Math puzzle for scope

[Don C L]

Ok, I was thinking about what happens when you let a weight down your anchor line to increase the effective holding power of the anchor and I posed this question to my mathematician friend. How can I calculate the effect of a given weight on a given length of rode? In other words, if I need more scope but I don't have the room, how much weight will be needed to keep the rode horizontal? ( I know there are many variables involved.) I intuitively believe there is a very complex formula for it, but I believe there IS a formula that can take all the variables into account. Anyone know what it is, or can figure it out? My friend said the beer had reduced his calculating skills. I did research threads here on scope but did not see any reference to it. Any mathematicians out there?

[noelex 77]

Don here are a couple of articles on the subject:

Rode - Static Behavior

Kellets or Anchor Angels / Sentinels: Uses and Applications

Kellets have some uses, but they have little effect in decreasing the angle of pull on the anchor in the sort of windspeeds that are likely to cause problems.

[Lake-Effect]

Not a full solution, but some direction: it's vector math.

The diagonal tension on the rode can be resolved into horizontal and vertical forces. Adding an angel weight at some point on the rode contributes that weight pulling down at that point.

The force vectors acting on a stationary point add up to zero, so you end up solving that equation to find a weight value that will hold the lower part of the rode at the desired angle.

But it gets messier when you have to consider the weight of the rode, whether you have any chain, etc etc. So there's probably a rule of thumb chart out there somewhere that says to use a weight of X if your boat is of size Y and you have Z ft of rode out at scope A:1...


..... aaaand noelex has just covered it well, so I'll just stop now.

[Don C L]

Thanks to you both. Noelex, that second article is the one that had what I was searching for. Looks like the only major benefit is shock absorption.

[clownfishsydney]

I use this method on my power boat when out scuba diving. We worked out how much weight we needed by a bit of trial and error. Works well, but this is on a rope anchor line so it is easy to slide down and pull back up.

[denverd0n]

Originally Posted by Don C L

Looks like the only major benefit is shock absorption.

Exactly. In a heavy blow or surge, when the anchor rode becomes fully extended, the weight will not make any difference in the angle between the sea bed and the rode. A short rode will still be a short rode, with a steeper angle, and a long rode will still be a long rode, with a shallower angle.

[barnakiel]

A suction device can also be used, esp. in muddy bottoms.

b.

[thinwater]

Originally Posted by denverd0n

Exactly. In a heavy blow or surge, when the anchor rode becomes fully extended, the weight will not make any difference in the angle between the sea bed and the rode. A short rode will still be a short rode, with a steeper angle, and a long rode will still be a long rode, with a shallower angle.

What he said. When you need it, it won't do anything, even shock absorption; while the chain will not be perfectly straight, the difference will be only inches. Neeves did a write up for Practical Sailor (pulled chain with winch), and the difference in length was trivial. The amount of strain required was also less than you would think (190 pounds to lift the last link of 100' of 5/16" chain--nothing).

Chain does help in soft mud for a number of reasons, and if the strain is tons you are dragging anyway! But a bigger anchor more chain seems far simpler than a kelet.

[seandepagnier]

using all line is much better than weights for absorbing the waves, and is a lot lighter and easier to handle and doesn't rust. I met someone who showed me how to anchor with only line so it can never risk cutting.

[Bulawayo]

Hi Don, I'm no mathmatician but common sense tells me that if the conditions get worse the anchor rode (be it chain, warp or a combination) shall eventually go tight. The angel shall help with reducing light snatch loads though under 'normal' conditions. We prefer to adopt different anchoring methods depending on the circumstances, usually involving a second anchor arrangement. We use lots of chain and heavy anchors. I have yet to discover a method that lets me anchor safely in the vicinity of coral - even chain can be cut by coral. Putting your faith in line only as has been suggested and you'll not have a boat for long in many places of the world. Of course, warp is fine if you stay out of warm waters, away from ice, away from rocks or jetties or.............

[CHAZ]

Originally Posted by boat_alexandra

using all line is much better than weights for absorbing the waves, and is a lot lighter and easier to handle and doesn't rust. I met someone who showed me how to anchor with only line so it can never risk cutting.

Ahoy boat alexandra,
could you tell how to achieve this?

Thanks, and fair winds
Martin

[noelex 77]

Originally Posted by CHAZ

Ahoy boat alexandra,
could you tell how to achieve this?

+1 There are no secrets on CF

There are a few options that allow rope rode to used in abrasive substrates. Usually some chain close to the anchor is still needed.

1. Buoy the rode.
This can work well in deserted anchorages. Floats keep the rope rode from contacting the abrasive bottom. If the wind picks up the floats will sink, but the rope will not contact the bottom. Unfortunately in light wind the floating rode is hazard to other boats.

2. Constantly adjusting the scope.
The pull of the anchor stock is the critical parameter. In very light wind even a small scope is fine. I have seen yachtsmen with rope rode constantly adjust the scope in an abrasive substrate. The adjustment ensures that the rope is above the seabed. In light wind the chain close to the anchor remains on seabed. This needs frequent adjustment, depending on the wind strength.

3. Take your chances
In many anchorages there is only a small chance of chafe damaging a rope rode. However, diving I see a lot of debris, natural and man made, which makes me nervous of this this approach.

4. Hi tech ropes.
Dyneema and similar hi tech fibres are abrasion resistant and provide a intermediate step between chain and normal rope rode.

More ideas would be great.

[barnakiel]

When the waves get big enough to need getting "absorbed" then perhaps neither rope nor chain but just bug out?

I, for one, would be on chain in any too much wind too much wave conditions. I do not want our boat to be everywhere and most of the time beams on to the gusts. I want our boat to stay put as much as viable.

I like what you are saying about "ultimately flat tine, no matter chain or line". I can see this picture.

I also like the drag from the chain - be it across the bottom or thru the water. Try it out, you may sense the difference.

Line is fine. When it is fine.

b.

[Jim Cate]

even chain can be cut by coral.

Not my experience. Never heard of such an event amongst all our cruising acquaintances.

Chew off galvo in time? Sure! Cut chain? I don't think so...

Jim

[Lodesman]

Originally Posted by Don C L

Thanks to you both. Noelex, that second article is the one that had what I was searching for. Looks like the only major benefit is shock absorption.

That article seemed to be a little biased. I grabbed the equations from the other article for determining the critical force [Fc=w*(L²-H²)/2H] and ran the numbers from Smith's first scenario (30m 10mm chain, 5m depth, 15 kg kellet) using the effective weight of steel in water. Chain alone required a force of 159.25 daN (kilos) to lift the entire rode; adding a 15kg kellet bumped that required force up to 197.1 daN. Getting 38 kilos more at the bowring (24% increase in "holding power") for adding 15 kilos to the rode suggests more value than just shock absorption.