You have a plane and a conveyor belt.

[waggy]

Tom.

Im curoius to know what changed your mind and why you now think it will take off.

 

[So]

Originally posted by: jagec

Originally posted by: Tom
I was reading a relatively recent post, and then the phone interrupted me..

So i can't attribute it to a particular person, which I would like to do, but I don't have time to find the post again..

But I think I'm convinced I've been wrong, and agree now that the force of the engine acting on the plane will make the plane move forward, regardless of the conveyor belt.

So let the lambasting continue !!

OK...here's the funny part...

I've been doing some calculations, using the numbers for a light plane.

It turns out that if you put a Cessna on a conveyor, and set it to full power until the fuel runs dry...assuming a 30% conversion of chemical to mechanical energy...

The conveyor can spin at a speed of 2152.8 km/h, and convert ALL of that energy into angular momentum in the three wheels of the plane, thus keeping it from taking off. They'll be spinning at over 17,000 RPM.

I hope I made a calculation error, or didn't have the right data on the plane, because those numbers aren't nearly as high as I expected. I didn't even take into account friction losses.

Crap, crap, crap. We might all have been pwned.

Show me a conveyor belt that cad do well over 2000kph and I'll show you a great deal on a Bridge in Brooklyn.

 

[chr6]

instead of asking that question, only try to realize the truth. there is no plane.

 

[JujuFish]

Originally posted by: chr6
instead of asking that question, only try to realize the truth. there is no plane.

There is only spork.

 

[jagec]

Originally posted by: So
Show me a conveyor belt that cad do well over 2000kph and I'll show you a great deal on a Bridge in Brooklyn.

I know it would never happen in a real-world situation, but just the fact that it's hypothetically possible weakens our argument.

Not to mention that the 2000kph accounts for ALL the energy in a fully fueled Cessna's tank...How long do they take to burn through that at full throttle? A few hours? Which means that the conveyor WILL be able to keep the plane from taking off for quite a long time, until finally it reaches its top speed and the plane starts coasting down the runway (or the wheels explode). Not to mention I didn't take into account friction losses (works against the Cessna, assuming the belt has a big enough motor).

Of course, the control system for the belt WILL have to be changed from that described in the OP. I suggest a PI control system based on aircraft position.

 

[JujuFish]

Originally posted by: jagec

Originally posted by: So
Show me a conveyor belt that cad do well over 2000kph and I'll show you a great deal on a Bridge in Brooklyn.

I know it would never happen in a real-world situation, but just the fact that it's hypothetically possible weakens our argument.

Not to mention that the 2000kph accounts for ALL the energy in a fully fueled Cessna's tank...How long do they take to burn through that at full throttle? A few hours? Which means that the conveyor WILL be able to keep the plane from taking off for quite a long time, until finally it reaches its top speed and the plane starts coasting down the runway (or the wheels explode). Not to mention I didn't take into account friction losses (works against the Cessna, assuming the belt has a big enough motor).

Of course, the control system for the belt WILL have to be changed from that described in the OP. I suggest a PI control system based on aircraft position.

Nah, it's all good, because the imaginary plane in the OP has infinite thrust.

 

[So]

Originally posted by: jagec

Originally posted by: So
Show me a conveyor belt that cad do well over 2000kph and I'll show you a great deal on a Bridge in Brooklyn.

I know it would never happen in a real-world situation, but just the fact that it's hypothetically possible weakens our argument.

Not to mention that the 2000kph accounts for ALL the energy in a fully fueled Cessna's tank...How long do they take to burn through that at full throttle? A few hours? Which means that the conveyor WILL be able to keep the plane from taking off for quite a long time, until finally it reaches its top speed and the plane starts coasting down the runway (or the wheels explode). Not to mention I didn't take into account friction losses (works against the Cessna, assuming the belt has a big enough motor).

Of course, the control system for the belt WILL have to be changed from that described in the OP. I suggest a PI control system based on aircraft position.

Therein lies the main point of contention. The OP is proposes an impossible control system. The plane begins to accelerate, so if the belt tries to match it's speed, you get an n = n+1 situation with the speeds raching infinity quickly.

Plus, if we're going into a theoretical world where we have belts that don't exist, why not put magnetic bearings on the wheels of the plane and make friction ~0, putting us back at the original 'the plane will take off' scenario?

 

[jagec]

Originally posted by: JujuFish
Nah, it's all good, because the imaginary plane in the OP has infinite thrust.

LOL, fair enough. Let's just hope the conveyor isn't capable of infinite speed :Q

 

[jagec]

Originally posted by: So
Plus, if we're going into a theoretical world where we have belts that don't exist, why not put magnetic bearings on the wheels of the plane and make friction ~0, putting us back at the original 'the plane will take off' scenario?

Unfortunately frictionless bearings aren't the issue. As long as the wheels have mass, it's *possible* for the conveyor to keep the plane from taking off

 

[So]

Originally posted by: jagec

Originally posted by: So
Plus, if we're going into a theoretical world where we have belts that don't exist, why not put magnetic bearings on the wheels of the plane and make friction ~0, putting us back at the original 'the plane will take off' scenario?

Unfortunately frictionless bearings aren't the issue. As long as the wheels have mass, it's *possible* for the conveyor to keep the plane from taking off

If there is no friction from bearings, what force is acting on the wheels? (I don't doubt you, I just can't think of a force).

 

[FoBoT]

just want to make sure i have a post in a historic thread like this

 

[So]

Originally posted by: FoBoT
just want to make sure i have a post in a historic thread like this

Buddy, you're in the crappy remake.

 

[jagec]

Originally posted by: So

Originally posted by: jagec

Originally posted by: So
Plus, if we're going into a theoretical world where we have belts that don't exist, why not put magnetic bearings on the wheels of the plane and make friction ~0, putting us back at the original 'the plane will take off' scenario?

Unfortunately frictionless bearings aren't the issue. As long as the wheels have mass, it's *possible* for the conveyor to keep the plane from taking off

If there is no friction from bearings, what force is acting on the wheels? (I don't doubt you, I just can't think of a force).

There is no FRICTION, however, the wheels are pushed forward by the plane, and pulled backwards by the conveyor, which creates torque. No horizontal force is transferred, but both these forces act to spin the wheel faster. The inertia of the wheel acts as a counterforce. If the conveyor exerts a greater angular force than the airplane, the intertia of the wheel will cause the plane to move backwards slightly, even with frictionless bearings. If you balance the forces correctly, you'll have 100% of the force of the plane AND conveyor pouring into angular momentum.
I did make one mistake in my calculations. I assuming that 100% of the useful energy of the fuel (30% of the chemical energy was my assumption) would be converted to angular momentum. Actually, it's 200%, because the conveyor adds an equal amount. I don't really want to do the calculations again, though...let's just say the conveyor speed has to increase, but not double, to make it work.

Anyone who wants to check my calculations, here are the figures I used:
light plane
mass 1000kg
takeoff speed 27.8 m/s
3 tires, of diameter .66m and mass 11.3 kg each
200L fuel tank, holding avgas with an energy density of 44 MJ/kg

 

[So]

Originally posted by: jagec

Originally posted by: So

Originally posted by: jagec

Originally posted by: So
Plus, if we're going into a theoretical world where we have belts that don't exist, why not put magnetic bearings on the wheels of the plane and make friction ~0, putting us back at the original 'the plane will take off' scenario?

Unfortunately frictionless bearings aren't the issue. As long as the wheels have mass, it's *possible* for the conveyor to keep the plane from taking off

If there is no friction from bearings, what force is acting on the wheels? (I don't doubt you, I just can't think of a force).

There is no FRICTION, however, the wheels are pushed forward by the plane, and pulled backwards by the conveyor, which creates torque. No horizontal force is transferred, but both these forces act to spin the wheel faster. The inertia of the wheel acts as a counterforce. If the conveyor exerts a greater angular force than the airplane, the intertia of the wheel will cause the plane to move backwards slightly, even with frictionless bearings. If you balance the forces correctly, you'll have 100% of the force of the plane AND conveyor pouring into angular momentum.
I did make one mistake in my calculations. I assuming that 100% of the useful energy of the fuel (30% of the chemical energy was my assumption) would be converted to angular momentum. Actually, it's 200%, because the conveyor adds an equal amount. I don't really want to do the calculations again, though...let's just say the conveyor speed has to increase, but not double, to make it work.

Anyone who wants to check my calculations, here are the figures I used:
light plane
mass 1000kg
takeoff speed 27.8 m/s
3 tires, of diameter .66m and mass 11.3 kg each
200L fuel tank, holding avgas with an energy density of 44 MJ/kg

Ah, okay. Well, that sounds reasonable (I haven't done moment of inertia stuff in 3 years) so I'll take your word for it. Plus, I'm exhausted right now.

 

[Chiropteran]

This made me think...

Increase the rotational speed of the wheel enough, and you increase it's apparent mass. Given an conveyor with infinite speed and frictionless wheels, eventually the wheels are spinning so fast that they become more massive than the rest of the airplane, and could prevent the plane from taking off.

This is based off of Einstein's formulars, which say that as an object's relative speed approachs the speed of light it's relative mass becomes infinite.

 

[BUrassler]

Can I ask something without getting bashed!?

Excluding everthing except what I am asking, to move forward at all, the speed of the wheels would have to be moving forward faster than the speed on the belt moving in the opposite direction, right?

So, as the OP said, if the belt will ALWAYS match the wheels in speed, NO MATTER WHAT, the plane cannot move forward, correct?

 

[Throwmeabone]

Originally posted by: deathkoba
You people are retarded. It will not take off as the sole lift mechanism (the wings) will not be getting any airflow. The engines only push the aircraft so that enough air can flow over the wings. Only then will the aircraft achieve any level of lift. I'm a private pilot with instrument license.

Now if there is enough headwind, even when the plane is visually stationary, it's possible that the headwind itself can push the plane up a bit but it would be very uncontrolled and will simply flip the plane over.

I agree with him. If the plane starts at a standstill and there is no wind, the forward force the engine provides is negated by the conveyor belt. Therefore the plane has no net movement, can't get air over its wings, and can't take off. It's like running up an escalator backwards that can change its speed to match yours. You can't win..

EDIT: Nevermind..I get it now. The plane does take off.
EDIT AGAIN: I'm not so sure now after thinking about it some more

 

[BIGk]

R....................and no

 

[So]

Originally posted by: BUrassler
Can I ask something without getting bashed!?

Excluding everthing except what I am asking, to move forward at all, the speed of the wheels would have to be moving forward faster than the speed on the belt moving in the opposite direction, right?

So, as the OP said, if the belt will ALWAYS match the wheels in speed, NO MATTER WHAT, the plane cannot move forward, correct?

Well, taking Jagec's comments into account, if we're assuming massless wheels then, no, you have a paradox and the conveyor belt asymptotically approaches infinite speed. If the wheels have mass then it depdends on a number of factors, including the maximum speed of the belt, the thrust output of the plane and the mass of the wheels.

You can either use a really simple model or not, you can't reasonably use huge simplifications for one thing and skip for another in order to get your desired answer.

 

[LTC8K6]

Why is it so hard to see that the treadmill has no effect on the plane?

For the life of me, I can't figure that out. Since the plane's wheels are free to spin, the treadmill cannot stop the plane from taking off.

If you have roller skates on*, I can probably hold you in place and push you forward on a treadmill that is set for 100mph, with just one hand. The treadmill cannot exert very much force on you at all.

It can't.

*Assuming skates and bearings and treadmill that can handle the speeds.

 

[Qwest]

the title reminded me of this excellent game.

Text

 

[daniel49]

yes, because I chained it to the 737 in front of me.

 

[mchammer]

jagec and SO, while you are correct that a very rapidly spinning tredmill could raise the RPM of the wheels to the point where they would have the "mass" to keep the plane still, in the OP it says that the treadmill would be limited to moving backward at the same speed the wheels (the plane) is moving forward. In that case, the wheels would spin at 2x what their normal RPM would be at any point throughtout the takeoff run. That would not be nearly enough to increase thier "mass" enough.

So basically, there is no way to argue under the terms of the OP that the plane would not take off, save wheel bearing with lots of friction.

Also :beer: to Tom for coming around.

 

[BUrassler]

Should this be a common sense thing.... or a physics thing?

I just cannot understand how the plane takes off.

 

[FoBoT]

lift

airplanes take off because they have lift

if the air above the wing is slower than the air below the wing, the air pressure under the wing pushes the wing up, hence lift

so the only thing you need to understand is airflow across the wing. if you have high airflow, you get lift, if you don't, then no lift. no lift, no airplane take off