Question for any instructor/examiner?

[Elessar]

Diagram seen, understood, and correctly makes the point it is supposed to make, which (per my last post) is not the point under discussion. Either you can address the correct problem, and do so formally, or not.

Nope can’t be bothered.

My position is simple.
1) If there is a cocked hat you are very probably near it or inside it.
2) It is more likely that you are near it than inside it. Don’t make the error (as some have done here) of assuming you are inside it.
3) the larger the cocked hat the less reliance you you place on your fix. With a large hat double check your bearings as with a large hat it is likely you have made an erroneous assumption on one or more of the bearings. Eg sighted the wrong red roof.

Some here have argued the opposite of 3. That is the larger the cocked hat the MORE likely it is that you are probably inside it. This is simply wrong. A large hat is an indicator of a mistake.

 

[Sharky34]

That's what we're doing every time. If the cocked hat is small, we should recognise there's strong probability we are outside. The larger it is, the more probably we are inside, but the less useful that is.

If position fixing is that nebulous, not much point any mariners doing any then.

 

[Elessar]

If position fixing is that nebulous, not much point any mariners doing any then.

little point if you don't understand it that's for sure.
Otherwise its served people well.

 

[RJJ]

Nope can’t be bothered.

My position is simple.
1) If there is a cocked hat you are very probably near it or inside it.
2) It is more likely that you are near it than inside it. Don’t make the error (as some have done here) of assuming you are inside it.
3) the larger the cocked hat the less reliance you you place on your fix. With a large hat double check your bearings as with a large hat it is likely you have made an erroneous assumption on one or more of the bearings. Eg sighted the wrong red roof.

Some here have argued the opposite of 3. That is the larger the cocked hat the MORE likely it is that you are probably inside it. This is simply wrong. A large hat is an indicator of a mistake.

As I said earlier, and which is partly consistent with the proper explanation you can't be bothered to read. Your (1) is correct. (2) is partly correct. The most likely POINT is inside IF you continue to assume your fixes are technically correct. The most likely AREA is outside for a small triangle, but the AREA inside becomes more likely as the triangle grows, partly displacing the AREA outside (3) At some point, I agree you should question the assumption, in which case go and start again.

Whether you have more, less or zero confidence in your bearings and plotting, it remains the case that the larger the triangle, the greater the proportion of possible positions in the possible sea area it covers. That gives you the probability you are in it. It's a problem of statistics not of geometry.

Either you have some confidence in your bearings, in which case you are very likely in or near the triangle, and the condition "within the triangle" better fulfils the 3x probabilistic relationship with the distance-to-bearing, and does so more strongly with increasing size. Or you have lost faith in your bearings, in which case we are looking at random uniform probability of being in any given position, and the larger the triangle the larger the proportion of possible positions.

It's not very complicated. But "can't be bothered" doesn't answer the question.

 

[lw395]

If position fixing is that nebulous, not much point any mariners doing any then.

To be fair, I don't think professional mariners very often take 3 point fixes with a hand bearing compass, or even used to before GPS.
That's why we have buoys and lighthouses.
Sailing direction are full of transits and soundings.

I'm struggling to think when I last actually needed to know my position accurately, and (in the absence of GPS) I'd have used 3 HB Compass bearings.
I can think of lots of pilotage situations where I've needed to know I'm on a line from point A to Point B, but not needed to know exactly how far along it I was, as it would become apparent when I reached Point B.

 

[lw395]

As I said earlier, and which is partly consistent with the proper explanation you can't be bothered to read. Your (1) is correct. (2) is partly correct. The most likely POINT is inside IF you continue to assume your fixes are technically correct. The most likely AREA is outside for a small triangle, but the AREA inside becomes more likely as the triangle grows, partly displacing the AREA outside (3) At some point, I agree you should question the assumption, in which case go and start again.

Whether you have more, less or zero confidence in your bearings and plotting, it remains the case that the larger the triangle, the greater the proportion of possible positions in the possible sea area it covers. That gives you the probability you are in it. It's a problem of statistics not of geometry.

Either you have some confidence in your bearings, in which case you are very likely in or near the triangle, and the condition "within the triangle" better fulfils the 3x probabilistic relationship with the distance-to-bearing, and does so more strongly with increasing size. Or you have lost faith in your bearings, in which case we are looking at random uniform probability of being in any given position, and the larger the triangle the larger the proportion of possible positions.

It's not very complicated. But "can't be bothered" doesn't answer the question.

I think the size of the triangle might usefully be view in angular terms. IF your bearings are from nearby objects and your 300m triangle implies angular errors of 15 degrees, it is a different case from a 300m triangle caused by small errors in the bearings to very distant objects.

But in crude basic terms, if the bearing you plot is your best guess, then the chances of being either side of the line are pretty much 50:50.
You can argue about whther the distribution around that line is Gaussian or some other thing.
But you don't get meaningful stats of two variables from 3 bits of data.
Take a fourth bearing and then you may see one is wrong?

 

[Muddy32]

Fixes are where you were, and I was taught that if you are unsure and it matters, "take another".

 

[[163233]]

To be fair, I don't think professional mariners very often take 3 point fixes with a hand bearing compass, or even used to before GPS.
That's why we have buoys and lighthouses.
Sailing direction are full of transits and soundings.

Even with babylon's fine chartwork a few pages back, he'd have done better if from his fix at 1400 taking a bearing on St A's Hd of about 250 and just staying slightly south of it say between 250 & 260. The second fix doesn't really help him out much.

If he'd done that, then he wouldn't have been so far south at 1445 as he apparently was and would have been able to spend more time in the cockpit looking out for the proverbial floating containers.

On the fix accuracy thing, imagine you were at the intersection of two transits, you know you are at that exact point. Then you take a bearing to another point, there will be some error which will create the "hat", if the hat is a sombrero then your error on that bearing is very large, if it's a zucchetto, then the error is small. However regardless of the error you are at the intersection of the two transits, which is one corner of the hat. That is, in this example you are always outside the hat despite two of your bearings being perfect.

 

[RJJ]

Even with babylon's fine chartwork a few pages back, he'd have done better if from his fix at 1400 taking a bearing on St A's Hd of about 250 and just staying slightly south of it say between 250 & 260. The second fix doesn't really help him out much.

If he'd done that, then he wouldn't have been so far south at 1445 as he apparently was and would have been able to spend more time in the cockpit looking out for the proverbial floating containers.

On the fix accuracy thing, imagine you were at the intersection of two transits, you know you are at that exact point. Then you take a bearing to another point, there will be some error which will create the "hat", if the hat is a sombrero then your error on that bearing is very large, if it's a zucchetto, then the error is small. However regardless of the error you are at the intersection of the two transits, which is one corner of the hat. That is, in this example you are always outside the hat despite two of your bearings being perfect.

That's partly true. First ,you have made a different assumption, that you have greater faith in two of your bearings, being "perfect" than the third.

Second, if you are 100pc certain of the two transits, you know you are not outside the triangle. You are at the apex of it.

 

[Sharky34]

To be fair, I don't think professional mariners very often take 3 point fixes with a hand bearing compass, or even used to before GPS.
That's why we have buoys and lighthouses.
Sailing direction are full of transits and soundings.

I'm struggling to think when I last actually needed to know my position accurately, and (in the absence of GPS) I'd have used 3 HB Compass bearings.
I can think of lots of pilotage situations where I've needed to know I'm on a line from point A to Point B, but not needed to know exactly how far along it I was, as it would become apparent when I reached Point B.

Of course mariners used a 3 point fix , surely you don't think it was especially invented for yotties.

 

[capnsensible]

Fixes are where you were, and I was taught that if you are unsure and it matters, "take another".

Bang on. If you are in a place where it takes 139 posts arguing pointlessly over the accuracy of it, either stay on the white bits or stay in harbour. Its easy, quick and confirmed with depth plus tide. Aint no magic at all.

 

[Spirit (of Glenans)]

But then one should add, or subtract, a healthy quarter fathom (~0.0005 km) or more to account for the storm surge you didn't include in the original calculation ;0)

If that data was given in the question!

 

[lw395]

Bang on. If you are in a place where it takes 139 posts arguing pointlessly over the accuracy of it, either stay on the white bits or stay in harbour. Its easy, quick and confirmed with depth plus tide. Aint no magic at all.

It's a set piece chartwork exercise.
The object of it is to learn and show the skill and understanding.
It doesn't have to bear any relation to practical use of the skill.

 

[Elessar]

That's partly true. First ,you have made a different assumption, that you have greater faith in two of your bearings, being "perfect" than the third.

Second, if you are 100pc certain of the two transits, you know you are not outside the triangle. You are at the apex of it.

If you have two transits you have a fix. No bearing necessary, thus no 3rd line and no cocked hat.

 

[Elessar]

Bang on. If you are in a place where it takes 139 posts arguing pointlessly over the accuracy of it, either stay on the white bits or stay in harbour. Its easy, quick and confirmed with depth plus tide. Aint no magic at all.

Yep. The worry is when people think they know where they are but they don’t. Ie when they think they must be in the cocked hat!!

 

[lw395]

Cocked Hat

 

[[163233]]

That's partly true. First ,you have made a different assumption, that you have greater faith in two of your bearings, being "perfect" than the third.

Yes, of course two of them are transits you don't get a better fix than that. I was using a perfect fix to illustrate the effect of error on the position and the hat.

Second, if you are 100pc certain of the two transits, you know you are not outside the triangle. You are at the apex of it.

That was the point, I thought that was a straight forward example of the way errors affect the fix.

You and Sharky have at least proven that it's much harder than I ever realised it was.

 

[capnsensible]

It's a set piece chartwork exercise.
The object of it is to learn and show the skill and understanding.
It doesn't have to bear any relation to practical use of the skill.

The question on the theory course includes a depth reading and invites the student to comment on how this does confirm or refute the accuracy of the position.

 

[[3889]]

Am a RYA CI and the idea of a quantative assessment value for a fix seems nonsensical.
A fix off a headland, lighthouse and mountaintop at night ain't gonna put you within 100yds of anywhere. Likewise, 100 yrds error from crossed transits is poor performance. That the instructor fails to consider this is cause for alarm.

 

[peter gibbs]

First mate is about to do her DS theory. Her instructor has told her that any innaccuracy in plotting a fix will lead to fail. in revising ahead of tomorrow's exam, she has just obtained a 100 yard "cocked hat" and is now convinced she will fail.

I am trying to say that a 100 yard margin of error (from an object 3.5m away) is acceptable. It's a fraction of a degree, the thickness of the lines on the plotter. A big cocked hat is a prompt that you made a significant plotting error, then you check again.

More importantly in real world, if visibility is such that you can see 3.5 miles, 100 yards in open water (which you've covered several times over in the time taken between fixes) is simply neither here nor there. If you are within 100 yards of an unmarked hazard and you don't know it's there or which way lies safe water, a far-off fix isn't much good to you.

Am I right? Or is the instructor right to indicate that all 3 lines must actually cross? Trying to help 1st mate through something she is finding quite tough.

The ‘dot’ should ideally be placed in what would be perceived as the most dangerous part of the triangle so that a plot can be worked away from that point.

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.

Don't get too fixated on this nicety. Cartographic precision is not what the examiner is about. Once the cocked hat is established, pencil a circle round it and examine for nearby hazards - to show awareness of the practicalities of navigation - ie to avoid hazards and stay afloat.

PWG