Question about Navigation Course

Re: Very nice and all that ....

Lemain, what independent variables are you talking about specifically (you did not mention them in your post)?

Also, I was not suggesting that navigation was breaking any natural or mathematical laws - just trying to explain a paradox arising from mathematical considerations.

I don't know if I successfully communicated my TP (thought process?) on the experimental setup I had in mind. I don't think so. I think I should have suggested turning the boat to starboard not port as I earlier suggested too. Sorry about that!

Still, if I am wrong, I'd like to understand, so let me know.

Cliff.
 
Re: Very nice and all that ....

p.s. the dependent variable I had in mind was M which is determined once you specify the compass reading and corresponding deviation D(C). In fact, M = C + D(C). That looks like a dependent relationship to me (M depends on C). Are you thinking that M is defined independent of your compass reading? If so, then we are not really talking about the same thing. If M = C + D(C) , then M depends on C as a mathematical function (even if the relationship arises in a different way, i.e. reading the equation the other way around). Eeek, this is getting too philosophical! /forums/images/graemlins/smile.gif
If the equation M = C + D(C) is valid, then there are definitely deviation functions D that I can construct that prove the claim about two compass readings corresponding to one Magnetic (and hence True) reading. That's a theorem! /forums/images/graemlins/smile.gif

Can you address the experiment I described and explicitly describe what you think is wrong with it?
 
Re: Very nice and all that ....

Cliff, there is no paradox if you do the maths correctly. By 'TP' I was referring to the 'Turning Point' you mentioned, not a 'thought process'. None of the variables are dependent - the deviation is neither a mathematical function of heading nor variation so you may not differentiate as though they are dependent variables. If you look at a deviation cards you find that some are fairly sinusoidal-looking and others are lumpy but there is no hard and fast rule.
 
Re: Very nice and all that ....

[ QUOTE ]
Cliff, there is no paradox if you do the maths correctly. By 'TP' I was referring to the 'Turning Point' you mentioned, not a 'thought process'. None of the variables are dependent - the deviation is neither a mathematical function of heading nor variation so you may not differentiate as though they are dependent variables. If you look at a deviation cards you find that some are fairly sinusoidal-looking and others are lumpy but there is no hard and fast rule.

[/ QUOTE ]

Lemain,

I thought deviation was a correction to your compass reading C that corrects it to the correct magnetic reading M. You do this correction by adding the deviation which you look up by plugging in C into your deviation table and then reading off the corresponding devation. That looks to me like deviation depends on compass reading (ships heading as measured on the compass).

Have I completely mis-understood the definition of deviation?

Looking back over your wording - I wonder if we are arguing over the definition of a function? By a function, all I mean is some rule that takes a set of inputs (the compass readings in this case) and outputs a corresponding set of readings according to the rule (the output readings being deviations in this case and the rule is the deviation graph/table). The sinusoids and lumpy graphs that you refer to all seem like graphs of functions to me.

Cliff.

Cliff.
 
Questions of Sign

i too hate the mnemonics.

Compass reading + Variation + Deviation = True ...holds firm in ALL cases PROVIDED that you take account of the "sign" of the variation or deviation.

Easiest to think of east positive, west neagtive which is fine - think as "left and right" being "negative and positive" as seen looking north-up.

Thus deviation or variation east means the compass starts counting real actual degrees a bit LATER than it should. hence add these positive values to the compass reading to get the true reading

Deviation or variation west means the compass starts counting "a bit too early" from when the real actuall degree should be counted from and the true value is less than the reading. Key point - you still add these values - BUT THEY ARE NEGATIVE.

er for clarity - devaition is the wrongness of the ships compass which varies with the direction in which the ship travels. Variation is location-dependent. There can't be a "graph" although i suppose you could mark up each chart compass rose for your own boat totals to be added (using the sign of course) but a bit painful..
 
Re: Very nice and all that ....

p.s. those lumpy deviation graphs you referred to are exactly the pathological scenario I was worried about - if the graph is tightly bunched up then that's a rapid change of deviation over a relatively small change in compass heading.
 
Re: Very nice and all that ....

[ QUOTE ]
The sinusoids and lumpy graphs that you refer to all seem like graphs of functions to me.

[/ QUOTE ]They are not continuous 'functions' - they depend on the combined effect of lots of bits of ferrous material around the vessel. You can't differentiate D with respect to C (or vice versa) as though it was a continuous dependent variable. You say that your 'paradox' is that you can have two 'correct' headings as a solution of the equations and you base that on d/dx=0 at a TP. That seems to be the mistake as you cannot legally perform the differentiation. I don't think that your argument is correct even if you could, but I haven't given it any thought as you are not allowed to do it in any case /forums/images/graemlins/smile.gif
 
Re: Very nice and all that ....

You seem now to be accepting that there is dependence of M (and hence T) on C? And hence that they are functions.

Assuming I am reading you right, then of course differentiability of these functions comes into question. The graphs I have seen look differentiable but maybe they are ideaslised?

Even if these functions are not differentiable, then it does not really rule out the phenomenon I am worried about. Forget about calculus altogether (I was just using it as a convenient tool in the differentiable case to illustrate the problem). Think about this: Suppose you are pointing the boat in different directions, taking your hand bearing compass reading and noting the deviation. Do this in a systematic way, increasing the true heading of the boat at increments of 5 degrees say. Suppose now that the deviation started off small and positive but maybe half way through the process, the deviation became rapidly negative. Plot your compass readings and your magnetic readings and you will see that the graph has gone up steadily and then come back down. You now have the problematic situation I was referring to. So, it seems the problem I am worried about has nothing really to do with calculus (that's a red herring).

Cliff.
 
Re: Very nice and all that ....

woops, I see you are not agreeing about them being functions. so forget about my initial response (although I still stand by it).
 
Re: Very nice and all that ....

The use of Calculus on the equation doesn't help, because that relates to the Rate of CHange of a function., and sure there will be a time when the rate of change of deviation is significant. What is the practical application? In a sailing yacht. How does deviation change? As boat heading changes. At what rate for navigation purpses does a boat heading change? ANswer very slowly and then only when you tack or reach a waypoint requiring a course change. In between these instances your boat is to all intents and purposes on a constant heading, therefore dD(C)/dC is always zero.
 
Re: Very nice and all that ....

[ QUOTE ]
Suppose you are pointing the boat in different directions, taking your hand bearing compass reading and noting the deviation. Do this in a systematic way, increasing the true heading of the boat at increments of 5 degrees say. Suppose now that the deviation started off small and positive but maybe half way through the process, the deviation became rapidly negative. Plot your compass readings and your magnetic readings and you will see that the graph has gone up steadily and then come back down. You now have the problematic situation I was referring to.

[/ QUOTE ]What is the problem? The deviation card is to be read against the indicated compass bearing. i.e. if the deviation card reads 'East 14 degrees' at N then when the compass shows N the actual Magnetic heading is 000 + 14, = 014 degrees. If the deviation card also shows 'West 13 degrees' at NE (045) then when the compass is reading 045 the Magnetic heading is 045 - 13 + 032 degrees. This would be an extreme and very unusual example but it wouldn't cause a problem in the scientific sense or be 'paradoxical' though it would be true to say that the compass is NBG for navigation /forums/images/graemlins/smile.gif
 
Re: Very nice and all that ....

I guess you meant to address that to Cliff?
 
Re: Very nice and all that ....

[ QUOTE ]
The use of Calculus on the equation doesn't help, because that relates to the Rate of CHange of a function., and sure there will be a time when the rate of change of deviation is significant. What is the practical application? In a sailing yacht. How does deviation change? As boat heading changes. At what rate for navigation purpses does a boat heading change? ANswer very slowly and then only when you tack or reach a waypoint requiring a course change. In between these instances your boat is to all intents and purposes on a constant heading, therefore dD(C)/dC is always zero.

[/ QUOTE ]

Larry, we're talking about different things. I am talking about a rate of change with respect to the ships heading, not how quickly this heading changes.

Cliff.
 
Re: Very nice and all that ....

[ QUOTE ]
I guess you meant to address that to Cliff?

[/ QUOTE ]

I cannot see who the previsous post came from (seems to be forarded by Lemain?) but it does not appear to be addressing the issue I raised.
 
Re: Very nice and all that ....

I've decided to stop posting and do the following. I am going to make up a deviation table and use it to plot compass versus magnetic and hopefully explain the problem using a simple picture. That should get rid of a lot of the mis-understandings. It'll take me a while to do because I need to figure out a website where I can post it. When I do , I will post back here witht the link.

Cliff.
 
Re: Very nice and all that ....

Cliff Please don't bother trying to work it out.I will draw a chalk line on the surface for you to follow.If you cant manage this make sure that you have a good selection of foreign language phrase books as it will be anyones guess where you end up.I go sailing to SAIL not play with numbers.
 
Re: Very nice and all that ....

Does this help at all?

CivilEngineering.jpg
 
Re: Very nice and all that ....

That reminds of Pythagorus's other theorum.
"heat of the meat times the angle of dangle equals size of the rise"
 
Re: Very nice and all that ....

Lakesailor, you did help (even if unintentionally!) - I did not realise you could insert images in posts.

Here's the plot I promised ... [image]http://www.badongo.com/pic.php?file=Magnetic+and+Deviation+Vs+Compass__2005-12-14_deviation.jpg[/image]
I plotted M versus C in green - you can also see the deviation I used in purple. I only showed the graphs out to 100 degrees as nothing new happens after that and it makes the graph easier to look at.

Now, I hope you can see the curiosity I raised originally. Looking at the green graph, you should see that a magnetic course of say 020 degrees corresponds to three compass readings; namely, 005, 015 and 025 approximately. This means there are three possible readings on the compass that correspond to exactly the same true heading. I found that initially surprising, but my earlier explanations now seem to be borne out by this kind of example.


This arose from an anomolous deviation near compass reading 000.

Cliff.
 
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