Question for any instructor/examiner?

Elessar said:
Yes. As I have said all along. You are probably outside the hat.
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Coming back to this thread as an economist and mathematician...(NB, also the OP, and my wife passed with 100pc)

You view the world in terms of what we know, how we interpret what we know, and what we assume.

If we assume our plotting is broadly correct, then we might indeed be 50pc either side of each line. But that's not really the point. Our probability of being "on or near" the line is hight. our three plotted lines work as a team. If, as it turns out, all three lines cross imperceptibly close together (our cocked hat is 1cm square on the ground) then it's fair to say we're probably outside it. But probably pretty close to it. If our three lines cross acceptably close together (1cm on the chart) then there's greater chance we're in it. If our three lines are massively apart, then there's a greater chance we're in the hat, but also that that information is of limited use to us.

Then of course we sensibly superimpose our dead reckoning.

If our DR and fix are wildly apart, or if our fix gives us a massive fix (that, using our experience, is greater than suggested by distance travelled between fixes and the thickness of the pencil) then we are rightly prompted to check our working.
 
Joker said:
Following on from that, I remember an Open University video from yonks back saying in effect:

You have a 50% chance of being either side of the line you have drawn. You draw 3 lines. The probability of being in the 'cocked hat' is therefore 50% of 50% of 50% = 12.5% or 1 in 8!
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I think I watched that! It also showed why lines should cross at the largest possible angle.
 
RJJ said:
Coming back to this thread as an economist and mathematician...(NB, also the OP, and my wife passed with 100pc)

You view the world in terms of what we know, how we interpret what we know, and what we assume.

If we assume our plotting is broadly correct, then we might indeed be 50pc either side of each line. But that's not really the point. Our probability of being "on or near" the line is hight. our three plotted lines work as a team. If, as it turns out, all three lines cross imperceptibly close together (our cocked hat is 1cm square on the ground) then it's fair to say we're probably outside it. But probably pretty close to it. If our three lines cross acceptably close together (1cm on the chart) then there's greater chance we're in it. If our three lines are massively apart, then there's a greater chance we're in the hat, but also that that information is of limited use to us.

Then of course we sensibly superimpose our dead reckoning.

If our DR and fix are wildly apart, or if our fix gives us a massive fix (that, using our experience, is greater than suggested by distance travelled between fixes and the thickness of the pencil) then we are rightly prompted to check our working.
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I agree with the spirit of all of what you said, and it's nearly all correct except the red bit. Which is wrong.
 
lw395 said:
They presumably set the exercises so they are easy to mark and so they expose not understanding the process.
That's normal in training and education.
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Arse about face. The excercises are set so the student understands the process. Easy to mark doesnt come into it. You havent got 100,000 students taking their GCSE in History all expected to get the results on the same day.
 
Meanwhile, back in the real world...

DSCF6794.JPG

... and the only real errors I made were not with my cocked-hat position fixes (plus what looks like a quick depth and bearing fix check previously off the head), but in failing to adequately allow for the southerly component of the tidal set and our estimated leeway to the south (wind from roughly NW) when I made my first course alteration at 1400.

DSCF6765.JPG

We were also cracking along nicely at just under six nerds... not bad for a fat heavy 27 footer! ;)
 
A healthier way of looking at this--what a scientist, engineer, or surveyor would do--is to look at the precision of each measurement. Sitting still, take several fixes (better yet, use several observers, without sharing information) and look at the scatter in the data. Determine the average error (or SD) and plot that as well. In some cases the cocked hat will be tiny but the error bands wide. In some cases the error bands will not cross within the cocked hat.

In this way you include variables such as distance from landmark, visibility, rolling, and relative plotting angles (are any lines near parallel?). Knowing the precision of the measurements is key, remembering that precision and accuracy are not the same thing.
 
Sharky34 said:
What is your experience of accuracy when doing a 3 point fix?
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Well because I have taught practical courses for the past 20 odd years, sh*t hot!

But seriously. The DS theory course does exactly what its meant to do. 3 point fixing is just part of the overall position fixing excercises showin the principles of how its achieved. And likely errors plus ideas of how you can also confirm you position like depth. Remember this is all mostly brand new stuff to people on this course so the concepts must be kept simple.

The practical course is the time when you can get people to understand more about those errors and how to deal with them. But thats still only the start. As one of ten million skills you can master as a skipper, practice, practice, practice is what counts. Ive been fabulously fortunate to do the job I do so that yes, I can generally be accurate in my fixing but really appreciate thats an unusual background. (y)

Oh, for the 'average' student on a practical course, most get quite good quite quickly at taking fairly accurate bearings. The problem is generally going below to plot it without vomming. :sick:

Which is why plotters in the cockpit can be a Good Thing!
 
Iliade said:
Iliade said:
View attachment 86398
I have never seen the exam, But is this the issue being found/considered? (fix points kept jumping to a grid so not perfectly aligned)
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The boat appears to be moving directly towards the object in line with the red star, so it will always be on this line. The (lower) blue star shows its exact position when that sight was taken and the green one denotes its position at the precise time when that( green) sight was taken. Conclusion; when taking a Three-Point Fix do not sight on a charted object directly in line with the boat's course. However, this is an excellent method of determining a boat's position when the objects sighted upon are not too distant.
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Babylon said:
Meanwhile, back in the real world...

View attachment 86554

... and the only real errors I made were not with my cocked-hat position fixes (plus what looks like a quick depth and bearing fix check previously off the head), but in failing to adequately allow for the southerly component of the tidal set and our estimated leeway to the south (wind from roughly NW) when I made my first course alteration at 1400.

View attachment 86555

We were also cracking along nicely at just under six nerds... not bad for a fat heavy 27 footer! ;)
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Why the sad face?
 
thinwater said:
A healthier way of looking at this--what a scientist, engineer, or surveyor would do--is to look at the precision of each measurement. Sitting still, take several fixes (better yet, use several observers, without sharing information) and look at the scatter in the data. Determine the average error (or SD) and plot that as well. In some cases the cocked hat will be tiny but the error bands wide. In some cases the error bands will not cross within the cocked hat.

In this way you include variables such as distance from landmark, visibility, rolling, and relative plotting angles (are any lines near parallel?). Knowing the precision of the measurements is key, remembering that precision and accuracy are not the same thing.
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I’m sorry Mr thinwater but that is completely over the top. I speak as an engineer with a career involving statistical variation and as a reasonably competent recreational navigator.

I’d take a step back and reconsider the primary objective of navigation and the purpose of a fix.?
 
Elessar said:
I agree with the spirit of all of what you said, and it's nearly all correct except the red bit. Which is wrong.
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Why wrong? There's near - zero chance you plotted yourself accurately within a pinprick. The greater the area, the bigger the chance you are within it.

To put more formally, the Open University probability challenge is only correct if all lines and possible positions are independent of each other and randomly distributed, which (in the case of a fix) is not the case. Assuming as I said that the lines are correctly but imprecisely plotted, you start with an expectation that you are near all of them; if they indicate a very small cocked-hat then you are likely outside it but not far away; if it gets larger, you are increasingly likely to be within it. To say you are likely still outside it, as it gets larger, implies technical distrust of at least one of your bearings.
 
RJJ said:
Why wrong? There's near - zero chance you plotted yourself accurately within a pinprick. The greater the area, the bigger the chance you are within it.

To put more formally, the Open University probability challenge is only correct if all lines and possible positions are independent of each other and randomly distributed, which (in the case of a fix) is not the case. Assuming as I said that the lines are correctly but imprecisely plotted, you start with an expectation that you are near all of them; if they indicate a very small cocked-hat then you are likely outside it but not far away; if it gets larger, you are increasingly likely to be within it. To say you are likely still outside it, as it gets larger, implies technical distrust of at least one of your bearings.
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Wrong because the likelihood of the error being + or - does not change as the error increases. There for the area inside the hat does not change the likelihood of being in it. Remember the area outside it is infinite.
 
Elessar said:
Wrong because the likelihood of the error being + or - does not change as the error increases. There for the area inside the hat does not change the likelihood of being in it. Remember the area outside it is infinite.
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...only if the lines and our position relative to the lines are random, which they are not. You believe you are on or very near each line (that's the whole point, or we wouldn't even start). If the area increases, then being outside the area means you are moving further away from at least one of the lines. You can choose whether to put that down to error or inaccuracy, and also whether it's "good enough" given what you know, what you can see, what are the risks, and what you reasonably assume.

Assuming correct plotting there is different probability associated with being 1 mile, 2 miles or 5 miles from the furthest line.

Equally, while the area outside is infinite, the probability of points on the area is not uniformly distributed. If 2 hours ago I knew I was in the central Solent heading east, and my fix puts me in a large triangle somewhere between Bembridge and Portsmouth, it is more likely that I am in that triangle than off Land's End or Cape Horn. In the Open University question, I have no starting point and the lines are random so I could indeed be anywhere.
 
RJJ said:
Why wrong? There's near - zero chance you plotted yourself accurately within a pinprick. The greater the area, the bigger the chance you are within it.....
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Still wrong. There's an area of possible error outside the perimeter of your cocked hat, imagine drawing round it with a highlighter pen. As your cocked hat gets bigger, that area gets bigger.
 
penberth3 said:
Still wrong. There's an area of possible error outside the perimeter of your cocked hat, imagine drawing round it with a highlighter pen. As your cocked hat gets bigger, that area gets bigger.
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Translated as, if your triangle gets bigger, the area within gets bigger.
Wow, I never knew that, mindbreaking mathematical discovery.:rolleyes:
 
RJJ said:
...only if the lines and our position relative to the lines are random, which they are not. You believe you are on or very near each line (that's the whole point, or we wouldn't even start). If the area increases, then being outside the area means you are moving further away from at least one of the lines. You can choose whether to put that down to error or inaccuracy, and also whether it's "good enough" given what you know, what you can see, what are the risks, and what you reasonably assume.

Assuming correct plotting there is different probability associated with being 1 mile, 2 miles or 5 miles from the furthest line.

Equally, while the area outside is infinite, the probability of points on the area is not uniformly distributed. If 2 hours ago I knew I was in the central Solent heading east, and my fix puts me in a large triangle somewhere between Bembridge and Portsmouth, it is more likely that I am in that triangle than off Land's End or Cape Horn. In the Open University question, I have no starting point and the lines are random so I could indeed be anywhere.
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You are still wrong.
 
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