I have never ben on any plane, from a commercial airliner to a t-38 trainer jet that can take off in 30 seconds - two minutes maybe, but definitely not 30 seconds. I don’t think even an F-15, with possibly the best TTW around, could jerk its way off the ground that fast.
[QUOTE=nerys]
Every Plane I have been in from Cessana’s to Airliners to C130’s was able to go from Standstill to airborne in under 30 seconds.
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Again, for the fourth time, it depends on your assumptions about the problem. If you assume the conveyor matches the fuselage speed of the plane with respect to the ground, as you’re doing, the plane will take off. Absolutely. In fact, so far as I can tell, no one disagrees with that at all.
Actually, quite a few of us disagree with that.
Not quite. Even a theoretical treadmill could not do so, since the turning of the airplane’s wheels (disregarding friction) would prevent any thrust being applied to the airplane, no matter how much acceleration the treadmill might have. Note, however, that if the airplane’s wheels were ATTACHED to the treadmill and did not turn, then the treadmill would exert thrust to the body of the airplane, and if the treadmill’s thrust against the airplane equalled the engines’ thrust against the ambient air, THEN the plane would not move.
I can only suggest that on the next flight you take, look at your watch. Or just look at it now. Let it count off 30 seconds… Try to remember the last flight you where on.
2 minutes? No way, you’d be off the runway, through the fence and starting emergency evac procedures.
Are you including the taxi to the runway?
I know it’s a lot of work to read all this stuff, but this has been covered many times.
I’m in the camp that interperates the question that the plane will fly.
BUT.
If the treadmill accelerated, and continued to accelerate, the inertial effects of the weight of the tire and wheel will be transfered to the plane.
Though it was shown that that type of acceleration would have to be so great that the whole thing would go up in flames in about 1 second.
Actually even that is not correct. if the treadmill were capable of going fast enough to create enough wheel friction to keep the plane in place LONG before it generated that kind of friction the airplane would simply leave the ground from the mass of air that the conveyor itself would be generating.
Remember an airplane only has 1 speed - Airspeed. there are no other indicators of speed in an airplane. that is why when the question says the speed of the airplane it can not possibly be talking about anything except airspeed because there is no other speed.
NOW the problem with this is that the question says the air is CALM so once the airplane takes off inside the conveyor boundary layer if it LEAVES this boundary layer and by the questions conditions enters CALM AIR its airspeed will not be almost zero. not good 
but it will have taken off and that is all the question asks.
Chris Taylor
http://www.nerys.com/
What enipla said. Cecil covers this in his column, and it’s touched on multiple times in this thread and others–the rotational inertia of the wheels will create a coupling between the treadmill and the plane, such that forces from the acceleration are transmitted. If you’re unsure just why this is true, ask and I’ll dig up some posts from the other threads.
Well of course that why most planes use wheels and not hunks of jagged metal. but this force is MINOR in the larger picture.
FOr the conveyor to turn this MINOR force into a force strong enough to equal the thrust of the airplanes engines it would have to move at an extraordinary speed (I would guess THOUSANDS of miles per hour) this is assume that the landing gear could withstand that. if we assume the conveyor can do this we assume the landing gear can take this.
at this point the conveyor would be moving such a huge mass or air at such a speed that the airplane would simply take off from its 0 ground speed and fly.
now how the pilot will STAY airborne is another issue all together since he would have to STAY in that boundary layer until he could crab sideways to enough of a ground velocity that when it HEAVES the boundary layer he will still have enough airspeed to stay in the air in the as described calm air around the conveyor. but the question does not ask if the airplane can FLY away successfully it only asks if it can take off and the answer is yes no matter which way you interprit the problem to be.
The whole point of the excercise is to make sure people understand force relationship. IE that the airplane pushes against the air and not against the ground.
this second iteration of the question does not exist. it was created by someone who WANTED to be right about the airplane not being able to take off so they tried to ALTER the question to make themselves right.
Chris Taylor
http://www.nerys.com/
A previous poster did the math.
A loose interpretation would be “For a small GA aircraft, the treadmill would have to accelerate to 636mph in one second to keep the plane in place.” And it would have to continue to accelerate.
Bada Bing, Bada BOOM.
I kind of agree with you here. But, folks like zut and many others have done a damn good job of getting the math on board here. Unfortunately, some new comers seem to just want to do an ‘I told ya so’ while not having the first idea of what is being talked about.
As I thought 636mph that would easily generate a boundary layer of air moving at likely over 150-200mph being conservative.
Ie the plane would easily take off but I sure would not want to be the pilot in that plane if that boundary layer was too small ouch.
if it tapers off you might be ok just climb till you find the slightly slower air without going into the calm air and accelerate till your ground speed is above your stall speed so that when you enter the calm air your airspeed will be sufficient but watch your trims its going to be a nasty transition
Chris Taylor
http://www.nerys.com/
Then I would suggest you have never been on any plane.
Christ, in two minutes a Dash 8 will have accelerated to over 240 kts and have travelled over 6 nautical miles.
If a Boeing 737 hasn’t rotated and lifted off (sea level or thereabouts) at right around 30 seconds, start to worry.
It’s not the speed, it’s the acceleration. Continuous acceleration produces extraordinary speed, of course, but it’s not the speed itself that transmits the force.
sigh The first time I personally saw this question it was phrased like so: Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? If you have your heart set on claiming that this “doesn’t exist” because planes have air speed indicators, then knock yourself out. But you do realize this is a semantic argument, I hope.
Oh, good. I was wondering about this. Can you show your calculations? I was wondering how quickly the air velocity dropped back to ambient, but I didn’t feel like researching the equations for something that was kind of esoteric.
I’ve wondered about this to zut To en-train (is that the right word?) air over the treadmill to lift the plane brings in so many other variables.
How rough is the treadmill for one. How long and wide for another.
Both sides are right, depending on the interpretation of the question, but how long might it take for a treadmill to get air going fast enough for a plane to take off?
I think that the folks that look to BR#2 as the answer are reaching a bit. But, it’s a good thought experiment. And I learned a lot.
Suggesting that the treadmill will accelerate enough air to get the plane to take off and hover is really reaching.
But. Since BR#2 pretty much disregards the ability of any plane to put up with such a force for more than a second or so. I guess we should also look at the air that the conveyor itself would generate.
Could it happen? Sure. Just like our hypothetical constantly accelerating treadmill. If you have one, I guess you have to have the other.
For myself. I’ll stick with BR#1. I think that’s the spirit of the question.
“Oh, good. I was wondering about this. Can you show your calculations? I was wondering how quickly the air velocity dropped back to ambient, but I didn’t feel like researching the equations for something that was kind of esoteric.”
"Suggesting that the treadmill will accelerate enough air to get the plane to take off and hover is really reaching. "
If we give a reality excemption to the treadmill we will assume the landing gear gets the same excemtpion otherwise the question is moot. SO the landing gear CAN take the force even if infinite. Otherwise there is no point discussing this as the plane would be obliterated instantly.
Have you ever used a belt sander ? even with super fine 1600 grit polishing paper ?
good now in a CALM AIR room put your hand NEAR it as its moving. (dont touch it that would hurt quite a lot most likely)
Notices the rather SIGNIFICANT amount of air moving ? yeah thats right thats the boundary layer.
at 636mph I bet its over 300mph but I was being exceedingly conservative. I dont ahve the ability to do that kind of math to figure out exactly what it would be and I dont care because we do not know what the treadmill is made of.
We can safetly assume some rubber like material since that is what almost all conveyor belts are made of that I am aware of and since its not stipulated we go with reality.
this means a VERY draggy surface not unlike the belt sander.
this means IT WILL (there is no room for argument here this is fact the question does not excemtp this) Move a massive volume of air at a massive speed with almost zero delay.
The airplane will probably take off faster on this conveyor than it would on a normal runway.
“sigh The first time I personally saw this question it was phrased like so: Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off?”
Sorry though I can not be certain I am 99.99% certain I am right in this regard. the question as you state it is illogical. it requires us to make too many assumptions and serves no educational purpose.
the first version DOES serve a purpose. it is my beliefe to 99.99% certaintly that somone who got stumped by the real question CREATED the second illogical question to satisfy themselves.
Chris Taylor
http://www.nerys.com/
I doubt the slickness of the surface would figure into the boundary layer, except perhaps very close to the treadmill itself. And the velocity of the entrained air will drop off with increasing distance from the treadmill. I was curious what the air velocity would be near the wings, as a function of the treadmill velocity. Ah, well. A real effect, but not exactly the main thrust of the question.
To my mind, the interpretation that requires the plane to stand still is more educational: to understand the answer, you have to know that the plane will not take off if it’s not moving through the air, even if its wheels are spinning madly. In the alternate interpretation, the plane moves forward, not much differently than normal, and of course it takes off–no special knowledge needed. However, the variations and interpretations are all muddled together by now, and I admit it’s kind of silly to contrast interpretations with perceived educational value.
No I am sorry that does not make sense at all.
it would make sense if a CAR was in the problem. NOW that second iteration would make sense.
for it to make sense with an airplane requires too many assumptions.
it requires you to assume the treadmill can do that.
that is can survive that.
that the plane can do that
that the plane can survive that
that the wheels can survive that
etc… etc…
the first one traps most people because they fail to realize the airplane pushes against the AIR and not against the GROUND.
There is NO feasible way for a treadmill to produce enough speed (and I am sorry your math is subject to me as I do not think 636mph would be fast enough)
The Friction differential is so great that we are forced to move the treadmill into PURE fantasy just to allow the problem to work.
Sorry I just dont except that. NO teacher would create that problem. it just makes no sense to do so. Problem #2 as far as I am concerned came froma disgruntled student or internet user who got stumped by problem #1 so they made up problem #2 so they could pretend they had a clue. This is what I will believe until someone can prove to me otherwise. there are just too many problems with the question. too many reality excemptions.
and the boundary layer on a runway sized treadmill would be QUITE substantial. probably over 100ft thick at least.
Look at how thick the boundary layer ona belt sander is. several inches.
Scale a plane down to those dimensions and it could fly all day withing that boundary layer. and thats only 6x3 inches or so.
Something the size of a runway would move quite a significant amount of air.
Chris Taylor
http://www.nerys.com/