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Old 08-31-2016, 11:36 AM   #1
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Anchor Circles

Do I dare post this? From Active captain this morning

Interesting article as we anchored a lot on our trip and only used the Raymarine Anchor alarm only twice. I also have the drag queen app, but I would forget about it and by the time the anchor was set it was too late to use it.


>>> Anchor Circles >>>

Last week's newsletter brought another large set of responses from the
ActiveCaptain community. We continue to be amazed at the quality and
abilities of boaters. It doesn't matter what type of boat you have, the
experience out there is much better than any other source we can find.
Especially when the topic is anchoring.

So the math major in me wants to bring up another topic. It's a detailed
one that nearly everyone ignores. You see, so many of the responses
involved explanations of how the navigation product or app used for
anchor alarms draws a circle. Other people watch the track their boat
creates and the circle drawn as they swing with wind and tide.

Circles, circles, circles.

And yet, none of them should look like circles.

So I checked a couple of anchor alarm apps to see what they do. And sure
enough, some draw perfect circles based on your alarm distance. In all
cases, the circles are drawn over Google Maps, satellite imagery, or
nautical charts. And all of them are drawing the swing area incorrectly.

By now, some of you are saying that I've lost my mind. Of course it's
a circle with the anchor in the middle and the radius equal to the alarm
distance. The thing being forgotten is that the Earth is not flat. It's
a sphere. And nearly all the map data, satellite imagery, and nautical
charts are drawn with a Mercator projection.

The Mercator projection of the Earth produces some exceptional features
that are perfect for navigation. The main one is that bearing lines
appear as straight lines. In nearly all other projections, maintaining a
constant bearing will create a curved line. Not so with Mercator.

The disadvantage of the Mercator projection is the distortion that
happens as you move away from the equator. This is what makes Greenland
look huge.

So the problem with many existing anchor alarms is that the alarm circle
itself needs to be projected through the Mercator projection too. But
doing that involves a lot of trigonometry and many of the developers
writing these apps don't have a good understanding of it. The reality
is, a proper anchor alarm circle projected through the Mercator
projection should look squashed and not perfectly round as long as
you're not near the equator. As soon as you start to get 30 degrees of
latitude away from the equator, the circle will not look like a perfect
circle.

So go check your anchor circles drawn by alarms. Are they squashed?
If not, perhaps you should be using a different anchor alarm.

A second fun exercise is to plot your track through tide cycles as you
swing around your anchor. That won't ever be a circle either - if you
look carefully, it will also be a little squashed.
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Old 08-31-2016, 11:49 AM   #2
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I totally agree with the concept that Mercator projection will distort the circles...but how much in latitudes below Labrador and Anchorage, Ak.?

Not doing that much work unless I have to....
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Old 08-31-2016, 11:49 AM   #3
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Doubt that it's even perceivable at that close of a distance. If you let out plenty of chain say 1 nm it might change a bit, but not for the distances we use.
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Old 08-31-2016, 12:05 PM   #4
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Doubt that it's even perceivable at that close of a distance. If you let out plenty of chain say 1 nm it might change a bit, but not for the distances we use.
I agree, the difference is not significant.
I was disappointed that he brought this up as being a major factor.
No way
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Old 08-31-2016, 12:11 PM   #5
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Fly stuff.
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Old 08-31-2016, 12:28 PM   #6
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Since he is a math major, I wish he would derived and provided a formula to quantify the error. Maybe he did the math and realized that it is immaterial.
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Old 08-31-2016, 12:44 PM   #7
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I agree, the difference is not significant.
I was disappointed that he brought this up as being a major factor.
No way
Nothing in the article indicated to me that the author thought it was a major factor, just an interesting detail.
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Old 08-31-2016, 12:51 PM   #8
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I am curious where it does really start to make a difference.

At the poles, the circles would become a straight line.... so without some research, maybe 45 degrees north, the circle is really 2 times taller than wide .....if you assume lat/long is the same like near the equator and draw the circle based on that, but then plot the lat/long per the real lines....

So maybe there is something to it when cruising upper lattitudes....if you set for a 200 for rode circle with errors, and you swing towards 90 degrees to that... you quickly go out of the circle.

Hmmm, don't want to do the research...and I did look quick for a calculator of lat/long...but the ones I found rounded off too much. Maybe I will over the weekend with some dead time.
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Old 08-31-2016, 01:37 PM   #9
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I'll add 5' and call it even!
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Old 08-31-2016, 01:48 PM   #10
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The wonderful thing about math is that it's one of those things that has definite answers. I love the off-the-cuff "it doesn't matter" postings here without a clue about what the error actually is or what it looks like.

I'd love to provide the trig formula to calculate the error but it would be a waste of time since no one was willing to even make any attempt at just drawing what happens. I don't see any of the characters here figuring out how to calculate hyperbolic trig functions on their vintage 1992 HP calculator.

The attached picture shows a grid at 0.06 minute intervals (360 feet) which is a pretty typical 180 foot anchor alarm distance. The area is one where I've anchored many times near Castine. So imagine a "circle" drawn perfectly inside one of the "squares" touching the top, bottom, left, and right. Think it would be noticeable as something a little out-of-round? The error is way outside the typical 15 feet of GPS error.

Should you lose sleep over this? Nah - I don't. Although I prefer using alarms that take the extra step to calculate the proper solution to the problem. The apps that do it correctly probably solve all the other issues correctly too which is why you purchase the app in the first place.

But mainly, I think it's an interesting mathematical side-note to anchoring that no one has really thought about.
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Old 08-31-2016, 01:58 PM   #11
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I see the anchor alarm thread is closed so I will ask this question here. Perhaps I'm not understanding all this but:

If I drop my anchor, let out the scope I desire and then take my iPhone or iPad to my stateroom and set the anchor alarm at that point I can then eliminate the error created by the distance from the anchor to my stateroom. Is this correct? And if so, can't I then set a distance composed of double the scope plus a "safety margin?" My head hurts from thinking about this.
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Old 08-31-2016, 02:04 PM   #12
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I am curious where it does really start to make a difference.

At the poles, the circles would become a straight line.... so without some research, maybe 45 degrees north, the circle is really 2 times taller than wide .....
The ratio of latitude distance to longitude distance is equal to the square root of the lattitude. So, at 45 degrees latitude its about 0.71
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Old 08-31-2016, 02:09 PM   #13
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If I drop my anchor, let out the scope I desire and then take my iPhone or iPad to my stateroom and set the anchor alarm at that point I can then eliminate the error created by the distance from the anchor to my stateroom. Is this correct?
No, it isn't. If your iPhone sits 25 feet back from the bow in your stateroom, the error will be 50 feet in the worst case.
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Old 08-31-2016, 02:18 PM   #14
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It may be that the error up where our AK are would be more signficant. Imagine what might happen for someone who wanted to transit the Northwest Passage some Summer? In that setting, but the potential for some very significant winds and anchorages that would be relatively unknown (not too many AC members have been through there yet), and accurate anchor alarm would be helpful.

Since I know nothing about programing, maybe this wouldn't work, but I think it would be relatively easy to have an alarm that would base it on the number of degrees from the GPS point. It would take some math, but most devices would have plenty of processing power I would imagine.

Again, not significant in my opinion for most of us, but I could create some scenarios where it could be important.
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Old 08-31-2016, 03:54 PM   #15
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The ratio of latitude distance to longitude distance is equal to the square root of the lattitude. So, at 45 degrees latitude its about 0.71
Thanks...so at just 45 degrees north...isn't that most of Puget Sound north, the northern Great Lakes and the Maritimes.....there is already a 30% error in the anchoring circle.

But isn't the square root of 45 closer to 0.67?

But I found a calculator that says at 45 degrees latitude, a degree of latitude is 60 and longitude is 42.57...which does work out to a 0.71 multiplier.

But at the equator, where the latitude is zero, the square root is zero but longitude is nearly a facto of 1.

Here's that calculator.... Length Of A Degree Of Latitude And Longitude Calculator

Either way...at higher latitudes, the error is worth considering....

Thank you Jeffrey, I will do some math before I head those places. .
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Old 08-31-2016, 03:57 PM   #16
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But isn't the square root of 45 closer to 0.67?
I should have written "square root of the cosine of the latitude". That gives .71
At 30 degrees, its about .87
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Old 08-31-2016, 04:01 PM   #17
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I should have written "square root of the cosine of the latitude". That gives .71
At 30 degrees, its about .87
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Old 08-31-2016, 05:03 PM   #18
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Originally Posted by hmason View Post
I see the anchor alarm thread is closed so I will ask this question here. Perhaps I'm not understanding all this but:

If I drop my anchor, let out the scope I desire and then take my iPhone or iPad to my stateroom and set the anchor alarm at that point I can then eliminate the error created by the distance from the anchor to my stateroom. Is this correct? And if so, can't I then set a distance composed of double the scope plus a "safety margin?" My head hurts from thinking about this.
Lets say you didn't add a "safety margin". If you put out 100' of road, and anchored in 25' of water. If your berth is 30' from your bow, you will be about 128' from your anchor when sleeping in your bunk. If you set an alarm and double your rode it would be set at 200'. With this, you could drag 200' before your alarm goes off. In many of the places I anchor, that would be bad. OTOH, if the wind or tide reverse directions, your bunk would be 128' on the other side of the anchor from which you set the alarm and about 56' beyond the alarm radius that you set. So you would need to set a "safety margin" of 56' (more if the tide drops) to keep you from tripping the alarm if the wind/tide reverse. That would mean that if the wind didn't reverse, you could drag 256' before the alarm would go off.

This may have already been answered as I have been typing this between patients for the past 5 hours.
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Old 08-31-2016, 05:13 PM   #19
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The best thing would be to take the iPad to phone to the bow and hit mark when the anchor hits bottom.

Most anchors according to the anchoring videos catch in their own length.

If you feel it has drug...then add a few feet.

Then in the app....use your rode plus the distance where the iPad or phone will reside in the boat.

Other than a few feet of drag and GPS error...that should be a reasonable circle less latitude differences.
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Old 08-31-2016, 05:28 PM   #20
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The best thing would be to take the iPad to phone to the bow and hit mark when the anchor hits bottom.

Most anchors according to the anchoring videos catch in their own length.

If you feel it has drug...then add a few feet.

Then in the app....use your rode plus the distance where the iPad or phone will reside in the boat.

Other than a few feet of drag and GPS error...that should be a reasonable circle less latitude differences.
Yup. Of course, I kind of want to check the anchor when the wind or current direction change significantly anyway. So an alarm that goes off in such a situation, even if the anchor has not dragged, is fine with me.

To be honest, it is all academic for me anyway. With the size of my prostate, I am up a few times in the night anyway, and always take the opportunity to check anchor position.
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