Low Frequency Radio Trilateration

[RadioEng]

Say your transmitter - receiver distance is 65 kilometres and your desired accuracy is 100 metres.

I see nothing in your proposals that would distinguish between the signal at 65Km and at 65.1Km.

As has already been discussed, it is a matter of computing the losses and gains of that signal. It is a matter of having the right information. So, its not that it cannot be done, its about how much money you have to solve a difficult problem.

 

[sophiecentaur]

RE Ad hominem
If Albert Einstein were to tell me he was trying this system I would be unlikely to question him, initially, in the absence of quoted figures. If our Milkman told me the same thing I would need a some numbers to back it up. If that is too "ad hominem" then I plead guilty. Which are you Albert or the Milkman? As it is, you have not given any figures so you could be either. I think you need some numbers to establish some credibility with the forum.

Spread spectrum is no more magical than noise (to quote you) and it is a method used to improve signal to noise ratio. Hence I ask by how much your system will improve the SNR and for some quantitative argument to show it has a snowball's chance in hell of working - and producing accurate enough measurements to make trilateration work. I was trying to point out that you will be looking for very accurate measurements of three or more path lengths in order to place your vehicle by calculations of range differences.

The label / modulation you will be using is the signal which is deviating the spread spectrum and the minimum bandwidth you are stuck with is related to frequency stability at both ends. Without finite bandwidth, how will you know that a lowering of the signal level is due to distance or drift out of the input filter? If your vehicle is to be operating in orbit then you would also need to know about and to eliminate the effects of all massive bodies that could affect its velocity. You want to integrate over a long time (weeks / months) then your bandwidth would need to have room for all the minor perturbations due to other craft and minor bodies which are not available in almanacs - and not even known.

So many questions and no figures for any of the vital quantities involved. Is there any wonder I am getting skeptical? What sort of financial budget would this have to involve if you just assume that any necessary measurements of perturbations can be taken care of?

 

[Studiot]

As has already been discussed, it is a matter of computing the losses and gains of that signal. It is a matter of having the right information. So, its not that it cannot be done, its about how much money you have to solve a difficult problem.

The deterministic view of the universe went out of the window more than a century ago now.

I have actually stood at the measurement end of such systems and made - yes - measurements. You had the benefit of that experience available, but you chose to be contemptuous of it - I wish you well however.

Since you know all the answers, why ask questions?

I look forward to reading about this great leap forward in science, since both the mathematics and the physics are against you.

 

[sophiecentaur]

I has worried me a lot that so many posts about circuits seem centred around the results of simulations. Now, we know just how well many circuit components can be characterised and I reluctantly have to accept that it is the way things tend to be done these days. And it is very often successful.
This, however, takes simulation to ludicrous lengths. It assumes the Solar System, the Ionosphere, Spread Spectrum systems and a host of other things can be characterised to unbelievable levels of accuracy. (That actual degree of accuracy of any of them is not, however, quoted.) Isn't it usual to do an analysis of overall accuracy very early on in a planned project?
I get the feeling 'that Bridge' in India had a firmer footing than this suggested project.

 

[RadioEng]

Spread spectrum is no more magical than noise (to quote you) and it is a method used to improve signal to noise ratio. Hence I ask by how much your system will improve the SNR and for some quantitative argument to show it has a snowball's chance in hell of working - and producing accurate enough measurements to make trilateration work. I was trying to point out that you will be looking for very accurate measurements of three or more path lengths in order to place your vehicle by calculations of range differences.

This is really the question that was posed at the beginning of this thread. The consensus was that there were a range of factors that needed to be accounted for. Thus, it comes down to what information you possess. Obtaining that information is a completely different question and each factor will have its own particular solution.

I have yet to see a problem that does not have a particular solution given the resources.

The label / modulation you will be using is the signal which is deviating the spread spectrum and the minimum bandwidth you are stuck with is related to frequency stability at both ends.

That's an engineering issue, but I agree in principle. Again, it comes down to resources and funding. According to the document from IEEE that I posted, it seems as though an E-Field receiver may be best.

Without finite bandwidth, how will you know that a lowering of the signal level is due to distance or drift out of the input filter?

An array of detectors would show if this was the case. The final calculations would be off revealing the source of the problem.

If your vehicle is to be operating in orbit then you would also need to know about and to eliminate the effects of all massive bodies that could affect its velocity. You want to integrate over a long time (weeks / months) then your bandwidth would need to have room for all the minor perturbations due to other craft and minor bodies which are not available in almanacs - and not even known.

Anything unknown will have a very small effect, but a real-time position can be calculated using timing signals exchanged across the array. Its just another trilateration.

So many questions and no figures for any of the vital quantities involved. Is there any wonder I am getting skeptical?

That's what I was looking for. I wanted too see where the pitfalls where. It looks like it just comes down to resources, rather than any physical impossibilities.

 

[sophiecentaur]

You still have quoted no figures.
The Victorians though the same way as you; that Physics was all sorted out and it was just a matter of improving on the accuracy of a measurement or two. Then along came QM and it all changed. There are, in fact, some fundamental limitations in Science.
I guess, by your arguments, you should be able to get round Heisenberg too?
It's very hard not be ad hominem in the face of such naivety. Only some facts and figures can prove your system.

 

[skeptic2]

That's what I was looking for. I wanted too see where the pitfalls where. It looks like it just comes down to resources, rather than any physical impossibilities.

What resources would it take to pull a signal out of noise at least 90 dB stronger?

 

[RadioEng]

The Victorians though the same way as you; that Physics was all sorted out and it was just a matter of improving on the accuracy of a measurement or two. Then along came QM and it all changed. There are, in fact, some fundamental limitations in Science.

I understand this, but you do not know what these limits are. This is what this thread was asking and no one had a definitive answer. You are trying to get me to answer the question I posed to you and others.

I won't be solving these issues only understanding that they are there and the methodology used to reduce them to acceptable level. I don't think you have shown how the accuracy is greatly effected by the factors you describe, also I've seen no attempt on your part to consider how they may be solved.

Perhaps its best to take the viewpoint of a project manager on this. I don't want to hear about the problems, only how they can be overcome. As it stands right now, the accuracy of the solution comes down to the quality of the experimental mapping. As such, you have not shown that this cannot be done and what level of error would impact the accuracy.

So, you are really giving us your opinion based on gut instinct and that's of little value.

 

[skeptic2]

I think I understand what you mean now by resources and I think we have been guilty of thinking too narrowly or too far inside the box. This project may work after all with a loop antenna encircling the Earth with a signal of a few hundreds of thousands of amps. It's just a matter of resources. Most of the problems we have been considering have been based on much more limited resources of antennas merely miles in length and transmitting perhaps only a few hundred kilowatts. Regardless of the problem, it really comes down to just increasing the resources, doesn't it?

 

[Studiot]

43 posts to have got nowhere, except insulting those trying to help you.

Congratulations.

Contemporaneously I have been going through a much more difficult thread, with another OP.
In half that number of posts we have achieved quite satisfying progress for all parties and goodwill all round.

 

[RadioEng]

43 posts to have got nowhere, except insulting those trying to help you.

Take it as an insult if you wish, but the fact remains I have been offered nothing more than vague speculation and inappropriate laws and formulas. There is no hard data to support the claims, such as those coming from Skeptic2.

You're trying to blame me for the inability of this group to answer a straight question. Perhaps it would have been simpler for all of you to initially admit that you did not know. This would have saved everyone's time.

 

[sophiecentaur]

Take it as an insult if you wish, but the fact remains I have been offered nothing more than vague speculation and inappropriate laws and formulas. There is no hard data to support the claims, such as those coming from Skeptic2.

You're trying to blame me for the inability of this group to answer a straight question. Perhaps it would have been simpler for all of you to initially admit that you did not know. This would have saved everyone's time.

That is not a fair appraisal of the replies you have been given. It is not up to other members to design your system for you or to tell you the numbers involved. You came up with an idea which, in the collected wisdom and experience of those replying, was not viable. You clearly didn't like the negative response and so you demand that 'we' supply solutions. It doesn't work that way. You supply some actual figures and 'we' comment on them. We've had no figures to comment on so or basic knowledge tells us the system is not workable. Give the forum some concrete (quantitative) questions and you may get satisfactory answers.
It seems that we have actually been fairly indulgent, considering how little of substance you have supplied. You have been the most "vague and speculative" of all contributors, I reckon.
Now, for an appropriate consultation fee . . . . . .;)

 

[RadioEng]

That is not a fair appraisal of the replies you have been given. It is not up to other members to design your system for you or to tell you the numbers involved. You came up with an idea which, in the collected wisdom and experience of those replying, was not viable.

No one has demonstrated that. This "collective wisdom" was only yourself, Studiot and Skeptic2, but none of you can state why. The reasons you have provided can be accounted for, or they were not really applicable to what was being described.

So, it is fair to state that you were unable to answer the question with science and made your comments based on gut instinct.

You supply some actual figures and 'we' comment on them.

You were being asked what potential sources of losses exist and what known methods there are to address them.

It was really basic stuff and the answers I received had very little to do with those questions.

You have been the most "vague and speculative" of all contributors, I reckon.

I've been quite specific in my requests. I did not ask about the viability of such a system, as I know that it is well beyond anyone's experience that would be a regular on this forum. Any pretense to the contrary is really insulting everyone's intelligence.

 

[sophiecentaur]

You have actually "accounted for" nothing, explicitly. You have merely assured us that things have been "accounted for". We should just take that as enough, should we? This is an Engineering Forum in which Measurements and Figures are needed. How many have you given? What distances, powers, noise figures, speeds etc etc have you given? Without that sort of thing, how can anyone give an opinion other than a general comment about the implausible sound of the project. How can people react differently to such a vague proposal except to be skeptical.
"Specific in my requests"? Have you asked about the situation with a given power, a given noise level, a given technology? You have just asked 'in principle'. Engineering isn't like that. You don't just design A Bridge. You design one with a certain span and to carry a certain load. I could predict that it will be hundreds of years before they put one across the Pacific ocean. In fact, without some stunning new technology, I can safely say it will never happen. I can't imagine anyone getting petulant about that reaction either.
As for "unable to answer using Science" there was no specific question which could be answered using Science - except to say, 'based on Science', that it is impossible to characterise or monitor a transmission path that you envisage to the degree of accuracy that you seem to imagine. Just take a look at any of the hundreds of publications about satellite transmission and reception and look at the uncertainties involved. You have no justification for saying that all the sources of error can be "accounted for".
I can ask a very specific question as to the distance measuring accuracy that you require and which will lead to an acceptable value for signal amplitude measurement. If your answer turns out to require better than +/-0.1dB then 'scientifically and practically speaking' you can say there's a serious problem.
You could easily work out the figures for that yourself. What dB accuracy do you need?

To your original request for an idea of variation due to 'other factors' (your f(lpm)), the answer is "several dB' and a large part of that figure can't be eliminated or corrected for because it's far too localised in position and frequency for adequate monitoring. - Hence the required error is, we can say very definitely, much less than you can hope to achieve. You can't seriously believe that there's no lower limit to the level of error, in a real world.

 

[RadioEng]

You have actually "accounted for" nothing, explicitly. You have merely assured us that things have been "accounted for".

I seem to remember only asking what factors need to be considered, not your opinion on whether or not this has been achieved.

You are answering questions that no one has asked, then taking exception when it is pointed out. That's rather bizarre.

Personally, I do not care about your opinion on this being achievable, its clear you do not have the expertise to provide such an opinion in the first place.

As for "unable to answer using Science" there was no specific question which could be answered using Science

Nonsense. There is a defined list of potential losses, that has a specific answer.

To your original request for an idea of variation due to 'other factors' (your f(lpm)), the answer is "several dB' and a large part of that figure can't be eliminated or corrected for because it's far too localised in position and frequency for adequate monitoring

That's just your opinion and there is no evidence that is the case. Whilst you may be an engineer, these are problems in physics and no engineer would be expected to solve them. As such, your opinion on what is achievable is not one that would be sought.

 

[Studiot]

So, my question is two-fold, what considerations must be made for f(lpm) and what would be your estimate of accuracy? Of course, I would ask that you leave any engineering points to one-side for the moment.

The references I supplied contain the full theory to answer your first question.

Every respondent has replied that in their estimate your accuracy will be very very low.

Both your questions were therefore fully answered, but you treated this and the responders with contempt.

It is a forum rule that you do not belittle other members. Should I report this infringement?

 

[RadioEng]

The references I supplied contain the full theory to answer your first question.

That was not really an answer, it was a way out of giving an answer.

Every respondent has replied that in their estimate your accuracy will be very very low.

...but without any evidence to back that claim up. Its just a gut reaction, nothing more and that's not particularly useful.

Both your questions were therefore fully answered, but you treated this and the responders with contempt.

It is a forum rule that you do not belittle other members. Should I report this infringement?

More indifference than contempt, especially when you were answering questions that were never asked. Keep in mind that one man's belittlement is another man's truth. If that makes you or anyone else feel inadequate, it is truly not my problem.

 

[sophiecentaur]

From your OP:

So, my question is two-fold, what considerations must be made for f(lpm) and what would be your estimate of accuracy? Of course, I would ask that you leave any engineering points to one-side for the moment.

This has been addressed qualitatively on several occasions. No one has been paid to give you actual figures but there is loads of info about the values and variations of the known transmission losses. Also, suggestions about imponderables. You can find those in more detail if you reject our ball-park 'estimates'. I think you need to consider that the estimates are of the order of dBs (which, given the geometry, make it a non starter), which should give a clue as to why the rest of the project is viewed with skepticism by those who have replied. It can't really be a surprise that people who have shown an interest should ask for some details about the required measurement accuracy. Why should anyone bother to stray from their 'gut reaction' without being given more to feed on - so far, any more input would seem to be a waste of effort.
I don't think you can demand that Engineers on and Engineering Forum can ignore glaring Engineering factors any more than you could expect to have a practical / feasible 'Faster than Light' discussion in a Physics Thread.

BTW, there are three main reasons why not many people reply to a particular thread. The topic may be too hard, the scenario may be viewed as ludicrous and not worth following or it may just be boring. As an initial idea, it could grab the attention (it's had 700+ views, with its intriguing title) so you may ask yourself why there haven't been many responders.

You seem to suggest that an Engineer would have no idea about such matters and that one would need to be a Physicist to 'understand' this stuff. Are you either of those beasts? In what way are you qualified to 'belittle' Engineers and insist that, per se, they would not know enough? Any project like the one you are describing would be a huge Engineering undertaking. Any other large experiment is the same. It wouldn't work if the Engineering wasn't right and you have given no reasons to believe in its feasibility.

Nonsense. There is a defined list of potential losses, that has a specific answer.

Why did you ask the question if you know this list? But, yes, there is a list of many losses, some of which have enormous random variations (in the region of dBs) and which are very localised in space and time (I may have mentioned this before). As you seem to know about this "defined list" then you will know the quantities involved. Do you really not appreciate that these imponderables will introduce unacceptable errors? It is just not good enough to assert that, given enough time and money, all errors can be eliminated - that's just naive. If you ignore the concept of bandwidth in the context of measurement then you clearly should get acquainted with the basics of experimentation.

Have you actually done any calculations about the effect on calculated Range from different degrees of error in Power measurement? In the absence of any figures in your posts (even less than from the rest of us) I conclude that you haven't. (No one else can do this as you haven't disclosed the geometry of the proposed system).

 

[Carl Pugh]

"Seriously - is this your first project or do you have a track record of successful novel measurement methods? This is a very relevant question because I should like to take this seriously but I am struggling."

I'm struggling also.

(Sorry I couldn't resist)

 

[sophiecentaur]

Ad hominem, I'm afraid!

 

[RadioEng]

This has been addressed qualitatively on several occasions. No one has been paid to give you actual figures but there is loads of info about the values and variations of the known transmission losses.

You dodge questions better than Neo dodged bullets. :)

Also, suggestions about imponderables. You can find those in more detail if you reject our ball-park 'estimates'. I think you need to consider that the estimates are of the order of dBs (which, given the geometry, make it a non starter), which should give a clue as to why the rest of the project is viewed with skepticism by those who have replied.

Not according to the document from the IEEE, the E-Field experiences relatively little loss at orbital distances. So, perhaps you have not been keeping up with the research.

It can't really be a surprise that people who have shown an interest should ask for some details about the required measurement accuracy. Why should anyone bother to stray from their 'gut reaction' without being given more to feed on - so far, any more input would seem to be a waste of effort.

Well, it was one of the questions I asked and someone else said they obtained 30m on higher frequencies.

So, once again, you're trying to get me to answer the question I posed.

I don't think you can demand that Engineers on and Engineering Forum can ignore glaring Engineering factors any more than you could expect to have a practical / feasible 'Faster than Light' discussion in a Physics Thread.

Perhaps, but then you only have your base knowledge of what sensors and processing solutions exist to solve the problem. So, while your gut instinct may have been correct 10, or even 20 years ago, it does not mean that is the current situation.

BTW, there are three main reasons why not many people reply to a particular thread. The topic may be too hard, the scenario may be viewed as ludicrous and not worth following or it may just be boring. As an initial idea, it could grab the attention (it's had 700+ views, with its intriguing title) so you may ask yourself why there haven't been many responders.

You could probably count in one hand the number of people that could provide an accurate answer. It doesn't come as a surprise.

You seem to suggest that an Engineer would have no idea about such matters and that one would need to be a Physicist to 'understand' this stuff. Are you either of those beasts? In what way are you qualified to 'belittle' Engineers and insist that, per se, they would not know enough? Any project like the one you are describing would be a huge Engineering undertaking. Any other large experiment is the same. It wouldn't work if the Engineering wasn't right and you have given no reasons to believe in its feasibility.

Engineers don't create the sensor equipment, they merely combine the work of other people to create their solutions. They are bound by what is on the market and what they have been exposed to.

You did not claim that you had designed sensors or DSP solutions for low frequency satellite radio links.

Let's leave feasibility studies to the experts.

Why did you ask the question if you know this list? But, yes, there is a list of many losses, some of which have enormous random variations (in the region of dBs) and which are very localised in space and time (I may have mentioned this before).

Which would have no effect over a large enough time period. This is not the major issue you are making it out to be.

As you seem to know about this "defined list" then you will know the quantities involved. Do you really not appreciate that these imponderables will introduce unacceptable errors? It is just not good enough to assert that, given enough time and money, all errors can be eliminated - that's just naive.

What "imponderables"? Please name one and how that will effect the final calculation.

If you ignore the concept of bandwidth in the context of measurement then you clearly should get acquainted with the basics of experimentation.

I strictly see bandwidth in terms of information, not finite ranges of frequencies and the associated physics of propagation.

So, this is a "you say tomato" issue...

Have you actually done any calculations about the effect on calculated Range from different degrees of error in Power measurement?

Final measurements do not come from a single calculation. More like a composite of time-stamped FFT images offset by real-time experimental data.

Transient errors are practically eliminated by this process.

In the absence of any figures in your posts (even less than from the rest of us) I conclude that you haven't. (No one else can do this as you haven't disclosed the geometry of the proposed system).

Only two questions were asked, what are the losses and what would the expected accuracy be?

Its a straightforward set of questions with a straightforward set of answers. Even if presented incomplete, it could be refined by other posters.

 

[sophiecentaur]

"Well, it was one of the questions I asked and someone else said they obtained 30m on higher frequencies. "

If you really think that a single figure of 30m in any way indicates required or achievable accuracy in this system then it isn't worth continuing this conversation; you clearly don't understand the situation. I think that your expertise in Software may not be matched in other directions.

I think most people are aware of the equivalence between frequency and time domains. Normally, where noise is concerned, because it is a random process, then problems would be dealt with in the frequency domain. Either way, you will hit a practical bandwidth / observation time limitation. Given a million years you may be able to extract some information from way down in the noise but what use is that in the context of navigating a spacecraft ? You'd be long dead before the information revealed itself.

I might also point our that Engineers are not Maintenance Men or Technicians and that any non-theoretical Physicist needs to be a competent Engineer at the same time if a complex experiment is to have any hope of working. I thought the IEEE (which you quote) was an Engineering Organisation. Surprised it manages to have any credibility with you - not being run by Physicists.

 

[RadioEng]

As I said before, I'm not really interested in your opinion of feasibility. Let's face it, you would not be posting here everyday if you were busy working in this field.

Also, you have made about 13 posts on this thread and not one of them contain any technical data to support your assertions. It just been talk about what you think, a complete lack of understanding of what is being described and inappropriate potential pitfalls.

I feel that it is clear that you are not qualified enough to be commenting on this issue. I have asked numerous times for you to stop being vague and show particular "imponderables" (as you like to call them), but you have failed to do so.

As such, this particular conversation is going nowhere.

 

[sophiecentaur]

" a complete lack of understanding of what is being described"
Rather 'a complete lack of description of the system'.

A bit too much of the "ad hominem", again. But then, when have you demonstrated any understanding about it either?

Could you, perhaps, explain what you mean by the "30m" figure and how, on it own, it could relate to received signal level?
Then we could call it a day.

 

[RadioEng]

What more do you need than trilateration of a spread spectrum signal in the sub-1000Hz range?

Two questions:

1. What are the potential sources of loss?
2. What is the expected accuracy?

Stop making up your own questions.

 

[sophiecentaur]

"What more do you need than trilateration of a spread spectrum signal in the sub-1000Hz range?"The distances involved are one of the major factors in the problem. The error will depend upon the distance. Do you not know that? Signal loss is not linear with distance so no one can comment on potential accuracy of position measurement unless there is some idea of the distances involved. Surely you understand that the 30m figure is totally irrelevant.
What you don't seem to realize about is that there is absolutely no point in doing any detailed theory unless there is some remote chance of a result. That is why an Engineer's experience can save you loads of time and money. If you deny the relevance of SNR then there is no hope for you.
(You have already said that there is a defined list of loss mechanisms and that they will all be accounted for - so why not just use the info that you have?)
You haven't yet declared your area of expertise.
I have spent decades in Research in the area of RF propagation and communications. I am not talking off the top of my head.

And, as for the fact that the reason that I am not "busy working in the field" could be that I am wheelchair or bed-bound. I could be writing this using my left eyelid. What difference could that make? As the first to introduce the ad hominem thing, you are pretty free with it yourself.
Could it be that you are a teenager? I could forgive some of that if you were.

 

[Studiot]

I calculate the answer to the question I posed in post #35 to be about 1 milliwatt per kilowatt of transmitter power.

Is your mathematics up to understanding this?

 

[RadioEng]

The distances involved are one of the major factors in the problem. The error will depend upon the distance. Do you not know that?

I didn't define the function f(PDs) to prevent compound errors for nothing. Have you been reading this thread at all?

Signal loss is not linear with distance so no one can comment on potential accuracy of position measurement unless there is some idea of the distances involved.

Again, we already defined this:

PDr = (PDs /4 pi R^2) - ASL

If you had been following the discussion, we were talking about trilateration of a signal anywhere on the planet.

Surely you understand that the 30m figure is totally irrelevant.

Not entirely, its a good baseline to have.

If you deny the relevance of SNR then there is no hope for you.

No one is denying it, its just that no one has shown it to be an issue.

I have spent decades in Research in the area of RF propagation and communications. I am not talking off the top of my head.

Given the complete lack of technical detail, jargon and analysis that would be expected of an engineer, I doubt it very much.

As the first to introduce the ad hominem thing, you are pretty free with it yourself.

So, you admit it? Interesting approach. Anything else you care to confess?

 

[sophiecentaur]

Given the complete lack of technical detail, jargon and analysis that would be expected of an engineer, I doubt it very much.

My quote:"As the first to introduce the ad hominem thing, you are pretty free with it yourself."

So, you admit it? Interesting approach. Anything else you care to confess?

Interesting that you managed to mis-parse that statement. It is the 'you' that is the related participle and not an implied 'I'. If I had meant what you imply, then I would have written something like.
"As the first to introduce the ad hominem thing, I would say that you are pretty free with it yourself." But I didn't.
Does your grasp of English grammar reflect your other abilities? I thought that computer languages were fairly fussy about how you they're used, regarding syntax.

I think you are becoming too offensive for me to continue this. Teenage behaviour can only be tolerated so far.

 

[Studiot]

This OP is obviously promoting a windup.

(S)he fails to respond whenever faced with a real comment about hard facts, such as in post #62.

 

[RadioEng]

I calculate the answer to the question I posed in post #35 to be about 1 milliwatt per kilowatt of transmitter power.

Is your mathematics up to understanding this?

Let's look at post #35...

Say your transmitter - receiver distance is 65 kilometres and your desired accuracy is 100 metres.

I see nothing in your proposals that would distinguish between the signal at 65Km and at 65.1Km.

Lets do the math and calculate the power density at 65Km (We will omit loss and interference for the moment):

PDr = 1000 / 4 * 3.1415926535897932384626433832795 * 65000^2
PDr = 1.8834904507916607783299853653552e-8

Now the power density at 65.1Km:

PDr = 1000 / 4 * 3.1415926535897932384626433832795 * 65100^2
PDr = 1.8777084420741732059254669452469e-8

and to determine the difference between 65.1Km and 65Km, or a 100m resolution, we need a power sensitivity of at least:

PDdiff = 5.7820087174875724045184201081228e-11 Watts

So, you couldn't be more wrong in your calculations. Also, this sensitivity is well within modern capabilities.

(Edit: Corrected typos)

 

[Studiot]

Yes, I got the 13 on the top of the fraction instead of the bottom.

$$Pdiff = \frac{{{{10}^3}}}{{4\pi {{10}^6}}}\left( {\frac{{{{65.1}^2} - {{65}^2}}}{{{{\left( {65.1} \right)}^2}{{\left( {65} \right)}^2}}}} \right) = 5.8x{10^{ - 11}}watts$$

Edit following recalculation.

I also suggest you take a hard look at the rest of your post #66.

I don't have to pass exams or satisfy a pernickety boss, but such work will do neither for you.

 

[RadioEng]

This seems to come out at 0.006 milliwatts per sq m per KW broadcast, rather than your figure.

Actually, that works out to be:

6.1213439650728975295724524374044e-6

Which is way off.

 

[Studiot]

I find it hard to take seriously a post which states

'the difference between 65.1 kilometres and 60 kilometres to be 100 metres'

and to determine the difference between 65.1Km and 60Km, or a 100m resolution

So I haven't checked the rest of your working, but I am now happy with mine.

There do, however appear to be further inconsistencies in it.

 

[RadioEng]

I find it hard to take seriously a post which states

'the difference between 65.1 kilometres and 60 kilometres to be 100 metres'

Its a typo...I'll correct it. The figures are correct.

So I haven't checked the rest of your working, but I am now happy with mine.

You should, its completely wrong, its not even the right formula.