Airplane physics question

i'm gonna go real simple here. gears. gears match speed to one another no mater how fast the other one tries to go. same with the wheels to the gound/treadmill.

 

I contend that a treadmill cannot possibly be built that will conteract the forward movement of an axle. It will only counteract the rotational movement of the axle. Therefore, if the driving force is external to the wheels, the treadmill cannot possibly match the speed of the wheel.

This is going on the assumption that if the object moves forward on the treadmill, it's wheels are moving faster than the treadmill. If this is not correct, I would like an explaination.

 

this is correct.

this is why the object CANNOT move forward IF we obey the rules of the original posit.

 

i see now where it is confusing you. the question poses that the treadmill will match the speed of the wheel. okay lets start there, lets use the disgination for the speed of the wheel as RPMs. the treadmill will match RPMs for RPMs, now the forward movement isn't RPMs it is displacment. whether or not the axle holding the wheel moves forward from point A or not, the wheel RPM is matched by the treadmill becouse the displacment is not a result of the wheels RPMs but of the thrust generated by the jet engine.

 

Okay, your explanation wasn't getting through to me, so I did an experiment to try and demonstrate it, and I think I figured it out.

Picture 1 below, shows my two soda caps, one directly above the other on the X-axis. The bottom one represents our treadmill, and isn't allowed to leave the box that I drew around it.

Picture 2 is after I move the top cap to the left along the X-axis using a directional force, not a rotational force, causing the bottom cap to rotate counterclockwise inside its box. It appears that the bottom cap is not rotating at the same speed as the top cap, since the top cap is still upright, and the bottom cap is rotated.

What I've learned is that the X-axis doesn't matter at all. If you look in picture 3, you can see that both caps have rotated the exact same distance in opposite directions.

I concede that the plane moves forward and takes off.

Excuse the poor photo quality. I used my camera phone.
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um, your top cap isn't rotating on it's axis, it's rotating in an orbit around the bottom cap. if they rotated the same on their own axis, they'd stay in the same spot.

 

Any of you that think this plane will take off.......................

I would not fly with you.


Take some physics classes and some flight instruction.

I didn't read all the posts but some had very good explainations.

No relative AS = no takeoff

 

I stopped reading at the beginning of page 4, so please excuse me if this has already been mentioned.

At first I agreed with the car on dyno analogy, but then I thought what if you put a plane on a dyno. Put an airplane on a dyno and the wheels will not move and neither will the dyno drums.

If it is assumed there is NO friction between the planes wheels and the treadmill runway, I say it never takes off. If there is the SLIGHTEST bit of friction between the two, the plane will eventually take off, but it will take a while (i.e. put a car on a dyno without straps and go as fast as you can, don't stand in front of it).

Since in reality there is friction, I say it takes off.

 

I think there are two points to the question. One is about relative location of two objects (plane to ground) and the other is about the lift of an object.

As far as an airplane goes, it cannot "take off" or leave the ground unless proper airspeed is achieved over it's wings to produce the required lift to overcome it's weight/gravity. This air speed theoretically could be achieved in any number of ways regardless of wheels or engines. A jet engine pushes the airframe through the air, a propeller driven plane gets pulled through the air, either way a plane flys by moving through the air. If there is no motion of air there wont be any lift.

If you put an airplane in a wind tunnel and produced the required airspeed to generate lift from the wings, the plane would lift off the ground regardless if the earth, wheels or anything else on the plane was moving. Similarly if while in the air the engine of the plane does not maintain it's minimum reqiured air speed the plane will "stall" and fall to the earth like any other object.

As far as I'm concerned if no air is moving over the wings or there is no forward motion through the air to produce lift, the plane will not leave the ground. (I'm assuming the the posit of the question is that the plane "stays" in one place).

The other point (and more complicated) is the planes relative position to the earth, the belt, f-chat, itself or whatever. The examples from the from the article seem to make it simple... if you are rowing upstream at 3mph on a river that is coming at you at 3 mph you should remain in the same place.

It would seem to be more about force than speed. That is if you are in a boat rowing at 3mph on a pond with minimal resistance, you will move forward. Rowing with the same level of force or effort which it took you to go 3mph on the pond would probably cause you to loose ground in an opposing 3mph head current. I would think in order to stay in the same relative position (to a fixed point) in a 3mph head current you would need to produce more force or effort than the opposing 3mph to counter the additional friction and drag of the vehicle to stay in one place.

I agree that the paper was not pulled out fast enough from under the skateboard, and the rubber band airplane from the artilce also overcame the opposing force that could be generated by the treadmil...

It would be my opinion, that if the forces were equal and opposing the plane would not move. The "speeds" may not be equal. Because of the weight and friction of the plane it's thrust or relative "speed" may have to be greater than the "speed" of the belt, but if they are producing the same amounts of opposing force, then the plane should have moving wheels, spinning prop but appear to be in the same location to someone standing aside this whole scenario.

We're also not taking into account the space time relationship. There is no such thing as the "same place", because place has both a time and space assignment. You or anything for that matter can only ever be in one place at one time, even if you don't move. The next time you are in the same spot it is in fact a different time... =)

Wow, F-chat is fun! =)

 

Jesus you guys are drastically overthinking this. The wheels on an airplane have NOTHING to do with forward propultion. The only counteracting force they have on forward motion is the rolling friction. That conveyor belt could be traveling at mach 3 in the opposite direction of the travel of the plane. Throttle those big turbines up and it will roll down the runway belt thing exactly as it would if it were a stationary concrete runway.

PLANES ARE NOT WHEEL DRIVEN, how hard is that to understand.

As stated put an RC plane on a treadmill and throttle it up, it will absolutely fly right off.

man some technically intelligent people are really dumb at times.

 

This is a cute question. Took me about 3 pages to understand the "plane will not take off"argument but now that I understand it, it has a certain charm. What this thread needs is a picture, and I'll be back in a few minutes with one.

 

No-E go-E.

 

The question has an impossible constraint. In a practical sense it won't take off simply due to wheel bearing not being able to take the rotational speeds.

SRT-10 sees it, why can't anyone else (other than ash and some select few)?


BTW, anyone that posted a link to another forum, YOUR SCENARIOS ARE DIFFERENT. THIS THREAD HAS WHEEL SPEED = CONVEYOR SPEED, NOT PLANE SPEED = CONVEYOR SPEED.

 

I think you should do just that........make sure the treadmill is going as fast as the planes wheels and report back.

........... Tell me about it.

 

The plane will take off because there is friction between the wheels and the treadmill. This entire problem relies the friction between the two, which wasn't even given in the thread question.

Edit: For those who think the plane won't move, imagine the plane on a flat, motionless, frictionless surface (close to ice). A plane with wheels will still take off because the thrust will push the plane and the wheels will just drag on the ground. Using an idea of a non-moving frictionless surface is the same as a having wheels on a moving treadmill that match its speed.

 

the original questoin says nothing about keeping the plane stationary, the reader assumes this inncorectly becouse of the asumption that wheels moving on the treadmill would keep it so. if it was a car then yes it would stay stationary. but bieng a plane the thrust is generated external to the wheels so it would take off. airspeed would be attained and liftoff would occur.

 

OK, here's the picture: this is a simple prolem in statics: for the plane to remain stationary the forward thrust on the plane due to the prop/jet must be balanced by an equal force backward on the plane through the wheel via the belt.

Are we all in agreement here?
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Hopefully this plane has a nose wheel because otherwise it's going to rotate into the ground due to the couple:
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If you followed that then you are really clever: the next bit is actually easier, but right now I'm going out for a quick cigarette. next up: fun with friction!

 

for the crowd in the it aint gonna fly camp, how much RWHP do planes have?

 

For it to remain stationary that is correct, basically just overcome the frictional forces in the wheel rotation. Even if the conveyor matches the plane speed as it accelerates this friction is relatively low, the plane will easily overcome this and travel down the runway in a standard fashion. As stated, wheel speed is practically irrevelant.

Now if you changed the wind speed and direction that could really mess things up. Hence how an aircraft can have an airspeed of say 300mph, but a gps speed of 340mph, 40mph tail wind is good stuff.

 

The problem says no wind, so we'll stick to that. And FWIW tailwinds are a BAD thing when you are trying to take off. Note that aircraft carriers turn INTO the wind to launch aircraft to create a HEADWIND. But that is irrelevant here: no wind.

 

So here we are with our plane with a nose wheel:
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So, the plane thusts backward, causing it to TRY to roll forward, but the belt moves backward at the same speed as the wheel is trying to move forward. At some point the forces are balanced: the plane is thrusting forward and the belt is thrusting backward equally, and the plane does not move.

So the question becomes, can the plane overcome the backward force of the belt and move forward relative to the ground? To do so it must generate more force than the belt is capable of generating.

So how much force can the belt generate? Again, simple. The belt is using the friction of the tire to generate its backward force, so the max it can generate is the weight of the plane multiplied by the friction coefficient of the tire. If the plane generates more thrust than that the tire slides on the belt, and the plane accelerates relative to the earth, and thus gains enough speed to take off.

So the question becomes, does the plane have enough power to drag its wheels as if they were locked by the brakes? Same deal.

Nitpickers may want to add the friction in the wheel bearings, but if we are postulating a belt that can roll at such high speeds I say we can also neglect the bearing friction. Or just do a Tim Taylor and add MORE POWER!

SO, does the airplane take off? Depends on whether it has enough power to drag its locked wheels down the runway, plus a bit more for bearing friction if you insist.

Cool question, had fun figuring it out!

 

But it wouldn't have to drag the wheels, they are fully capable of rolling. That being said the friction is extremely low, ever see one of those little airport trucks pull a loaded 747 around?