Bird & Train: Solving the Mystery

[Mephisto]

this questions has been bugging me for a long time now:
Imagine you are in a train, in a compartment, sitting there. Then suddenly you see outside of the window a bird that flies exactly at the speed of the train. It gets closer and closer, until it flies into the compartment through an open window, while still maintaining the constant velocity in forward direction. What happens to that bird as it enters?

 

[russ_watters]

It accelerates forward in the train.

 

[mgb_phys]

A useful thing to know if for instance you ever have to drive a mini cooper full of stolen Italian gold into the back of a converted bus!

Anyone who has watched British TV at christmas in the last 40years could have told you this!

 

[Mephisto]

It accelerates forward in the train.

yes obviously it accelerated because its flapping, but there are basically 3 outcomes i can see:

smashes to front wall
smashes to back wall
suspended in air

now i think i can rule out suspended in air... but anyway. I think the problem is that the air in the room is actually stationary, but it is moving at train's speed. The air outside is stationary, but the bird is moving through it... I still don't get it

 

[kudoushinichi88]

If the train and the bird are in vacuum or the train is moving really slowly, then the bird will appear stationary.

At higher speeds... erm... I need to think first.

 

[pixel01]

Think opposite way. The train is at rest, outside, the wind is very strong, say 80km/h and the bird is trying to fly head on the wind and it can only as fast as the wind, so it appears to be stationary with the train. If the bird some how is closer and closer and finally be in the train, it would hit the front wall if still flapped and just dropped down if it stopped flapping. There's no way it hit the wall behind. But I should think the tubulence of air in the window must be very complicated.

 

[kudoushinichi88]

Yeap, thinking about the air turbulence at the windows made me imagine that the bird wouldn't be able to enter the train that easily...

 

[mgb_phys]

If the train and the bird are in vacuum

Typical physicist answer = first we assume a spherical bird flying in a vacuum !

 

[dst]

Typical physicist answer = first we assume a spherical bird flying in a vacuum !

I wonder if a biologist was ever studying chickens and had to make assumptions about the Earth


Another way to think of it - if you jump upwards on a train, the path you sweep is parabolic (observed by someone not on the train, of course). When in the air, you would have a velocity equivalent to the train and assuming the train doesn't accelerate, you land exactly where you jumped up from. The bird moving at the same velocity as the train should be treated no differently once they are in the train. Any more flapping would accelerate them relative to the train.

Doesn't matter how fast, as long as the functions describing their movement match up.

 

[Mephisto]

yea, dst & pixel you make valid points. I tried to think about it like that before... I think you are right. Still, i really wish i could see it happen in real life :) It would probably be almost as funny watching the confused bird, as it is watching a cat in zero-g environment.

Oh and... how on Earth would a bird FLY in vacuum, let alone survive! haha

 

[Ash17]

It accelerates forward in the train.

Hang on a minute, I'm confused. He said the bird maintains constant velocity so surely it won't accelerate? I would have thought that the bird would be seen to flap but would appear stationary because of its relative position to the walls, ceiling and floor of the train carriage.

 

[Mephisto]

Hang on a minute, I'm confused. He said the bird maintains constant velocity so surely it won't accelerate? I would have thought that the bird would be seen to flap but would appear stationary because of its relative position to the walls, ceiling and floor of the train carriage.

you have to keep in mind how flapping works. You force air particles backwards to push yourself forwards. Hence flapping will always accelerate you forward. The only reason you are seeing birds fly at seemingly constant rate is because their acceleration forward from flapping exactly balances out the air friction they are facing

 

[mgb_phys]

If the bird takes off from a perch does the weight of the plane change if it is running on a treadmill - and how long does it take for a moderator to notice?

 

[bsimmo]

It doesn't matter what people assume would think in real life, it is the question that matters..

'It maintains constant velocity'
Since velocity is direction & speed then it will
a) hit the other side of the train.
b) be lucky if the other side of the trains window is open ;)

It's just two lines crossing each other.

Velocity already tells you the direction it will be traveling.

 

[Hootenanny]

If the bird takes off from a perch does the weight of the plane change if it is running on a treadmill - and how long does it take for a moderator to notice?

 

[dst]

It doesn't matter what people assume would think in real life, it is the question that matters..

'It maintains constant velocity'
Since velocity is direction & speed then it will
a) hit the other side of the train.
b) be lucky if the other side of the trains window is open ;)

It's just two lines crossing each other.

Velocity already tells you the direction it will be traveling.

No, you misread. It's two lines that are parallel to each other, and one goes inside the other and continues straight at some point by making a sharp turn.

The question is whether the air inside the train will keep accelerating the bird. Assuming a spherical bird mounted with a jet engine in a vacuum, it's clear that the bird has to maintain acceleration in step with the train, as long as it's in the air. Air effects aside, there is no difference between a bird outside the train moving at the same velocity, and a bird inside the train.

If it slows down when going into the train, it will slap into the back. Speeding up, it will slap into the front. If it moves at the exact same rate, then it'll look stationary for some period of time, and very very, very strange.

 

[bsimmo]

I cannot see how they are two parallel lines.

In velocity terms the train is traveling in its direction at a speed
The bird is traveling towards the train at an angle (getting closer and closer) at it's speed.

It is one of the normal relativity questions.

To passenger who is stationary (wrt him/herself) the bird is just moving striaght towards the train.

Velocity does not care for air or the surroundings, if it is constant then it cannot change, otherwise it would not be constant.

But the trick part of the question in my opinion depends on how you interperet forward.
Since the bird continues forward with constant velocity, forward has no specific direction so I interpret it wrt to the bird since we are talking about the bird. hence it keeps going in a stright line and out the other side (if lucky)
But if you say forward wrt the direction of the train, the bird will hit the front of the compartment.
If it is forward wrt the passanger, then the bird is hovering, since the passenger is not moving wrt him/herself.

Note the question mixes relativities by speeking from the passanger point of view but talking like a 3rd pesrons point of view.

 

[capnahab]

You did not say if theoretical bird that flew into the theoretiacl railroad car was anticipating it, like landing on a perch? Did he put his air brakes on?

 

[TVP45]

Think of the old Feynman trick (well, he probably didn't invent the technique, but I learned it from him) and run the scenario backwards. A bird is hovering stationary inside the carriage and suddenly goes out the open window. What happens?

 

[capnahab]

Does the open window lead to the next car or to outside environment? You must be specific to get the correct answer.

 

[dst]

I cannot see how they are two parallel lines.

In velocity terms the train is traveling in its direction at a speed
The bird is traveling towards the train at an angle (getting closer and closer) at it's speed.


Note the question mixes relativities by speeking from the passanger point of view but talking like a 3rd pesrons point of view.

Ah, two different approaches.

How I was thinking of it, is that the bird flies parallel to the train, and then swoops inwards when it lines up with a window, or a strong side wind blows it in. It's going to be a different scenario if it's going diagonally of course.

 

[Mephisto]

i was thinking of it originally as dst describes: the bird flies as fast as the train, and then swoops in through the window. Although, its a very interesting idea to consider what happens if it flies in perpendicularly... I have no idea. This seems like it should be an EASY problem but yet I just can't wrap my head around it!

 

[Cyrus]

Why is this on page 2?

Why does the bird flap its wings when outside? -DRAG

When the bird flies inside the train, is there any forward air causing drag on the bird? NO The air in the train is moving at the same speed as the bird. Relative velocity of air to bird is now zero.

As russ said, it accelerates forward inside the train.

-The End.

 

[bsimmo]

Not true, the window is open so you'll either have air pulled out of the train or air blowing into the train (depending on the speed of the train) hence the air is not stationary. That and the air conditioning is going crazy as you should have the windows closed for them to work properly...




... a bird flaps it wings for many reasons... To counter the effects of gravity (and hence make flight much easier) using the air and the wind to propel itself, hover, turn and cool itself down. Also to poo on people.

 

[Mephisto]

Why is this on page 2?

Why does the bird flap its wings when outside? -DRAG

When the bird flies inside the train, is there any forward air causing drag on the bird? NO The air in the train is moving at the same speed as the bird. Relative velocity of air to bird is now zero.

As russ said, it accelerates forward inside the train.

-The End.

:) Yes Cyrus that's correct. Its a pretty good explanation too :) Oh and when the bird flies perpendicularly inside the window, I think it will just hit the back wall because the bird has no velocity in forward direction like the train does.

 

[Cyrus]

No. Once the bird is inside the train it has the same velocity as the air inside the train. That air is moving forward at the speed of the train. So the bird will move foward the same as the air, but it will also move side ways. If I were standing outside looking down on the train from the sky, I would see the bird move forward, and to the left. The bird moves to the left because it is flapping in that perpendicular direction.

If I were inside the train, I would just see the bird come into the window, and fly out the other side. It would just go left.

 

[Cyrus]

Not true, the window is open so you'll either have air pulled out of the train or air blowing into the train (depending on the speed of the train) hence the air is not stationary. That and the air conditioning is going crazy as you should have the windows closed for them to work properly...




... a bird flaps it wings for many reasons... To counter the effects of gravity (and hence make flight much easier) using the air and the wind to propel itself, hover, turn and cool itself down. Also to poo on people.

Well, I am dealing with the hypothetical train that has open windows and stationary air.

 

[Mephisto]

No. Once the bird is inside the train it has the same velocity as the air inside the train. That air is moving forward at the speed of the train. So the bird will move foward the same as the air, but it will also move side ways. If I were standing outside looking down on the train from the sky, I would see the bird move forward, and to the left. The bird moves to the left because it is flapping in that perpendicular direction.

If I were inside the train, I would just see the bird come into the window, and fly out the other side. It would just go left.

i think you misunderstood? The case I am talking about now is if the bird is just flying along perpendicular to the train's motion. But instead of crashing into the train flat on, there is an open window there so it will go right in. The bird has no velocity component in train's forward direction, only in the perpendicular direction, so it will hit the back wall of the compartment, or more precisely - the train will hit the bird with its walls.
Anyway, I'm all for letting this thread die :)

 

[Cyrus]

No, I fully understood what you said. You did not understand what I said.

 

[shawshank]

if he keeps flapping he'll accelerate in the train right?

 

[msmsmanu]

Hmmm...

Remember, the train and the bird are traveling at the same velocity! Therefore, when the bird is in the train, the speed of the train wouldn't effect the bird. So, the bird will be at the same stationary point in the train, provided it maintains the same velocity. Similarly, if it is flying in the frame of the window, it will remain flying at the same point in the frame. There would be no change in its velocity, and nor will it hit any wall and stop since it has the same velocity as the train...

 

[Mephisto]

No, I fully understood what you said. You did not understand what I said.

ok well I'm totally confused then. The first case was that train goes along line x=0 upwards, and the bird flies at x=-1 or something right beside it, but it also has a very slight component in the x direction, so that it eventually gets into the train.

This next one is that the train is again going upwards on line x=0, but now we have a bird flying on the line y=0 in the positive x-direction (it has no component in the y-direction!), and the bird and train meet at (0,0) and the bird flies into the train through the open window. You are telling me that it will not hit the wall in this case? The x and y directions are completely orthogonal to each other. The only way the bird can survive is if there is another window on the other side of the train which it can quickly pop out of before the wall gets there.

I'm sorry... i went through your explanation a couple of times I can't make sense out of it

 

[arunbg]

Remember, the train and the bird are traveling at the same velocity! Therefore, when the bird is in the train, the speed of the train wouldn't effect the bird. So, the bird will be at the same stationary point in the train, provided it maintains the same velocity. Similarly, if it is flying in the frame of the window, it will remain flying at the same point in the frame. There would be no change in its velocity, and nor will it hit any wall and stop since it has the same velocity as the train...

True, if the train is in space, and the bird is wearing a jet pack. When on earth, if the bird continues to flap its wings as before in the train, then it accelerates relative to the train as well due to moving air within the train.

This next one is that the train is again going upwards on line x=0, but now we have a bird flying on the line y=0 in the positive x-direction (it has no component in the y-direction!), and the bird and train meet at (0,0) and the bird flies into the train through the open window. You are telling me that it will not hit the wall in this case? The x and y directions are completely orthogonal to each other. The only way the bird can survive is if there is another window on the other side of the train which it can quickly pop out of before the wall gets there.

Correct, but I don't see where such a scenario popped up in the first place

 

[kudoushinichi88]

Oh, so I misunderstood the question right from the beginning...

I think Cyrus is right. Once the bird enters the train, the air inside the train causes the bird to accelerate. The air will push the bird in the direction of the motion of the train.

And I also agree that the bird will exit the train through the window right opposite the window which the bird initially enters (assuming that it's open).

I remember that if I put my arms out the window when I'm on a fast moving train, i feel my arms being pushed back by the air... I suppose it works the other way round as well since motion is relative.



Now let's complicate matters...

What if the train is going around a bend?? Will the bird exit the train through the window right opposite the window it entered?

 

[arunbg]

I think Cyrus is right. Once the bird enters the train, the air inside the train causes the bird to accelerate. The air will push the bird in the direction of the motion of the train.

And I also agree that the bird will exit the train through the window right opposite the window which the bird initially enters (assuming that it's open).

If the window is large enough and the bird laterally fast enough yes, otherwise no. The bird after entering the train through one window moves forward w.r.t the train for some time before reaching the opposite window.

Now let's complicate matters...

What if the train is going around a bend?? Will the bird exit the train through the window right opposite the window it entered?

Too little data.

 

[kudoushinichi88]

ok well I'm totally confused then. The first case was that train goes along line x=0 upwards, and the bird flies at x=-1 or something right beside it, but it also has a very slight component in the x direction, so that it eventually gets into the train.

Lemme try answering this question again.

Let ground be our frame of reference.

Let a car of a train start at coordinates (0,-a) where a is a large number and the train is moving at a velocity, v along the the line x=0 (the y-axis) in the positive direction.

At the start, let the bird be at coordinates (1,-a).

Now I am slightly confused here because, if the bird is moving at the same velocity as the train, the bird and the train will never meet. So, I'm assuming that the y-component of the velocity of the bird is the same as the train.

So let the y-component of the velocity of the bird equals the train and the x-component of the velocity of the bird is in the negative direction and has a low magnitude.

Let the bird enters the car of the train through one of the side windows at coordinates (0,0).

The line traced by the moving car of the train is x=0 for y > -a if the train continues move indefinitely.

The line traced by the flying bird is

y = -ax \ \mbox{for} \ 0 > x > 1

Now, if I'm sitting inside the train and looking out the window, I will see an almost stationary bird that is moving closer and closer to the window, wouldn't I?

Switching back to the original frame of reference (the ground),

Once the bird enters the train, the y-component of the velocity of the bird increases (the bird accelerates) if the bird retains the same flapping as it does outside the train. Since the air inside the train is moving wrt to the ground, it should cause the bird to accelerate compared to the bird flying in still air, outside the train.

The x-component of the velocity of the bird remains the same.

The bird should exit the train through the window a few windows in front of the window opposite the window it entered. (exits through the window closer to the front of the train than the window that it used to enter the train)

So, the line decribed by the bird would be

y = -ax \ \mbox{for} \ 0 < x < 1

and

y = -ax + b \ \mbox{for} \ x < 0

Where b is caused by the acceleration of the bird in the train and

assuming that the width of the train is infinitesimally small.

Anyway, in reality, the width of the train wouldn't be infinitesimally small, but, because of the acceleration of the bird inside the train, the line described by the bird while it's flying inside the train in our frame of reference should have a steeper gradient compared to the line it described when it's flying outside the train. That is what I think of this question, for now...

 

[capnahab]

But what if the bird was trying to get into the bar car? He/She would certainly be flapping their his/her wings faster.

 

[kudoushinichi88]

into the what??

 

[capnahab]

The point is that the bird would be applying its air brakes and could make the transition.

 

[kudoushinichi88]

This next one is that the train is again going upwards on line x=0, but now we have a bird flying on the line y=0 in the positive x-direction (it has no component in the y-direction!), and the bird and train meet at (0,0) and the bird flies into the train through the open window. You are telling me that it will not hit the wall in this case? The x and y directions are completely orthogonal to each other. The only way the bird can survive is if there is another window on the other side of the train which it can quickly pop out of before the wall gets there.

Lemme try this one too.

Let the ground be our frame of reference.

An infinitely long train is moving along the line x = 0 (the y-axis) at a velocity, v1 in the positive direction.

Let our bird start at coordinates (-c,0) and is flying along the line y=0 (the x-axis) at velocity, v2 which has the same magnitude as v1 but in the direction perpendicular to v1 and towards the positive direction on the x-axis. (means it's flying towards the train in the direction perpendicular to the train.) The bird has zero velocity in the y-component.

The bird enters the train through one of the side windows at coordinates (0,0).

The bird now is in the train. Because of the air in the train is moving wrt to the ground, it causes the bird to accelerate and have a velocity in the positive direction of the y-axis.

The bird now exits the train through the window opposite the window it enters.

Hence the line our bird describes on our frame of reference is

y=0 \ \mbox{for} x<0

and

y=d \ \mbox{for} x>0

where d is caused by the acceleration of the bird while it's flying in the train, assuming the width of the train is infinitesimally small.

The bird is assumed to maintain a constant flapping throughout and all windows are assumed to be open.From these lines of thought, what I can deduce is, if I am in the train, I would observe the bird entering a window and exiting the window right opposite the window through which it entered but it exits from a position slightly closer to the rear of the train.

 

[kudoushinichi88]

Well, I'm assuming the bird didn't do that. If the bird applies 'air brakes' then it's velocity would change and the whole thing would be messed up.

 

[capnahab]

Instead of a ground frame of reference I prefer coordinate or at least cartesian.

 

[Hootenanny]

How on Earth has this thread reached 42 posts?

 

[kudoushinichi88]

I wonder too.

 

[capnahab]

I say neuter all of the cats. Let's see it that gets a rise.

 

[Hootenanny]

I say neuter all of the cats. Let's see it that gets a rise.

I wasn't trying to get a 'rise', I was merely commenting that the OP's question was answered in the second post (and clarified again in post #9). Since then, the thread has just been misinterpreted, taken out of context and over-complicated.

 

[Mephisto]

I wasn't trying to get a 'rise', I was merely commenting that the OP's question was answered in the second post (and clarified again in post #9). Since then, the thread has just been misinterpreted, taken out of context and over-complicated.

that's actually a quite correct insight :)
anyone feels like discussing the cases where the train moves at 0.99c ? :)
just joking, let it die. The questions were answered.

 

[Shooting Star]

Typical physicist answer = first we assume a spherical bird flying in a vacuum !

I disagree. A typical physicist's answer would have been a point mass moving only along the x-axis in vacuum.

(Hey Hootenanny, this is another way how the number of posts increase. If the number still continues to rise, I promise to contribute more. This thread is a gold mine...)

 

[algis.j]

I think Mephisto assumed initial paths are parallel. The bird will enter the train and accelerate toward the front because air resistance is much lower.
If he keeps going sligthly transversally; passing by one other side window and enter another train crossing in the other way; he will go toward the end of this second train - and if he finally goes out by a fourth window he will keep his way as before entering his set of trains.

But if I were to be him; I just stop at the first bar having half bottle of Vodka to cheer my luck :p

 

[kudoushinichi88]

What if the train is going in the opposite direction of the bird but the magnitude of the velocity is about the same? It means the bird decelerates in the train, right