The old airplane/treadmill revisited

[woodturner]

How is an airplane any different from a car when it's accelerating on the ground?

Similar, but different acting force. In the plane, the prop is pulling on the air - like the propeller of a boat pulls or pushes the water. In the car, the force is applied by turning the wheel against the resistance of the ground.

[JeffG78]

The reason pilots have to pull back on the stick is that they are pushing forward on the stick during the takeoff roll. They don't want the airplane to go airborn too soon and stall, so they use the stick to push the plane down toward the ground. When air speed is attained, they pull back a bit, causing the nose to lift, changing angle of attack on the wings and increasing lift under the wings.

That proves my point. They hold the plane on the ground, thus keeping a high load on the tires which proves that the engines can easily overcome the rolling friction of the tires and bearings. It's only after they change the angle of attack that the load is removed from the tires. By that time, the plane is travelling quite fast.

[Alex Franke]

By frictionless wheels, do you mean no friction with respect to the ground? So if I sneeze on the plane, it slides across the ground?

If so, then yes, because the airplane will move forward along the ground.

No, I mean that there is no friction in the wheel bearings. They still function as wheels (meaning they would still turn and not skid on the ground) but they are "perfect" wheels -- always perfectly round, and if you hold one up in the air and give it a spin, it will just keep spinning and spinning.

So if you sneezed on it with enough force to get the plane moving in the first place, it would keep moving. (AHHH-CHOO!)

[woodturner]

No, I mean that there is no friction in the wheel bearings. They still function as wheels (meaning they would still turn and not skid on the ground) but they are "perfect" wheels -- always perfectly round, and if you hold one up in the air and give it a spin, it will just keep spinning and spinning.

So if you sneezed on it with enough force to get the plane moving in the first place, it would keep moving. (AHHH-CHOO!)

But there is friction between the wheel and the ground, and the ground is resisting the movement of the wheel through that frictional force. So if you get the plane moving, it will decelerate, unless force is added to maintain its speed. Just like pushing a car on a flat surface - it doesn't roll forever, it stops.

[Alex Franke]

But there is friction between the wheel and the ground, and the ground is resisting the movement of the wheel through that frictional force. So if you get the plane moving, it will decelerate, unless force is added to maintain its speed. Just like pushing a car on a flat surface - it doesn't roll forever, it stops.

I'm having trouble with this one. There has to be friction between the wheel and the ground or the wheel wouldn't function as a wheel. In fact, the more friction the better. The very bottom of the wheel never moves in relation to the ground -- if it did there would be no traction.

But we're talking about a perfect wheel (on a perfect surface) -- always perfectly round. I don't see how the friction that creates traction could resist a rolling wheel.

Cars stop because they don't have frictionless bearings, or perfectly round wheels (they're spongy) -- and because of my far-from-perfect driveway.

I'm just trying to take some variables out of the equation here. If the wheel and surface are impossibly perfect (round, rigid, frictionless bearings, but still operates as a wheel with perfect traction), and the treadmill is perfectly fast and flat, then wouldn't a plane be able to take off regardless of how fast (or which direction) the treadmill is running?

[Kristofor]

But there is friction between the wheel and the ground, and the ground is resisting the movement of the wheel through that frictional force. So if you get the plane moving, it will decelerate, unless force is added to maintain its speed. Just like pushing a car on a flat surface - it doesn't roll forever, it stops.

This is true in the real world, but in the real world bearings do have friction, the tires deform and sap energy, there is wind resistance etc.

If we assume that a "perfect" wheel would eliminate the bearing friction, not the tire/surface friction then the ground would not "resist" the movement of the object once started...

Draw your force diagram. Where is there acceleration?

As the perfect wheel rotates only a single point on the wheel will ever be touching the surface. Put a white dot on the side of the wheel to mark one of those points. It will rotate around the wheel and then very briefly touch down on the surface (an infinitely short time on a perfectly circular wheel but don't let that confuse you the same thing happens with a wheel that does distort). While this dot is "on" the surface it does not move either forward or backwards relative to the surface. In other words it was neither accelerated nor decelerated. Moment's later it rotates up at the same speed it was always moving, there was no acceleration, and thus no force exerted on it. In fact with frictionless bearings if the plane rolled on to perfectly slippery ice the wheels would continue to rotate at the same rate.

You cannot use real-world examples to apply to massless frictionless pulley, frictionless infinite plane, and massless inextensible string problems as such do not exist in the real-world...

[gsmittle]

To Review…

Here's what we know so far:

1. There's an airplane.

2. There's a treadmill.

3. Said airplane is moving on said moving treadmill.

4. Said airplane either takes off or it doesn't.

5. Igniting a rocket pack on the back of a roller blader is a "Hey, hold my beer and watch this!" moment.

6. We need more beer.

Tautology Class dismissed.

g.

[Mr__Bill]

And we also know:

1. Some people see the light

2. Some do not see the light

3. Some do not believe there is a light

4. Some see the light and with glee in their eyes try to convince others that that the light is a false light

5. Some people don't care if there is a light or not but they'll be darned if they'll ever get into an airplane that's sitting on a conveyor belt!

6. I think Niki and a few others up there are talking about how it's a good thing that some of us will never change but at least we can make things out of wood....


Bill
well it's 9 am, the sky is blue and I'm walking the dog, without a conveyor belt.

[woodturner]

I'm just trying to take some variables out of the equation here. If the wheel and surface are impossibly perfect (round, rigid, frictionless bearings, but still operates as a wheel with perfect traction), and the treadmill is perfectly fast and flat, then wouldn't a plane be able to take off regardless of how fast (or which direction) the treadmill is running?

I think I see your point. Maybe another analogy is a hovercraft - it's contact with the ground is nearly frictionless. If you could push hard enough to overcome momentum, you could push a hovercraft around. Another analogy is an air hockey puck - blowing on them is enough to move them, takes very little force.

So, if that is what you mean - that the plane has essentially no frictional contact with the ground - I agree the plane would move forward and take off. I think the one part we all agree with is that in still air, the plane must have forward movement relative to the ground. If the airplane can move fast enough to achieve the required airspeed, it will take off.

[cabinetman]

6. I think Niki and a few others up there are talking about how it's a good thing that some of us will never change but at least we can make things out of wood....

Bill

Hear, hear!!
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