Ben Lanterman

I haven't visited this site in some time, things get busy. Concerning the airplane tires and conveyer belt.

1. Take the question stated such that the belt speed matches the airplane speed.

As the airplane gets a little power from the prop and slowly tries to move, the belt moves in turn to oppose it and the airplane remains stationary. The tire/belt interface contact point is moving at the same speed - ie, the aft linear speed at the contact point is the same. No problem here. The frictional force in the longitudinal directional from the tire/belt contact is toward the rear and will cause this to happen at low power.

Remember in the case of airplanes that the prop power can be much greater than the friction due to the tires on the conveyer belt. At the time when the prop power is increased to greater than the longitudinal frictional force aft, the correlation between airplane motion and the tire/belt contact speed is lost. The belt can no longer constrain the airplane. That is the key to the problem.

But in the spirit of the question you must change the speed of the belt to whatever is necessary such that the tire/belt contact point speed will be the same no matter what the airplane's speed is. As the airplane moves forward on the conveyer belt, change the speed of the belt such that the wheel/belt contact speeds stay the same and watch the airplane takes off. This is what happens in the typical thing like the MythBusters did.

Indeed if we let the belt run in reverse the airplane can takeoff with zero wheel speed.

2. If the question is stated such that the belt moves to try to keep the airplane body in place in space.

That is easier - It is the same as above except when the prop power is increased to greater than the longitudinal frictional force aft, then the belt simply can't do the job any more and the airplane takes off.

These are easy to check out with a Vapor indoor airplane and an exercise machine. Well not easy but relatively easy, better than a car and a tarp on a runway.

Ben

pimmnz

I have one question, how will the belt know the tyres are turning? I mean, at any point where the wheels are touching the belt, there is no relative motion between the belt and wheel, otherwise the tyre will be skidding. So far as the belt knows, the tyres do not move, relative to the belt. The only thing that happens is that the tyres change position on the belt, but as there is no force generated between the belt and tyre (neither is driving the other) to tell the belt which way, or how fast, the wheel is moving. Simply, the point of pressure where the wheel and tyre meet changes as the airplane/belt moves, but there is no other indication that anything is happening, or have I got something wrong, again?
Evan, WB #12.

Ben Lanterman

Hi Evan,

The belt won't know unless there is a slight lag in the system - the airplane starts to move and the belt moves in response. Indeed as I noted if the belt is allowed reverse motion the airplane can take off with zero rotation of the wheels. Makes me think of taking off of an aircraft carrier in a high wind in an old biplane. But I think the spirit of the question is akin to trying to take an airplane off of a treadmill like a big exercise walker.

I wrote this because it so happens I can duplicate this in the basement. First I found a low throttle setting that would allow my Vapor (everyone should have one of these great little airplanes) to just take off consistently. This is a pretty slow speed. I tried to remember it. I put my fingers on the front of the Vapor's wing and felt the amount of force being generated.

Then I set the walker belt to a very slow speed and increased the throttle on the Vapor from the slowest point to the point where the Vapor would remain stationary. The grooves in the belt tended to grab the wheels so steering by the rudder didn't work. Instead I steered the Vapor by hand - applying forces across the front of the wing - two fingers on each side of the centerline. Then I could concentrate on working the throttle and also feel if the airplane had forward force. In this setup the wheels are definitely turning.

Then the belt speed was increased (by my long suffering lovely bride) slowly while I tried to keep the airplane stationary with the throttle speed. There wasn't any forward force at the slowest speeds. But fairly quickly there came a belt speed where I felt a small forward force. Then as the belt speed was continually increased and the throttle increased I felt a forward force that was much higher than I had noted (based on throttle stick position) that the Vapor had previously needed for takeoff and slow-flight speed. At that force/throttle setting there was a definite tendency to accelerate forward meaning that the belt no longer would restrain the airplane.

Sometime in the experiment the forward thrust of the airplane overcame the aft frictional force of the wheel/belt. Remember the grabbing of the wheel by the belt kept the belt/wheel contact point moving at the same speed nicely, but, no matter what speed the belt might try to move at it was be unable to restrain the airplane. The airplane take would take off and, in my case, nailed the front walker brace.

I think almost any real attempt to work the problem will turn out this way.

Ben

pimmnz

Thanks Ben, I had imagined much the same thing.
Evan.

combatpigg

My Feedback: (3)

Once the plane breaks traction with the belt and skids ahead, the whole concept is lost. The plane can not make progress on the moving belt without scrubbing its' way forward. At that point, there is no concept, there is no scenario.

Might as do away with all the other paradoxes as well so that the "reality majors" will be happy.

A Vapor will leap off a lilly pad in the middle of a pond, not my best choice for a test subject.

pimmnz

I'm confused, what 'traction' is there between the belt and the airplane? There is no 'drive' or 'scrubbing' unless the wheels are driven (which we know they are not) and 'scrubbing' could only come from the airplane being turned, perhaps with one wheel braked and the airplane pivoting on the stationary wheel. Such maneuvering is not mentioned anywhere in the question. How can the airplane 'skid ahead' unless the brakes are on? The pilot would have to have a lot of power on, and I have to report that I have never taken off with any wheel 'skidding' on the runway, applying brakes at the point of take off is not considered 'good form' unless there is a dire emergency.
Evan.

combatpigg

My Feedback: (3)

The natural rates of feed between the belt and the tire has no scrubbing effect.........as long as both are in sync. If the tire is forced to break that pace and speed up, it has to chew it's way forward along the belt. You might even see wheel hop, even though the ideal belt is flat. Our "perfect model" is not supposed to have this problem, if the tire tries to speed up, the belt instantly matches it to infinity.

Sport_Pilot

In mythbusters the belt was moving faster than the planes takeoff speed before it throttled up. No fancy speed changes as mentioned here. The only thing giving the plane a negative force is the tire and wheel bearing friction, which is much much lower than the thrust of the prop.

Ben Lanterman

There is no scrubbing or hopping - rather it would be a smooth system. In my case it would have been smooth except for the groves in the belt and even with them it would not have prevented the Vapor from taking off.

In the idealized version as well as my test, the airplane remains stationary with no force felt on the wing leading edge as low speeds. Only when the airplane reached the transition between equal forward thrust and maximum aft force due to the tires rolling friction, will the wheels (airplane) try to move forward. The rolling friction is dependent on several things but it does have a maximum value which is less than the thrust. After the transition the wheels will try to speed up and the belt will increase in speed to match them but there is no longer a constraint on airplane position or takeoff.

There is simply no correlation between wheel/belt speed and airplane forward speed when the transition point is reached. Once the forward force for takeoff was felt, the treadmill could be set at any speed and not effect the airplane other than make the wheels turn faster (and equal to the treadmill speed).

Sometimes these kinds of questions are proposed and in the process leave out some important factors that will effect the outcome. It becomes a bad question, not a bad answer.

I have spent many hours in a wind tunnel chasing answers to questions that luckily had answers. Actually the Vapor was an excellent subject for this since it was easy to pick the stick position where it would be airborne with a constant horizontal tail setting. I picked the lowest speed possible - not a leap off the ground speed. I picked a setting such that takeoff happens in about twice the length of my treadmill - a bit arbitrary agreed. This throttle stick position was repeatable on the belt. Using finger tips to measure the forces from the wing leading edge was valid also since we have very sensitive pressure sensors in them.


Ben

topspeed

Ben,

What is a Vapor ?

Juke

cyclops2

The foggy mass between my ears...

rmh

The VAPOR is the BEST example of what has evolved in the modeling world
It is a tiny model weighing much les than anounce - which has electric power and very accurate servo control- it will fly at a walk- true and can easily fly in a very small room with perfect control. The entire porportional radio weighs a few grams
The structure is carbon fibre and the flyig urface are flat pieces of film stetched oer the carbon frame
all very high tech and very inexpensive and the radio is a 2.4 DSM2
.
Go to Horizon model site and type in Vapor in the query box.

andrew66

ive only skimmed through this. but no matter what speed the belt is turning, the plane will still take off, cause of the realative wind. remember that planes rely on airspeed to take off. the belt would have to move the air too, to get the plane to "leap" off the ground. kinda like taking off in a 50kt headwind if the lift off speed of the plane is 50kts.

Sport_Pilot

Nobody is moving air with the belt. The prop pulls the airplane regardless of the belt.

andrew66

i know, but the belt would HAVE to move the air. otherwise, the plane will take off in a normal fashion

Ben Lanterman

Andrew66,

The belt (again going with the experiment that I did do) doesn't move the air except for an extremely thin layer next to the belt. In the range of a 1/15 of an inch or so. You can feel that at the end of the belt but it is nowhere near the height of the wing.

The plane does take off in a normal fashion - after - it has gone through the transition from stationary to being able to move as I noted in my responses above. Remember that the friction of the airplane on the belt will keep it stationary if the prop is just idling. If the belt moves the airplane will move aft. Then you increase the power and the airplane will start to remain stationary with the belt moving.

Do the process in increments (in your head) until the transition takes place. Then the plane will move forward and take off. It won't take off in a vertical fashion since the belt won't generate enough air speed at the wing.

And the Vapor is something everyone should have. Like Dick said it is a great little airplane. I fly mine in the living room, it can go around in a level flight, do figure eights and is a ball to put into a high angle of attack flight mode and creep around the living room. The angle of attack will be around 40 degrees or so and the power needed is much greater than level flight. It is cheap and a ball to fly. Everyone should buy one. I bought the Bind and Fly version and use it with my JR12X.

Another must have is the Blade MCX. It is in the same category of tinyness (is that a word). The control is precise and the gyro works great. It is fun to drive it around the living room in various geometric figures or to take it for a walk through the house. I can't fly a normal single blade helicopter but the little MCX is like driving a car. Easier to fly than the Vapor.

Ben

Sport_Pilot

<i>i know, but the belt would HAVE to move the air. otherwise, the plane will take off in a normal fashion </i>

I does take off in a normal fashion that is the point.

Sport_Pilot

Everybody has their own taste's and put putting around the living room seems boring to me. I'd rather watch TV. Well OK it would be intresting for a while but I would probably put it down after a few minutes and never go back to it.

rmh

Try one - before you knock it
I have had models up to inc 42% -and for the bang for the buck none are as much pure fun as this little wonder
From a purely technical standpoint -it is a dream come true for those who worked throuugh the various advancements in radios engines airframe construction etc..
The heli actualy has two working gyros -VERY accurate and all up under one ounce!

topspeed

Ok Ben

I see then it is not the size of the ac that matters but the wingloading.

I realized that VmaxProbe snapped just like all four the small winged Bede-5 with A model wing ( all on first flite and resulting 4 fatalities ).

Shoe

I've watched this discussion for years and, until today, was smart enough to stay out of it. Let me start by defining which problem I'm talking about...

Suppose you place a wheeled vehicle on a treadmill and control the speed of the treadmill so that the belt ALWAYS translates at exactly the same rate as the bottom of the wheels (i.e. the instantaneous treadmill speed -in ft/sec- is equal to the instantaneous wheel rotational speed -in radians/sec- times the height of the center of the wheel's axle above the treadmill -in feet-). If you are able to do this, then as long as the wheels remain in contact with the treadmill, the vehicle cannot move forward or backward. Notice that I said wheeled vehicle. As long as the treadmill speed is controlled as described above, it doesn't matter whether you're talking about a bicycle, a firetruck or an airplane, the vehicle CANNOT move forward or backward if it remains in contact with the treadmill. Notice also that this has nothing to do with friction or torque or thrust or anything having to do with forces (in Physics speak, it is a kinematic constraint).

So if the vehicle happens to be an airplane, can it take off from the treadmill? The answer is: only if it's the kind of plane that can start its takeoff with PURELY vertical motion (remember that the treadmill prevents ANY forward or backward motion as long as a wheel is in contact). Are there airplanes that can do this? There certainly are... a Harrier can do this with no problem. How about a "conventional" airplane? The way the question was posed, it said nothing of the wind conditions. Certainly if the wind blowing over the treadmill was strong enough (and in the right direction) ANY airplane could start its takeoff vertically. OK, how about if you specify that there is no wind when the treadmill belt is at rest. In that case, it's POSSIBLE that a "somewhat conventional" airplane could take off from the treadmill. In order to do so, the propulsive part of the airplane (i.e. its jets or propellers) would have to create/induce enough flow over the wing(s) and control surfaces in order for them to generate lift equal to the airplane's weight. If you look at some specialty STOL airplanes, they could probably do this while still being considered "somewhat conventional". For most airplanes, however, it isn't possible or them to start their takeoff with purely vertical motion under "no wind" conditions.

So why do thrust and torque and friction so often come into the discussion? I think it's because it is hard to imagine how the treadmill is able to maintain the condition described above. If the airplane's propulsion system exerts some thrust on the airplane then surely the treadmill must exert an equal and opposite force on the airplane. Is it possible for a treadmill to exert such an opposite force on the airplane? Absolutely. OK, but what if the airplane has no friction in its wheel bearings? The answer is still "yes". The wheels (and treadmill) will just keep rotating faster and faster as long as thrust is applied to the airplane. In reality, this couldn't go on forever, because at some point the wheels will come apart, but at that point you no longer have a wheeled vehicle and all bets are off.

But "wait" you say, "the airplane in the Mythbusters episode flew". True, but that airplane was NOT subject to the constraint I described above. If you were standing on the ground, the Mythbusters airplane would have been moving forward relative to you. Still an airplane on a treadmill, but on a treadmill that wasn't moving (really accelerating) fast enough.

Top_Gunn

My Feedback: (6)

If the airplane isn't moving forward, how will the thrust of the engines cause the wheels to turn at all? It's only the forward motion of the plane plus the friction between the wheels and the ground that makes the wheels turn. This version of the problem is just a set of contradictory assumptions.

Are we all agreed that in the Mythbusters version of the problem (speed of the treadmill equals the forward speed of the airplane) the plane takes off as normal, except that its wheels turn twice as fast as they would on a fixed surface?

victorzamora

You've hit the nail on the head, Top Gunn. It's Zeno's paradox all over again. THAT is what's so good about it.

Shoe

Absolutely not! Because the plane is on a treadmill, there is NO forward motion required to make the wheels turn. As the problem was stated, the plane must remains stationary as long as it is in contact with the treadmill... only the wheels and treadmill can accelerate. The thrust of the engines causes the wheels (and the treadmill) to accelerate because the treadmill must exert a force on the airplane to keep it from accelerating. The treadmill exerts the force on the airplane through its wheels. The force (and resulting unbalanced torque) on the wheels causes them to spin faster. As the wheels spin faster, the treadmill also spins faster (until the wheels come apart). No paradoxes here (Xeno's or otherwise).

It may be helpful to think of this part of the problem in reverse... Suppose you put the airplane on the treadmill, but instead of controlling the treadmill speed to keep the airplane in place, you allowed the treadmill to turn at any speed it wanted, and you very carefully modulated the thrust of the airplane to keep it in place. If the treadmill were to speed up, (or accelerate faster in the frictionless case) you would have to open the throttle in order to keep the airplane in place. I think this is pretty intuitive, and it illustrates the connection between airplane thrust and wheel/treadmill speed.

Ben Lanterman

Shoe - read through the comments I have made above and think it over. You have got it wrong.

You state... "it doesn't matter whether you're talking about a bicycle, a firetruck or an airplane, the vehicle CANNOT move forward or backward if it remains in contact with the treadmill. Notice also that this has nothing to do with friction or torque or thrust or anything having to do with forces (in Physics speak, it is a kinematic constraint). "

You speak of the movement of the contact point of wheel and treadmill and the position of the airplane body as if they all are physically connected for all time. They are not. The wheel and belt are connected - but and it is a big but - When the thrust exceeds the aft frictional force that the treadmill can exert on the airplane (and there is a definite limit) the kinematic constraint no longer applies.....

You say the problem is stated, "the treadmill moves to keep the airplane stationary", but it does not say that physical laws are violated to do it. We are allowed to have the rest of the problem obey the laws of physics. You say, "As the problem was stated, the plane must remains stationary as long as it is in contact with the treadmill... only the wheels and treadmill can accelerate."

The Mythbusters statement of problem was, "An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff." They don't say the airplane "must" remain stationary as long as it is in contact with the treadmill. There is no kinematic constraint in the problem as stated and there is none in real life.

A point is reached where the treadmill can try to do anything it can, run at any speed it can, and although the wheels will respond to it equally, the airplane can move forward - the kinematic constraint no longer applies and the airplane will eventually take off.

You say it might be helpful to think of the problem in reverse. I performed that exact experiment in my basement!! The maximum force the treadmill could exert aft was small even though the wheels were turning at the maximum treadmill speed (which was wide open and much faster than the Vapor's flying speed) and the airplane took off with no effort (and hit the front support of the treadmill). It had no problem doing it over and over. The Vapor is sturdy.

You can have a kinematic constraint with a car. The frictional force of a car's tires on the treadmill is considerable and if the treadmill is capable of all of the speeds that the car can produce it can be stationary no matter what. A car is designed to maximize friction between tire and ground. You can do this experiment in the basement too.

An airplane is designed to minimize friction between tire and ground while having a great deal of thrust forward. For example, take the wheels off the airplane and put on small skids. The problem becomes the same as above - but we don't have a pesky wheel to get in the way.

The treadmill will try to keep the airplane stationary. As you apply power the body tries to move forward and the treadmill speeds up. The aft force on the airplane is the sliding friction force of the skid-treadmill interface which is proportional to the speed until - you guessed it - a maximum sliding friction force is reached. It can't get any higher no matter what happens. Exceed that maximum sliding friction force by enough and the airplane takes off - all the while sliding forward on the treadmill.

Don't fall into the trap that the treadmill-wheel contact point has unlimited force producing capability.

Ben