Airplane physics question

The original post is a repost and rewording of a puzzle that apparently began circulating in English around mid-2005. If you search you will find a lot of differently worded versions.

However, the "original" wording of the problem was apparently posted in Russian in August 2003. Even then it was a posting of a conundrum apparently posed at a school, so that could also have been a variant. Still it is the earliest and most original recorded instance so far.

http://forum.ixbt.com/topic.cgi?id=64:417

 

I think you left out a key portion of the translation:

"The aircraft (reactive or screwed) stands on the runway with movable coating (type of conveyor), the cover can move against the direction of take-off of the aircraft, it has a control system that tracks and adjusts the speed of the web so that the speed of rotation of the wheels of the aircraft is equal to the speed movement of the canvas. The question is: will the plane be able to scatter on this canvas and fly off?"

 

Not me, the browser translator.

 

If you understand the parameter "moving in the opposite direction of rotation" to mean the spin of the wheels, then you would need to have the conveyor constructed as a giant wheel, that also spins. The conveyor is not being described this way.

The question was meant to be about physics, not semantics.

 

Moving in the opposite direction of rotation cancels wheel rotation.

Doesn't matter if it's a conventional type conveyor with drums at each end or a sheet of material pulled along the ground, the above remains true.

If it's about physics and not semantics I think we already agree the plane would fly regardless

 

No way it takes off, the ground speed would not be high enough.

 

Lol. More of this! It’s all about airspeed not groundspeed. They are called airplanes not groundplanes for a reason!

 

IIRC, Tillman lives by a private airstrip. Gives him time to observe, which he does quite well.

Regardless, Pitot Tube would say "No groundspeed *or* airspeed for you!"

It won't fly.

Sent from my SAMSUNG-SM-J727A using FerrariChat.com mobile app

 

I wasn’t even aware pitot tubes *ever*....*measured*....ground speed.

Cool stuff.

 

LMAO

 

It will fly, I can't find the exact video, but there was an larger RC plane they did this with and a large treadmill (This link has the mythbusters version). But it will take off.

https://jalopnik.com/here-s-the-actual-science-behind-that-plane-takeoff-mem-1797763299

 

A possible problem might be exceeding the maximum tire speed and resulting tire failure.

 

Even though the question is badly phrased, the real key to understanding the dynamics is that the conveyor belt speed must be constantly increasing ... a conveyor belt that moves rearward at a constant speed will not exert a rearward force on the plane, but a rearward-accelerating conveyor will exert a rearward force on the plane. All the "experiments" that i've seen fail to understand this essential point (more broadly, fail to understand inertial vs non-inertial frames of reference).

In brief, the question essentially "inverts" F=ma

If the conveyor belt actually accelerates rearward at the correct rate, applying a rearward force on the plane to match the forward thrust of the engines, the plane can & will remain stationary relative to the ground and surrounding air.

 

nah the wheels don't really matter.

Heck, throw a brick on a conveyor belt. If the belt (and brick) move at a constant speed, the conveyor belt is imparting no force on the brick (no force is required to move an object at a constant velocity). If, however, the conveyor speed is increasing ... then the conveyor is indeed imparting a net force on the brick (a net force is required to accelerate a mass).

A constant-speed conveyor belt cannot keep a plane stationary, but a rearward-accelerating conveyor can.

 

Correct, this is key to the question. Also essential, as you initially said, that the question is badly phrased, which explains the strong opposite reactions of people. Anyway the rearward-accelerating conveyor would need to accelerate infinitely almost instantly, so totally ficticious. A real world setup that tried that would result in wheel and conveyor destruction in seconds.

 

Can't believe folks can't get this. The wheels have nothing to do with the ability of a plane to move forward. They only keep the belly from scraping on the ground during take off and landing. The rearward-moving conveyor belt that matches the wheel speed is doing nothing more than setting up a pseudo zero friction scenario. Analagously, imagine the plane taking off on a frozen lake where the wheels have zero friction and therefore can not do anything to help propel the plane forward (not that they ever do anyway). The engine/propellor will still drag the plane forward across the ice and it will eventually reach take-off speed. No different on the conveyor belt. Unless you somehow believe that the conveyor belt moving beneath the rotating wheels somehow exerts a massive rearward force on the plane. The rearward force is essentially zero, particularly relative to the force exerted by the engine/propellor.

 

A rearward moving conveyor ... moving at a constant speed ... exerts zero force on the plane. Can't possibly balance the forward thrust of the motors/engines.
A rearward moving conveyor ... that is accelerating ... exerts a rearward force on the plane. If the acceleration is fast enough (infinite acceleration is certainly not required, since infinite force is not required), the rearward conveyor force can balance the forward thrust of the motors/engines and keep the plane stationary.

The difference between a constant-speed conveyor belt, and an accelerating conveyor, is no small matter. The difference is huge, and quite fundamental ... as different as a body moving at a constant velocity versus a body that is accelerating.

 

The problem statement starts with the plane at rest, so acceleration of the conveyor belt is a necessary implication from the conditions.

 

No wind and the conveyor matches the ground speed of the plane exactly means that the acceleration due to thrust from engines is the same as the acceleration of the conveyor in the opposite direction so no forward velocity. No forward velocity means no air speeds over the wings means no lift is generated, means no flight, therefore plane is essentially a noisy rock.

 

Jeez, even the myth busters demonstrated that the plane will take off. The only thing the conveyor belt does is spin the wheels at twice the speed they would normally spin on a take-off roll. The wheels don't drive the plane, the engine thrust does. And the wheels turn freely (essentially) on the conveyor belt meaning they do not get dragged backwards by the conveyor and do not impede the forward thrust of the plane.

 

Mythbusters test was fatally flawed. Constant-speed conveyor does nothing.

I'm shocked at how many people don't get the essential, fundamental difference between an accelerating conveyor and a constant-speed conveyor ... the fundamental difference between an accelerating body, and a body moving at a constant velocity ... an inertial frame of reference, and a non-inertial frame of reference. These are most definitely not pretty much kinda the same things ...

 

Wow, let's try another analogy that might be simpler to understand. The engine/propellor create thrust which ultimately acts as a force in the forward direction. Instead of the engine/propellor, consider a sufficiently powerful winch with cable attached to the front of the plane which can exert the exact same force as the engine/propellor would. Do you really think you could not winch the plane forward on free-wheeling tires over a conveyor moving backwards, regardless of the conveyor speed. Likewise, the engine/propellor are doing nothing other than winching the plane forward. The force due to friction between the conveyor and tires is so small compared to engine thrust as to be negligible. Laughable really.

 

You still don't get the real, fundamental difference between:
- a body moving at constant velocity, versus a body that is accelerating
- a conveyor moving at a constant velocity, versus a conveyor that is accelerating

The difference between "constant velocity" and "acceleration" is not small, nor something to just "gloss over" (as you have been doing). The difference is HUGE, and fundamental to ALL of physics. Pretending that there is no difference, does not help your case. So far, you have not acknowledged or understood that there even IS a difference


Once more: throw a brick on a conveyor belt.
IF the conveyor belt is moving at a constant speed, THEN the conveyor belt is exerting NO force on the brick. Why? Because no force is required to move an object at a constant speed.
IF the conveyor belt is accelerating, THEN the conveyor belt IS exerting a net force on the brick. Why? because a net force IS required to accelerate an object.


In one case, there is NO net force. In the other case, there IS a net force. Can't get much clearer than that!


(It's OK that you don't understand the difference between "constant velocity" and "acceleration" ... the mythbuster guys were equally clueless)