Beating a Dead Horse - Airplane on a Treadmill

[BuffCyclist]

Okay, so to stop threadjacking that other post, I want to explain to people where I was coming from, in my thinking that a plane CAN NOT take off on a treadmill. There are two answers to this question, both of them are correct, but they are based on the initial conditions of the problem.

Scenario 1:

Can a plane take off if placed on a treadmill? This answer is NO. Everyone who thinks of this problem, thinks of this:

http://graphics8.nytimes.com/images/2006/12/11/technology/poguespan.jpg

Which is literally, a plane on a treadmill. In this scenario, the plane does not have enough room to move forward and since the wheels can spin freely, the plane will just sit there (assuming the engines power the plane at the same speed as the treadmill, so as to keep the plane stationary). The wheels do not generate forward thrust and thus, if a blindfold is put on this plane, they will be at rest relative to the air surrounding them.

Now, if you want to look at the actual scope of the problem, which took me quite a bit of googling to actually find the DETAILED, well written problem, it is this:


Scenario 2:


Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

In this scenario, because the wheels spin freely, as long as the engines are turned on and powering the plane, will it be able to take off? YES. This is because the engines see speed relative to the air, and therefore the wheels can spin at 500mph and the plane will still be able to take off because the air is not moving at 500mph.

And here is the MythBusters' episode on this situation:


http://www.youtube.com/watch?feature=player_embedded&v=YORCk1BN7QY


Conclusion:

So there you have it, two scenarios where the plane is able to both take off and not take off from a treadmill. This was not a matter of the plane being able to take off or not, it was a matter of the initial conditions of the problem and the problem not being explained correctly.

Lastly, for the record, I have absolutely no idea how I have never heard of this problem before. It appears to have been floating around like crazy in 2006, when I was in college for my first degree.



And now I'm ready: [Flame]

[00tec]

Mythbusters tested it

[BuffCyclist]

Mythbusters tested it

Yes, mythbusters tested Scenario 2. And they saw exactly what I saw I described (editing first video to include the video).

But Scenario 1 is still a valid scenario of this problem.

[merl]

but what about a sea plane in an endless pool? :)

[BuffCyclist]

but what about a sea plane in an endless pool? :)

Do you mean Scenario 1 or Scenario 2? An "endless pool" is a brand name for a pool that has a turbine at one end to simulate a current in the 20ft long pool. If the plane is a normal sized plane, then NO, the plane will not take off.

Here is their website: http://www.endlesspools.com/

How do I know about them? My Dad had one installed at our house so we could train for triathlons easier than having to go biking around our house, stop at the YMCA for the pool (and leave the bike there), then run around the neighborhood. With the Endless Pool, we could go on our swim, hop out of the pool and get on our bikes, then end up back home and head our running.


If however, by "endless pool" you mean a pool that is simple endless in nature (ie an ocean) then YES, the plane will take off.

[Ridge]

It's not about how fast the wheels are moving, or how fast air is moving through the engines. It's about how fast air is moving across the WING.


http://www.youtube.com/watch?v=uUMlnIwo2Qo

[BuffCyclist]

It's not about how fast the wheels are moving, or how fast air is moving through the engines. It's about how fast air is moving across the WING.

(video removed to lessen clutter)

Correct, but the two scenarios I laid out are both correct in and of themselves. You are furthering my explanation as to the reason why a plane can or can not take off.

If there was a fan in front of the treadmill in scenario 1, that changed speed according to the tread, would the plane be able to take off? YES. The airspeed over the wings would reach the 80mph or whatever speed required to achieve lift and it would become airborne. However whether or not the plane would start moving forward once it got out of the way of the plane is an entirely different question. It would depend on the achievable acceleration
of the plane (in that if you drop a plane at 30k feet with its engines at max speed, it will still fall below 30k feet before moving forwards).

[Ridge]

Yes, that is true. At least until the plane moved out of the fan's area of influence, at which point it would probably stall and crash and burn.

[asmo]

Please god make it stop..

[BuffCyclist]

Yes, that is true. At least until the plane moved out of the fan's area of influence, at which point it would probably stall and crash and burn.

Yes, that is what I was trying to say after I said YES. The plane would have no lift but the engines would be at their max capacity, it would probably fall down but if put high enough into the atmosphere, it would be no different from the engines stalling and could, in theory, recover. If the plane was able to accelerate at an ungodly high rate (think UFO going from stop to superfast in a second), then it could fly.

This type of problem is exactly how a lot of problems in special relativity are laid out.

For example, two twins are on earth and one gets on a spaceship, to fly at the speed of light, towards a star that is 4 light years away. When she gets there, she realizes there are no planets and returns the 4 light years to earth. When she gets there, she has aged only 8yrs, however her twin sister on earth aged something like 20yrs. But the twin on earth sees it a different way. Long story short, the spaceship is in an accelerating reference frame, because it is physically impossible to travel the speed of light from one point to another and return without accelerating and therefore is not the valid reference frame to use for this situation. But this type of problem gives hundreds of physics students a run for their money every semester.

[clublights]

Yes, that is true. At least until the plane moved out of the fan's area of influence, at which point it would probably stall and crash and burn.


Unless it was moving forward at the above the stall speed of the wing + the fan speed.. IE an effective airspeed of both combined.. if the stall speed was ~60mph ( what is typical of most light aircraft) and the fan was blowing at say 100.. if it was going at an indicated airspeed of 160mph then you removed the fan it would still be moving at 60mph and would continue to fly .

[clublights]

Also wanted to add.. in scenario 1 .. if the engines were off and the treadmill was turned on .. the friction drag would push the aircraft off the back of the treadmill... unless it was held in place by something ( tied down or the like)

[BuffCyclist]

Unless it was moving forward at the above the stall speed of the wing + the fan speed.. IE an effective airspeed of both combined.. if the stall speed was ~60mph ( what is typical of most light aircraft) and the fan was blowing at say 100.. if it was going at an indicated airspeed of 160mph then you removed the fan it would still be moving at 60mph and would continue to fly .

Exactly.

Now I'm starting to see why this thread could be millions of pages long, however the only line of thought that is wrong is thinking that a plane WILL NOT be able to take off from a sufficiently long treadmill.

Another scenario, flip the plane around and chock the wheels. As you turn on the treadmill, the plan would start moving, nose first and the airspeed over the wings could reach the speed required to achieve lift. This is effectively launching the plane using the treadmill.


Also wanted to add.. in scenario 1 .. if the engines were off and the treadmill was turned on .. the friction drag would push the aircraft off the back of the treadmill... unless it was held in place by something ( tied down or the like)

Yes also true, should have clarified that the engines move at the speed of the treadmill, so as to remain stationary relative to the ground.

[clublights]

\
Another scenario, flip the plane around and chock the wheels. As you turn on the treadmill, the plan would start moving, nose first and the airspeed over the wings could reach the speed required to achieve lift. This is effectively launching the plane using the treadmill.



Yes also true, should have clarified that the engines move at the speed of the treadmill, so as to remain stationary relative to the ground.

This is how airplanes are shot off aircraft carriers basically.

[BuffCyclist]

Yup. A good friend of mine used this theory for his phd thesis (aerospace engineering). He collaborated on a project to develop a fleet of self-launchable UAVs that could fly pre-determined aerial patterns. The theory behind it was to have dozens of them around a large city. A plume of gas is attacking the city, and they need to study where the plume is moving, so these UAVs launch themselves, flying around the city and avoiding each other, taking air measurements. It was really freaking anticlimactic to watch the first time he tested the launcher. Long story short, it didn't have enough spring power and the plane nose-dived into the dirt.

[clublights]

It was really freaking anticlimactic to watch the first time he tested the launcher. Long story short, it didn't have enough spring power and the plane nose-dived into the dirt.

HAHA
Gotta have enough energy to accelerate the mass of the aircraft above stall speed. at least .. more the better .. unless the acceleration rips the aircraft apart of course...

you learn about that fast enough when using line launching of RC gliders.

[generalmeow]

Here's another brainbuster: is it possible to make an aircraft stand still on a moving treadmill, relative to a person standing directly at the side of the plane (but not on the treadmill)?

It seems to me that either the aircraft will not be producing any thrust, and will be taken backwards by the treadmill, or it will be producing thrust, and moving forward on the treadmill (faster than the treadmill is going backwards). How can a balance be struck? And for simplicity, let's say this is taking place in a vacuum and there is also zero friction on the wheels, landing gear, ball bearings, etc.

Edit: crap, I guess if it was in a vacuum thrust wouldn't be possible via propeller. But you get the idea: no other factors except the speed of the wheels, the thrust of the airplane, and the motion of the treadmill.

[BuffCyclist]

Here's another brainbuster: is it possible to make an aircraft stand still on a moving treadmill, relative to a person standing directly at the side of the plane (but not on the treadmill)?

It seems to me that either the aircraft will not be producing any thrust, and will be taken backwards by the treadmill, or it will be producing thrust, and moving forward on the treadmill (faster than the treadmill is going backwards). How can a balance be struck?

How do you maintain the same speed as cars on the highway? You apply just enough gas to get up to their speed and let off when you start going too fast.

If the treadmill is able to go fast enough, there will be a point where the plane engine speed can match the treadmill speed and therefore sit in equilibrium.

[generalmeow]

How do you maintain the same speed as cars on the highway? You apply just enough gas to get up to their speed and let off when you start going too fast.

If the treadmill is able to go fast enough, there will be a point where the plane engine speed can match the treadmill speed and therefore sit in equilibrium.

NO! I reject this. The plane engine speed is completely independent of the treadmill speed. That's why the plane can take off! It will move forward with any amount of thrust. The speed of the treadmill is irrelevant.

[BuffCyclist]

NO! I reject this. The plane engine speed is completely independent of the treadmill speed. That's why the plane can take off! It will move forward with any amount of thrust. The speed of the treadmill is irrelevant.

Oh gotcha, I see what you're saying. Hmm...



Oh I know, START YOUR OWN STUPID THREAD! [LOL]

[clublights]

Here's another brainbuster: is it possible to make an aircraft stand still on a moving treadmill, relative to a person standing directly at the side of the plane (but not on the treadmill)?

It seems to me that either the aircraft will not be producing any thrust, and will be taken backwards by the treadmill, or it will be producing thrust, and moving forward on the treadmill (faster than the treadmill is going backwards). How can a balance be struck? And for simplicity, let's say this is taking place in a vacuum and there is also zero friction on the wheels, landing gear, ball bearings, etc.

Edit: crap, I guess if it was in a vacuum thrust wouldn't be possible via propeller. But you get the idea: no other factors except the speed of the wheels, the thrust of the airplane, and the motion of the treadmill.

I'd say yes.. but it would take a fraction of the power needed for a standard take off... since all you would be trying to overcome is the friction and drag of the treadmill against the wheels .

[generalmeow]

The treadmill can be moving at 100 mph, and if I apply even 5mph of thrust to my airplane, I'm going to be moving forward at 5mph. My wheels will be spinning at 105mph, but I'm moving forward.

[generalmeow]

I'd say yes.. but it would take a fraction of the power needed for a standard take off... since all you would be trying to overcome is the friction and drag of the treadmill against the wheels .

No friction and drag. They don't exist in my scenario.

[clublights]

No friction and drag. They don't exist in my scenario.


with no friction and no drag the plane would sit still with no thrust . since the treadmill would turn under the wheels with no friction they would just slide along like they were not touching

[generalmeow]

with no friction and no drag the plane would sit still with no thrust . since the treadmill would turn under the wheels with no friction they would just slide along like they were not touching

Ha! Brilliant. I didn't think of that.

[J]

Was trying to delete posts that were out of order trying to merge from the hydrophobic nano-tech thread. Accidentally deleted the whole thread. Its back now. Sorry, my bad.

[BuffCyclist]

Was trying to delete posts that were out of order trying to merge from the hydrophobic nano-tech thread. Acidentally deleted the whole thread. Its back now. Sorry, my bad.

P.S. I thought BuffCyclist was an Engineer.... Maybe not?

Ahh cool, its back! Thanks!

I am a Telescope Operations Specialist, but I've studied all levels of physics and have a degree in Astrophysics (basic physics, E&M, Special/General Relativity, etc).

I am going back to school to get another degree in Mechanical Engineering (which I did for 2 years at my current job before becoming an observer), and one of the classes I am currently taking is dynamics. One of the things we're studying is projectile motion and initial conditioned problems. So when I read an airplane on a treadmill, I instantly started applying constraints to it and made one assumption (like many do to this problem) and then decided to start the thread and stop hijacking that other one.

Which by the way, I am sorry for hijacking that thread so much, I didn't want to start a new pointless thread but once I saw how lengthy the discussion was, I thought, what the heck, we could use some more fun posts right now that aren't about gun grabbers.

[Drucker]

[facepalm] ohh Gawd, I saw a 100+ page thread on this at AGW a few years ago...

[BuffCyclist]

[facepalm] ohh Gawd, I saw a 100+ page thread on this at AGW a few years ago...

Really, you think we can get this thread to go 100+ pages? Alright...

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTQHaOH0dRWqTI9529Ee5c8Mql_81iYk m5xKg6c_Tu2dpK20S7N

(Saw this pic in another thread and love it!)

[J]

So, to understand Situation #1 better. Is there something / physical lip or object at the front of the treadmill that is keeping the plane from moving forward?

[BuffCyclist]

So, to understand Situation #1 better. Is there something / physical lip or object at the front of the treadmill that is keeping the plane from moving forward?

The size of the treadmill and the fact that treadmills have bars on the front, like the picture. Otherwise it wouldn't be a treadmill, but a conveyor belt.

As in, when I first thought of the scenario, I immediately imagined that picture and said no, if a plane moves forward it will crash into the bars since the end of the treadmill is not much farther in front of the front plane wheel. Scenario 1 assumes a treadmill that is of a similar length as the plane. Just like humans don't run on 30ft long treadmills when their stride is 3-5ft, a plane that is 50ft long wouldn't be on a 5000ft treadmill.

[J]

Makes sense. Though it really is the bars/obstructions/discontinuance of the level ground rather than the length. If there was nothing in the way, and the treadmill was level with the ground (sunken in) it would simply power off the end of the treadmill and continue on the ground.

[clublights]

Makes sense. Though it really is the bars/obstructions/discontinuance of the level ground rather than the length. If there was nothing in the way, and the treadmill was level with the ground (sunken in) it would simply power off the end of the treadmill and continue on the ground.


unless it was able to reach a speed above stall speed and became airborne before the end of the treadmill

[BuffCyclist]

Makes sense. Though it really is the bars/obstructions/discontinuance of the level ground rather than the length. If there was nothing in the way, and the treadmill was level with the ground (sunken in) it would simply power off the end of the treadmill and continue on the ground.

Yes, again another initial condition that the treadmill is level with the ground and no obstructions on either end of the treadmill. What my post was trying to get at, is that the initial conditions and the assumptions we make when we start discussing the problem make all the difference in the world.

By the way, J, where did you 3Million posts go? Did someone delete all of your history or just boot you back to noob status? [LOL]

[J]

It was 2 Million, and I keep setting it to some absurd negative number, somewhere between -25000 and -66000. Some index process, that I haven't had the time or energy to isolate, occasionally doesn't like the negative number and resets me to zero automatically. My actual count is retrievable from the database, and last I checked was somewhere near 1500.

[BuffCyclist]

Haha, thats weird it doesn't like the negative number. Any chance you can add an "i" to the end of it and make it an imaginary number of posts? Must be fun screwing with individual things like that!

Was just talking with a co-worker about this (he has a phd in astrophysics) and his first answer was no, a plane can not take off. I asked him why and what his assumptions were, and he said he didn't make assumptions. After we talked more, he understood what I meant by the initial conditions of the treadmill, etc. That if it is sufficiently long enough for a plane to take off, it isn't a treadmill, it is a conveyor belt.

Then he told me about a question he had on his graduate exams.

Which person will get wetter, a person walking for cover, or a person running for cover, during a rainstorm?

[J]

Too many variables to answer generically. Wind, therefore non direct downward fall of rain?

[BuffCyclist]

Too many variables to answer generically. Wind, therefore non direct downward fall of rain?

Ah yes, my bad. Assuming a steady downfall (constant number of drops per square inch per second) and no wind.

[J]

Hrmm.... Not sure, but on first thought, I would say walking gets you more wet:

The amount of vertical area on your body that you get wet will stay consistent. It is the integral of drops per inch at any given time of your vertical surface as considered over the inteval of distance you travel. We assume this because at any given time the spread of rain drops will be roughly uniform, so no matter how fast or slow you cross through them you cross the same plane of drops.

So, what is then un-constant is the drops that fall on horizontal surfaces, like the top of your head. That is proportional to time. So running will reduce that time.

[mitch]

No one mentioned this yet? Slackers....


http://dwfttw.blogspot.com

[BuffCyclist]

Hrmm.... Not sure, but on first thought, I would say walking gets you more wet:

The amount of vertical area on your body that you get wet will stay consistent. It is the integral of drops per inch at any given time of your vertical surface as considered over the inteval of distance you travel. We assume this because at any given time the spread of rain drops will be roughly uniform, so no matter how fast or slow you cross through them you cross the same plane of drops.

So, what is then un-constant is the drops that fall on horizontal surfaces, like the top of your head. That is proportional to time. So running will reduce that time.

Somewhat correct, however as you run faster, your cross sectional area increases to not just the top down view of your body, but includes the front cross sectional area, as the rain will start to come at you at an angle (think of driving in a car and rain comes at you at an angle). This is also assuming you aren't clumsy and trip while running, in which case you'd fall and would get more wet.

Another scenario though is that if the rain storm stops halfway to the cover, you'll get more wet by running. But assuming it rains continuously for both people, the walker will get more wet.

[clublights]

Then he told me about a question he had on his graduate exams.

Which person will get wetter, a person walking for cover, or a person running for cover, during a rainstorm?


Didn't Mythbusters do this one too ????

[BuffCyclist]

Didn't Mythbusters do this one too ????

Probably, they do nearly everything.

Then again, I haven't seen any real evidence to using rotating cylinders in place of airfoils to generate lift. Rotating cylinders are more efficient at creating lift than an airfoil is, but the problem arises when the cylinders stop rotating, in which case you fall like a rock. With airfoils though, you glide somewhat.

However, if you slap a rotating cylinder on the face of an airfoil (carve out the airfoil a bit so the leading half of the rotating cylinder is the front edge of the airfoil), it should, in theory, create a more efficient airfoil and allow for a greater amount of lift to be produced.

[clublights]

Then again, I haven't seen any real evidence to using rotating cylinders in place of airfoils to generate lift. Rotating cylinders are more efficient at creating lift than an airfoil is, but the problem arises when the cylinders stop rotating, in which case you fall like a rock. With airfoils though, you glide somewhat.




Sort of like a helicopter.... a collection parts flying in formation to the scene of the crash ?

[clublights]

here we go ....

http://www.youtube.com/watch?v=HtbJbi6Sswg


http://www.youtube.com/watch?v=HtbJbi6Sswg

[BuffCyclist]

Ah, interesting results. They say its better to walk than run in the rain and my understanding was its better to run. There is definitely a distance factor that comes into play, and maybe the course of 100ft was not enough to show the significance of that.

[generalmeow]

I've got another threadjack scenario: If there's a wall 10 feet in front of me, and I move 1/2 the distance to it. And I move 1/2 the distance to it. And I then move 1/2 the distance to it. I should be able to do this an infinite number of times without ever reaching the wall. And therefore it should take me an infinite amount of time.

How can I ever reach the wall? How can I ever touch anything? It doesn't matter if I'm stopping and saying, "ok, I've gone half the distance", every time I go half the distance. It's happening whether I think about it or not, or whether I stop or not.

Someone with a camera with an infinite number of frames could film me in real-time approaching the wall, and then they can watch it and after an infinite amount of time watching it they could verify that I'm never able to touch the wall. What gives?

[BuffCyclist]

I've got another threadjack scenario: If there's a wall 10 feet in front of me, and I move 1/2 the distance to it. And I move 1/2 the distance to it. And I then move 1/2 the distance to it. I should be able to do this an infinite number of times without ever reaching the wall. And therefore it should take me an infinite amount of time.

How can I ever reach the wall? How can I ever touch anything? It doesn't matter if I'm stopping and saying, "ok, I've gone half the distance", every time I go half the distance. It's happening whether I think about it or not, or whether I stop or not.

Someone with a camera with an infinite number of frames could film me in real-time approaching the wall, and then they can watch it and after an infinite amount of time watching it they could verify that I'm never able to touch the wall. What gives?

Here's the philosophy answer:

Zeno's Paradoxes: The Dichotomy Paradox
http://en.wikipedia.org/wiki/Zeno's_paradoxes

But relating to physics, we never really "touch" anything. The atomic forces always repel, so the nucleus of an atom in our fingertip will never touch the nucleus of an atom on the wall.

What you describe though is the easily understandable concept of infinity.

[Gman]

Are you suggesting coconuts migrate?

[J]

Maybe it was carried by a swallow?

[Gman]

What? A swallow carrying a coconut?

[BuffCyclist]

Ants can carry up to 50 times their body weight, so in theory, a swallow could very well be able to carry a lot of weight too.

Something tells me my threadjack-turned-standalone-post has just been threadjacked...

[Gman]

It's not a question of where he grips it! It's a simple question of weight ratios! A five ounce bird could not carry a one pound coconut.

[clublights]

It's not a question of where he grips it! It's a simple question of weight ratios! A five ounce bird could not carry a one pound coconut.



not always ... like already pointed out .. an ant can carry 50 times it's own weight... now true the ant is not flying ...

[Irving]

Buffcyclist, I wholly reject your first airplane scenario as invalid. No one would ever ask the question describing the set-up of scenario #1 because it introduces elements that are outside of the concepts of wheel speed vs air speed. It'd be like asking if you could, while wearing rollerskates, while on a treadmill, pull your body forward, but oh yeah there is a lead pipe directly across your chest that you will run into.

Instead, I purpose another interesting scenario to think of, but I don't think it is as capturing as the airplane on a treadmill question.

You are standing still on a street, and a vehicle passes you at 100 mph.
You are traveling in a vehicle at 100 mph, and a vehicle passes you at 200 mph.
Each time the vehicle will be passing you at 100 mph. Will you perceive the speed of the passing vehicle the same each time?

This was presented to me a long time ago (back in college) by my much smarter roommate. My answer is No, they will not look the same, but I'm not sure if I am correct.

[Irving]

Ants can carry up to 50 times their body weight, so in theory, a swallow could very well be able to carry a lot of weight too.



A lot of weight is not the same as 50 times the weight.

[Gman]

If you are in a spaceship that is traveling at the speed of light, and you turn on the headlights, does anything happen?

[BuffCyclist]

Buffcyclist, I wholly reject your first airplane scenario as invalid. No one would ever ask the question describing the set-up of scenario #1 because it introduces elements that are outside of the concepts of wheel speed vs air speed. It'd be like asking if you could, while wearing rollerskates, while on a treadmill, pull your body forward, but oh yeah there is a lead pipe directly across your chest that you will run into.

Instead, I purpose another interesting scenario to think of, but I don't think it is as capturing as the airplane on a treadmill question.

You are standing still on a street, and a vehicle passes you at 100 mph.
You are traveling in a vehicle at 100 mph, and a vehicle passes you at 200 mph.
Each time the vehicle will be passing you at 100 mph. Will you perceive the speed of the passing vehicle the same each time?

This was presented to me a long time ago (back in college) by my much smarter roommate. My answer is No, they will not look the same, but I'm not sure if I am correct.

And that is perfectly within your right to reject anything I say, hell, my Fiancee does it to more than half the stuff I say! [LOL]

However, the burden of describing the problem does not weigh on the student, it weighs on the teacher. I approached the problem from both angles. If you want to change the problem to whether or not a plane can take off from a runway-length conveyor belt that moves backwards, then feel free to. With that said, the question is can an airplane take off from a treadmill. A treadmill is an exercise machine meant for running, and therefore has the bars in front to "hold on" to while starting/slowing/drinking/etc.

Now, to answer your new scenario:

Standing still, watching a car drive by at 100mph yields the relative motion of the car (A) with respect to the you standing on the sidewalk (B), call this value v_A/B (which is the velocity of A with respect to B) as the following: v_A = v_B + v_A/B . Therefore, 100mph = 0mph + v_A/B, which yields that v_A/B = 100mph.

Solve this again with the other scenario, where the 200mph car (A) and you are in the 100mph car (B). 200mph = 100mph + v_A/B. Again, yielding v_A/B = 100mph.

That is assuming that the cars are already traveling at those speeds and not accelerating. If they start accelerating, or approach the speed of light, things change. The equation above for relative motion was taken from my Dynamics textbook, but can be found in nearly every other textbook.

If you want to start a discussion about special relativity, we can play that game too. There are a lot of very interesting thought problems in SR, involving the speed of light and reference frames.




A lot of weight is not the same as 50 times the weight.

No, but say a swallow COULD carry 50 times it's weight. The average Barn Swallow weighs 16-22g. The average coconut weighs, say, 1kg. 50 times the weight is between 800g and 1.1kg. So in theory, if there was a buff enough swallow, it could carry a smaller coconut. :P


If you are in a spaceship that is traveling at the speed of light, and you turn on the headlights, does anything happen?

I will reply to this one first, because its the easiest. Assuming you could ever get a spaceship UP to the speed of light (the closer you get to the speed of light, the more energy is required to speed up and it takes roughly an infinite amount of energy to get anything with mass to the speed of light).

But that aside, assuming you COULD get a spaceship to the speed of light and rigged it with headlights, the light would travel ahead at the speed of light.


Final eta: yes, I said "roughly an infinite amount".
Final Final eta: In the new scenario that irving introduced, the assumption was made that the two cars in the second instance, are traveling directly parallel to one another. If there is a slight angle involve, these values change.

[spyder]

Holy shit... Really? Football season has only been over for less than a week, and you guys are already losing your minds......

[BuffCyclist]

Holy shit... Really? Football season has only been over for less than a week, and you guys are already losing your minds......

It's not losing our minds, its recovering from all of the blows to the helmet that were sustained this past football season...




Aww who am I kidding, I'm a geek. This stuff is fun for me!

[Irving]

No one mentioned this yet? Slackers....


http://dwfttw.blogspot.com

This site is messing with me right now. I watched the #4 video and was initially amazed. I would like to see how the experiment works with thimbles and wheels of different sizes though to see how the result changes.




Now, to answer your new scenario:

Standing still, watching a car drive by at 100mph yields the relative motion of the car (A) with respect to the you standing on the sidewalk (B), call this value v_A/B (which is the velocity of A with respect to B) as the following: v_A = v_B + v_A/B . Therefore, 100mph = 0mph + v_A/B, which yields that v_A/B = 100mph.

Solve this again with the other scenario, where the 200mph car (A) and you are in the 100mph car (B). 200mph = 100mph + v_A/B. Again, yielding v_A/B = 100mph.

That is assuming that the cars are already traveling at those speeds and not accelerating. If they start accelerating, or approach the speed of light, things change. The equation above for relative motion was taken from my Dynamics textbook, but can be found in nearly every other textbook.



I can discuss these topics conceptually, but unfortunately I can't do the math at all. If something goes over my head conceptually, then I'll have a difficult time understanding. That being said, I believe what the math is telling me, that the difference between you and the vehicle is 100mph in both scenarios. However, does that still mean that I will be able to perceive this in the same way?

For example, let's say that I can see the passing vehicle until it gets to 1 mile away from me. While standing on the sidewalk, I will be able to see the vehicle traveling at 100mph until it gets 1 mile away, then I can no longer see it. For every foot the vehicle travels away from me, I travel 0 feet in the same direction.

In scenario #2, I'm traveling at 100mph, the passing vehicle at 200mph; and again I can see the passing vehicle until it gets 1 mile away from me. In this scenario, for every foot the passing vehicle travels passed me, I travel 6 inches in the same direction. Does this mean that I will be able to see the passing vehicle for twice as long as in the first scenario? If so, I would say that I would perceive the speed of the passing vehicle differently.

Please let me know if I am adding unrelated elements to this, such as the airplane on an actual treadmill example.

[clublights]

but the Real question to this current line of questioning is .......


What is the air speed velocity of an unladen swallow?

[def90]

An airplanes thrust has nothing to do with it's wheels.. it is about pushing air and air movement over it's wings.. treadmill or not the thrust from a propeller or jet is pushing air not spinning tires on the ground as a driveshaft on a car does.

[clublights]

This site is messing with me right now. I watched the #4 video and was initially amazed. I would like to see how the experiment works with thimbles and wheels of different sizes though to see how the result changes.



I can discuss these topics conceptually, but unfortunately I can't do the math at all. If something goes over my head conceptually, then I'll have a difficult time understanding. That being said, I believe what the math is telling me, that the difference between you and the vehicle is 100mph in both scenarios. However, does that still mean that I will be able to perceive this in the same way?

For example, let's say that I can see the passing vehicle until it gets to 1 mile away from me. While standing on the sidewalk, I will be able to see the vehicle traveling at 100mph until it gets 1 mile away, then I can no longer see it. For every foot the vehicle travels away from me, I travel 0 feet in the same direction.

In scenario #2, I'm traveling at 100mph, the passing vehicle at 200mph; and again I can see the passing vehicle until it gets 1 mile away from me. In this scenario, for every foot the passing vehicle travels passed me, I travel 6 inches in the same direction. Does this mean that I will be able to see the passing vehicle for twice as long as in the first scenario? If so, I would say that I would perceive the speed of the passing vehicle differently.

Please let me know if I am adding unrelated elements to this, such as the airplane on an actual treadmill example.


The time / distance to not being able to see the other car would be the exact same since speed of separation is the exact same. What would change is that the standing still to 100 guy the 1mile loss of sight is 1 mile away from the point of passing. with the 100 to 200 car scenario the distance between passing and loss of sight would be greater .. but the TIME would be the exact same .

The time for him to get to 1 mile of seperation is equal but would happen 1/2 mile farther down the road since the 100 mile an hour car would be 1/2 mile father down the road compared to the standing still guy

Make sense ? my explanation kinda sucks I think LOL

[BuffCyclist]

This site is messing with me right now. I watched the #4 video and was initially amazed. I would like to see how the experiment works with thimbles and wheels of different sizes though to see how the result changes.



I can discuss these topics conceptually, but unfortunately I can't do the math at all. If something goes over my head conceptually, then I'll have a difficult time understanding. That being said, I believe what the math is telling me, that the difference between you and the vehicle is 100mph in both scenarios. However, does that still mean that I will be able to perceive this in the same way?

For example, let's say that I can see the passing vehicle until it gets to 1 mile away from me. While standing on the sidewalk, I will be able to see the vehicle traveling at 100mph until it gets 1 mile away, then I can no longer see it. For every foot the vehicle travels away from me, I travel 0 feet in the same direction.

In scenario #2, I'm traveling at 100mph, the passing vehicle at 200mph; and again I can see the passing vehicle until it gets 1 mile away from me. In this scenario, for every foot the passing vehicle travels passed me, I travel 6 inches in the same direction. Does this mean that I will be able to see the passing vehicle for twice as long as in the first scenario? If so, I would say that I would perceive the speed of the passing vehicle differently.

Please let me know if I am adding unrelated elements to this, such as the airplane on an actual treadmill example.

Okay, so conceptually speaking, and this is the same premise behind police officers radaring you while they're driving. The difference in speed between two vehicles (or particles) traveling in the same direction, parallel to one another, is simply taking the faster vehicles speed and subtracting the slower vehicles speed. So yes, you are correct in extracting that the speed difference in both situations is 100mph.


However, perceptions vary from person to person. If you ask 100 people to guess the distance from them to a sign across the street, you'll get 100 answers. Same thing goes for speed, time and weight. As you will be stationary in one situation, and traveling at 100mph in the other, you will most likely perceive the two instances differently. This is because in the second scenario, you have the surrounding things, houses/buildings/etc to compare with your speed, and then the other car will speed past you.


Now, with your new scenario. No, you will not perceive the time to be different in the second scenario. All said and done, the car you are in will travel 1 mile, the other car will travel 2 miles. I can break out more math to prove this, but I don't think that would help (again though, its pretty simple math).


The basic equation is: x_B = x_A + (v_x)*(t)


Where, x_B is the final x position, x_A is the starting position, v_x is the velocity in the x direction and t is obviously time. If you think about this equation, say you are traveling at 10mph for a time of 1 hour. How far will you have traveled? (this is x_B).


For scenario 2, x_B = 5280ft, x_A = 0ft, v_x = 100mph = 146.67 ft/s


5280 ft = 0 + (146.67 ft/s)*t which gives a time of t = 35.9992 seconds for the 100mph car
10,560 ft = 0 + ( 293.34 ft/s)*t which gives a time of t = 35.9992 seconds for the 200mph car


Scenario 1 is similar, in that the time it takes a particle to travel a distance is simply t = distance/velocity. Since the car disappears at 1mile, you can simply take the distance it travel, of 1mi and divide that by the speed it travelled, 100mph.


t = 5,280 ft / (146.67 ft/s) = 35.9992 seconds once again.


So thats another entirely different set of equations, proving the same basic thing, that if the 2nd car travels twice as far as you, twice as fast as you, the time it takes for both cars to cover that distance is the same.


And getting back to answering whether or not you would perceive the passing vehicle differently in both scenarios goes back to the first part where perceptions vary for everyone.


For instance, a car passes you on the street at 20mph. It seems rather slow. But a car passes you at 80mph on a highway when you're traveling 60mph, everyone always "swears" the car flew past you at going AT LEAST 100mph, at least thats how my friends always told those stories lol.

And not at all, there is no such thing as unrelated elements when dealing with thought experiments. Yes, this thread has strayed off the initial path of an airplane on a treadmill, but correct me if I'm wrong in saying that thinking about these things is pure entertainment. No?

[BuffCyclist]

but the Real question to this current line of questioning is .......


What is the air speed velocity of an unladen swallow?

Is this unladen swallow traveling under its own power, or piloting the fictitious airplane that took off from the treadmill?

[clublights]

Is this unladen swallow traveling under its own power, or piloting the fictitious airplane that took off from the treadmill?


No Airplane but the swallow may or may not have landed on a treadmill near a coconut at some point.

( and you just lost geek points by not catching the monty python reference... tho you gained SOME back with the loop back to the treadmill . )

[BuffCyclist]

No Airplane but the swallow may or may not have landed on a treadmill near a coconut at some point.

( and you just lost geek points by not catching the monty python reference... tho you gained SOME back with the loop back to the treadmill . )

Oh I caught the reference, I just didn't think I needed to point it out, since I thought my reference to the treadmill was better. Then again, Monty Python was quite a few years before my time (the show ended 2 years before I was born).

[Irving]

The time / distance to not being able to see the other car would be the exact same since speed of separation is the exact same. What would change is that the standing still to 100 guy the 1mile loss of sight is 1 mile away from the point of passing. with the 100 to 200 car scenario the distance between passing and loss of sight would be greater .. but the TIME would be the exact same .

The time for him to get to 1 mile of seperation is equal but would happen 1/2 mile farther down the road since the 100 mile an hour car would be 1/2 mile father down the road compared to the standing still guy

Make sense ? my explanation kinda sucks I think LOL

Of course! Your example makes perfect sense and I actually feel silly for not having thought of it that way myself.

Thank you for the math BuffCyclist.

[BuffCyclist]

Of course! Your example makes perfect sense and I actually feel silly for not having thought of it that way myself.

Thank you for the math BuffCyclist.

This is what math/physics is all about, looking at problems from different angles. Just because an approach works for one problem, doesn't mean it'll work the same for another. You have to think about things differently and trust me, I've been wrong plenty of times because I got stuck in my ways of understanding a problem.

In going back to school for another degree, I've discovered a new way of approaching all problems, and honestly that comes from work where we constantly have to diagnose something, figure out what is at fault, determine what we know about the situation and the causes, and then figure out how to fix it.

And no problem for the math help, math never lies (until you screw up a minus sign somewhere [LOL])

[Irving]

And no problem for the math help, math never lies

Yeah, you've never seen any of my math...

[BuffCyclist]

Yeah, you've never seen any of my math...

LOL, perhaps not, but having a conceptual understanding of a problem is still more than most college freshman have taking classes, they just start deriving until they get to a point where they're confused and then question what they were solving for in the beginning.

[sniper7]

but the Real question to this current line of questioning is .......


What is the air speed velocity of an unladen swallow?
What do you mean, African or European?

[Gman]

but the Real question to this current line of questioning is .......


What is the air speed velocity of an unladen swallow?
What do you mean? An African or European swallow?

ETA: Beat me to it.

How do know so much about swallows?

[sniper7]

As far as the first airplane post is concerned, they are both correct. Plane 1 will not fly because the takeoff distance required is not available on a very short distance. It will fall off the treadmill and crash. Much the same as if an airliner tried to take off on a 1000 foot airstrip.

The second scenario the airplane will take off at its normal airspeed but the tire speed will be double that of a normal takeoff. So a typical rotation speed is 150 knots of airspeed. Assuming a standard day at sea level, the groundspeed will be 150 knots also but the wheels will be spinning at 300 knots. Realistically they will blow as most tires rated speed is under 200 knots.

[sniper7]

Yeah, you've never seen any of my math...

Groundbreaking stuff?

[DFBrews]

Yes in all scenarios.... Vectored thrust.../thread