The old airplane/treadmill revisited

[Alex Franke]

To be practical and consider things like the friction in the wheel bearings, we should also be practical with respect to the treadmill. Can a reasonably viable treadmill hold a plane back if it has a reasonably efficient set of wheels. My guess is probably not -- the plane will move forward with respect to an observer on the ground and take off with perhaps a little extra effort -- the worse the wheels, the more the effort.

Or you can do it the fun way and just take out some variables. Assuming the wheels are perfect and completely frictionless, and assuming you have a huge treadmill that goes zillions of miles per hour, and that tires will never explode or bearings won't melt away, then the plane will move forward with respect to an observer on the ground and take off.

In any case, if air is moving over the wings at the speed required for lift-off, then the plane will lift off. The air can be caused by a big fan, it can be pulled along by a zipping treadmill, or whatever. Or if you can guarantee that there will be no air over the wings, then the plane will not take off.

At the end of the day it's all about the air and the wings. That's it. Air and wings. If the air and wings are there and sufficient, then it will take off. If the air and wings are not there or are insufficient, then it will not lift off. Put the plane on ice, in the river, on a runway, on a treadmill, or even on a lava flow -- doesn't matter.

Air and wings. That's it.

[leehljp]

The fundamental question comes down to this:

Can the plane/jet, as stated, achieve ANY forward motion relative to the ground?


If ANY forward motion is achieved then it will progress to take off speed.
(Of course it will if there is nothing to hold it back which the wheels will not.)

Friction and conveyor/roller speed is irrelevant to this first presupposition.

[Mr__Bill]

And, if you don't believe all us fine folk who may or may not know what we are talking about, will you believe Cecil Adams? Who the heck is Cecil Adams you ask, well he is the Straight Dope answer guy. Just click here and read his answer the the question.




Bill
over here in the fog

[chopnhack]

I think a light when on in my head Doc R. Thanks

[docrowan]

I think a light when on in my head Doc R. Thanks

I'm not sure, but I think I argued the plane would NOT take off in our previous thread on this topic many moons ago. It took crokett's post early on in this thread for me to get the light on in my head.

[JeffG78]

A simple test could be conducted to prove this once and for all. The Straight Dope guy mentioned roller blades on a treadmill using a rope to pull yourself forward.

The experiment (with proper authorizations) would be to strap a very small rocket engine onto a person's back who is wearing roller blades. The rocket is capable of moving the person from a standstill up to a speed of 5mph while wearing roller blades. Now take the same guy with the same rocket and put him facing the wrong direction on a moving sidewalk in an airport. Those sidewalks travel around 5mph, so it would simulate an equal speed, but the opposite direction, the same as with the plane on a conveyor. The test subject should, and will, accelerate up to 5mph with respect to the airport terminal. The only extra resistance when he is on the treadmill will be the slight friction of the bearings. For those who rollerblade know, friction losses are not substantial. Air friction is a much larger factor.

To an observer standing in the airport terminal, they would have no idea that there was even a moving sidewalk under the rollerblader. He would accelerate due to the thrust of the rocket.

Once you accept this, you will understand how the plane would do exactly the same thing and accelerate up to takeoff speed the same as on a normal runway. Like the rollerblader, the only difference will be the speed of the wheels.

[docrowan]

A simple test could be conducted to prove this once and for all. The Straight Dope guy mentioned roller blades on a treadmill using a rope to pull yourself forward.

The experiment (with proper authorizations) would be to strap a very small rocket engine onto a person's back who is wearing roller blades. The rocket is capable of moving the person from a standstill up to a speed of 5mph while wearing roller blades. Now take the same guy with the same rocket and put him facing the wrong direction on a moving sidewalk in an airport. Those sidewalks travel around 5mph, so it would simulate an equal speed, but the opposite direction, the same as with the plane on a conveyor. The test subject should, and will, accelerate up to 5mph with respect to the airport terminal. The only extra resistance when he is on the treadmill will be the slight friction of the bearings. For those who rollerblade know, friction losses are not substantial. Air friction is a much larger factor.

To an observer standing in the airport terminal, they would have no idea that there was even a moving sidewalk under the rollerblader. He would accelerate due to the thrust of the rocket.

Once you accept this, you will understand how the plane would do exactly the same thing and accelerate up to takeoff speed the same as on a normal runway. Like the rollerblader, the only difference will be the speed of the wheels.

Good analogy, Jeff. The key to understanding this conundrum is that the conveyor does not impede forward motion as seen by a stationary observer if one is using a propulsion method that does not act by pushing on the ground (or particularly the conveyor.)

If tried in real life, a propellor driven model airplane engine could probably do the job as well, with better throttle control and fewer safety concerns.

[Alex Franke]

If tried in real life, a propellor driven model airplane engine could probably do the job as well, with better throttle control and fewer safety concerns.

Not nearly as fun, though.

[chopnhack]

I'm not sure, but I think I argued the plane would NOT take off in our previous thread on this topic many moons ago. It took crokett's post early on in this thread for me to get the light on in my head.

Nope, the light came on, it was the analogy that made me see the difference. It was a point of reference issue

[TK421]

I'm sure you have all seen gliders. The ones with long skinny wings that look like U2 spy planes. They get into the air by being towed either by a plane or a car/truck. What if you replaced the plane in question with a glider, which is attached via cable to a truck on the road running alongside the conveyor belt (theres gotta be road next to it, right?). Now the truck starts down the road. The conveyor starts spinning. The glider wheel is spinning. Whats going to happen? Is the truck going to be held in place? No. Its going to pull the glider down the conveyor belt just like normal except that the wheel in the glider will spin faster than it would over stationary ground. In fact you could have the conveyor belt spinning at whatever speed you want, the wheel in the glider is just going to spin x times faster, the glider itself will still move at whatever speed the truck is pulling it until lift > gravity and glider is flying.

[woodturner]

The key to understanding this conundrum is that the conveyor does not impede forward motion as seen by a stationary observer if one is using a propulsion method that does not act by pushing on the ground (or particularly the conveyor.)

I agree that the propeller is acting on the air, not the ground. However, the wheels cause an opposing force. So, if the convey speed is adjusted to offset the acceleration of the plane, the plan remains motionless, does not achieve the required air speed, and thus cannot take off.

The key here is that in still air, the plane's motion relative to the ground is essentially the air speed. Unless an observer on the ground sees the plane moving, it can't take off. The conveyor thwarts the plane's efforts to move and that's why the plane doesn't take off.

[docrowan]

I agree that the propeller is acting on the air, not the ground. However, the wheels cause an opposing force.

What force do the wheels cause, other than a minor amount of friction in the bearings? The wheels on an airplane spin freely, forwards or backwards, just like the wheels on a dolly, wheelchair, or in-line skate.

[woodturner]

What force do the wheels cause, other than a minor amount of friction in the bearings? The wheels on an airplane spin freely, forwards or backwards, just like the wheels on a dolly, wheelchair, or in-line skate.

The friction of the wheel in contact with the ground provides the opposing force - that's what allow a car to move. So the conveyor is providing a force that counteracts the attempted forward movement of the airplane, generated by the propeller.

[JeffG78]

The friction in the bearings would be insignificant. If it were substantial, every plane would struggle to move down a runway. The only difference is that the wheels would turn twice as fast as normal.

[master53yoda]

just a point that i made earlier anyone motion can be obtained if enough energy is exerted on the components. every example given has used an energy source that far exceeds the friction losses of the interface between the moving conveyor and the person airplane etc.

this is like saying that all rockets can go straight up. That only applys if the thrust of the engine exceeds the weight of the rocket. otherwise it will just sit on the launch pad and go nowhere.

Take the roller blades off of the man at the airport and put on ice skates and he will not move against the conveyor. because the engine does not deliver enough power to overcome the friction of the ice skates.

in any case that the engine has excess power then the conveyor interface and inertia requirements the airplane will take off at some point.