This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
This is why these things get so much traction. That document/picture asks all the wrong questions, making so many false assumptions, that have nothing to do with physics. Going through the whole thing is far too much work, there are so many errors, but I will do a couple to help you understand what I mean.
Does lunar lander look like it could launch off the moon and intercept and dock with the lunar orbiter?
Your answer was "Not really."
The real answer is, it's an absolutely nonsense question. What does it mean to "look like" it can do something? It either has enough fuel, and efficient enough rockets to do what it needs to do or it doesn't. That would be determined by calculation, not by visual inspection. Even the answer given was not definitive, but one of biased guessing because there is no way to actually answer it. There are several nonsense "leading" questions in there designed to manipulate bias.
Have you ever tried to park a vehicle in a garage while driving at 3500 MPH?
3500 MPH relative to what? The orbiter and the landing vehicle were going at the same speed (or close enough) when they docked. When a rocket takes off it doesn't go straight up, it follows a curved path, which means as it accelerates its direction changes. This launch to a particular orbit (the orbit the orbiter vehicle was in) was done by launching at a slight angle, so gravity pulling down changed the total path into a curve with respect to the starting condition on the moon.
These questions make this mistake a ton, not taking into account what travel in a gravity well is actually like. Like this one:
If satellites are travelling so fast that they "fall around" the Earth in an orbit...
This is not the best way to look at orbit paths as it creates a lot of false ideas. It is better to think of an orbit as an equipotential. Think of a round hill. If you travel around the hill you can go all the way around without going up or down. If there is no friction, and you have path, you can go around the hill forever without any energy expenditure.
If a rocket is travelling at 25,000 MPH and cuts its engines, would you expect the rocket to "coast" uphill to the Lagrange point for another hour?
Similar to the equipotential around the hill, a rocket will travel in a curved path which could be an equipotential. Regardless of the path this rocket took, it travelled in a curved path that was not "uphill" even if it was not an equipotential. Just like a car going up hill that you take your foot off the gas, the car can in fact coast up the rest of the way if it had enough kinetic energy to overcome the remaining potential energy it would gain by attaining the top of the hill. In every case the car, or the rocket, will follow the path of least energy required to get there (similar to an equipotential curve, though including an exchange of its initial kinetic energy to the potential energy it gains as it goes up the potential well). These paths are calculated, they aren't difficult, and every physics student calculates them. They are done all the time.
There is no voodoo here. This is not complicated stuff. That questionnaire asks a lot of the wrong questions in a way that confirms bias without addressing actual physics. It takes the familiar physics (what we experience on Earth) and applies it to orbital mechanics or more specifically, rocket science. While those things are related, they are not the same. They require different equations, and a better understanding of a curved space. Its a very similar problem to the difficulties some people are having in this particular paper interestingly. Thinking that things that work in flatland, apply to curved land.
Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
I picked that up immediately. In engineering, calculations are sometimes simplified by 'nullifying' them out or disregarding it when not a factor. After all the report is about a 'Linear' aircraft model.
so... they had to take into account the curvature of the earth when engineering the golden gate bridge, but they can just safely ignore the curvature of the earth when trying to land an airplane? seems legit.
Bridge design is not linear and is distantly related to "linear" aircraft model as you are to a detritus rock..... Well, may be not. Nevertheless, the designs are radically different and take into consideration very different forces. Did you read linear in the title? Do you understand linear? Why would it include "linear" aircraft model, if they were going to consider non-linear considerations?
As I said, to change it to a rotating spherical reference frame you take the equations of motion in the Euclidian frame (flat, non-rotating) and transform them into the new reference frame (spherical rotating) using the appropriate transformation matrix.
I apologize if this doesn't make any sense to you, but just to show you what I'm talking about: Transformation Matrix.
Your snarky rhetoric does not strengthen your position, it just proves that you don’t understand the physics and math involved.
There are people here with degrees in physics, engineering and mathematics telling you what this means, but no, I’m sure your degree in music appreciation is just as valid to evaluate this stuff, right?
Insults, mockery and ridicule are the only appropriate responses to flat-earthism, and prove nothing other than we’re all making fun of your abject ignorance.
i was taught about flat earth in school, but in a slightly unusual way. we were told that Columbus's crew were all flat earth'ers, but that the visionary Columbus knew better. then we all had a good laugh about how stupid Columbus' crew was.
looking back on it now, it seems to me that the only reason we were even taught about Columbus, was to mock the flat-earth model. because they set up Columbus, just to knock him down.
because later we are taught that Leif Erickson actually came before Columbus,
that Columbus didn't actually prove the earth was round, BUT Magellan did later,
oh, and Columbus was a terrible person who burned Indians at the stake, in the name of Jesus Christ.
so you tell me... whats the point of teaching us about Columbus at all? so we memorize worthless trivia?
The thing I can't figure out is what difference does it make? Round, flat, square....why does one way or the other hurt some people's feelings? I have a feeling that the real problem here is that the ones throwing all the stones must feel like they have been lied to their whole life and they have to take it out on anyone with a different opinion. It's a shame really that just because we are all here on GAW doesn't mean we can be one big "family". There are always the people that must attack no matter what. I could really give a shit what shape the earth is, I haven't trusted the "ones in charge" since an early age. I can only speak for myself when I say I'm 100% sure no matter the shape, the world will be completely fucked if we don't come together and use this energy against the ones trying to destroy it.
I used to work at a flight training place, for maths purposes the earth is flat in many calculations. The reason being is that in one exact moment of time u are essentially in a column of air calculated like the earth is flat.
No. The math ur applying is lift weight balance etc. Navigation is a different subject and yes you calculate curvature. Its possible to do a triangle with 2 90 degree turns on the globe
I love how all the early experiments to prove globe earth with a distant sun can also prove flat earth with a close sun, that is what got me into this like I am.
Smooth, like many words has other words that mean the same thing. These are called synonyms. One synonym for smooth is Flat. Because of this I postulate that "curve" can be disregarded all together because the Earth is Smooth is Flat and frankly, literally everyone can disregard the curve without much consequence, even though it is said to be 8 inches for every 81 feet, I think. 8in per 3meter^2 (I could be wrong it has been a while)
My question now is, HOW THE HELL DID THEY KNOW that the Earth was smooth way back when. So I did some looking and came across a man named Hu, thanks to a "typo" in one of Trump's twitter posts back in the day. Hus story instead of History. So I looked for Hu's Story and this is what I found. https://historyofyesterday.com/historys-first-astronaut-c27f32b3e8b5
I might be grasping but shortly after Wu Han had released a virus that threatened the world. This guy named Wan Hu is probably not connected at all.
Everything we learned about atoms is already outdated. They are on quantum theory now. Now they teach light and matter have both wave and particle characteristics at the atomic and subatomic levels.
Read further. Explains why these models assume no atmosphere or gravitational forces. This doesn't prove what you think it does.
To elaborate a little bit:
This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
hmm, so what you are saying is that pilots are too stupid to understand the math, but you do?
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
yeah, it took me a couple of years to do the math...
most people can't get past question 4 without resorting to a thought-terminating cliche
https://i.redd.it/g287hbmcb94z.png
This is why these things get so much traction. That document/picture asks all the wrong questions, making so many false assumptions, that have nothing to do with physics. Going through the whole thing is far too much work, there are so many errors, but I will do a couple to help you understand what I mean.
Your answer was "Not really."
The real answer is, it's an absolutely nonsense question. What does it mean to "look like" it can do something? It either has enough fuel, and efficient enough rockets to do what it needs to do or it doesn't. That would be determined by calculation, not by visual inspection. Even the answer given was not definitive, but one of biased guessing because there is no way to actually answer it. There are several nonsense "leading" questions in there designed to manipulate bias.
3500 MPH relative to what? The orbiter and the landing vehicle were going at the same speed (or close enough) when they docked. When a rocket takes off it doesn't go straight up, it follows a curved path, which means as it accelerates its direction changes. This launch to a particular orbit (the orbit the orbiter vehicle was in) was done by launching at a slight angle, so gravity pulling down changed the total path into a curve with respect to the starting condition on the moon.
These questions make this mistake a ton, not taking into account what travel in a gravity well is actually like. Like this one:
This is not the best way to look at orbit paths as it creates a lot of false ideas. It is better to think of an orbit as an equipotential. Think of a round hill. If you travel around the hill you can go all the way around without going up or down. If there is no friction, and you have path, you can go around the hill forever without any energy expenditure.
Similar to the equipotential around the hill, a rocket will travel in a curved path which could be an equipotential. Regardless of the path this rocket took, it travelled in a curved path that was not "uphill" even if it was not an equipotential. Just like a car going up hill that you take your foot off the gas, the car can in fact coast up the rest of the way if it had enough kinetic energy to overcome the remaining potential energy it would gain by attaining the top of the hill. In every case the car, or the rocket, will follow the path of least energy required to get there (similar to an equipotential curve, though including an exchange of its initial kinetic energy to the potential energy it gains as it goes up the potential well). These paths are calculated, they aren't difficult, and every physics student calculates them. They are done all the time.
There is no voodoo here. This is not complicated stuff. That questionnaire asks a lot of the wrong questions in a way that confirms bias without addressing actual physics. It takes the familiar physics (what we experience on Earth) and applies it to orbital mechanics or more specifically, rocket science. While those things are related, they are not the same. They require different equations, and a better understanding of a curved space. Its a very similar problem to the difficulties some people are having in this particular paper interestingly. Thinking that things that work in flatland, apply to curved land.
Math and logic are a beautiful thing to behold....just another reason to praise God for his wonderful works.
Kek.
Your argument lacks, care to explain? I already know. Anyone with eyes to see soon will too. Especially if this is the best plug for all these leaks.
Please see my response about changing reference frames above. It does not "lack".
You can't reference your claimed matrix calculations or any curvature calculations. I understand.
You didn't ask.
Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
I understand the matrixes busywork that may be completely ignored in operation.
https://image1.slideserve.com/1902429/transformation-matrix-continue1-l.jpg
I picked that up immediately. In engineering, calculations are sometimes simplified by 'nullifying' them out or disregarding it when not a factor. After all the report is about a 'Linear' aircraft model.
so... they had to take into account the curvature of the earth when engineering the golden gate bridge, but they can just safely ignore the curvature of the earth when trying to land an airplane? seems legit.
Bridge design is not linear and is distantly related to "linear" aircraft model as you are to a detritus rock..... Well, may be not. Nevertheless, the designs are radically different and take into consideration very different forces. Did you read linear in the title? Do you understand linear? Why would it include "linear" aircraft model, if they were going to consider non-linear considerations?
As I said, to change it to a rotating spherical reference frame you take the equations of motion in the Euclidian frame (flat, non-rotating) and transform them into the new reference frame (spherical rotating) using the appropriate transformation matrix.
I apologize if this doesn't make any sense to you, but just to show you what I'm talking about: Transformation Matrix.
our advanced calculations are far too difficult for mere mortals to understand, so just take our word for it.
Your snarky rhetoric does not strengthen your position, it just proves that you don’t understand the physics and math involved.
There are people here with degrees in physics, engineering and mathematics telling you what this means, but no, I’m sure your degree in music appreciation is just as valid to evaluate this stuff, right?
this 30 second NASA video debunks your moon landing myth
https://youtu.be/9HQfauGJaTs?t=8s
No it doesn’t. That’s your opinion given limited knowledge. Have a great thanksgiving!
Keep believing lol
Ok, Cleetus
people weight less at the equator than they do at the poles, because of centrifugal force, right?
No, because they are a little further from the center of mass, because the earth is not perfectly round, it bulges at the equator.
It's funny how quickly a little thinking can produce so many plot holes.
Becuase you don't account for that during everyday physics calcs
Oh the Flat Earthers are back. What are we supposed to be forum-slid from this time?
do you realize posting 8+ times with nothing but insults just proves my point...
Insults, mockery and ridicule are the only appropriate responses to flat-earthism, and prove nothing other than we’re all making fun of your abject ignorance.
SADS - Sudden Adult Death Syndrome
This is gonna piss some people off!!!! I am here for it!
i was taught about flat earth in school, but in a slightly unusual way. we were told that Columbus's crew were all flat earth'ers, but that the visionary Columbus knew better. then we all had a good laugh about how stupid Columbus' crew was.
looking back on it now, it seems to me that the only reason we were even taught about Columbus, was to mock the flat-earth model. because they set up Columbus, just to knock him down.
because later we are taught that Leif Erickson actually came before Columbus,
that Columbus didn't actually prove the earth was round, BUT Magellan did later,
oh, and Columbus was a terrible person who burned Indians at the stake, in the name of Jesus Christ.
so you tell me... whats the point of teaching us about Columbus at all? so we memorize worthless trivia?
what year did Columbus sail?
you get an A+ for regurgitating 1492
The thing I can't figure out is what difference does it make? Round, flat, square....why does one way or the other hurt some people's feelings? I have a feeling that the real problem here is that the ones throwing all the stones must feel like they have been lied to their whole life and they have to take it out on anyone with a different opinion. It's a shame really that just because we are all here on GAW doesn't mean we can be one big "family". There are always the people that must attack no matter what. I could really give a shit what shape the earth is, I haven't trusted the "ones in charge" since an early age. I can only speak for myself when I say I'm 100% sure no matter the shape, the world will be completely fucked if we don't come together and use this energy against the ones trying to destroy it.
The flat earthers typically believe that a flat earth “proves” the existence of God, and the cabal uses “globe earth” to suppress…
Because if we see every other planet as a globe, but our planet is flat, that makes us special and “proves” God.
Basically they’re all just really, really, (REALLY) stupid. Pray for them.
Let me give it to you straight...
I used to work at a flight training place, for maths purposes the earth is flat in many calculations. The reason being is that in one exact moment of time u are essentially in a column of air calculated like the earth is flat.
Yeah so you never calculate for curvature, and they tell you to do the math assuming a flat Earth.
No. The math ur applying is lift weight balance etc. Navigation is a different subject and yes you calculate curvature. Its possible to do a triangle with 2 90 degree turns on the globe
https://s3mn.mnimgs.com/img/shared/discuss_editlive/5956792/2013_11_18_09_51_46/image1477904103093019129.jpg
only on paper.
They are using FORTRAN FFS. That programming went out with the ark.
NASA has never had the technology necessary to go to the moon.
I love how all the early experiments to prove globe earth with a distant sun can also prove flat earth with a close sun, that is what got me into this like I am.
I also love the language used.
It was once said to me that the Earth is smooth. This person has done some maths to prove a smooth Earth : http://www.curiouser.co.uk/facts/smooth_earth.htm
Smooth, like many words has other words that mean the same thing. These are called synonyms. One synonym for smooth is Flat. Because of this I postulate that "curve" can be disregarded all together because the Earth is Smooth is Flat and frankly, literally everyone can disregard the curve without much consequence, even though it is said to be 8 inches for every 81 feet, I think. 8in per 3meter^2 (I could be wrong it has been a while)
My question now is, HOW THE HELL DID THEY KNOW that the Earth was smooth way back when. So I did some looking and came across a man named Hu, thanks to a "typo" in one of Trump's twitter posts back in the day. Hus story instead of History. So I looked for Hu's Story and this is what I found. https://historyofyesterday.com/historys-first-astronaut-c27f32b3e8b5
I might be grasping but shortly after Wu Han had released a virus that threatened the world. This guy named Wan Hu is probably not connected at all.
Yea, it was a common viewpoint that was used. Nothing special about it.
did you know that the only reason they still teach the admittedly-wrong Bohr model of the atom, is because they can't come up with a better model?
Everything we learned about atoms is already outdated. They are on quantum theory now. Now they teach light and matter have both wave and particle characteristics at the atomic and subatomic levels.
This website,
https://dizzib.github.io/earth/curve-calc/?d0=30&h0=10&unit=imperial
Florida, 113 Sears Towers, and 100,000 feet.