A discussion on TFES forum

[brimstoneSalad]

Come on now! You don't have to use the unknown to explain the unknown.

I'm not. I said I might be able to explain a standard lens to you, but either way this would take too much time to explain. It shouldn't be necessary, because you already know these distortions can and do occur.

It shouldn't matter if Santa Clause is causing them, because they are real, and the reality of the distortions in lenses (regardless of the cause) explains the apparent non-convergence of short shadow segments in such a photo with those distortions.

If you want to understand why, it will take a lot longer. It's an important question to ask IF you're interested in studying optics. If not, it's probably irrelevant to your daily life.

Magnifiers we all have at home also make the straight lines appear curved. Why?

Depends on the lens and the situation, but generally lenses cause some distortions.

Why do you think lenses cause distortions?
I can give you a hint: Your confusion has to do partially with the method in which you are modeling these light paths (as a cross section of the lens), which is virtually incapable of clearly illustrating distortions across three dimensions (particularly the two dimensions of the camera's sensor plane).
You're making a lot of mistaken assumptions here.

[teo123]

Look, I now have a lot of cognitive dissonance in my head. Back when we were learning about optics in school, I assumed with great confidence that the distortion of a magnifier is caused by the Petzval field curvature. But, obviously, at least if I draw the diagrams the right way, Petzval field curvature doesn't affect the lines parallel with the optical axis, when, as you have shown me, they are also curved. And, if I have correctly understood the diagram of the wide-angle lens you've shown me, they correct the Petzval field curvature, yet, obviously, the distortion still happens. I don't know, I just don't like having contradictory beliefs in my head.

[teo123]

Well, when I think about it, I think that what's actually been going on is that I thought I understood what we were learning at school, when, in reality, I didn't (even though I've always had an A in physics). Maybe I have a wrong conception of what even is a light ray, what is an image, what is a lens, what is a reflection, what is a refraction, and so on. Just like many people think they understand what is a force, what is a weight, what is a free fall, when, in reality, they don't. Ever watched this video:
https://www.youtube.com/watch?v=Yf0BN0kq7OU
What do you think about it? Have I simply got very close to the fractal wrongness when it comes to this? Should I read about optics, from, let's say, Encyclopedia Britannica and think about each thing I read much more carefully than I did at school if I want to understand it? I mean, now I can't even guess what I got so wrong that my predictions don't match the reality at all.
I will not do it right now, I now have problems in real life. When my mother ended up on a psychiatry, I moved to my father's place and had to change the school, and almost everything else I knew, and, you know what comes with that.

[brimstoneSalad]

Wikipedia has a page on optical distortions that may help: https://en.wikipedia.org/wiki/Distortion_(optics)

Just like many people think they understand what is a force, what is a weight, what is a free fall, when, in reality, they don't. Ever watched this video:
https://www.youtube.com/watch?v=Yf0BN0kq7OU
What do you think about it?

Right, most people are making incorrect assumptions. It's impossible to assume you understand the technical meaning of a term based on intuition.

Whenever your beliefs disagree with scientific consensus, the safest assumption is that you got something wrong somewhere. It's not always easy to figure out where that mistake lies, however, so correcting it is easier said than done.

I mean, now I can't even guess what I got so wrong that my predictions don't match the reality at all.

Because I don't know what mistaken assumptions you have, I don't know how to easily correct you. I assume it's because you're looking at a cross section of the lens and only receiving a one dimensional image through that with your diagram, which would not make the distortion particularly obvious because it's only shortening the line along its length. See the radius illustration on Wiki. Using that model may help you see the distortion more clearly with your diagrams.

[teo123]

I've read about the distortion on Wikipedia, they don't even try to explain where it comes from.
Actually, I think I know one thing I got wrong. See, I used an analogy with a magnifier. That's a false analogy: the film and the eye don't actually "see" the same way.

Now, if the real image of an object is curved towards an eye, the eye will see the curvature. But the same doesn't go for a film. A film would simply "see" the closer points of that curve as sharp and farther points as blurred.

I think I now even have an intuitive explanation for the distortion: in order to appear sharp, that curve has to be projected by some other lens exactly on the film, however, you can't project a parabolic surface on a flat surface without, well, some distortion. That curve is obviously bigger the wider the angle is, so a wide-angle lens is going to have more distortion.
But, again, this is based on the assumption that the distortion visible when you look through a magnifier is due to the Petzval field curvature. Is it?
And, again, the Petzval field curvature, as far as I can tell by drawing the diagrams, doesn't affect the lines parallel with the optical axis.

[brimstoneSalad]

I've read about the distortion on Wikipedia, they don't even try to explain where it comes from.

The Wikipedia page does explain it. It's caused by differential amounts of zoom in the center of the lens vs the edges.

In order to understand these distortions, it should be remembered that these are radial defects; the optical systems in question have rotational symmetry (omitting non-radial defects), so the didactically correct test image would be a set of concentric circles having even separation—like a shooter's target. It will then be observed that these common distortions actually imply a nonlinear radius mapping from the object to the image: What is seemingly pincushion distortion, is actually simply an exaggerated radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be steeper in the upper (rightmost) end. Conversely, barrel distortion is actually a diminished radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be less steep in the upper (rightmost) end.

Here's another page explaining it in different words:

https://support.nikonusa.com/app/answer ... -happen%3F

as far as I can tell by drawing the diagrams, doesn't affect the lines parallel with the optical axis.

Why are you assuming the lines are parallel to the optical axis?

Because it is a radial effect, if you angle the camera so the vanishing point is precisely in the center of the camera, and all lines are precisely parallel to it, the bowing may be eliminated. In practice, this is never the reality in photography. The camera is always angled up, down, or to the side a little bit.

You can test this if you like.

[teo123]

Because it is a radial effect, if you angle the camera so the vanishing point is precisely in the center of the camera, and all lines are precisely parallel to it, the bowing may be eliminated. In practice, this is never the reality in photography. The camera is always angled up, down, or to the side a little bit.

Yes, I never actually thought about it. If you look at those photographs, you can clearly see that the camera is not aligned with the horizon. It's still hard to tell whether the effect would be what we see on those photographs or exactly the opposite, but I can't use that as an argument.

So, let's try to talk about the reaction mass. You know, we have learned about it at school, and I managed to, as always, get an A in physics, but, in reality, I didn't understand it very well. First of all, if a balloon is broken when it's still in the air, it starts moving because of the reaction mass, right? Well, it obviously doesn't move at a straight line as rockets are supposed to. How is that a false analogy? The answer that immediately comes to my mind is that the rocket is, whenever it's not aligned exactly vertical, pressurized by the air to do so. Well, the air would pressurize it to be aligned exactly horizontal, as it does it with the airplanes, right? Besides, there is no air in space, yet it's still supposed to be moving at a straight line, right? Also, if I correctly understand the fluid mechanics (and I got an A in it also), an engine that bases itself on the reaction mass would have to break the law of conservation of energy. Let me explain: the reaction fluid runs out of the fuel tank because it's pressurized, correct? Then it would be governed by the Bernoulli's equation:
p1+rho*g*h+rho*v1*v1/2=p2+rho*g*h+rho*v2*v2/2
p1 would, of course, be the pressure made by the tank. rho*g*h is, in this case, negligible, since the rho of the hydrogen is very small and there wouldn't be a significant difference on the top and in the bottom of the tank. The speed v1 of the hydrogen in the tank is clearly zero, right? p2 can also be crossed out, because as long as it is smaller than p1, and since the hydrogen runs out of the tank it clearly is, this negative proof will work. So, what we end up with is:
p1=rho*v2*v2/2
Let's try to express v2 out of it.
2*p1=rho*v2*v2
v2*v2=2*p1/rho
v2=sqrt(2*p1/rho)
So, what would be the potential energy of the reaction mass? Well, it is equal to the kinetic energy that reaction mass has upon leaving the tank, right?
Ek=m*v2*v2/2
m=rho*V
Ek=rho*V*2*p1/(rho*2)
Ek=V*2*p1/2
Ek=V*p1
So, since Ep=Ek in this case, the Ep=V*p1. And by the volume of the reaction fluid decreasing in the tank, the kinetic energy of the reaction fluid of the tank increases, right? However, since the formula for the potential energy of the reaction mass can be derived from the Bernulli's equation, which tells us exactly what is the speed of reaction mass upon leaving the tank, all that potential energy has to be spent on accelerating the reaction mass, and no energy is left for accelerating the rocket. Let me try to be a little move convincing: it is possible for a tank to create a jet of fluid, even when it's not moving because of being fixed to the ground, right? That's because it does some work on it, and that work is W=F*s. Well, if the tank itself is not moving, then the work done on it is exactly zero, and all the energy is spent on accelerating the fluid to form a jet. Now, suppose that the tank itself is moving. Can it accelerate because of creating the jet? Keep the Newton's 1st law in mind. It can't. If there were any difference caused by the tank moving at a constant speed, or even being able to move, it would violate the law of inertia, right?
To be more clear, let me make an example. Suppose you have a tank with 3 m2 reaction fluid pressurized at 100000 Pa more than the outside pressure, and that the tank itself is 10 kg mass and that the density of the reaction fluid is 1 kg/m3 (I know that's probably not an accurate description of what's supposed to happen in rockets, but the analogy should still apply).
First, let's assume that the tank can't move.
Ek=Ep=V*p1=3*100000=300000 J
And that's all.
Now, let's assume it can move without friction.
Ekf<-Kinetic energy of the fluid.
Ekt<-Kinetic energy of the tank.
Ekf is again going to be Ekf=Ep=300000 J.
But, from the Newton's third law it follows that mt1*vt1+mf1*vf1=mt2*vt2+mf2*vf2, known as the conservation of momentum. In this case, mt1 is the sum of the mass of the tank and the fluid, vt1 and vf1 zero, and mf1 is irrelevant because it is multiplied by zero. So, what we end up with is mt2*vt2+mf2*vf2=0. Let's calculate the unknown variables.
mf2=V*rho=3*1=3kg
Ekf=mf2*vf2*vf2/2
300000=3*vf2*vf2/2
600000=3*vf2*vf2
vf2*vf2=200000
vf2=447.21 m/s
mt2 is, from the description, 10 kg.
Let's solve the equation with 1 unknown variable.
10*vt2+3*447.21=0
10*vt2=-1341.63
vt2=-134.16 m/s
Ekt=mt2*vt2*vt2/2=10*(-134.16)*(-134.16)/2=89994.53 J.
So, the total Ek is going to be Ek=Ekf+Ekt=300000+89994.53=389994.53 J.
So, the total energy would have to be different in the beginning (where there is only potential energy) and at the end, and that violates the law of conservation of energy. Also, the change of the kinetic energy would have to be different depending on whether the tank can move at a constant speed or not, and that goes against the law of inertia, which states that there is no way to determine whether something is moving at a constant speed or not moving at all. Therefore, the rockets would have to break two well known laws of physics.
And this is exactly what you've been asking for, right? I have done the math and I have ended up with a conclusion that rockets are (epistemically) impossible. Or is my belief still somehow irrational?

[brimstoneSalad]

First of all, if a balloon is broken when it's still in the air, it starts moving because of the reaction mass, right?

If it's released by its 'nozzle', yes. If it's broken, it probably explodes because the material rips from the puncture. Look at slow motion film of balloons popping.

Well, it obviously doesn't move at a straight line as rockets are supposed to. How is that a false analogy? The answer that immediately comes to my mind is that the rocket is, whenever it's not aligned exactly vertical, pressurized by the air to do so.

Rockets can fly in non-vertical directions.

How are balloons different from rockets?
Which direction does the reaction mass exit the balloon in? Does is wobble around and spray in all different directions? If so, how does this affect angular momentum?

What's going on here? https://youtu.be/Pvk84Sh0D5I?t=195
(you can probably find better slow motion footage if you look around)

Besides, there is no air in space, yet it's still supposed to be moving at a straight line, right?

Moving in space is easier, because there's no drag from the air, but you still have to make adjustments in flight.

What is torque? What is the center of mass? Where does the rocket have to be positioned? Is it possible to position a rocket exactly over the center of mass? If not, how can this be corrected during flight (through human or computer control)?

an engine that bases itself on the reaction mass would have to break the law of conservation of energy.

Water rockets and balloons work on a function purely of stored pressure. This has limits based on the ability of real materials to contain that pressure.

Hydrogen and Oxygen based rockets add energy to their reaction mass by increasing the heat through chemical reaction, which creates more pressure as the reaction occurs (rather than having to store all of that pressure at once). This allows a sustained production of pressurized reaction mass.
Solid state rockets burn and create both heat and gas (from the solid), thus creating pressure for the reaction mass (the gas) while in flight too.

If the pressure gets too high, the rocket explodes (happens sometimes). If it's not high enough, the rocket falls to Earth.

There are dangers to these rockets, but the benefit is that the reaction mass exits at a much higher velocity than the max pressure the container could hold would allow, giving them more thrust.

You can calculate the velocity of the reaction mass exiting a chamber where it is combusted based on the heat energy produced from an amount of material reacting.

all that potential energy has to be spent on accelerating the reaction mass, and no energy is left for accelerating the rocket.

Equal and opposite forces. The rocket gets 'half' the force. This is not the same as the rocket getting half of the energy.

Let me try to be a little move convincing: it is possible for a tank to create a jet of fluid, even when it's not moving because of being fixed to the ground, right?

Your goal should not be to convince me you are right, but to understand why you are wrong.
Have you still not understood this point?
You are demonstrating fractal wrongness here.

No. In this case you are moving the Earth slightly, and the tank with it. The Earth is not fixed to the biblical firmament. There is no special frame of reference, and nothing is immobile no matter how large it is. If there WAS such thing as a fixed object, then you could probably find a way to violate the laws of physics using it.

Force on rocket (or and plant) = Force on reaction mass.

Force = Mass * acceleration

For the "planet", we can say 1 arbitrary force unit = 1,000,000 (mass) * 1/1,000,000 (acceleration)
For the reaction mass, we can say 1 arbitrary force unit = 1/1,000,000 (mass) * 1,000,000 (acceleration)
(we'll assume this force is applied for one second to make things easy, the mass is an arbitrary hypothetical unit, acceleration is m/(s^2))

Kinetic energy = 1/2 m v^2

Kinetic energy added to the planet = 1/2 * 1,000,000 * (1/1,000,000)^2 = 0.0000005
Kinetic energy added to the rocket = 1/2 * 1/1,000,000 * 1,000,000^2 = 500000

As you can see, the force is shared equally, but the kinetic energy imparted to the reaction mass is MUCH larger. A trillion times larger.

What happens if the rocket is the same mass as the reaction mass?
Obviously, if they have the same mass, they share the kinetic energy equally too.

But this isn't the case:

http://coolcosmos.ipac.caltech.edu/ask/ ... tle-weigh-

The Space Shuttle weighed 165,000 pounds empty. Its external tank weighed 78,100 pounds empty and its two solid rocket boosters weighed 185,000 pounds empty each. Each solid rocket booster held 1.1 million pounds of fuel. The external tank held 143,000 gallons of liquid oxygen (1,359,000 pounds) and 383,000 gallons of liquid hydrogen (226,000 pounds). The fuel weighed almost 20 times more than the Shuttle. At launch, the Shuttle, external tank, solid rocket boosters and all the fuel combined had a total weight of 4.4 million pounds. The Shuttle could also carry a 65,000 payload.

In fact, the reaction mass is much heavier than whatever we put into space. We're launching light weight hollow tubes of fuel into space. Why? Because we need the rocket to get as much kinetic energy out of it as possible to overcome gravitational drag and obtain orbit velocity.
This is also why the rocket falls apart in stages (it would be a waste to carry empty tanks into space).

Now, suppose that the tank itself is moving. Can it accelerate because of creating the jet?

Yes. It certainly can.

Keep the Newton's 1st law in mind. It can't. If there were any difference caused by the tank moving at a constant speed, or even being able to move, it would violate the law of inertia, right?

What do you think Newton's laws are, exactly?
Can you list them?
What assumptions have you been making that violate these laws?

Therefore, the rockets would have to break two well known laws of physics.

Rockets clearly do not break the laws of physics, so you are misunderstanding something here.

The problem here is that you are still assuming it is the rockets that are wrong, and not your understanding of physics (which is the much more likely situation).
I believe that you made an A in physics, but that really just speaks to the poor quality of public education.

And this is exactly what you've been asking for, right? I have done the math and I have ended up with a conclusion that rockets are (epistemically) impossible.

You used the wrong equations, and based your calculations on mistaken assumptions which themselves clearly violate the basic laws of physics.
Attempting to do the math has helped identify your mistakes, since your results clearly do not match reality -- it is at least easier to point them out now.

You may want to look into billiards to have a more accessible demonstration of the basic laws of physics. Once you understand basic Newtonian physics (which you clearly do not yet), you can move on to gas laws and thermodynamics.

[teo123]

I don't know now. Look, if I believed in rockets, I would make a simple rationalization that the v in the Bernoulli's equation is the speed of the jet relative to the tank, in other words, the difference of the speed of the jet and the speed of the tank, and not the speed of the jet relative to a staying observer as I assumed. That would make the argument hilariously nonsensical.
But I don't think that learning about rockets can actually help. See, when I learn more about rockets, there will be even more things I realize I don't understand and I will simply be able to make more arguments of type "I don't know, therefore conspiracy!". I know that's probably irrational, but giving up the conspiracy theories would be giving up everything I know and love. I don't know how to stop believing in conspiracies. Maybe there are a few geniuses who can learn and understand rocket science, but I am certainly not one of them.
Though I do think it would be interesting to understand the physics a bit better. Would you help me?
I think I understand the Newton's laws of motion, at least they appear sensical to me. But I probably misunderstood the conservation of momentum. I have tried to make my question as simple as possible.

So, the conservation of momentum apparently predicts that if you, let's say, cavort a lasso, you should be pushed perpendicular to it. That's false, you feel you are pulled by the centrifugal force. So, where is the error in my reasoning? It can't be the inertial forces because the whole system itself isn't accelerating, right?
And the reason I assumed it is impossible for the rockets to fly vertically, or in any non-horizontal direction, is because, well, I assumed that the lift force, being always perpendicular to the oncoming flow direction, is canceled by the gravity only when an airplane is flying horizontally. Is it true? Are rockets supposed to somehow eliminate the lift?
Anyway, I was trying to debate flatearthers by showing them the refutations of their "evidence", and, luckily, I noticed that one of the refutations I was about to show them is false. See, the evidence of the flat Earth sunrays being non-parallel has a well-known (at least on that forum) refutation that the sunrays seem to converge only because of the perspective. But that's, as you like to call it, an ad-hoc hypothesis: it sounds scientific and makes perfect sense until you analyze it.

In this photograph, it's obvious that some of the rays, ones in the middle, are exactly perpendicular to the ground. Yet others obviously aren't. They can't be parallel. The perspective obviously doesn't make the vertical lines appear to converge.

I think I even know the math behind it, but I also don't think that's relevant now. And if it were lenses again, it would make the sunrays appear curved, right? I don't know, and you don't need to know the right answer to recognize the wrong ones (the Earth being flat or the perspective somehow making the vertical lines appear to intersect).

[brimstoneSalad]

I don't know now. Look, if I believed in rockets, I would make a simple rationalization that the v in the Bernoulli's equation is the speed of the jet relative to the tank, in other words, the difference of the speed of the jet and the speed of the tank, and not the speed of the jet relative to a staying observer as I assumed. That would make the argument hilariously nonsensical.

No, that would be correct. There is no such thing as a stationary observer. Thinking v defines the speed relative to some arbitrary observer would be nonsensical. But you are using the wrong equations here, as I explained. You don't really need to be relating pressure to velocity yet, you just need to understand the concept of equal and opposite forces for now.

But I don't think that learning about rockets can actually help. See, when I learn more about rockets, there will be even more things I realize I don't understand and I will simply be able to make more arguments of type "I don't know, therefore conspiracy!". I know that's probably irrational, but giving up the conspiracy theories would be giving up everything I know and love. I don't know how to stop believing in conspiracies. Maybe there are a few geniuses who can learn and understand rocket science, but I am certainly not one of them.

That's what I've been saying all along. You can't understand everything; you need to learn to be sensible and trust experts.

Now that you finally admit and recognize your bias in favor of conspiracy theories, you may be able to overcome it.
This is the same kind of problem that plagues theists and carnists, who simply want to believe something, and so will in spite of any evidence. You can't criticize others for being irrational -- whether that means thinking animals don't have souls, or that Muhammad rode a flying horse to heaven -- when you're engaging in the same thought process.

Though I do think it would be interesting to understand the physics a bit better. Would you help me?

I can help you a little, but if you really want to understand this stuff, you need to study at at the university level.

I think I understand the Newton's laws of motion, at least they appear sensical to me. But I probably misunderstood the conservation of momentum. I have tried to make my question as simple as possible.

This means going back to the drawing board. You actually don't understand any of the laws of physics at all, but have been mistaken for a long time.

So, the conservation of momentum apparently predicts that if you, let's say, cavort a lasso, you should be pushed perpendicular to it. That's false, you feel you are pulled by the centrifugal force. So, where is the error in my reasoning? It can't be the inertial forces because the whole system itself isn't accelerating, right?

The force is inward, and so is your acceleration (because you're changing direction), so if you're sitting in Dumbo...

...you feel pushed out (just as in the case of sitting in a car, and feeling pushed in the opposite direction of the car's acceleration, back against the seat behind you when you're speeding up, because the seat is pushing on you).

This is probably your false assumption.

On Earth, due to gravity your body is trying to accelerate down, but the ground is pushing back up at you with the normal force (like the car's seat pushing on you when you're "stationary" in the car, just the reference frame is shifted to an 'accelerated' [in a conventional sense] body being "stopped" rather than a "stopped" body being 'accelerated'), so that's what you feel.

And the reason I assumed it is impossible for the rockets to fly vertically, or in any non-horizontal direction, is because, well, I assumed that the lift force, being always perpendicular to the oncoming flow direction, is canceled by the gravity only when an airplane is flying horizontally. Is it true? Are rockets supposed to somehow eliminate the lift?

It's called gravitational drag. The force on the rocket from the escaping reaction mass is higher than the force of gravity upon the rocket. That's how rockets ascend, and it wastes a huge amount of fuel.
You can fairly easily calculate the gravitational drag on a rocket based on the time it takes to ascend. Most of the fuel is spent doing that (pushing against gravity).

See, the evidence of the flat Earth sunrays being non-parallel has a well-known (at least on that forum) refutation that the sunrays seem to converge only because of the perspective. But that's, as you like to call it, an ad-hoc hypothesis: it sounds scientific and makes perfect sense until you analyze it.

The sun rays are not parallel because of perspective; this is a theory which can be easily confirmed by evidence.

The sun is too far away for the rays
[...]
In this photograph, it's obvious that some of the rays, ones in the middle, are exactly perpendicular to the ground. Yet others obviously aren't. They can't be parallel. The perspective obviously doesn't make the vertical lines appear to converge.
[...]
I think I even know the math behind it, but I also don't think that's relevant now.

Do the math. How tall are those buildings? The one in the middle looks like 500 or so feet. How many blocks do they represent?
How tall are those clouds? Low-balling it, they may be 4,000 feet. Could easily be a lot higher. How broad an image is that ocean photo?

seriouslynow.jpg

Photographic framing can be very deceptive, just based on zoom, irrespective of lenses.
Also, what angle are they being seen at? Because of the scale, the clouds are far above, being seen from below from a fairly wide angle lens. The buildings are being photographed from a distance along a level horizontal ray using an optical zoom (or the image has been cropped).

Also, you're doing the same thing with the lines again: in this case, making the lines seem to be parallel when they aren't. There is obviously some slight perspective in those edge buildings that the thick lines are covering up.

And if it were lenses again, it would make the sunrays appear curved, right?

They probably are curved. If not, the image may have been corrected on the computer. Kind of irrelevant, though, given the differences in scale of those images.