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Displacement of an anchor
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The Publisher
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Mar 6, 2013, 8:22 AM

Post #1 of 12 (28041 views)
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How smart are you feeling today? Let's find out...

Does anchoring a boat cause the sea-level to be:
(a) higher
(b) lower
(c) no change


Answer below


The Publisher
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Mar 6, 2013, 8:22 AM

Post #2 of 12 (28039 views)
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To the question, "Does anchoring cause the sea-level to be (a) higher, (b) lower, or (c) no change", the answer is (b) lower.

First consider that FLOATING things displace a volume of water EQUAL to their mass. The anchor sinks because when it's in the water, it displaces LESS volume than the water it's competing with. So while the anchor is in the boat, it's displacing MORE water than the anchor's volume. So tossing out the anchor, the anchor now displaces water EQUAL to the anchor's volume, so the sea-level FALLS by that difference in volume.

Corollary: if civilization is in danger because climate change will cause seas to rise, we all need to go out and anchor to compensate.


The Publisher
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Mar 6, 2013, 8:24 AM

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Tue, 05 Mar 2013 19:36:05 -0800 (PST)
Date: Tue, 5 Mar 2013 22:36:05 -0500
Subject: Concerning the question of a anchor rising or lowering, or keeping it the same
From: Kirk Robertson
To: editor@sailingscuttlebutt.com


I think the answer is wrong. (and I could be wrong too).The mass of the anchor stays the same in the boat or in the water. That means the displacement of water will also remain the same.


The Publisher
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Mar 6, 2013, 8:24 AM

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From: Chris Field
Date: Tue, 5 Mar 2013 23:08:55 -0500
To: editor@sailingscuttlebutt.com


As far as the anchoring question goes the answer seems a little simplistic. What if there's current? Doesn't the boat displace more water? Most probably more that the difference in the density of the anchor and water.


The Publisher
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Mar 6, 2013, 8:27 AM

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Tue, 05 Mar 2013 20:50:13 -0800 (PST)
Date: Tue, 5 Mar 2013 20:50:13 -0800
Subject: SCUTTLEBUTT 3789 - Wednesday, March 6, 2013
From: Bill Barham
To: editor@sailingscuttlebutt.com


ANCHORING ANSWER
To the question, "Does anchoring cause the sea-level to be (a) higher, (b)
lower, or (c) no change", the answer is (b) lower.

First consider that FLOATING things displace a volume of water EQUAL to
their mass. The anchor sinks because when it's in the water, it displaces
LESS volume than the water it's competing with. So while the anchor is in
the boat, it's displacing MORE water than the anchor's volume. So tossing
out the anchor, the anchor now displaces water EQUAL to the anchor's
volume, so the sea-level FALLS by that difference in volume.

Corollary: if civilization is in danger because climate change will cause
seas to rise, we all need to go out and anchor to compensate.


This would be true if anchoring with no wind and no current (but then, why anchor, just drift)

When anchoring with those horizontal forces in place, the boat is subjected to both horizontal and vertical forces based on the scope of the anchor rhode. It is quite likely the downward component would exceed the anchors weight, and the net result will be an increase in effective displacement. Thus, the sea-level would increase.


The Publisher
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Mar 6, 2013, 8:30 AM

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From: rob tomkies
To: "editor@sailingscuttlebutt.com" <editor@sailingscuttlebutt.com>
Subject: Anchor and flotation
Date: Wed, 6 Mar 2013 21:25:43 +1300

Archamedes would have some dispute with your anchor/ displacement theory. He would have a Eureka moment and state that removing the anchors weight from the boat would cause the boat to have less volume (float higher) so the end result would be that the sea level would remain the same. To save the planet, on the basis that some boats somewhere in the world are always sailing, it is compulsary to go foiling as often as possible.


The Publisher
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Mar 6, 2013, 9:50 AM

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Tue, 05 Mar 2013 18:51:57 -0800 (PST)
Date: Wed, 6 Mar 2013 10:51:57 +0800
Subject: Re: Scuttlebutt 3789
From: paul baker
To: editor@sailingscuttlebutt.com

In response to the trivia question: how do you account for the fact that an anchor's purpose is to keep a boat's position stationary?

The anchor imparts a vertical and horizontal ("gripping") force on the seabed, with the opposite force vector's direction is up the chain and into the boat. The external forces on the boat however (the reason why you're anchored in the first place: ie. tide, wind, current) will impart only a horizontal force on the boat (less than that of the anchor "gripping", or you'd be "slipping"). This horizontal force will cause the angle between the seabed and the anchor chain to decrease (pushing them closer to being parallel) and therefore push the boat deeper into the water displacing more volume.

I suppose the answer must then take into account outside forces and how big and your anchor gear is...




The Publisher
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Mar 6, 2013, 11:41 AM

Post #8 of 12 (28028 views)
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To: editor@sailingscuttlebutt.com
From: sean purdy
Subject: Anchoring for climate change
Date: Wed, 06 Mar 2013 17:57:36 +0000 (GMT)


I enjoyed the wishful thinking of your "anchoring against climate change" suggestion, but I fear the problem is rather bigger and more intractable than that. As Randall Munroe recently pointed out, global sea-level is rising so quickly that we could remove the entire merchant shipping fleet from the oceans, and sea level would be back up to its previous level in about 16 hours.


The Publisher
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Mar 6, 2013, 11:53 AM

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From: Kenneth Voss
Subject: Re: Scuttlebutt 3789
Date: Wed, 6 Mar 2013 09:58:51 -0500
To: editor@sailingscuttlebutt.com


The answer will be more complicated depending on the wind conditions, and the anchor scope.

Steel density is about 490 lbs/ft3 (to keep English units to make it easy for us to relate to). so a 30 lb anchor is about 0.06 ft3. This will displace 3.7 lbs of water, and in the absence of everything you say, the boat will float higher as it had to displace 0.48 ft3 of water to keep it floating in the boat.

But assuming the purpose of the anchor is to keep the boat in one place, if there is wind, the anchor will be pulling on the boat to keep it in place. Since the anchor is pulling downward (depending on scope, wind strength and boat windage), the water will be forced to put slightly more upward buoyancy force to keep the boat from sinking, this will cause the boat to displace more water, thus raising the overall water level.

So depending on the situation you might gain or lose by being anchored…….for a 5:1 scope this is about 130 lbs of force on the anchor line, for a 10:1 scope more like 260 lbs.




Andrew Troup
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Mar 6, 2013, 6:27 PM

Post #10 of 12 (27995 views)
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People are overthinking this.

The given answer is correct, and this is why:

When you start feeding the anchor over the bow, very little changes in terms of the sealevel (easiest if you imagine a small inland sea aka lake) :
This is because the boat + anchor + chain don't change mass, AND the system is still floating (crucially) so they still need to displace the same volume of water

However this all changes once the anchor (and perhaps some of the chain) rest on the bottom: at this point, Archimedes principle no longer applies, because that proportion of the total weight of boat + anchor + chain is NO LONGER floating.

The boat will sit higher in the water because the lake floor is now supporting that weight. The displacement of the b + a + c system reduces to support only the floating entities. Hence the lake level will drop by the volume corresponding to that displacement loss.


Andrew Troup
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Mar 6, 2013, 6:31 PM

Post #11 of 12 (27992 views)
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oooops - accidentally posted before I was quite finished ...

less the volumetric displacement of the anchor and any chain supported by the bottom.

However this will be considerably less than the volume change of the boat's displacement, because the anchor is considerably heavier than the same volume of water. (In other words, it occupies a lot less volume than the same mass of water)

So the lake's shoreline level will go down


redler
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Mar 8, 2013, 10:21 AM

Post #12 of 12 (27801 views)
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Only a physicist or a mathematician would be concerned with how much the water level actually changes. An engineer would claim that it is insignificant and unmeasurable. Therefore the water level remains the same.


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