The old airplane/treadmill revisited

[jking]

If the air is still and the plane is not moving relative to the ground, it's no different than a plane sitting on the ground motionless - it cannot take off. As originally stated, the problem is misleading because it implies that the plane is stationary to the ground, when it really is not. The point is that the conveyor cannot match speed quickly enough so that it cannot hold the plane in a stationary location, so the plane accelerates and moves, achieving air speed.

OK, I confess - I wanted to make sure this was correct, and we happened to be testing model airplanes in the wind tunnel yesterday, so I tried it (with the model airplane). As expected, when the plane remained stationary relative to the ground, the plane did not take off.

Bottom line, the airplane needs sufficient air flow over the wings to achieve takeoff. That can be due to wind or due to travel along the ground - but without achieving the air flow over the wings, it won't take off.

Think about an airplane that stalls - it's completely free of ground contact, but air flow has reduced to the point that the wing stalls.

Confusing, it seems you're contradicting yourself in the two middle paragraphs. What exactly did you test in the air tunnel? In order to remain stationary to the ground, the airplane must be tethered somehow. Even if it's tethered, it doesn't mean there is no lift on the wings. It just means the force of the lift is less than the strength of the tether.

As far as a stalled airplane, you're right that it happens because of lack of air flow. Stalling generally occurs because of too much angle of attack. This can occur at takeoff when the pilot tries to gain altitude to quickly, or, in the air when angle of attack is too great for the air speed. It seems this is a rabbit trail, though. I don't see how it applies to the treadmill question.

[Alex Franke]

Suppose the plane is on rollers that trap the wheels -- like what they put cars on to test them at speed without them moving. The plane's engine would need to provide enough power to pull the wheel up over the roller in order for it to break free and move forward (and take off), but the wheels and the rollers would still not roll, right? (except maybe 1/8 turn as the plane breaks free)

And I can't help but add this, too: Now suppose there were two planes, side by side going up a hill with the same ground speed, and one is in a lower gear. Which one is doing more work?

Oh and here's another serious one: Say the plane needs 50mph air speed to take off. If there's a 50 mph wind at the front of the plane, the plane is not tied down, and the wheels are well lubricated (or on ice, etc), then the plane would still not lift off but be pushed backward. But if the wind were 50 + some amount to overcome drag then it would lift off? is that how drag works?

[cgallery]

is that how drag works?

I'm not sure. But there is a guy in drag that visits the shop from time to time. Next time I see him, I'll ask him whether he has ever been picked up on a windy day.

[Alex Franke]

I'm not sure. But there is a guy in drag that visits the shop from time to time. Next time I see him, I'll ask him whether he has ever been picked up on a windy day.

ROFL -- See if he'll buy me a new keyboard, too. Mine's now soaked in coffee! thanks for that one.

[jking]

Suppose the plane is on rollers that trap the wheels -- like what they put cars on to test them at speed without them moving. The plane's engine would need to provide enough power to pull the wheel up over the roller in order for it to break free and move forward (and take off), but the wheels and the rollers would still not roll, right? (except maybe 1/8 turn as the plane breaks free)?

In that case, yes, the engine (prop or jet) would have to provide enough thrust to get over the rollers. The rollers & wheel would move only when the plane moves forward over the roller. And the pilot would curse when the gear breaks...

Oh and here's another serious one: Say the plane needs 50mph air speed to take off. If there's a 50 mph wind at the front of the plane, the plane is not tied down, and the wheels are well lubricated (or on ice, etc), then the plane would still not lift off but be pushed backward. But if the wind were 50 + some amount to overcome drag then it would lift off? is that how drag works?

Basically, yes.

[sailor55330]

5 pages? I'm surprised.

I guess here's my take and how I interpreted the meaning of the test. When a plane is put on a conveyor that moves equally and opposite of the plane, then I expect that the plane does not move forward. In reality, what each of you are saying is that it does because the wheels are rolling.

My original vision was that the plane was not moving. So, lets try this.

If a plane's wheels were on rollers (imagine a dyno machine for cars) and the plane was tethered to stationary object that could withstand the load, would the plane take off and fly in place?

[JeffG78]

If a plane's wheels were on rollers (imagine a dyno machine for cars) and the plane was tethered to stationary object that could withstand the load, would the plane take off and fly in place?

No, but that's not the question. The plane is not tethered and DOES move forward.

[Alex Franke]

If a plane's wheels were on rollers (imagine a dyno machine for cars) and the plane was tethered to stationary object that could withstand the load, would the plane take off and fly in place?

No unless it's really windy.

Dyno machine? Is that the thing they roll cars on? New word for me...

[Kristofor]

Oh and here's another serious one: Say the plane needs 50mph air speed to take off. If there's a 50 mph wind at the front of the plane, the plane is not tied down, and the wheels are well lubricated (or on ice, etc), then the plane would still not lift off but be pushed backward. But if the wind were 50 + some amount to overcome drag then it would lift off? is that how drag works?

This depends on how you arrive at that state... If the plane is sitting motionless (unpowered) in still air and suddenly there's enough wind to reach the amount of lift needed to take off it would jump up in the air (assuming it's ballanced correctly, etc.). However it will also be accelerating in a negative direction due to the force of the wind. As it accelerates the relative velocities between the plane and the wind will decrease until the velocity of the wind over the wings is no longer enough to lift the plane and it will come back down while still continuing to accelerate in a negative direction until it reaches the wind velocity (less friction, etc.).

If the wind was rampped up gently then the plane would simply accelerate in a negative direction until it matched the wind velocity (less frictional losses, etc.).

[Alex Franke]

As it accelerates the relative velocities between the plane and the wind will decrease until the velocity of the wind over the wings is no longer enough to lift the plane and it will come back down while still continuing to accelerate in a negative direction until it reaches the wind velocity (less friction, etc.).

I see -- with a sudden 50 mph wind, the plane would instantaneously and imperceptibly lift but then immediately fall back to the ground as it begins to accelerate backward due to drag (air speed <50 mph again). With a 51 mph sudden wind, the plane would lift only until its backward speed reaches 1 mph. It makes sense that the drag isn't there unless the wind is there.

So if you wanted to keep it in the air as efficiently as possible, you'd need to ramp up the wind exponentially -- so that it is always 50 mph plus the ground speed of the plane as it's continually being accelerated backward by the wind due to drag.

[woodturner]

What exactly did you test in the air tunnel? In order to remain stationary to the ground, the airplane must be tethered somehow.

....

As far as a stalled airplane, you're right that it happens because of lack of air flow. ...
I don't see how it applies to the treadmill question.

The plane does not have to be tethered to remain stationary. The propeller is pulling the airplane through the air. The contact with the ground is the wheels on the conveyor. If the conveyor speed is constantly adjusted such that the plane remains motionless relative to a point on the ground, the airspeed is 0 and the plane does not take off.

In the wind tunnel, we tied down the model plane with expandable tethers. This allows the plane to move about a foot in any direction with no restriction, but if it moves more than a foot, it is constrained. This just keeps the plane from hitting the walls, etc.

The wheels were placed on a conveyor belt and the controls were set so that the conveyor speed matched the motion of the plane. Thus the plane remained stationary.

We did not turn on the fan, so there was no "wind". As we accelerated the engine to maximum throttle, the propeller tried to move the plane forward, but the conveyor adjusted speed to overcome the forward motion and keep the plane stationary (more or less, small variation as the conveyor compensated).

The stalled wing is essentially the same issue, it just removes the conveyor and wheels from the experiment. The wing stalls when air speed is too low. This can be due to angle of attach changing and thus changing the required minimum air speed, as you noted.

[sailor55330]

See, that's where I had some interpretation questions. When I envision the the plane on a treadmill, I envision the plane not physically moving forward in relation to any stationary object, which would not allow for airflow over the wings other than what is provided by the prop.

I guess in my simple mind it seems that if the treadmill is truly matching the exact motion of the plane, then airflow over the wings will not exist and it will not take off.

Think of it like this. When you run on a treadmill, the motion of the treadmill is keeping you from moving forward, but do you feel wind in your face? No, therefore, no airflow, no lift for the plane. How does this example differ from the plane? If I am understanding it (and I may not be), the plane is lifting off from airflow over the wings. WHere is the airflow coming from if the plane is not moving forward (again, use the running example)

[Alex Franke]

We did not turn on the fan, so there was no "wind". As we accelerated the engine to maximum throttle, the propeller tried to move the plane forward, but the conveyor adjusted speed to overcome the forward motion and keep the plane stationary (more or less, small variation as the conveyor compensated).

Um.....

[LarryG]

Think of it like this. When you run on a treadmill, the motion of the treadmill is keeping you from moving forward, but do you feel wind in your face? No, therefore, no airflow, no lift for the plane. How does this example differ from the plane? If I am understanding it (and I may not be), the plane is lifting off from airflow over the wings. WHere is the airflow coming from if the plane is not moving forward (again, use the running example)

In the original thread, I was arguably the one who took home the trophy for thick-headedness (just ask Loring). In retrospect, I now realize that this is precisely what was bothering me.

As has been discussed, the problem as originally stated omits one critical stipulation: the speed of the airplane relative to what? It is absolutely true that the treadmill cannot keep the airplane's wheels from rolling, and that the thrust generated by the plane's engines will propel it forward no matter what the conveyor belt is doing. The plane would move forward relative to the ground; when it reached takeoff speed, it would fly. No argument about that.

However, I question whether the real intent of the question was: what if the conveyor belt could keep the plane's speed at zero, relative to the ground? If that were somehow possible, then No, the plane would not fly.

Re: your running-on-a-treadmill question, the answer is really the same. You adjust the speed of the treadmill to match the speed at which you wish to run. But there's nothing to keep you from applying more "thrust" (e.g., running faster and faster) and outrunning the treadmill. You'd feel the wind in your face, and you'd run off the front end of the moving belt (or into the control pedestal, since it's usually right in front of you). But if the treadmill was tracking your speed and adjusting itself to compensate for your running faster and faster, you would not move forward, would not feel any wind, would not be able to run off the front end of the machine. The key difference, however, is that your feet are moving you "forward" because they have traction on the treadmill. With the airplane, whatever traction the wheels have on the conveyor belt is immaterial since they are not the means of propulsion.

[sailor55330]

I love this discussion. Everyone is right, no one is wrong and everyone could be wrong and no one could be right.

Until we are able to make a lifesize conveyor belt/treadmill and get someone to donate the airplane and I'm riding in it, in my own mind, it won't take off and I'm ok with that!