OK, this is how I'm figuring this:

A plane has a forward FORCE of 10,000n
My treadmill can also produce an opposing Force of 10,000n

The plane's tires have a CRF (coeffecient of Rolling Friction) of 0.006

At that force, the plane will taxi on a static runway at 9,040n
(10,000 - 60 = 9,040)

Ex1.
Put the plane on a treadmill that's in 'neutral' ie 'freewheeling'

The plane keeps it's wheels locked with the brakes. There is no rolling friction, since the tires aren't rolling.
The plane throttle's up to 10,000n. Again, the wheels do not move.

However, my freewheeling treadmill DOES start to move. The force of the plane's thrust is transmitted through the locked tires, and the treadmill starts to move forward at 10,000n.
10,000n (plane's force) - 0 (treadmill's force) = 10,000n (plane moves the treadmill's belt forward)

Now, I counteract the plane with the treadmill. I bring the treadmill up to 5,000n. The belt slows it's forward progress, but it's still moving forward at 5,000n:
10,000n(plane's force) - 5,000n(treadmill's force) = 5,000n(plane moves treadmill's belt forward)

Looks like I need more power, so I raise the treadmill's opposing force to 10,000n.
Now we have the following:
10,000(from plane) - 10,000n (opposing force from treadmill) = 0n of forward progress.

What I just did was 'freeze' the plane on the treadmill.
The plane does not move in relation to the belt.
The belt does not move in relation to the plane.
Neither the plane nor the belt moves in relation to the ground.
Both equal and opposing forces have 'balanced' each other out.
The plane's engines whine. The treadmill's motor humms...both are producing 10,000n of force, opposing each other!
Everything is 'locked up'....'Frozen in time'..so to speak.


Now for the Magic!!! Brake Release!
(keep the treadmill and the plane reved up to 10,000n!!)

The first thing that happens when the brakes are released is obvious...the 10,000n from the plane starts to turn the tires. But since the tires have a rolling resistance of 60n, the plane moves forward at only 9,040n NET FORCE. (Right?)

Now, what might NOT be so obvious, is what is happening on the treadmill.

See, the before plane's brakes were released, the treadmill's 10,000n was holding back the plane's 10,000n. But something just happened! The plane's NET FORCE was just DECREASED to 9,040n.
But the treadmill is STILL pumping out 10,000n!
Think....what affect does this have on the treadmill?

9,040n (NET Plane Force) - 10,000 (treadmill's force still) = (- 60) Belt Movement!!!!

So, now we know that the belt is moving at NEGETIVE 60n! (backwards)
This is due to the tires rolling resistance of 60n

Now, since the treadmill's belt is moving now, it is no longer pushing out 10,000n of force. The treadmill's motor is now producing a NET force of 9,040n
10,000n (from treadmill's motor) - 60n(belt's movement) = 9,040 (backwards)


But Wait! Didn't we also just say that:
The plane is moving at POSITIVE 9,040n!? (forwards)


So, now the plane has a Net forward force of 9,040n AND the belt has a NET backwards force of 9,040n.

Resultant Forces:
9,040(plane's force forward) = 9,040(treadmill's motor's force backwards)
Equal and Opposite Forces (those are the ones that create equalibrium, the plane dosn't move)


Resultant Movement
60n (plane forward) = 60n (treadmill backwards)

So, the plane is moving forward at 60n

The treadmill is moving backwards at 60n

Let's just say that at this weight, 60n is 10mph

Thus, the plane moves at +10mph in relation to the belt
The belt moves at -10mph in relation to the plane

The belt has matched the SPEED of the plane!

But the plane remains 'motionless' over the actual earth, and therefore, since the wind is calm, 'motionless' through the 'Air'.

Challenge yourself to Re-read this 4 times before responding, and try to make your rebuttals relevent to this post.

THAT is why the plane will never fly.

On a normal takeoff -- no conveyor involved -- if there is a 20 mph headwind, Manfred and the J-3 will lift off at 45 mph indicated airspeed; but relative to the ground, it is only 25 mph. Should the wind increase to 45 mph and if Manfred can get to the runway, he can take off without rolling an inch. His airspeed is 45 and groundspeed is zero. It is not necessary to have any groundspeed to fly, just airspeed. Conversely, if Manfred has a lot of runway and nothing to hit, and takes off downwind in a 25 mph tailwind, the propeller will have to accelerate the airplane to a zero airspeed, which will be a 25 mph groundspeed, and then on to a 45 mph airspeed, which will have him humming across the ground at 70 mph. The speed over the ground, or a conveyor belt, when an airplane takes off is irrelevant; all that matters is its speed through the air, and unless the pilot sets the brakes, a moving conveyor belt -- under the freely turning wheels -- cannot stop the process of acceleration.

Conveyer-Belt Runway


What I learned from Old Hack was that an updated version of a question aimed at confusing folks over relative measurements of airplane motion and the medium in which it operates had shown up on the Internet, and it was causing the fracas in the Lounge.

The question that has been going around is not particularly artfully worded, and I think that has caused some of the disagreements, but I'll repeat it as it is shown: "On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?"

My comment: Notice that the question does not state that the conveyor's movement keeps the airplane over the starting position relative to the ground, just that it moves in the direction opposite to any movement of the airplane.

Initially, about a third of the folks here said that the airplane could not ever takeoff, because the conveyor would overcome the speed of the airplane and it could never get any airspeed. The rest said the airplane would fly.

The "It won't fly, Rocky" group said that the conveyor would hold back the airplane. They asked us to imagine a person running on a treadmill. As he or she sped up, the treadmill would be programmed to speed up, just as the conveyor in the problem, and the person would remain over the same locus on the earth, while running as fast as possible.

The argument was that if the airplane started to move forward, the conveyor program was set up to move the conveyor at exactly that speed, in the opposite direction, thus, the airplane would never move relative to the ground, and, because the air was calm, it could never get any wind over its wings. One of the analogies presented was the person rowing at three mph upstream in a river on a calm day. However, the current was flowing downstream at three mph, so the resultant speed with reference to the stream bank and air was zero, and thus there was no wind on the rowboat.

I watched and listened to the disagreement for a while and was fascinated to see that the argument seemed to split between those who had some engineering or math background, all of whom said the airplane would takeoff and fly without any problem; and those with some other background, who visualized the airplane as having to push against the conveyor in order to gain speed. Because the conveyor equaled the airplane's push against the conveyor, the airplane stayed in one place over the ground and in the calm air could not get any airspeed and fly.

It was an interesting argument, but as things progressed, more rational heads prevailed, pointing out that the airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff. One guy even got one of those rubber band powered wood and plastic airplane that sell for about a buck, put it on the treadmill someone foolishly donated to the Lounge years ago, thinking that pilots might actually exercise. He wound up the rubber band, set the treadmill to be level, and at its highest speed. Then he simultaneously set the airplane on the treadmill and let the prop start to turn. It took off without moving the slightest bit backwards.

Manfred In The 21st Century


OK, let's figure out why the airplane will fly.

We'll use Manfred again. Although we're bringing him forward into the 21st Century, we'll still let him use the 65 hp J-3. It doesn't really matter what airplane he flies, but he got used to the J-3 while he was demonstrating downwind turns and this one happens to have lifting rings on the top of the fuselage. It's also been modified with a starter so no one has to swing the prop.

Manfred's in the airplane. Old Hack has the Army-surplus crane fired up and he's picking up the J-3 and Manfred and carrying them over to Runway 27, which has been transformed into a 3,000-foot conveyor belt. It is a calm day. The conveyor drive is programmed so that if Manfred can start to move in the J-3, if he can generate any airspeed or groundspeed, the conveyor will move toward the east (remember Manfred and the J-3 are facing west) at exactly the speed of the air/groundspeed. Because the wind is calm, if Manfred can generate any indicated airspeed, he will also be generating precisely the same groundspeed. Groundspeed, of course being relative to the ground of the airport surrounding the conveyor belt runway. So, the speed of the conveyor belt eastbound will be the same as Manfred's indicated airspeed, westbound.

Manfred does his prestart checklist, holds the heel brakes, hits the starter and the little Continental up front clatters to life. Oil pressure comes up and stabilizes and Manfred tries to look busy because the eyes of the world are upon him, but all he can do is make sure the fuel is on and the altimeter and trim are set, then do a quick runup to check the mags and the carb heat. He moves the controls through their full travel and glares at the ailerons, doing his best to look heroic, then holds the stick aft in the slipstream to pin the tail and lets go of the brakes.

Baron of the Belt

So far the J-3 has not moved, nor has the conveyor. At idle power, there's not enough thrust to move the J-3 forward on a level surface, so Manfred starts to bring up the power, intending to take off. The propeller rpm increases and the prop shoves air aft, as it does on every takeoff, causing the airplane to move forward through the air, and as a consequence, forward with regard to the ground. Simultaneously the conveyor creaks to life, moving east, under the tires of the J-3. As the J-3 thrusts its way through the air, driven by its propeller, the airspeed indicator comes off the peg at about 10 mph. At that moment the conveyor is moving at 10 mph to the east and the tires are whirling around at 20 mph because the prop has pulled it to an airspeed, and groundspeed, of 10 mph, westbound. The airplane is moving relative to the still air and the ground at 10 mph, but with regard to the conveyor, which is going the other way at 10 mph, the relative speed is 20 mph.

Manfred relaxes a bit because the conveyor cannot stop him from moving forward. There is nothing on the airplane that pushes against the ground or the conveyor in order for it to accelerate; as Karen -- one of our techies here at the Lounge -- put it, the airplane freewheels. In technical terms, there is some bearing drag on the wheels, but it's under 40 pounds, and the engine has overcome that for years; plus the drag doesn't increase significantly as the wheel speed increases. Unless Manfred applies the brakes, the conveyor cannot affect the rate at which the airplane accelerates.

A few moments later, the roaring Continental, spinning that wooden Sensenich prop, has accelerated the J-3 and Manfred to 25 mph indicated airspeed. He and the airplane are cruising past the cheering spectators at 25 mph, while the conveyor has accelerated to 25 mph eastbound, yet it still has no way of stopping the airplane's movement through the air. The wheels are spinning at 50 mph, so the noise level is a little high, but otherwise, the J-3 is making a normal, calm-wind takeoff.

As the indicated airspeed passes 45 mph, groundspeed -- you know, relative to where all those spectators are standing beside the conveyor belt -- is also 45 mph. (At least that's what it says on Manfred's GPS. Being brought back to life seemed to create an insatiable desire for electronic stuff.) The conveyor is also at 45 mph, and the wheels are whizzing around at 90 -- the groundspeed plus the speed of the conveyor in the opposite direction.

Manfred breaks ground, climbs a few hundred feet, then makes a low pass to see if he can terrify the spectators because they are Americans, descendants of those who defeated his countrymen back in 1918.

It's All About Airspeed


(Don't try this at home!)
(Don't try this at home!)

While the speed of the conveyor belt in the opposite direction is superficially attractive in saying the airplane cannot accelerate, it truly is irrelevant to what is happening with the airplane, because the medium on which it is acting is the air. The only time it could be a problem is if the wheel speed got so high that the tires blew out.

Put another way, consider the problem with the J-3 mounted on a hovercraft body (yes, similar things were tried about 30 years ago). The hovercraft lifts the airplane a fraction of an inch above the conveyor belt, and so no matter how fast the conveyor spins, it cannot prevent the propeller -- acting on the air -- from accelerating the airplane to takeoff speed. It's the same with wheels rolling on the conveyor belt. Those wheels are not powered and thus do not push against the belt to accelerate the airplane. Were that the case, the vehicle could not reach an airspeed needed to fly, because then the conveyor, the medium acted upon by the propulsive force, would be able to negate the acceleration relative to the air and ground.

I'm reminded of the New York Times editorial when Robert Goddard's rocket experiments were first being publicized. The author of the editorial said that rockets can't work in space because they have nothing to push against. It was laughably wrong, ignoring one of Sir Isaac's laws of physics that for every action there is an equal and opposite reaction. Here the propeller is pushing against the air, as it does every time an airplane takes off. How fast the airplane is moving over the surface on which its wheels rest is irrelevant; the medium is the magic. On a normal takeoff -- no conveyor involved -- if there is a 20 mph headwind, Manfred and the J-3 will lift off at 45 mph indicated airspeed; but relative to the ground, it is only 25 mph. Should the wind increase to 45 mph and if Manfred can get to the runway, he can take off without rolling an inch. His airspeed is 45 and groundspeed is zero. It is not necessary to have any groundspeed to fly, just airspeed. Conversely, if Manfred has a lot of runway and nothing to hit, and takes off downwind in a 25 mph tailwind, the propeller will have to accelerate the airplane to a zero airspeed, which will be a 25 mph groundspeed, and then on to a 45 mph airspeed, which will have him humming across the ground at 70 mph. The speed over the ground, or a conveyor belt, when an airplane takes off is irrelevant; all that matters is its speed through the air, and unless the pilot sets the brakes, a moving conveyor belt -- under the freely turning wheels -- cannot stop the process of acceleration.

Things eventually calmed down as the number of "it won't fly" folks dwindled as they began to understand that the airplane would take off. Old Hack looked at me and suggested we depart as the few holdouts showed no sign of changing their position. So, we headed out into the night to watch the guys take the conveyor out and reinstall the runway.

See you next month.