Can the plane take off?

[Fit of Rage]

Big edit: It's a big yes. I re-read it and didn't notice the bit about "sensing" the speed of the plane. This means it starts from a stand-still, so the only thing that is going to happen is that the runway will have to be very slightly longer (a few metres) or slightly more thrust will be needed. I'll leave in what I originally wrote

The plane will be able to take off.

It, will, however, take a longer time as the engines will have to accelerate the plane from whatever speed they are pulling it back to the required take-off speed.

You'll also have to take into consideration the tyres. I'm not too clued up on the regulations regarding tyres, but it's probable they will be able to withstand the increase in heat from the faster rotation speed.


Also you have to consider the way turbofan engines work. The require a starter motor to get them going to a high enough speed that they can "suck" in the air from the front and be self sufficient (ofc they have to burn fuel). If you're starting the conveyor belt at the same time as the engines, this probably won't be an issue. If, however, you wait until you're travelling backwards at some speed before attempting to start the engines, it's likely you won't be able to get the compressor (intake) spinning enough to "suck" any air in, and thus won't be able to get started.

Big ups, Ewan's got it right. It will take off, albeit it will take a much longer time.

PS: Fluffz, shut the fuck up about infinite acceleration.

[D1st0rt]

I agree with Ewan from a theoretical standpoint (once he made me realize I had to ditch the deus ex machina keeping the plane stationary -- I misread that as a given).

I also did some internets research and number crunching:

The static coefficient of friction for rubber on rubber is 0.84. A 747 has an EMPTY weight of 180,000 kg. This makes the maximum frictional force 1,483,272 N

Now, the Pratt & Whitney PW4000-94 engine has a takeoff thrust of about 253,000 N.

So even though it conceivably could, I don't think this plane is going anywhere.

[Ewan]

The static coefficient of friction for rubber on rubber is 0.84. A 747 has an EMPTY weight of 180,000 kg. This makes the maximum frictional force 1,483,272 N

This would be correct if the plane had a rubber belly and simply sat on that and not the wheels.

The value you've given there is the friction on the wheels, not the whole plane. The wheels turn, and thus the majority of the friction is "absorbed" and not transferred to the plane. The only friction force which matters really is the friction between the wheels and their axles.

[D1st0rt]

Rubber and Aluminum: 0.51

It's still 900,558 N for a plane with NOTHING in it

[Bioture]

Are you just not reading what I say, I am aware of how planes fly thank you.

The FORWARDS MOTION of the plane is provided by the engines. The running on a treadmill argument is not valid as the only thing pushing you forwards are your feet, WHICH RELY ON THE SURFACE TO PUSH YOU FORWARDS, engines on a plane aren't PUSHING AGAINST THE GROUND like your feet are.

The engines are like you running on a treadmill with a rope tied to you. This rope is tied to a car, the car drives, you move forwards.

I'm not sure if you're agreeing with me here or something - but what is the purpose of your "FORWARDS MOTION" again?

[Ewan]

Rubber and Aluminum: 0.51

It's still 900,558 N for a plane with NOTHING in it

Ok, now your argument only works if the plane simply has no wheels and is sitting on the runway on its belly.

Or maybe it uses Skis?

I'm not sure if you're agreeing with me here or something - but what is the purpose of your "FORWARDS MOTION" again?

Normal Scenario

The engines push the plane forwards
Forwards motion = wind over wings
= Liftoff


Treadmill
The engines push the plane forwards
The treadmill pushes it back slightly, but at NO WHERE NEAR the force required to counter the sheer magnitude of thrust from the engines
Forward motion = wind over wings
= Liftoff



The treadmill just means it takes a little longer to reach take-off speed (or a little more thrust)

[Fluffz]

First of all, [...] if you take the literal meaning, then yes, unless the plane is stationary, the tangential speed wheels will always move faster than the speed conveyor belt

Now let's forget about that contradiction.

...

[Fit of Rage]

ENGINEERING = MAGIC AND VOODOO.

Seriously, if you haven't taken physics, get out of this thread.

[Fit of Rage]

Rubber and Aluminum: 0.51

It's still 900,558 N for a plane with NOTHING in it

The first frictional value you gave was for rubber on concrete, which essentially would be if you were sliding the plane on its tires across the runway. The contact point (or area) is essentially motionless at each time instant, so the plane doesn't have to overcome that friction.

The second value you listed was for rubber on aluminum. (Landing gear is usually made from steel due to impact impulses being too powerful for aluminum.) It's not the rubber/aluminum contact that makes a difference, that would be where the tire and the wheelbase meet. What matters is the wheelbase (steel) around the axle (steel) and this friction is also reduced from lubrication and ball-bearings.

[Zeebu]

wording prevents a correct answer i think...

so, im chillin on a treadmill with rollerskates on

i turn on the treadmill and i start goin backwards because they arent rolling yet

i hook a rope to the front of this treadmill and hold that shit when i turn it on

i now am using the correct amount of "thrust" to counteract the resistance of the skates

i pull on the rope giving me a relative velocity to the ground. shit yeah

assuming i can pull the rope hard enough for a long enough time, i can reach enough "thrust" for takeoff

that is all fine and good... but its still kinda a trick question. its almost like in the wording, it says that wheel speed = conveyor speed
and if wheel speed = plane speed then its all broken due to a given statement that plane speed = conveyor speed in the opposite direction or whatever. i dont think this problem can be set up correctly

[Pressure Drop]

this is not a normal conveyor belt , it matches the wheels at all times ...


so lets keep it simple. the wheel has a circumference off say 1 m and revolves at 1 time a second. The conveyor belt is moving at 1 m a second in the opposite direction. Net movement forward = 0


this causes the wheels to speed up
they accelerate
so does the treadmill

they are now turning 100 times a second
treadmill = 100 m a second
net movement of plane = 0

this continues exponentially till the wheels fail

Skidding is and example of failure, if the wheels skid this is no garentee of take off and more likely to cuase the plane to have a critical failure mechanicaly or just in control and not take off.

How can a plane mounted on wheels when the treadmill matches their speed at all times move forward?

You cannot compare this treadmill to a fixed rate treadmill and pushing something forward on that which has wheels ....

[Aquatiq]

Rubber and Aluminum: 0.51

It's still 900,558 N for a plane with NOTHING in it

You really think that's how plane and car wheels work? Rubber sliding against whatever it's attached to, like you're driving 4 big belt sanders?

[Hero*]

Stop taking it so literal!! When you do a riddle, you don't use a calculator..or what you learned in grade 11 physics. Seriously its not what its about. The speed of the plane is always matched by the speed of the conveyor belt. therefor it cant fucking move. Goddman. The wheels must spin faster to move forward because the engine is pushing it forward. Its too bad the conveyor belt is going just as fast as the engines. Yeah, thats right..its got engine power too! ITS NO ORDINARY CONVEYOR BELT.

[Jeansi]

Guys, GET OVER IT!

[Fluffz]

The speed of the plane is always matched by the speed of the conveyor belt. therefor it cant fucking move.

laugh, after 3 pages you still didnt get it. the pain. im happy you werent around when the wheel was invented, it would have beed a disaster