Anchoring Mathematics – again!

Jeff Seigel, founder of ActiveCaptain, writes…

This week we decided to reach into the archives and pulled out one of our most popular topics, an article from almost two years ago. Of the 250 newsletters we've written (which amazes us), the subject of anchoring math was in the top 5 for comments, arguments, and discussions. Since there have been so many new ActiveCaptain members in the last 2 years, we thought we'd revisit the subject to get everyone thinking about what really happens when you anchor using an anchor alarm.

Some of you will think there are logic and mathematics errors in this article. There aren't. Read it all and study the linked reference document. If you want to debate it, make sure to reference the linked graphic document and show how it's not correct (it is correct though!).

It should be simple. Pick the spot to anchor; come to a stop; drop the anchor and set the anchor alarm. Then pull back until the anchor sets.If you pull away further from the anchor set point than the distance you specified, alarms should go off. Simple, right?

Well, not exactly. The mathematics are surprisingly a lot more complex.

We know. It seems easy and obvious. We've been involved in many debates until the pencil and paper come out and then, "oh yeah" is heard.

Here's the missing magical point. You've got to notice that the point where the anchor position is set in the alarm is the position of the GPS and not the position of the bow/anchor. That one small point ends up bringing a whole bunch of trigonometry into the calculation.

When the boat swings 180 degrees, the error created by that offset equals twice the distance from the bow to the GPS. (Honest, twice.)

Let's take an example for a typical 42 foot sailboat with a GPS on the stern rail. This is the worst case scenario but is very typical and demonstrates what happens very well.

Assume you're anchoring in 10 feet of water with a bow that's 5 feet off the water's surface. A good scope for a night without much weather expected would be 5:1. This means 75 feet of rode will be let out and pulled back to set hard (we call that power setting). Then the anchor alarm is set at 125 feet, far more than the 75 put out. And since you power set the anchor, you couldn't possibly move 50 feet, right?

At 3 am, because these things always happen at 3 am, the anchor alarm goes off. You're 127 feet back. You remember that you way over added to the 75 feet so you start planning what you're going to do in the total black of night with the moderate wind that's now blowing. But in reality you don't need to do anything. Your anchor is not dragging.

What really happened is that the tide changed at 1 am. During the next 2 hours you slowly swung around and moved back. Not knowing this new math for anchor alarms you didn't realize that the GPS displacement caused 84 feet of position error in the anchor alarm. Your alarm went off after moving back only 52 feet. In reality, your anchor alarm should watch you move back another 32 feet without your anchor moving 1 inch on the sea floor. The anchor alarm should have probably been set at about 75 + 84 + 10 + 10 = 179 feet. The two 10's are for GPS accuracy error and slop since the anchor doesn't set immediately. Can you imagine setting an anchor alarm at almost 200 feet with only 75 feet of rode out? And yet, that's the right number for this boat.

This unexpected error is the reason we wrote DragQueen (available for free in the Apple app store and Google Play). Since the anchor alarm is on a phone, the GPS position is the phone itself. When deploying the anchor, we stand with the iPhone at the bow to eliminate one half the GPS position error. There's still another position error based on where the GPS is located while we sleep at night (25 feet back in our stateroom).

Remember too that this positional error happens at all angles. Swing about 90 degrees to the side and the error is about 1 times the GPS displacement distance. Even that can be significant. Given a heading/fluxgate sensor and a few configuration settings, 100% of this GPS positional error could be eliminated (DragKing?).

If you're still saying, "wait a second – there's not a 2x error in the position" – check out this graphic proof of what happens. We'll wait to hear the "oh yeah":

Happy anchoring!

By Jeff Seigel

Guest Author & Founder of ActiveCaptain



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