OT: Any mensa members here? ;)

[John Miller]

Originally Posted by Ben Winter

A good comparison is wearing roller blades on a running treadmill, hands on the rails on either side.

To "simulate" the thrust of the jets, simply pull yourself using the handrails. You will have no problem rolling yourself off the treadmill.

That's the most concise, clear and correct explanation I've seen yet!

[Dylan Couper]

Just to clarify... (or further confuse?)
I'm in agreement with the plane on the runway being able to take off regardless of the wheelspeed/conveyorbelt speed.

But I'd like some clarity on this scenario, just to make sure I have the physics right.

1) A small plane is sitting *STILL* on a massive conveyor belt travelling 100mph backwards.
2) The plane (sitting still, travelling backwards) has -100mph windspeed and 0mph wheelspeed (relative to the conveyor belt).
3) The plane normally needs +50mph windspeed to achieve lift.

So... The pilot kicks the throttle up to what thrust would under normal circumstances give him 50mph (I don't know plane RPM vs. speed figures at all, sorry)...

Which of the following is true?
A) The plane, not giving a rats ass about what's happening around it... simply because it is a plane and does not have a mind of its own... moves from -100mph to +50mph because the force of its engine is pushing against the universe, not the negtive windspeed nor the conveyor belt.
...and takes off!


B) The plane, again still not caring about the massive 20 mile long conveyor belt miracle of human engineering under it... generates a positive 50mph thrust... but because it is already moving backwards at -100mph airspeed... finds itself with a -50mph windspeed (still moving backwards in relation to the earth regardless of its now +50mph wheelspeed on the conveyor belt.)
And doesn't take off.

Love to hear an answer on that one.

[Dylan Couper]

Oh, and regarding Mythbusters... I haven't seen the full episode yet, but I wish they had experimented to see what they could have done to make the plane NOT take off.

[John Miller]

Originally Posted by Dylan Couper

Which of the following is true?
A) The plane, not giving a rats ass about what's happening around it... simply because it is a plane and does not have a mind of its own... moves from -100mph to +50mph because the force of its engine is pushing against the universe, not the negtive windspeed nor the conveyor belt.
...and takes off!

If it is moving with an airspeed of +50mph, it will take off. This is what you have described.

However, if at the start the plane is moving backwards with an airspeed of -100mph, it will be just like a 100 mph wind blowing up the (rat's) ass. Odds are the plane would be blown off/over etc.

B) The plane, again still not caring about the massive 20 mile long conveyor belt miracle of human engineering under it... generates a positive 50mph thrust... but because it is already moving backwards at -100mph airspeed... finds itself with a -50mph windspeed (still moving backwards in relation to the earth regardless of its now +50mph wheelspeed on the conveyor belt.)
And doesn't take off.

Love to hear an answer on that one.

Right - it won't take off.

Whether it takes off or not is all about airspeed and nothing to do with groundspeed. That's why airports switch runways/change direction according to the wind. Taking off into a wind requires less groundspeed, a shorter runway, less fuel etc.

BTW, there isn't such a thing as a 50mph thrust. Thrust is a force and makes the aircraft accelerate. As long as the thrust is maintained, the acceleration will continue. Just like a car's accelerator - you cut back on the acceleration when you get to the desired speed.

If you reverse the situation - i.e., the conveyor belt runs in the forward direction, then the aircraft will take off with less thrust required. If the belt is fast enough, no thrust will be needed.

This is just how the steam catapults on aircraft carriers work. They accelerate the aircraft quickly to take-off velocity. The speed of the ship and the head wind also contribute.

[Richard Alvarez]

For our non-pilot friends, it can be kind of confusing, seprerating GROUND SPEED from AIR SPEED from INDICATED AIRSPEED... all of these are distinctly different things. (Indeed, apparently more than one pilot was confused over this as well... ah well, plenty of drivers don't know how an engine works either).

The important thing to remember, is that the engines apply thrust to the airframe NOT the wheels. SO its just like someone standing OFF the treamill, pushing or pulling on the skater. Also, in the original thought experiment, and pretty much on the mythbusters, there is 'no apparent wind'... that is it is assuming 'still air'.

Here are some interesting go/no go thought experiments, that illustrate the importance of the SPEED and DIRECTION of the airflow in relation to the wings, and the difference between TAS, IAS and GS.

Put your plane on the treadmill... in a wind tunnell. The treadmill, the engine and the wind flow can all be controlled independently OR simlutaneously in synch. The wind tunnell can generate flow in either direction.

Assume a nominal 'take off speed' of the aircraft at 100mph.


Is it possible for the airplane to liftoff, without 'moving forward' in relation to the observer standing outside the tunnel?

If so, describe what speed and directions the wind and belt must travel.

IS it possible for the airplane to remain stationary ON THE RUNNING TREADMILL without lifting off?

If so, describe the speed and direction of the wind and belt.

Is it possible for the plane to take off while 'travelling backwards' in relation to the independent viewer?

Again, describe speed and direction for belt and airflow re: aircraft.


Or better yet - just lock this thread and I'll get back to editing. ;)

[Dylan Couper]

Originally Posted by John Miller

BTW, there isn't such a thing as a 50mph thrust. Thrust is a force and makes the aircraft accelerate. As long as the thrust is maintained, the acceleration will continue. Just like a car's accelerator - you cut back on the acceleration when you get to the desired speed.

I figured it was easier to simplify it down to that rather than to go through xRPM to lb/ft-thrust to acceleration/time/velocity. :)


Anyway, thanks for the feedback, it's definitely something to wrap your mind around, especially for us non-pilots. But what none of us factored into the equation though is...

how many hours does the plane have to sit on the runway before control clears it for takeoff? :)

[Daniel Vanniekerk]

Originally Posted by Richard Alvarez

Put your plane on the treadmill... in a wind tunnell. The treadmill, the engine and the wind flow can all be controlled independently OR simlutaneously in synch. The wind tunnell can generate flow in either direction.

Assume a nominal 'take off speed' of the aircraft at 100mph.


Is it possible for the airplane to liftoff, without 'moving forward' in relation to the observer standing outside the tunnel?

If so, describe what speed and directions the wind and belt must travel.

IS it possible for the airplane to remain stationary ON THE RUNNING TREADMILL without lifting off?

If so, describe the speed and direction of the wind and belt.

Is it possible for the plane to take off while 'travelling backwards' in relation to the independent viewer?

Again, describe speed and direction for belt and airflow re: aircraft.


Or better yet - just lock this thread and I'll get back to editing. ;)

1. Yes, if the wind speed in the tunnel is 100mph towards the nose of the aircraft. Belt direction and speed of no consequence providing you compensate for rolling resistance of the tyres
2. Yes, if the wind speed is opposite to the direction of the belt and high enough to counteract rolling resistance of the tyres of the plane - obviously below 100mph if the wind speed is towards the nose of the aircraft.
3. Yes. The wind speed must be 100mph plus the speed it is travelling backwards in relation to an independent viewer.

[Adrinn Chellton]

Another great way to prove this is to put a little toy car on a treadmill and hold onto it. Then turn the mill on and see how easy it is to push the car forward against the treadmill. That's very similar to the type of thrust generated by an airplane engine, jet or prop.

The only way you would have any difficulty is if the toy's wheel bearings failed.

[Carl Hayes]

Originally Posted by Sharyn Ferrick

A jet flying at mach 3 crosses over laser tower on the ground. At the same precise moment a laser beam is flashed from the Jet and the tower on a target the same distance ahead. Which laser beam hits the target first ?

Sharyn

In a vacuum, the beams would hit simultaneously, because they're going the same distance and the speed of light is constant. In air, however, the tower's firing path, being at a lower altitude and therefore in thicker air, will yield a slower lightspeed, because light moves more slowly in air than in thinner air or vacuum.

Let's assume they're both in vacuum, or both at the same density altitude.

Lightspeed is the same regardless of the observer or his motion. Because of the Lorentz-Fitzgerald contraction, the distance to the target will seem (and actually be) shorter as seen by the airplane [or its crew]. To them, the laser beams travel shorter paths, so take less time, but still go equal times and distances, and arrive at the target simultaneously. The difference in distance (for the observer in the plane and the observer in the tower) is exactly the same percentage-wise as the difference in the times the observers measure. That's relativistic time dilation and distance contraction.

Bottom line: If the two beams are fired when the distances are equal, then each observer will see the two beams arrive simultaneously, and they will be right. But the two observers will not see the same distance, or measure the same time interval, or concur about the speed of the airplane.

-- Carl Hayes, Mensan since 1965. Old fuddy-duddy.

[Carl Hayes]

Originally Posted by Sharyn Ferrick

A fixed wing (Non Harrier) plane takes off based on the air flow over and under the wings. Lift off speed is typically measured in terms of speed over the ground but only for convenience. This is why the plane takes off into the wind, and air craft carriers point into the wind, and power head.

If the airflow over/under the wing is not sufficient to create lift, the plane will not take off

Sharyn
Having flown turbo prop/jet aircraft for years ;-)

This deserves a somewhat deeper analysis, although Sharyn is precisely correct.

(1) The question is ambiguous. Does the treadmill's speed (let's call the runway a treadmill) equal the airplane's forward airspeed, or the speed determined by seeing how fast the wheels turn?

(2) If the treadmill's speed is determined by the airplane's forward airspeed there is no problem. At, say, TAS=100 knots [for you ground-pounders, TAS is True AirSpeed] (let's say north), the treadmill goes 100 kt south, and the wheels roll at 200 kt. The airplane takes off when it reaches its normal Vr (rotation speed).

(3) If the treadmill's speed is determined by how fast the wheels are rolling, the question is inherently self-contradictory. Proof: assume the wheels are going at speed Vw, the airplane is going at speed Vp, and the treadmill is going at speed -Vt.

Then, Vw = Vp + Vt because the wheels are assumed not to skid.

Also, Vt = Vw

Then, Vw = Vp + Vw, from which Vp = 0. This means the plane does not move, but the statement of the problem inherently assumes that it DOES move. Contradiction! Another way of saying it is that, if the plane moves, the treadmill cannot behave the way the problem statement says it does. Reductio ad absurdum!

My goodness, these are simple problems.

Incidentally a Harrier is, by definition, not an airplane when taking off vertically. It's a hovercraft, and becomes an airplane only when it gaines airspeed enough to support its weight by aerodynamic lift instead of thrust.

What do you fly, Sharyn? I fly only small taildraggers.

-- Carl

[Lee Roberts]

I've read the entire post, gotten a migraine because math was used by someone, took my medication, and have reached the following conclusion:

If I go to the airport to catch my flight and my 747 is on a big treadmill, I'm going to get back in my car and drive to my location. I really hate running on my treadmill, and the plane probably doesn't like it, either - I DO NOT want to piss off the plane.

Since we're talking about planes: Now that Amtrak has received however many zillion dollars to upgrade their system, it begs the question:

If Train A and Train B are on the same track 400 miles apart, and Train A is travelling 60mph while Train B is travelling 80mph, how long will it be before Amtrak is broke again?

[Brian Huey]

Originally Posted by Carl Hayes

(3) If the treadmill's speed is determined by how fast the wheels are rolling, the question is inherently self-contradictory. Proof: assume the wheels are going at speed Vw, the airplane is going at speed Vp, and the treadmill is going at speed -Vt.

Then, Vw = Vp + Vt because the wheels are assumed not to skid.

Also, Vt = Vw

Then, Vw = Vp + Vw, from which Vp = 0. This means the plane does not move, but the statement of the problem inherently assumes that it DOES move. Contradiction! Another way of saying it is that, if the plane moves, the treadmill cannot behave the way the problem statement says it does. Reductio ad absurdum!

-- Carl

Almost spot on except the part about the case where the plane doesn't move being absurd. It is a valid solution to the problem.

What if you replace the plane with a car like on Mythbusters?

Their reasoning for why the car won't move is incorrect. If you measure 'speed' for the car as Vp (speed with respect to the air) then it will drive off of the tread mill with the tires spinning twice as fast as the car drives off the belt, Vp (airspeed).

It's just a vector problem. 'Speed' is an ambiguous term in the problem and depending on what you define it as you either get an object moving off of the belt or you do not. The matter of propulsion doesn't matter.

[Mugurel Dragusin]

This is an entirely different thing...based on the initial question on this forum, most likely the plane would not fly simply due to the plane being stationary in relation to an Earth observer.

Based on the wheel speed, we need not even talking :)

While I didn't bring anything new, my initial assessment was that the plane would not fly, based on the initial formulation. The, reading through the thread I see all these contradictions to an obvious thing (for me)...thus, reading all and seems Mr. John Miller (#155) spotted the formulation issue.

Anyway...heh :) Long thread, thanks for confirming I am still sane though :)