Distance from Anchor = Rhode Length

[ost]

Well within 3.2% that is.

So taking the Pythagorean Theorem and right triangle stuff...

a^2 + b^2 = c^2

a = Keel Depth + Draft + Height of Bow Roller + Tide
b = Distance from Anchor
c = Rhode Length

We want c to equal a*scope (such as 4:1, 5:1, 10:1...) so:

c=scope*a

Going back to the original equation and fill in with the data from thus far:

(Keel Depth + Draft + Height of Bow Roller + Tide)^2 + b^2 = (scope*(Keel Depth + Draft + Height of Bow Roller + Tide))^2

Solving for b:

b = [(scope*(Keel Depth + Draft + Height of Bow Roller + Tide))^2 - (Keel Depth + Draft + Height of Bow Roller + Tide)^2]^1/2

blah blah blah so what does all this mean?

For my boat:
Draft = 5ft
Bow Roller Height = 5 ft.
Tide = 3ft

A Keel Depth of 10 feet and a scope of 5:1 would yield a distance from the anchor (b) equal to 113ft.

If you do the traditional calculation of scope*(Keel Depth + Draft + Height of Bow Roller + Tide) you end up with 115ft.

A difference of 2%. The greater the scope the less error.

Scope - Error
4:1 3.2%
5:1 2.0%
7:1 1.0%
8:1 0.8%
10:1 0.5%

The moral of the story is if you place a waypoint (or MOB button) on your chartplotter when you drop anchor, the distance from your boat to that waypoint as you are laying out rhode is equal to the length of the rhode (or close enough). Or if the distance from the waypoint is greater than the rhode you are dragging or have drug.

Of course, if your anchor does not set immediately (like my CQR...) it would do you well to have your rhode marked.

This also does not take into effect any catenary. Using this method in a low wind/current situation, would have you playing out more rhode than your distance to anchor (waypoint) would suggest. However, it could prove to be a quick check when things pipe up.

Standing by to be out mathed.

[Stu Jackson]

The math is reasonable, the complexity is unnecessary though, 'cuz as the triangle gets "stretched" the difference between the hypotenuse and the long side becomes less and less, as you've shown.

[ost]

Originally Posted by Stu Jackson

The math is reasonable, the complexity is unnecessary though, 'cuz as the triangle gets "stretched" the difference between the hypotenuse and the long side becomes less and less, as you've shown.

I had figured that, but I didn't think it would be this close.

[StuM]

> but I didn't think it would be this close

Instead of messing around with feet, just let a be 1 "unit"
Then it is apparent that b = Sqrt(c^2 -1).
At 4:1, c = 4, b = Sqrt(15) = 3.87,
Since 3.87/4 = 96.8% , the difference as you say is only 3.2%

And at 10:1, you get Sqrt(99)/100

[brazenarticle]

My better subject in elementary school was spelling. You are calculating the scope of the "rode", not the rhode.

[Vasco]

Originally Posted by brazenarticle

My better subject in elementary school was spelling. You are calculating the scope of the "rode", not the rhode.

You're both wrong. Scope is how much anchor line you have out based on bow to sea bottom. e.g. Bow to bottom at high tide 15'. 1:1 scope -15 feet let out,
10:1 scope -150 feet out.

And to add to the complexity sometimes even with 10:1 scope you might end up sitting on top of your anchor. This happens frequently when wind opposes tidal current. Distance from anchor varies greatly depending on conditions.

Rather than placing a waypoint when anchoring I set the hook and then have a sundowner. If you need a waypoint to know if you're dragging you have no business anchoring or cruising.

What is this, April 1st already?

[ost]

Originally Posted by Vasco

Rather than placing a waypoint when anchoring I set the hook and then have a sundowner. If you need a waypoint to know if you're dragging you have no business anchoring or cruising.

What is this, April 1st already?

I'll put my boat in the classified section tomorrow. Thanks for the help.

[brazenarticle]

Originally Posted by Vasco

You're both wrong. Scope is how much anchor line you have out based on bow to sea bottom. e.g. Bow to bottom at high tide 15'. 1:1 scope -15 feet let out,
10:1 scope -150 feet out.
What is this, April 1st already?

To mangle the bard - "What's in a name? That which we call a rode by any other name would smell as sweet."

[noelex 77]

Originally Posted by ost

The moral of the story is if you place a waypoint (or MOB button) on your chartplotter when you drop anchor, the distance from your boat to that waypoint as you are laying out rhode is equal to the length of the rhode (or close enough). Or if the distance from the waypoint is greater than the rhode you are dragging or have drug.

As the calculations show the hypotenuse and base length of the anchoring triangle can be considered the same for practical purposes when anchoring.

However, you do need to take into account the distance from the GPS aerial to the bow. The centre of the circle needs to displaced so the swing circle it is centred on the bow. If you don't do this the GPS will report a variable distance with a change of wind direction without any dragging.

If setting the GPS waypoint when dropping the anchor you also need to consider the distance the anchor takes to set. For older generation anchors this can be significant.

Originally Posted by Vasco

If you need a waypoint to know if you're dragging you have no business anchoring or cruising.

The GPS is very useful to tell if you are dragging. A waypoint is not always needed (which is perhaps what you mean) as the track trace shows what is happening, but distance to a waypoint at the anchor can be very useful for those that will read in metres and feet (instead of cables which is a bit crude)

Transits will show finer discrepancies than a GPS, but the visibility has to be enough to see them (thunderstorms for example can obscure transits).
They also take time to establish so with a significant rapid change in wind direction they are less useful.
Finally you need to look out of the window. With the GPS you can stay in bed.

A good anchor and anchoring technique is the most important thing to get right, but no anchor is 100% secure so monitoring your position is important. The GPS is a great tool to do this and will even alert you automatically (via the anchor alarm) if things change.

[Vasco]

Originally Posted by noelex 77

The GPS is very useful to tell if you are dragging. A waypoint is not always needed as the track trace shows what is happening, but distance to a waypoint at the anchor can be very useful for those that will read in metres and feet (instead of cables which is a bit crude)

Transits will show finer discrepancies than a GPS, but the visibility has to be enough to see them (thunderstorms for example can obscure transits).
They also take time to establish so with a significant rapid change in wind direction they are less useful.
Finally you need to look out of the window. With the GPS you can stay in bed.

A good anchor and anchoring technique is the most important thing to get right, but no anchor is 100% secure so monitoring your position is important. The GPS is a great tool to do this and will even alert you (via the anchor alarm) if things change.

Have never used GPS to see if I'm dragging. In weather when dragging is possible I'm in the cockpit on anchor watch. When a sailboat drags it goes sideways, very easy to tell when you're dragging. I do try to line up a couple of points (transit) but usually in dragging conditions the visibility is poor. Also in dragging conditions the boat will yaw going from one tack to the other. Hard to keep an eye on the GPS easier to watch the boat. The trick is to get out of bed before **** happens. My wind generator is my alarm. I sleep in the aft cabin right below the nice hum from my windgen. I can tell windspeed from the sound and wake up when it honks. Or my wife wakes me up. She's more sensitive than I am. As can be seen from my reply to the math question. What happened to seamanship?

[zeehag]

not always do boats drag sideways,. do not fool self. i watched as boats have slid gently back past the length of scope...ie, patricia belle in mazatlan, december 2011....straight backwards. pacific jade in la cruz...straight backwards. journey a 54 ct ketch,la cruz, ..straight backwards. no sideways, merely straight back.
it is true that MOST OF THE TIME one will find the boat will go sideways, BUT NOT ALWAYS. be alert and take bearings near as well as distant.
i do not do math, but i count how much chain is left on deck when i am done laying out my chain. i usually have 150 ft on bottom in most pacific mexican anchorages.

[Paul Elliott]

Why use keel depth? That makes sense if your depthsounder is displaying "depth below keel", but (for example) I have mine set to display depth from the water surface. I know my anchor roller is roughly five feet above the waterline so I add that to the depth when figuring my scope.

[Vasco]

Originally Posted by zeehag

not always do boats drag sideways,. do not fool self. i watched as boats have slid gently back past the length of scope...ie, patricia belle in mazatlan, december 2011....straight backwards. pacific jade in la cruz...straight backwards. journey a 54 ct ketch,la cruz, ..straight backwards. no sideways, merely straight back.
it is true that MOST OF THE TIME one will find the boat will go sideways, BUT NOT ALWAYS. be alert and take bearings near as well as distant.
i do not do math, but i count how much chain is left on deck when i am done laying out my chain. i usually have 150 ft on bottom in most pacific mexican anchorages.

It's been my experience that once the hook breaks free a sailboat will go sideways. That's how sailboats go. They just don't go straight backwards. It may be in the cases you cited the hooks were not set properly and the boats crept backwards slowly. Also in some cases due to the nature of the bottom and the type of anchor a boat might creep backwards. In these cases it's usually slower and nothing like a good anchor drag where a boat takes off.

[zeehag]

most DO go sideways, HOWEVER many can slide without crossing up and going sideways. watch the boats around you.
i used to believe that ALL boats went sideways until i saw those boats slide straight back.
have fun, reality can suck if you are not receptive to it.

[noelex 77]

Originally Posted by Vasco

Have never used GPS to see if I'm dragging.

Give it a try. Seamanship is about effectively using all the resources at your disposal. Ignoring technology because our forefathers managed without is not sound practice.

Originally Posted by Vasco

In weather when dragging is possible I'm in the cockpit on anchor watch.

An anchor watch is sometimes necessary, but when spending winter in the Mediterranean I would be a tired, frozen cruiser if I set an anchor watch every time the windspeed reached this stage.
In rare circumstances it is also possible to drag in low windspeed say 25 knots even if you have done everything right.

Originally Posted by Vasco

it goes sideways, very easy to tell when you're dragging.

Yes this is a very good clue, but it is not foolproof. It works when the anchor breaks out and the resistance from the bow is minimal. This is the most common type of drag, but sometimes an anchor will remain set and gradually pull through the substate. The boat does not alter its attitude in this sort of drag.

Originally Posted by Vasco

I do try to line up a couple of points (transit) but usually in dragging conditions the visibility is poor.

Agreed transits are the best. You can use them to reliably pick even a couple of metres movement backwards. However, as you note they not always usable and need considerable effort for frequent monitoring

Originally Posted by Vasco

My wind generator is my alarm.

This is an alert for windspeed rather than dragging.

In summary I think it is important to use all the tools at our disposal to detect the boat dragging as early and reliably as possible. The GPS is one of these tools and should not be ignored.