Plane on a Treadmill, redux

Cecil's Columns/Staff Reports
81

This question is not answerable as its presented here are the many reasons why.

First some assumptions. the only way to make this work is to assume that the conveyor is as wide as a runway and as long as a runway if not infinite in length for the purpose of this discussion.

Lets assume everything else falls within the realm of reality as we know it. the impossible conveyor will be our one reality excemption.

SO lets move on - there are several questions I have to have answered before I can even try to answer this question.

What aircraft are we using ? (this is critical) Thurst to weight ratio ? Minimum Takeoff speed ? Gear Failure speed and time limitations ?

The Conveyor ? how much laminar type airflow movement will it create ? anything that large moving on the ground WILL move the air above it ? how much how fast how thick and how turbulent ?

Several possible scenarios.

The drag imparted by the conveyor may be too much to allow the plane to reach flight speed (the plane WILL move how fast is the question)

I have seen small planes unable to achieve take off speed because of a muddy field. so if mudd can keep it on the ground the conveyor has at least a chance of creating just as much drag.

the drag on the wheels is critical. if it exceeds the propeller and engines ability to overcome it the plane could be prevented from reaching take off speed.

also the gear itself. if the conveyor works as advertised it will make the wheels sping at TWICE the speed of the airplane if not more.

so if you need 200mph to take off the wheels will be going 400mph just before take off. What happens if your landing gear FAILS at 350mph ? well then you dont take off now do you :slight_smile: since your airspeed will only be 175mph or 25mph short of the minimum needed.

Now what about the AIR the conveyor is moving - at first glance this might actually HELP the airplane since ground speed is not what it required it needs AIRSPEED

but how THICK is this accelerate air flow and how fast is it and MORE importantly how TURBULENT is it. air that will barely faze an F-14 would tear a Cessna 152 to shreds.

If the air is to turbulent the airplane might crash before taking off.

Lets assume the airflow is smooth well now you have another problem. when you reach the end of your conveyor runway OR flying higher than the airflow created by the conveyor you are changing enviroment.

Let me explain this in a different way.
0 wind
Stall speed 120mph
Ground speed 121
Airspeed 121mph

Result you take off

40mph headwind
Stall Speed 120mph
Ground Speed 81mph
Airspeed 121mph

Result you take off.

Scenario #2 again but this time the headwind STOPS once you leave the ground

result your airspeed is not suddenly 81mph Woops your stall speed is 120mph

Result you stall and crash.

So what happens when you Reach the end of this runway or rise more than 20-40 feet off the ground (assuming a bubble of 20-20 feet)

All of a sudden the AIRSPEED you got as a bonus headwind from the conveyors effect vanishes. if your now below your stall speed you crash.

For a little deviation from the subject as you note airspeed and groundspeed can and almost always do DIFFER. this is critical for pilots since they require BOTH peices of information. airspeed tells you if you will stay aloft while ground speed tells you how far you will get with the fuel you have onboard IE if the headwind is too high you might not be able to make it to your destination airport if fuel is tight :slight_smile:

this also means airplanes can fly “backward” or “hover” from the perspective of a Ground observer.

if an ultralight flies forward at 35mph and encounters a 40mph headwind to the pilot his airspeed is 75mph and his ground speed is -5mph yup if you look up he would appear to be flying backwards at 5mph

or that a plan with a max speed of 200mph can in fact go 250mph ground speed if he has a tailwind of 50mph :slight_smile:

if the ultralight flyer flies at 35mph and hits a 35mph headwind he can quite easily “hover”

So once again I need a lot more information to answer this question properly.

the only way to make this question work is to supply all this information OR reword the question to ask these question.

Will the airplane move forward relative to your non conveyor stationary position and could it in theory take off.

Yes and if conditions are right Yes would be the answer.

Ask the question is asked now you can not answer it with a yes or a no.

No I am not an Aerospace engineer Yes I am obsessed with physics and anything that is capable of flight :slight_smile:

And no I don’t thing I would ever consider paying $15 to post on a public forum ?? what the heck is that all about?? :slight_smile: IE what is offered here that is worth $15 a year. No offense intended but I have never heard of a pay public forum and am having difficulty thinking of what one could offer for such access.

Chris Taylor
http://www.nerys.com/

82

“So the issue is the mass of the air…not how fast the tires are spinning…besides…the tires would disintegrate around 250 knots anyway.”

So answer me this. what is the takeoff speed of your airplane. if its more than 125knots you wont take off since your wheels will disintegrate before reaching take off speed :slight_smile:

:slight_smile:

Chris Taylor
http://www.nerys.com/

83

I have landed some aircraft close to 200 knots. All have taken off at lower airspeeds by design (somewhere around 150 kts)…however in an emergency there are situations where you will land at a much higher speed than you took off…and use about 2 miles of runway to stop.

84

And the answer depends on your interpretation of the problem and your original assumptions. You appear to be interpreting the original question as allowing the plane to move forward with respect to the ground, while the treadmill moves backwards and trhe wheels spin twice as fast as they normally would. Nothing wrong with that interpretation, and of course the airplane would take off (assuming the tires don’t blow).

However, other people interpret the original question as requiring the treadmill to keep the plane in place with respect to the ground (although it “moves” with respect to the treadmill belt). Nothing wrong with that interpretation either, but it leads to very different conclusions.

85

No, unfortunately, you’re not right. The length of the treadmill means nothing. The key is the speed of the treadmill and its ability to match the expected forward speed of the plane.

Am I right?
[/QUOTE]

86

As I was reading the post about tires having to “grab” the runway, I was thinking, “In this person’s plane is there a fanbelt running from the propellor to the wheels or do the wheels have their own little motors?”

How about this. Instead of a big treadmill with a canvas or asphalt runner, try to imagine a conveyor made of ice and the plane does not have wheels but instead skids and, this is a real stretch, there is no friction between the ice and the skids. Yeah, I know some people might start discussing the lack of feasability of having a conveyor made of ice since the ice would crack as it went around the conveyor since ice is notoriously hard to bend, but lets just Assume it’s so.

Does that make the problem easier?

87

[/QUOTE]

No, you are not. Pay attention to the earlier posts. What do you mean by matching speed? Is that the same thing other people mean?

88

One would hope: reading comprehension, but from what we have seen in this and the several similar threads that is unlikely.

Are you asking the same question as people who disagree with you? Are you sure?

89

I agree. It seems to me that this is the kind of net brainteaser that is aimed to get people to say, “Oh, hey, airplanes take off by pulling themselves through the air, not pushing against the ground like a car. I get it!” This is by no means immediately evident to the majority of people, even smart people, and that lightbulb going on pays for the price of admission, so to speak. The discussion going on here, about friction and infinite wheel speeds, is interesting but much more complicated than the initial puzzle is “worth”—it requires a lot of information we don’t have (about the particulars of the airplane and the conveyor), it necessitates specific assumptions about which bits of the airplane are magical and which are real-world, and it’s only answerable by a very tiny fraction of net folks. From a sociological standpoint, it seems much more likely to me that BR#1 is the intended aim of the thought experiment—it would not have propagated as far as it has if the audience were as limited as BR#2’s is.

Those of you for whom BR#1 was obvious: congrats, you’re smarties. Party! But the answer to the Monty Hall puzzle (or any other net brainteaser) is obvious to some, too, but that doesn’t prevent it from propagating and being interesting to plenty of people.

90

“If the plane’s forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH”

Bad math - the wheels rotate at 100MPH

Imagine the wheel and the surface of the conveyor belt as a set of gears - they both “move” at the same speed.

The speed of the plane through the air is 0mph (100 forward over the surface of the conveyor minus 100 backward of the conveyor)

Look at these cases:
Plane = 100 fwd on conveyor in opposite direction of 100 = wheel speed 100, air speed 0
Plane = 100 fwd on stopped conveyor = wheel speed 100, air speed 100
Plane = 100 fwd on conveyor in same direction of 100 = wheel speed 100, air speed 200

“imagine you’re standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you”

That changes experiment with a third force (the rope) not present in the original question (only 2 forces = rotation of conveyor and thrust of engines) and is invalid.

“The unwary tend to reason by analogy to a car on a conveyor belt”

The plane operates like a car until enough air passes over the wings to create lift. Only then does it become an airplane.

“the plane moves forward at pretty much the usual speed relative to the ground–and more importantly the air”

Here’s your flaw - the plane moves forward reletive to the ground (the conveyor) but since the conveyor is going backwards by the same amount, it is not going through the air.

91

No. Absobloodylutely not.

I do not know of any aircraft in history that employed drive wheels. At the most, aircraft wheels have brakes. Aircraft are propelled on the ground either by their jets of props, or (when maneuvering at large airports) by a tug.

92

Not really bad math, no. Just different assumptions about what the problem means. You’re assuming the plane’s forward speed is measured with respect to the conveyor. Nothing wrong with that. Other people are assuming the speed is measured with respect to the ground. Nothing wrong with that either.

93

It makes it easier becuase it eliminates friction between the plane and the treadmill. On a regular treadmill there is friction between the wheels and the surface that potentially could counteract the force of the engines.

94

Thats not possible though and the quetion makes no reality allowance for that. the treadmill must go the same speed as the airplane so in order for the treadmill to have ANY speed the plane MUST move forward. if the forward motion of the airplane is 0mph then the rearward motion of the treadmill MUST by definition set forth in the question be ZERO mph

So we MUST assume the airplane DOES in fact begin to move forward. Since a treadmill moving backward would have to move at MANY multiples of the airplanes speed in order to impart enough physical trag to prevent it from moving forward we know the airplane will accelerate since the treadmill is limited to the speed of the airplane.

since the drag this imposes is far lower than the THRUST the engine provides we know the airplane will in fact move forward without much effort.

Remember it does not say it will move backwards equal to the thrust of the airplane but equal to the SPEED of the airplane.

Again very poorly written question but this part is QUITE clear in the question with no ambiguity. the treadmill can never exceed the take off speed of the airplane since at that moment the airplane will take off (baring the other issues I describe)

Chris Taylor
http://www.nerys.com/

95

[/QUOTE]

Technically your right but I chose to extend the question to the plane successfully attaining flight not just leaving the ground since the quetion does say Take Off not just leave the ground.

if the conveyor is too short and the wind from the conveyor is significant and the pilot can not attain still air airspeed needed to stay up the moment he rises too high or passes the end of the runway the plane will crash since at that moment as per the question he will encounter CALM AIR at which point if his ground speed is not higher than his stall speed it wont be a take off so much as a hop and crash :slight_smile:

Chris Taylor
http://www.nerys.com/

96

No assumptions. The wheel’s speed doesn’t change depending on how you measure it.
The wheel is in contact with the surface of the conveyor. If the plane’s thrust moves it forward, the wheel is turning a 10mph in relation to the conveyor top. If the conveyor is not moving then the plane (and wheels) are moving at 10mph in relation to the air (and ground around the conveyor).

The conveyor starts up and starts going backwards at 10mph. If you were a bug sitting on the belt, you’d see the wheels of the plane go by at 10mph. But that same bug and the belt are also moving at -10mph (negative in comparison to the plane). Standing outside the whole contraption you seeing the belt going 10 one and the wheels going 10 the other way. The plane goes 0.

People are somehow saying the the wheels should be spinning at 20mph but 10 plus -10 is 0.

97

I am sorry but you are woefully mistaken (no offense just statement of fact)

you are right when your speed is directly CONNECTED to the ground. since a car transfer engine power into rotation of tires which translates into motion on the ground X number of tire rotations equals distance over time.

so a CAR on this runway would never move from its starting point.

at 50mph the cars wheels would be at 50mph the treadmill would be at 50mph as well but its TRUE ground speed (think of the treadmill as airspeed or “treadmill speed” so its treadmill speed and car wheel speed would be 50mph but its ground speed would be 0mph IE if you were standing to the side off the treadmill the car would appear motionless (think the DYNO at your local Inspection Station)

this is because the car derives is locomotion from direct contact with the ground. it does not have any “thrust”

an airplane is not pushing against the ground there is ZERO correlation between ground speed and wheel speed to an airplane so long as you dont exceed the mechanical limits of your landing gear.

BY the way this question would not work for a car since the cars speed and the treadmills speed would always be ZERO since the CARS speed IS the cars WHEEL SPEED

the question says speed of the airplane NOT speed of the airplanes wheels.

the ONLY effect that a treadmill would have on an airplane is to make it wheels spin faster a pilot would not even notice this unless he had a sensor on the wheels to detect how fast they were spinning (barring the other issues I raise above)

the airplane is thrusting. this thrust works regardless of the ground below it. (think a FAN its not moving but its producing THRUST now in the case of the fan the friction of its BASE on the FLOOR is greater than the thrust from the fan so it does not move.)

Chris Taylor
http://www.nerys.com/

98

This is a hilarious thread.
Remember that a body in motion tends to stay in motion…so since the acft is in motion (motionless) relative to the earth…by having the treadmill spinning means the acft will remain stationary.
If the entire argument is that there is friction within the bearings of the wheels, and the tires to the treadmill, and therefore the treadmill will pull the acft backward…

…then the question no longer matters…because you are changing the variables…I can make up any imaginary infinite resistance and keep any object from moving.
However, if you are arguing from a physics standpoint…

The airmass is stationary in relation to the earth/powered off acft.

Once power is applied to the aircraft, the it will “pull itself along” just like the rope rollerblade scenario. It will fly.

99

Actually both of you are slightly mistaken. the question is rather clear on this. since the question says CALM air you would be correct in assuming the point of reference is non moving ground (relatively speaking) ie the earth since that is the frame of reference we use to determine CALM AIR.

Flight is determined by airspeed not ground speed. thrust is determined by the pressence of an atmosphere to draw against Action reactions. the airplanes shoves a grap load of air backwards so equal and opposite force is applied to the propeller in the forward direction since the propeller is attached to the rest of the airplane it goes along for the ride. the ONLY initial impact of the conveyor will be to make the wheels spin exactly twice as fast as the groundspeed of the airplane. Nothing more (again not counting the many other issues I mention above)

Chris Taylor
http://www.nerys.com/

100

Sorry the only reality exclusion the question stipulates is that this conveyor exists.

it makes no OTHER exclusions. it does not say we can assume the wind the conveyor will create is to be ignored. it does not say the failure limits of the gear are to be ignored it does not say we can assume the this wind to be stable or turbulent. it does not say that the extra drag imposed by this extra motion is to be ignored.

so we no choice but to assume what it says that this is REAL in which case reality and the extra crap that comes along with it also exists.

again it was a rather poorly written question :slight_smile: For example if they added this line to the question “You can assume there are no other side effects from the conveyor and it is infinite in length” THEN you could answer this question more easily since THAT would excempt us from having to consider drag mechanical failure or extra airflow and airspeed groundspeed discrepencies.

at which point it would then be able to answer YES the plane will take off with 100% certainty.

but that is not what the question said. :slight_smile:

Chris Taylor
http://www.nerys.com/