something that has minimal angular momentum – a skateboard, say.

So imagine a skateboard on a sloped treadmill – will it roll off the end?

(Obviously there’s the limiting case, as with the airplane, where the treadmill runs at 1,000,000mph and everyone bursts into flame)

Like i said it is time dependent the conveyor would need to accelerate

Okay, so again we have the limiting situation where the only time the skateboard doesn’t run off the end (or the airplane doesn’t take off) is when the treadmill runs insanely fast.

Lads would it not be easier to just e-mail each other 😉

Eventaully, in early stages, the conveyor does not actually have to go that fast. We the reach the ral world limits of rolling resitance and axle resitance, which inguess is knowable

That would be awfully selfish Junkyard

In the video on the previous page the treadmill is moving slower than the plane’s wheels, we know this because it moves forwards. So yes, a plane can take off from a surface which is moving slower than it is, there’s a surprise. If the speed of the towed belt had indeed been equal and opposite to the speed of the plane it would have remained static and so not taken off. All that video showed was that a plane can out-accelerate a truck.
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anyway, as you were gents.

You have seen it with your own eyes, had the physics explained to you and you still want to deny it.

There is nothing I can do to convince you it will take off, though it will, as the evidence and theory shows

It can take off from that treadmill but not the one in my head. I think we are all defining the question slightly differently, which is what makes it so much arguing about it 🙂

Imagine a skateboard ona treadmill and me placing my hand on it …no matter what speed the treadmill goes the skateboard stand still and if i push it it goes forward- which you seem to conceptualise wrongly in your head as impossible

A plane just does this with an engine instead of my hand. the speed of the conveyor belt is irrelevant as it has no impact on the planes ability to propel itself forward just like the conveyor belt speed has no impact on my ability to move the skateboard

How hard would you have to push down on the board to hold it in place?
If you pushed the skate board on a static conveyor would it behave in the same way?
if you pushed the skateboard gently only, which end would you expect it to fall off?

How hard would you have to push down on the board to hold it in place?

You don’t push down, you push forward – well, hold it from moving backwards, which is the same thing – with a force equivalent to the wheel drag.

If you pushed the skate board on a static conveyor would it behave in the same way?

If you pushed the same skateboard, with the same force, on a conveyor that was now static, it’d move forwards at the speed the conveyor had been moving.

if you pushed the skateboard gently only, which end would you expect it to fall off?

How gently? If the force you push at is greater than the wheel drag, it’ll fall off the front of the conveyor. If it’s less, it’ll fall off the back.

It can take off from that treadmill but not the one in my head

This is the problem – your common sense is failing you.

Ben, your model doesn’t seem to take into account the time component

Comapring the static model you talk about pushing with the same force. How do these compare? One. Is a constant force

What time component?

It’s a simple balance of forces. The force pushing backwards is wheel drag. The force pushing forwards is your hand (or the aircraft’s engines). If the forward force is larger than the backwards force, the skateboard (aircraft) moves forwards.

The time component comes in because, i assume JY was talking about giving the board a ‘shove’ and so it moved forward and this looks different on a static and running conveyors. Holding a board in place is applying a constant force so simulating that on a conveyor would mean applying a continual force, not a shove or ‘impulse’

Furthermore your balance of forces model assumes a static drag, in fact what happens is that the wheels are spinning and the spin speed increases, with constant force. Like the ball rolling down a conveyor

Stop it now boys. Ben, I admire your dedication to education, but Charlie is just winding you up. It is painful to watch. I know, I could step away from the thread, but it’s like a car crash..

The time component comes in because, i assume JY was talking about giving the board a ‘shove’ and so it moved forward and this looks different on a static and running conveyors.

No, it doesn’t. In both cases, the board goes from zero speed in the rest frame to a speed V.

Or if you want to do it in the frame of the conveyor surface, it goes from a speed C (the conveyor speed) to a speed of C+V.

Furthermore your balance of forces model assumes a static drag, in fact what happens is that the wheels are spinning and the spin speed increases, with constant force. Like the ball rolling down a conveyor

Indeed – so the only way it can’t work is if the drag increases at a faster rate and to a higher level than the thrust of the engines. Since the engines have a lot of thrust, and the drag only comes from bearing and tyre resistance, the conveyor speed has to be truly colossal to stop the aircraft from moving forward.

Stop it now boys. Ben, I admire your dedication to education, but Charlie is just winding you up. It is painful to watch. I know, I could step away from the thread, but it’s like a car crash..

I know, but I’ve got a toddler lying on my other arm so I can’t move, and this is more entertaining than Peppa Pig 😉

Have we discussed whether on not the pilot has remembered to take the handbrake off. He probably hasn’t, they’re usually drunk. That might explain why he’s taxied the plane into baggage reclaim and is trying to take off from there.

If the conveyor belt is going at th espeed of light [ and therefore so are the wheels] and I push the skateboard will it move?

Nothing can go faster than the speed of light so I assume I am speeding the wheels up- would the wheels actually slow down as they were pushed forward?

Or if you want to do it in the frame of the conveyor surface, it goes from a speed C (the conveyor speed) to a speed of C+V.

so the plane would move at the speed caused by thrust plus the conveyor speed too?

NO

so the plane would move at the speed caused by thrust plus the conveyor speed too?

Yes, in the frame of the conveyor belt. If you were standing on the conveyor belt, the plane would appear to be moving faster because you’d be moving backwards.

But that’s not relevant to the aircraft taking off – assuming there’s no headwind, it’s the rest frame that matters.

Or if you want to do it in the frame of the conveyor surface, it goes from a speed C (the conveyor speed) to a speed of C+V.
so the plane would move at the speed caused by thrust plus the conveyor speed too?

So why are the skateboard and the plane different?

Now, you see what happened there? Even though JY and ben seem to agree about the outcome, they are completley opposed about the underlying physics

so the plane would move at the speed caused by thrust plus the conveyor speed too?
Yes, in the frame of the conveyor belt. If you were standing on the conveyor belt, the plane would appear to be moving faster because you’d be moving backwards.

Good, so we know that the thrust speed of cessna is about 100 km/h, because that is its take off speed. So with a conveyor at -100 km/h how fast would the plane be going in the rest frame?

Have we covered the treadmill powering the wheels to drive a propeller and making it take off that way?
[video]http://www.youtube.com/watch?v=7xL8gRJ5F6k[/video]

Nice one Ian. That shows that if we match conveyor speed and wheel speed then iit will not move. If that had wings it would still not take off. It will only take off if the plane moves faster than the conveyor, which negates the whole question, we know planes can take off from things which move slower than them, like runways for example.

Good, so we know that the thrust speed of cessna is about 100 km/h, because that is its take off speed. So with a conveyor at -100 km/h how fast would the plane be going in the rest frame?

100km/h

In the conveyor frame, it’d be going at 200km/h – but since the atmosphere is not moving with the conveyor, the conveyor frame doesn’t matter.

But hat is not thrust speed plus conveyor speed. Thrust speed plus conveyor speed is zero