Physics of falling objects
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Mr Optimistic
As this is a technical forum I was hoping you would flesh this out by showing the calculations. I really don't think it is fair comment to label the guy as unintelligent and expect forum users to simply take your word for it. Has he done something to your sister or do you have another reason for the ad-homs approach?
As neither yourself or awblain have shown any inclination to do the sums I thought I'd do them myself:
According to his paper g is adjusted by the following equation:
gₐ = gₑ x (rₑ ÷ rₐ)²
It is obvious that at low altitudes this is going to make no difference. But what is the upper limit where a tool such as this would be used? A case study would be the Columbia disaster.
The altitude of that break-up was ≈ 64km. The Earth radius is ≈ 6380km at the equator (WGS84). So, rₑ is 6380km and rₐ is 6444km. Using 9.81 for gₑ in the above equation and evaluating for gₐ results in 9.62ms⁻².
By using the equation:
R = V₀ x √(2h ÷ g)
..we can get a feel for how much difference this would make to horizontal range, using the velocity at break-up ≈ 6000ms⁻¹ and evaluating R when g = 9.81 and then again when g = 9.62
This would not include drag. The answers are 685.4km and 692.1km
So, up to about 7km would be the maximum difference this technique would make, before drag. Clearly, drag would reduce this.
Whether or not you think that is trivial depends on one's point of view. I think that if his model allows him to make such a correction he may as well have it. Even if it isn't necessary.
The problem with the poor professor's paper is that it is quite simply unintelligent to include the range variation of gravity as its very small perturbing effect relative to a constant model is less than trivial when compared to the other forces acting and the inherent limitations of the model.
As neither yourself or awblain have shown any inclination to do the sums I thought I'd do them myself:
According to his paper g is adjusted by the following equation:
gₐ = gₑ x (rₑ ÷ rₐ)²
It is obvious that at low altitudes this is going to make no difference. But what is the upper limit where a tool such as this would be used? A case study would be the Columbia disaster.
The altitude of that break-up was ≈ 64km. The Earth radius is ≈ 6380km at the equator (WGS84). So, rₑ is 6380km and rₐ is 6444km. Using 9.81 for gₑ in the above equation and evaluating for gₐ results in 9.62ms⁻².
By using the equation:
R = V₀ x √(2h ÷ g)
..we can get a feel for how much difference this would make to horizontal range, using the velocity at break-up ≈ 6000ms⁻¹ and evaluating R when g = 9.81 and then again when g = 9.62
This would not include drag. The answers are 685.4km and 692.1km
So, up to about 7km would be the maximum difference this technique would make, before drag. Clearly, drag would reduce this.
Whether or not you think that is trivial depends on one's point of view. I think that if his model allows him to make such a correction he may as well have it. Even if it isn't necessary.
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This centre of mass will also be mobile as the moon revolves around the earth.
Thus, a person standing on the earths surface will be moving in and out relative to the centre of mass of the earth/moon pair and will experience (very tiny! 2micro m/s2) variations in gravity.
They would also be moving in and out relative to the L1 Lagrange point, ie varying their range from a point of zero g
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Oggers,
The Columbia situation is the same point point again there's wood to focus on before worrying about the trees. You don't need to do irrelevant sums, you can just say that different sums need to be done. You don't ask for sums at a PhD exam, you ask for insight, intuition and an understanding of the issues.
Here's one reason why - and one is sufficient to drop the point and think more about it.
Vertical changes in gravity by 1% are a minor detail, since the break up was not at a point - it took tens of seconds, and spread over tens of kilometers. Thus your uncertainty in initial position makes a potential 1% shift in a 700km track neither here nor there.
Remember that the drag for the whole shuttle brings it down in Florida about 4000km after substantial contact with the atmosphere, and the actually distance from break up to debris hitting the ground was only 100-200km, so saying anything numerical "without drag" is like focussing on a flea while missing a bear it is sitting on.
The Columbia situation is the same point point again there's wood to focus on before worrying about the trees. You don't need to do irrelevant sums, you can just say that different sums need to be done. You don't ask for sums at a PhD exam, you ask for insight, intuition and an understanding of the issues.
Here's one reason why - and one is sufficient to drop the point and think more about it.
Vertical changes in gravity by 1% are a minor detail, since the break up was not at a point - it took tens of seconds, and spread over tens of kilometers. Thus your uncertainty in initial position makes a potential 1% shift in a 700km track neither here nor there.
Remember that the drag for the whole shuttle brings it down in Florida about 4000km after substantial contact with the atmosphere, and the actually distance from break up to debris hitting the ground was only 100-200km, so saying anything numerical "without drag" is like focussing on a flea while missing a bear it is sitting on.
Awblain's address is Pasadena. Judging by his accurate responses I guess he works in an engineering capacity for a tech company perhaps associated with JPL. I studied for a couple of years at a place down the road there on California Blvd. Not sure why anyone would expect to learn much physics on pprune though when there's a world of introductory texts out there.
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Y'know, it isn't all that difficult ...
warmer ...
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awblain
No such things as a "natural frame"
Discussion of moon tides is obfuscation. These are due to an eliptic orbit, ie the moon does not face the exact same side to the earth at all times and the tides due to the sun.
Neither of these take away from the explanation.
I'll give you that about the L1 point. I was being simplistic.
In an inertial frame the zero g point is a little further out than L1.
No such things as a "natural frame"
Discussion of moon tides is obfuscation. These are due to an eliptic orbit, ie the moon does not face the exact same side to the earth at all times and the tides due to the sun.
Neither of these take away from the explanation.
I'll give you that about the L1 point. I was being simplistic.
In an inertial frame the zero g point is a little further out than L1.
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ANCPER,
I miss your entertaining style.
How did you go with conjuring up another mathematical proof that the mass of different objects has no effect on the time taken for those objects, (aircraft pieces in this discussion) to reach the ground?
Quote:
Not a pilot yourself then? And if you are a pilot, then I apologise. You have proved yourself correct with that put-down.
And why on earth would you disagree with A squared?
The post he/she delivered was clear, humorous, accurate and well written and based on "basic physics".
Eagerly awaiting more of your entertaining posts.
I miss your entertaining style.
How did you go with conjuring up another mathematical proof that the mass of different objects has no effect on the time taken for those objects, (aircraft pieces in this discussion) to reach the ground?
Quote:
"What's the world coming to, when pilots don't know basic physics"
And why on earth would you disagree with A squared?
The post he/she delivered was clear, humorous, accurate and well written and based on "basic physics".
Eagerly awaiting more of your entertaining posts.
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ANCPER,
I miss your entertaining style.
How did you go with conjuring up another mathematical proof that the mass of different objects has no effect on the time taken for those objects, (aircraft pieces in this discussion) to reach the ground?
Quote:
Not a pilot yourself then? And if you are a pilot, then I apologise. You have proved yourself correct with that put-down.
And why on earth would you disagree with A squared?
The post he/she delivered was clear, humorous, accurate and well written and based on "basic physics".
Eagerly awaiting more of your entertaining posts.
I miss your entertaining style.
How did you go with conjuring up another mathematical proof that the mass of different objects has no effect on the time taken for those objects, (aircraft pieces in this discussion) to reach the ground?
Quote:
Not a pilot yourself then? And if you are a pilot, then I apologise. You have proved yourself correct with that put-down.
And why on earth would you disagree with A squared?
The post he/she delivered was clear, humorous, accurate and well written and based on "basic physics".
Eagerly awaiting more of your entertaining posts.
I do hope nothing has happened to him.
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A Squared
Glad to see your concerned for my health!
No, I hadn't slunk off anywhere. I was waiting for response higher up the food chain, so had to wait out the w/end to get a response and yes I concede. Damn!
Yes, it's too dumb to say anything further!
No, I hadn't slunk off anywhere. I was waiting for response higher up the food chain, so had to wait out the w/end to get a response and yes I concede. Damn!
Yes, it's too dumb to say anything further!
Last edited by ANCPER; 17th Mar 2014 at 10:12.
Thanks for being a good sport about it.
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All is not lost ANCPER.
If you are a pilot, which doubtful in my opinion, then there may be truth to your assertion that some pilots don't know basic physics.
You being one of them.
But back to the thread...
It is turning out like we need to discuss the physics of disappearing objects rather than falling ones.
If you are a pilot, which doubtful in my opinion, then there may be truth to your assertion that some pilots don't know basic physics.
You being one of them.
But back to the thread...
It is turning out like we need to discuss the physics of disappearing objects rather than falling ones.
Unfortunately I have made some posts which only contributed to the noise so would be hypocritical to comment. Strange that so many people lost their lives in a manner which may have been awful (hope not) and we are indulging our technical curiosity...and I am guilty of it too.
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I just read the first 10 posts of this thread. Man, this internet thingy, it is really something, isn't it?
Any high school physics student could set you all straight; good thing high school physics isn't needed to fly airliners...
Any high school physics student could set you all straight; good thing high school physics isn't needed to fly airliners...
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Ok, this is on the matter of actual falling objects; airplanes in fact.
To start with: I am NOT entering the weird world of tin foil hats. I could not care less about what happened. The return of Elvis. Evil gnomes. Alien abductions. AlQaeda, IRA and PLO joint operation or any government cover up. I really really DO NOT CARE.
I am only interested in the physics, ok?
So, with this in mind, I would like to know if anyone here knows of ANY kind of calculation that would make, say TWA800, drop its nose and then continue to climb a few hundred metres (thousands of feet). I have tried different ballistic calculations but can only get the plane up to some tens of metres (about hundred feet actually). Some scenarios I tried:
- Approximating a B747 fuselage shortened with the length of the nose but CoG intact from official documents of a whole 747.
- As above but with different CoG.
- Approximating a B747 without a nose, instead a metal skin at the point of breakup, CoG intact from official documents of a whole 747.
- As above but with different CoG.
In all scenarios I assumed that all four engines after-the-fact were providing equal amounts of climb thrust and constant climb ratio per official documents, although I know that may not be the case depending on what wires may or may not have been severed.
Ballistic calculations are not the best way to approach this case because you have to take into account the various drag forces that would make a noseless plane do strange things, but statistically analyzing my calculations I still can't get the plane to make such an extraordinary trajectory even with significance 5%.
Do anyone here know if that animation of the trajectory after (whatever happened) is based on scientific calculations or if it is just a conjecture based on eyewitnesses statements?
Please, no endless tirades about your preferred theory about what happened. CFT explosion sounds good enough for me. I am just baffled by the trajectory - that is my only concern.
To start with: I am NOT entering the weird world of tin foil hats. I could not care less about what happened. The return of Elvis. Evil gnomes. Alien abductions. AlQaeda, IRA and PLO joint operation or any government cover up. I really really DO NOT CARE.
I am only interested in the physics, ok?
So, with this in mind, I would like to know if anyone here knows of ANY kind of calculation that would make, say TWA800, drop its nose and then continue to climb a few hundred metres (thousands of feet). I have tried different ballistic calculations but can only get the plane up to some tens of metres (about hundred feet actually). Some scenarios I tried:
- Approximating a B747 fuselage shortened with the length of the nose but CoG intact from official documents of a whole 747.
- As above but with different CoG.
- Approximating a B747 without a nose, instead a metal skin at the point of breakup, CoG intact from official documents of a whole 747.
- As above but with different CoG.
In all scenarios I assumed that all four engines after-the-fact were providing equal amounts of climb thrust and constant climb ratio per official documents, although I know that may not be the case depending on what wires may or may not have been severed.
Ballistic calculations are not the best way to approach this case because you have to take into account the various drag forces that would make a noseless plane do strange things, but statistically analyzing my calculations I still can't get the plane to make such an extraordinary trajectory even with significance 5%.
Do anyone here know if that animation of the trajectory after (whatever happened) is based on scientific calculations or if it is just a conjecture based on eyewitnesses statements?
Please, no endless tirades about your preferred theory about what happened. CFT explosion sounds good enough for me. I am just baffled by the trajectory - that is my only concern.
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Well, for what it's worth, I wondered the same thing while reading the official explanation of the airplane "streaking" upward after the CWT explosion.
Without going thru the numbers again, what I recall was that if you assumed that the airplanes velocity was suddenly directed upward, without significant loss of energy the altitude gain suggested was at leas semi-plausible.
The problems with that of course was that the reason the airplane suddenly turned up was the CWT explosion blew the nose off.
This introduces two problems:
1) The huge amount of drag from having a gaping hole in the fuselage instead of the forward half would not be a low drag feature.
2) The post explosion airplane was assumed to achieve a stable zoom climb following the loss of of the forward fuselage. This is inconsistent with the part of the theory which says that the loss of the forward fuselage caused it to depart stable flight upward. The loss of the forward fuselage either caused it to become unstable, or it didn't. It can't really do both, which is what the theory requires.
You can only figure that it climbed thousands of feet if you completely neglect drad and aerodynamics and focus only on how high the kinetic energy would take it in a vacuum.
The "zooms upward" scenario fails on an entirely different level. The raison d'etre for the "zoom upward" theory was to explain why so may people reported seeing something "streak" upward. It serves no other purpose, other than to provide an explanation for the witness accounts of a fire streak going up. The theory being that the post-explosion airplane was what they saw "streak" upward. The problem with that was the distance, altitude and speeds involved. From memory, the airplane was at 14,000 ft (or was it 15K?) when the explosion occurred, and (again from memory) it was something like 40 miles away from the nearest witness who reported something 'streaking upward"
We have all watched airplanes fly. an airliner at 14,000 ft altitude, and even just 10 miles away does not "streak" across the sky. It crawls. So if from the observers perspective it appears to be crawling across the sky, if that same airspeed is suddenly directed perfectly upward without loss of speed, it's not going to appear to "streak" upward any more than it was "streaking" across the sky horizontally.
Now, I'm not trying to start a conspiracy theory discussion either. I have no idea what happened to TWA 400, There are all kinds of reasons why a shoot-down is really implausible, and there are all kinds of reason why a CWT explosion seems the most plausible explanation.
I'm just saying that the post-explosion climb as an explanation for witness reports of fiery streaks going up to the airplane is a complete farce. And that is the only reason it exists.
Without going thru the numbers again, what I recall was that if you assumed that the airplanes velocity was suddenly directed upward, without significant loss of energy the altitude gain suggested was at leas semi-plausible.
The problems with that of course was that the reason the airplane suddenly turned up was the CWT explosion blew the nose off.
This introduces two problems:
1) The huge amount of drag from having a gaping hole in the fuselage instead of the forward half would not be a low drag feature.
2) The post explosion airplane was assumed to achieve a stable zoom climb following the loss of of the forward fuselage. This is inconsistent with the part of the theory which says that the loss of the forward fuselage caused it to depart stable flight upward. The loss of the forward fuselage either caused it to become unstable, or it didn't. It can't really do both, which is what the theory requires.
You can only figure that it climbed thousands of feet if you completely neglect drad and aerodynamics and focus only on how high the kinetic energy would take it in a vacuum.
The "zooms upward" scenario fails on an entirely different level. The raison d'etre for the "zoom upward" theory was to explain why so may people reported seeing something "streak" upward. It serves no other purpose, other than to provide an explanation for the witness accounts of a fire streak going up. The theory being that the post-explosion airplane was what they saw "streak" upward. The problem with that was the distance, altitude and speeds involved. From memory, the airplane was at 14,000 ft (or was it 15K?) when the explosion occurred, and (again from memory) it was something like 40 miles away from the nearest witness who reported something 'streaking upward"
We have all watched airplanes fly. an airliner at 14,000 ft altitude, and even just 10 miles away does not "streak" across the sky. It crawls. So if from the observers perspective it appears to be crawling across the sky, if that same airspeed is suddenly directed perfectly upward without loss of speed, it's not going to appear to "streak" upward any more than it was "streaking" across the sky horizontally.
Now, I'm not trying to start a conspiracy theory discussion either. I have no idea what happened to TWA 400, There are all kinds of reasons why a shoot-down is really implausible, and there are all kinds of reason why a CWT explosion seems the most plausible explanation.
I'm just saying that the post-explosion climb as an explanation for witness reports of fiery streaks going up to the airplane is a complete farce. And that is the only reason it exists.