Anchor rode length calcs
- Thread starter vyv_cox
- Start date
jdc
Well-Known Member
The formula for chain, for the chain to be just horizontal at the anchor, is:
L = sqrt(D^2 + 2 x Lambda x D);
Where L = length in m
D = depth in m
Lambda = horizontal pull in kg you want to sustain / weight of chain per m in water.
That this has the correct characteristics is clear: for low force and very deep water all formulae must approach L = D (more precisely, dL/dD ==1 for large D). It is also dimensionally correct. It can be derived it from first principles, allowing only that the chain be flexible, using integral calculus and using the identity sinh(x) = (e^x - e^-x)/2.
Some measured numbers for Lambda:
On my boat chain weight is approx 2kg/m in water, and I estimated horizontal force at 13kts wind (F4 mean) as 64kg (I count in wenches, 64kg = 1 wench). So Lambda = 32. This is eerily close to L = 12 sqrt(D) and not too far from L = 3xD + 10, which is why these other formulas are reasonable approximations.
Don't forget that the force increases with the square of wind velocity. Graphs available if interested.
L = sqrt(D^2 + 2 x Lambda x D);
Where L = length in m
D = depth in m
Lambda = horizontal pull in kg you want to sustain / weight of chain per m in water.
That this has the correct characteristics is clear: for low force and very deep water all formulae must approach L = D (more precisely, dL/dD ==1 for large D). It is also dimensionally correct. It can be derived it from first principles, allowing only that the chain be flexible, using integral calculus and using the identity sinh(x) = (e^x - e^-x)/2.
Some measured numbers for Lambda:
On my boat chain weight is approx 2kg/m in water, and I estimated horizontal force at 13kts wind (F4 mean) as 64kg (I count in wenches, 64kg = 1 wench). So Lambda = 32. This is eerily close to L = 12 sqrt(D) and not too far from L = 3xD + 10, which is why these other formulas are reasonable approximations.
Don't forget that the force increases with the square of wind velocity. Graphs available if interested.
saltwater_gypsy
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An alternative approach is to find out the maximum angle to the sea bed that your particular anchor will tolerate before breaking out. As I recall this angle for a Bruce anchor is about 8 to 10 degrees.
If you are in shallow water (say typically 3metres in the Med.) there is a good likelyhood, in a strong wind, that the chain will be pulled taut so that there is no appreciable catenery.
If you do the trigonometry, this means that the scope of the chain will be about eight times the depth to keep within the 10degrees limit. I would be quite happy , if space allows to put out 30metres.
In deeper water, the calculation becomes more complicated as the chain will take up a catenery curve before terminating at the anchor at the required angle and this is where the three to five times depth rule comes from.
I previously had a spreadsheet which allowed these calculationsto be made with a mixture of chain and rope and also with a "chum". I can dig this out on another computer given a little time.
PS found it! http://alain.fraysse.free.fr
If you are in shallow water (say typically 3metres in the Med.) there is a good likelyhood, in a strong wind, that the chain will be pulled taut so that there is no appreciable catenery.
If you do the trigonometry, this means that the scope of the chain will be about eight times the depth to keep within the 10degrees limit. I would be quite happy , if space allows to put out 30metres.
In deeper water, the calculation becomes more complicated as the chain will take up a catenery curve before terminating at the anchor at the required angle and this is where the three to five times depth rule comes from.
I previously had a spreadsheet which allowed these calculationsto be made with a mixture of chain and rope and also with a "chum". I can dig this out on another computer given a little time.
PS found it! http://alain.fraysse.free.fr
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noelex
Well-Known Member
A suitable amount of scope to put out is dependent on many factors such as:
How much scope have other boats got out?
What is the expected wind strength?
What is the holding like?
What Fixed hazards will I swing into with more scope?
If there are no boats and hazards close why not let out lots, chain in a locker is not going to do any good. The point of diminishing returns for the maximum holding power of an anchor is not reached in until you have something like 14/1 out.
In practice other boats and hazards often limit the amount of scope that is desirable.
3X max depth (to the bow roller)+ 10m is a good formula (and avoids mental square root calculations), but let out more if you can.
How much scope have other boats got out?
What is the expected wind strength?
What is the holding like?
What Fixed hazards will I swing into with more scope?
If there are no boats and hazards close why not let out lots, chain in a locker is not going to do any good. The point of diminishing returns for the maximum holding power of an anchor is not reached in until you have something like 14/1 out.
In practice other boats and hazards often limit the amount of scope that is desirable.
3X max depth (to the bow roller)+ 10m is a good formula (and avoids mental square root calculations), but let out more if you can.
jimbaerselman
Well-Known Member
Your formula is fine. However, it very rarely applies - only in light and steady wind conditions. The normal situation is an oscillation. Initially a boat at anchor will set up a small fore and aft surging oscillation, which, in stronger winds, becomes a side to side 'tacking' oscillation.
The forces in the rode when movement is reversed (reversing the boat's momentum) are many times higher than any static forces, making static forces irrelevant. And they will routinely remove all significant catenary from the chain. Bar taught, you might say. Hic.
jdc
Well-Known Member
I agree! Except not necessarily that it applies to light conditions only. The issue I think is more that gusts and snatching make a huge difference. especially in shallow water. However where I do think it at least qualitively useful is that it shows that in deep water (say 25m - a depth I do anchor in from time to time, mostly in Scotland) one needs less chain than most rules of thumb would predict. Hence I encourage people to be less worried about anchoring in deep water - 3 to 4x depth is over pessimistic, you don't actually need as much chain as you think.
However Vyv asked for the formula, and I'm a physicist, and it was lunch time...
However Vyv asked for the formula, and I'm a physicist, and it was lunch time...
jdc
Well-Known Member
PS:
I've been wondering about this for some time. I have even designed a strain guage and inclinometer for my chain to measure Horizontal and Vertical components of the force, but as yet am too lazy to actually make it and record the data. Do people think it worthwile doing this experiment? The modelling done by Alain (surname escapes me) is fantastic, but is modelling only, whereas I want to know what it is in practice for my boat.
Instead what I have done is put a very long and light line out into shallow water, so the rode is weightless and horizontal, and use this to estimate horizontal component of anchoring force. I was surprised that I could hold it, the force being only about 60kg peak I estimate in a wind gusting to 20kts (this was in the Isle of Muck: great place). So in summary while the force is clearly not uniform while shearing around, peak force may not be as much as several times the static force; that must be a function of the period and amplitude of the oscillation, which are in turn dependant on the Q or damping, which is probably affected by the hull form and boat windage. Thus techniques to increase damping may be more useful than longer rode; in the Isle of Muck anchorage mentioned above I let chain from my bower lie on the bottom while lying to the kedge, and the damping effect was astounding with shearing all but stopped.
I've been wondering about this for some time. I have even designed a strain guage and inclinometer for my chain to measure Horizontal and Vertical components of the force, but as yet am too lazy to actually make it and record the data. Do people think it worthwile doing this experiment? The modelling done by Alain (surname escapes me) is fantastic, but is modelling only, whereas I want to know what it is in practice for my boat.
Instead what I have done is put a very long and light line out into shallow water, so the rode is weightless and horizontal, and use this to estimate horizontal component of anchoring force. I was surprised that I could hold it, the force being only about 60kg peak I estimate in a wind gusting to 20kts (this was in the Isle of Muck: great place). So in summary while the force is clearly not uniform while shearing around, peak force may not be as much as several times the static force; that must be a function of the period and amplitude of the oscillation, which are in turn dependant on the Q or damping, which is probably affected by the hull form and boat windage. Thus techniques to increase damping may be more useful than longer rode; in the Isle of Muck anchorage mentioned above I let chain from my bower lie on the bottom while lying to the kedge, and the damping effect was astounding with shearing all but stopped.
jimbaerselman
Well-Known Member
The forces exerted when tacking are very much dependent on the elasticity of the rode, and the characteristics of that elasticity.
All chain rode offers trivial horizontal force as it first lifts off the ground, insufficient to stop the boat paying off from the wind. Then a first significant force comes in by the time it's angled at 30 degrees to the horizontal, shown by the yaw rate slowing. From then, force increases asymptotically over a mere further metre of movement as the rode lifts from 30 degrees to 15 degrees from the horizontal (simple geometry). The jerk detected standing at the foredeck (yes, that's me) is sufficient to unbalance most people in 20 to 25 kts of wind in fin keel yachts.
You're right, damping helps enormously. Yaw rate damping is high in long keel boats, so it takes a lot more wind for them to build up an oscillation in the first place. I guess hanging a long loop of chain over the bow would have some damping effect too. But both just postpone the wind speed at which unacceptable yawing sets in. Better is a forked moor.
Exerting that yaw force over a longer period of time also helps - 20m of nylon give you a linear increase of force over a 4m stretch, a much easier ride than applying the same momentum change over 1m distance!
It's all simple mechanics and geometry.
I've never looked at the deep anchoring situation (>20m) and why the ratio of scope to depth is commonly reduced. But I'm sure the explanation will lie in the fact that there's a greater roaming area, so a longer time to apply smaller forces, and lots of water damping hauling all that chain backwards and forwards. I still suspect, however, that a critical windspeed will be reached when that all counts for nothing.
All chain rode offers trivial horizontal force as it first lifts off the ground, insufficient to stop the boat paying off from the wind. Then a first significant force comes in by the time it's angled at 30 degrees to the horizontal, shown by the yaw rate slowing. From then, force increases asymptotically over a mere further metre of movement as the rode lifts from 30 degrees to 15 degrees from the horizontal (simple geometry). The jerk detected standing at the foredeck (yes, that's me) is sufficient to unbalance most people in 20 to 25 kts of wind in fin keel yachts.
You're right, damping helps enormously. Yaw rate damping is high in long keel boats, so it takes a lot more wind for them to build up an oscillation in the first place. I guess hanging a long loop of chain over the bow would have some damping effect too. But both just postpone the wind speed at which unacceptable yawing sets in. Better is a forked moor.
Exerting that yaw force over a longer period of time also helps - 20m of nylon give you a linear increase of force over a 4m stretch, a much easier ride than applying the same momentum change over 1m distance!
It's all simple mechanics and geometry.
I've never looked at the deep anchoring situation (>20m) and why the ratio of scope to depth is commonly reduced. But I'm sure the explanation will lie in the fact that there's a greater roaming area, so a longer time to apply smaller forces, and lots of water damping hauling all that chain backwards and forwards. I still suspect, however, that a critical windspeed will be reached when that all counts for nothing.
T
timbartlett
Guest
One of the funny things (I think) about these kinds of calculation is that factors such as the size and material of the chain or the buoyancy of the anchor seldom get a look in.
Buoyancy of an anchor?... imagine two identical anchors, one of steel and one of aluminium. If the steel one weighs 15kg, the ally one is probably about 5kg. But when immersed in water, they both experience a reduction in weight due to buoyancy. It's probably about 2kg each, so the steel one reduces to 13kg, while the ally one drops to just 3kg
The maths for different sizes or densities of chain is more complicated -- but it is sufficiently significant that the Admiralty Manual of Seamanship quotes different formlae for wrought and forged cables (forged cable needs 33% more than wrought cable)
Buoyancy of an anchor?... imagine two identical anchors, one of steel and one of aluminium. If the steel one weighs 15kg, the ally one is probably about 5kg. But when immersed in water, they both experience a reduction in weight due to buoyancy. It's probably about 2kg each, so the steel one reduces to 13kg, while the ally one drops to just 3kg
The maths for different sizes or densities of chain is more complicated -- but it is sufficiently significant that the Admiralty Manual of Seamanship quotes different formlae for wrought and forged cables (forged cable needs 33% more than wrought cable)
neil1967
Well-Known Member
What complicates things, at least to my mind, is where the bottom slopes - eg last week in Turkey (SO 36i) I dropped my anchor in 20m, but by the time I had let out 50m of chain, I was in 5m, with a line ashore about 20m long. I felt secure, but would be interested in any rules of thumb for dealing with sloping bottoms.
Regards
Neil
Regards
Neil
Artic Warrior
Well-Known Member
right with ya there....let it all out, if there's space..can do no wrong
noelex
Well-Known Member
It is the depth of water where the anchor is that is important. So if you anchor was dropped in 20m (from anchor roller to the bottom) you only had a ratio of 50/20 :1 (2.5 : 1) despite ending up in 5m water.
Anchoring into a slope (as you did) does however significantly help the anchors holding, conversely anchoring down the slope hurts holding. The effect of the slope is difficult to quantify and is very dependent on the local bottom topography directly at and behind the anchor.
I would not have felt secure in your situation, unless I was confident that the wind was going to stay from behind, or remain reasonably light.
ChrisE
Well-Known Member
apart from having to lug 100m of 10mm chain back in again? You guys must have forearms like gorillas unless you are softies with electric winches
Vyv, excellent post. It's not something that had occured to me.
FWIW, I use 200-300 foot of rope plus 30 foot of chain when anchoring in 100+ foot when I'm fishing. The 20 x sq root depth makes sense.
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boatmike
Well-Known Member
There are many formulas and rules of thumb. In truth none are truly scientifically derived and many based on poor data. The correct amount of rode is dependent on the weight of anchor chain, weight and displacement of the vessel, type of bottom, type of anchor, wind and tide strengths and wave action. There is no single answer. In calm conditions and relatively shallow water the minimum is usually considered to be 3 times depth. This should be increased, if space allows, when conditions worsen and there is no theoretical maximum.
In practice the maximum is determined by how much chain you can reasonably carry. If this is not enough the effectiveness can be increased by using and angel or chummy as discussed in a recent thread.
vyv_cox
Well-Known Member
Thanks again to everyone who responded. Sorry for delay, have been travelling back from Greece for the past week and was not able to get online.
The question relates to an upcoming question/answer in YM. I have used the Alain Fraysse, John Knox and Racnor pages on this subject many times, for answering other YM questions and for my own benefit. However, the calculation method I recall has not come up this time. It was possibly something the RYA came up with originally, and has been posted several times to my recollection. I have enough info to answer the question but would still like to see the method I recall, unless everyone has now had enough of the topic.
On the post about comparisons between calculated and measured load values, I answered a query on this topic in YM a year or so ago. The ABYC theoretical method seems to have several safety factors built in and it consequently predicts high loads. YM printed an article a couple of years ago, written by a man who runs a sailing school on W coast of Scotland. He had monitored actual loads using Anchorwatch permanently monitored by an onboard computer, in parallel with directly measured wind speeds. The article included a graphs of measurements over two years. Measured loads were surprisingly low, less than 200 kg in wind speeds to force 9 for a boat between 35 - 40 ft. I tend to agree with these figures, as I have used the same nylon snubber for nearly 20 years, a length of 11 mm nylon doublebraid with a breaking force of about 2.5 tonnes. In this time I have anchored several times in winds of 50 knots but the line has never given any concern. Most theoretical predictions would have snapped the snubber and probably pulled the cleat out of the deck.
The question relates to an upcoming question/answer in YM. I have used the Alain Fraysse, John Knox and Racnor pages on this subject many times, for answering other YM questions and for my own benefit. However, the calculation method I recall has not come up this time. It was possibly something the RYA came up with originally, and has been posted several times to my recollection. I have enough info to answer the question but would still like to see the method I recall, unless everyone has now had enough of the topic.
On the post about comparisons between calculated and measured load values, I answered a query on this topic in YM a year or so ago. The ABYC theoretical method seems to have several safety factors built in and it consequently predicts high loads. YM printed an article a couple of years ago, written by a man who runs a sailing school on W coast of Scotland. He had monitored actual loads using Anchorwatch permanently monitored by an onboard computer, in parallel with directly measured wind speeds. The article included a graphs of measurements over two years. Measured loads were surprisingly low, less than 200 kg in wind speeds to force 9 for a boat between 35 - 40 ft. I tend to agree with these figures, as I have used the same nylon snubber for nearly 20 years, a length of 11 mm nylon doublebraid with a breaking force of about 2.5 tonnes. In this time I have anchored several times in winds of 50 knots but the line has never given any concern. Most theoretical predictions would have snapped the snubber and probably pulled the cleat out of the deck.
tudorsailor
Well-Known Member
My biggest problem in anchoring around Mallorca is that the anchorages are quite crowded. I let out 5:1 scope but doubt that my neighbours do, so worry that when we swing with the changing wind that we may meet. No real answer to this other an watch as others anchor and try and calculate how much they have let out and estimate the distance from them to me! No formula for this!
Generally hate anchoring as a result.
Tudorsailor
Generally hate anchoring as a result.
Tudorsailor
Poignard
Well-Known Member
Yes that bothers me too. Only way round it that I can think of is to ask people nearby how much chain they have out [assuming they are onboard to ask] and if I don't like it, I move somewhere else.
I don't hate anchoring - only anchoring near anybody else!
silver-fox
Well-Known Member
Vyv
Not central to your current research on rode but it has been mentioned that yawing/sailing at anchor can be a big problem that increases loads on the anchor significantly. This is a much worse problem with the modern short keel fin and skeg designs
Some recommend a riding sail as a cure.
I would love to know what the trade off is when you fly a riding sail. Clearly that will keep the bow to the wind which reduces forces but also increases windage which will increase them again!
Does anyone know of any information on this. Are riding sails a good idea or is the cure worse than the problem?
Not central to your current research on rode but it has been mentioned that yawing/sailing at anchor can be a big problem that increases loads on the anchor significantly. This is a much worse problem with the modern short keel fin and skeg designs
Some recommend a riding sail as a cure.
I would love to know what the trade off is when you fly a riding sail. Clearly that will keep the bow to the wind which reduces forces but also increases windage which will increase them again!
Does anyone know of any information on this. Are riding sails a good idea or is the cure worse than the problem?