- Dec 11, 2002

- 18,408

- 39

- 91

**did you not get the hint when the previous thread was locked?**

Anandtech Moderator

--------------------------------------------------------------------------------------

Anandtech Moderator

--------------------------------------------------------------------------------------

So the main argument that the plane would still take off is that there's no counter force keeping the plane from moving forward as the thrust of the plane is independent from the wheels. So as long as the wheels roll freely, the plane will still take off.

However, there is a counter force! Rotational friction. There is a frictional force in the bearings of the wheels. It does not roll completely freely without any opposing forces. The thrust force the plane puts out would be needed to counteract this frictional force.

Therefore, the quicker the wheels spin, the more force the plane would have to put out to spin the wheels.

But isn't the conveyer belt pushing the same amount of force on the wheels in the opposite direction?

So when would the plane actually move forward relative to the air?

Well first, let's imagine this situation:

The plane is on a conveyer belt that's moving backwards at 100mph. The plane is moving forwards at 100mph also. So right now, the plane isn't moving relative to the air right? But what would happen if the plane suddenly stopped all its engines? The coveyer belt would begin to move the plane backwards. It would no longer be able to maintain the static air speed.

Therefore, we can reasonably deduce that it does indeed take some force from the plane's thrust in order to counteract the motion of the conveyer belt.

So how much force would it take to keep the plane stationary with the air when the belt is moving backwards at 1000000000000 miles per hour? Would the plane have enough power to keep it stationary? Probably not.

But then again, is it even possible for the tires to still be in contact with the treadmill at 100000000000 miles per hour? According to newtonian physics, once the frictional force of the bearings exceed the frictional force between the tires and the surface of the conveyer belt, wouldn't the tires lose grip with the surface? Once the tires lose surface, the plane will only have to generate enough thrust to counteract the frictional force between the tires and the surface of the belt in order to move forward.

So therefore, the plane will move forward, but only when the plane is able to generate enough thrust for the friction of the tires to break free from the belt.

But is there any plane that has a powerful enough engine that can generate enough force to break free?

Let's look at the Boeing 777.

According to wikipedia, it generates 418,000N of thrust, and has a mass of 139,225kg.

The coefficient of static friction between tires and tarmac is about 0.7.

If you work out the math, µmg is (0.7)(139225)(9.8) = 956,058N.

This is over twice as much force as what the 418,000N of thrust the engines put out.

And if you consider the hundreds of opposing forces that I haven't accounted for, it's even less likely to be able to break free from the friction.

But what if you had a plane with a better weight to thrust ratio?

Well, I let's look at the F22 Raptor.

According to wikipedia, the two turbofan engines generates a total of 311,000N of thrust. The plane when empty has a mass of 14,365kg.

So given that, let's work out the math again. (0.7)(14365)(9.8) = 98,544N

In this case, the 311,000N of thrust is significantly greater than 98,544N of frictional force. So in this case, the plane would take off!

In conclusion: THE PLANE MAY OR MAY NOT TAKE OFF DEPENDING ON WHICH PLANE IT IS!