Probability of being in a Cocked Hat

[B27]

Checking the depth on your echo sounder can often give some confidence to your fix.

We usually have a lot more information than just the 3 lines of the 'fix'.
As you say, depth.

But also a bit of simple DR from the last fix can show whether it's credible or not.



But in the case of the plot in post 94, the answer is 'a few miles South of Bournemouth' and that's all you need to know.

 

[zoidberg]

We usually have a lot more information than just the 3 lines of the 'fix'.
As you say, depth.

And if your depth-meter is indicating more than 300 metres ..... 'that's all you need to know'.

 

[B27]

And if your depth-meter is indicating more than 300 metres ..... 'that's all you need to know'.

I'm not familiar with anywhere 300 metres deep where there's 3 things to take a handbearing compass fix from, but if there was such a place, someone might manage to sail into one of the things they took the fix from?

 

[AntarcticPilot]

I'm not familiar with anywhere 300 metres deep where there's 3 things to take a handbearing compass fix from, but if there was such a place, someone might manage to sail into one of the things they took the fix from?

Plenty places on the West Coast of Scotland where the depth is greater than the maximum reading on a leisure echo sounder, but surrounded by land.

 

[capnsensible]

That's why I said 'often' and not 'always'......

Unless you happen to be on one of His Majesty's war canoes.

 

[DFL1010]

Oh, dear, Mark-1.

What a can of worms you've opened.

'Back in the day' there was a brigade of wizened RAF Staff Navigators arguing away incessantly about the optimum way to use Statistics and Probability Theory* to refine a position indicated by multiple Lines of Position ( LOPs ). In some circumstances, this mattered. For example, the sub-hunter Nimrod's tactical navigator may have several LOPs displayed on a very large 'tactical screen' derived from sources as abstruse as a vague bearing from a passive sonobuoy, a visual bearing on what MAY have been a fleeting periscope wake, a range from an active sonobuoy that was 12 minutes and 36 flight-miles old and not repeated. The question is 'Where exactly does one drop a depth charge?'

The need for accuracy in the answer may vary considerably if the depth charge intended is a nuclear one......

I have it on very good authority that the best sub hunter tac navigators were masters of the Stats arguments and Bands of Error calcs, but would use their experience and judgement to put a fingertip or cursor on a point and state 'There'. It would be a brave 'noobie' who would challenge them.

The WavyNavy types could get up before dawn and do a 'round of sights' using up to 7 Selected Stars, then go and quibble together about tenths of a nautical mile ( 'chains' for them wot's done the long course ) for half an hour before boiled eggs and coffee in the wardroom. Sweaty navs in a V-bomber 7 miles higher up would 'shoot' multiple sights on just two stars ( day or night ) - one ahead, one to the side - and use that to tweak the autopilot to better than one-tenth of an nm..... then continue doing that kind of star fixing in a continuous twelve-minute cycle.

The objective was to guarantee to bring the aircraft, after a 2000nm transit, down a half-mile wide 'alley in the sky' within 30 seconds of pre-briefed time. The good 'uns could do this within a quarter-mile and 15 seconds - and did, once every month. The very best crews, with a lot of tweaking and years of practice, could reliably do even better, regularly demonstrated in NATO Bombing Competitions with sub-200 metre CEPs and within 5 seconds of planned time.

The Americans simply couldn't believe it. The Russians did.

* I understand ( almost ) that the deeper depths of Probability Theory tells us that our position in space may be 'here' or may be 'there', but when we try to measure that precisely, we change it. And when we try to measure it twice, or go for 'best of three', we change it again. Cue bits of the Uncertainty Principle.....

So perhaps we should stop worrying about whether we're just inside a 'cocked hat' or just outside it, move along a bit and take another fix..... and later still, another. They're likely ALL right, enough for our purposes. And we should always end up following a Single Line of Position - a Leading Line - into our safe haven. That's usually unambiguous.

Cables, non?
Chain is the lengh of a cricket pitch, apparently.

Anyway, when are we going to discuss the benefits of HSAs and station pointers?

 

[zoidberg]

Don't know nuttin about cricket.....

 

[TLouth7]

Ooof, I was fully on my high horse back in 2019! However I did write this which I stand by:

If you are good at taking bearings/sights then you should expect to see small cocked hats, but if for a particular fix you get a small cocked hat it doesn't mean your bearings were good.

 

[MisterBaxter]

One technique I was shown (by my dad, sometime around 1988 in thick fog off Minehead) is to take a bearing with a hand bearing compass, but don't draw it onto the chart; instead, decide on a reasonable margin of error based on experience (say 5%*) and draw on two lines, one +5% and one -5%* of the bearing line. This gives you a gradually widening space that you probably are inside. Multiple bearings define an assymetric polygon that you may well be inside.
The advantage of the system is that it recognises that the further you are from the reference point, the wider your zone of uncertainty becomes.
EDIT 5 degrees not 5%...

 

[B27]

With Navionics on a tablet, it's easy to plot a single position line using the 'divider' function.
That at least shows how bad we are at using the handbearing compass.
But it also shows whether we've identified a landmark correctly.

This Angel nav seems to allow putting in more PLs and finishing the job, which is nice, but I'm not sure how much I'm willing to pay for that.

Much of the time, I am not actually that bothered about knowing exactly where we are.

 

[Baltika_no_9]

...... to take a bearing with a hand bearing compass, but don't draw it onto the chart; instead, decide on a reasonable margin of error based on experience (say 5%) and draw on two lines, one +5% and one -5% of the bearing line...............

5% of what? I'm not clear what you mean there.

 

[B27]

5% of what? I'm not clear what you mean there.

I assume 5degrees.

 

[Baltika_no_9]

I assume 5degrees.

Nothing to do with percentages then, that makes sense.

 

[MisterBaxter]

Oops yes, 5 degrees, symbol selection failure on my part! Will add a clarification to the post...