Is There Such a Thing as 1:1 "Scope?"
- Thread starter Kings Gambit
- Start date
How do we estimate the direction and magnitude of the resultant vector? That’s what is going on in our heads, isn’t it? Don’t we wish to diminish the angle between ground and the slope of the rode leading to the bow? It just so happens that angle is one of three, i.e., of a “tri”, that define the one we are most interested in.
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But ve must include zee catenary uf ze rode if ve vish to understand ze fool depth of ze problem. No ?
How precise do you want the answer? Direction is irrelevant because it changes all the time.
For students and most of us the KISS principle works in application. 5:1 scope, when bar tight the boat will be about 1.5 times the length of rode let out from the anchors position if raised to the surface. This will give you the radius of the swing circle which is the only time one needs to be concerned the hypotenuse of the right triangle. Thus if anchoring in 10 feet of water, put out 50 feet of rode, the swing circle will have a radius of about 75 feet.
If you make this as complicated as you seem wont to do, you will turn off more potential sailors than encourage them. Our sport doesn't need that.
I’m not talking to students right now. I asking the experts about a technical interpretation of “scope”, a topic often covered in this forum. We insert a vertical chain into the concept of scope with its (the scope’s) function being one of holding power at the anchor. I suppose zero scope means not anchored. Scope of 1:1 means the chain is vertical with no holding power. More than that it might be laying on the bottom in a heap. So, the instruction begins at a scope of, say, 2:1; 2x the length of rode over bottom depth. KISS me! I shouldn’t explain why scope of 5:1 has greater holding power b/c I might have to use a “math” term, the angle? Maybe I should say “the angle of the dangle” to get them listen for 30-50 seconds.
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The best teachers are those who can take complex ideas and present them in understandable ways using common language. Let the engineers and mathematicians argue about the language and the formulas, ordinary sailors don't want to do that and frankly most of us don't have the facility with complex mathematics to even try.
If you're not sure how to present this in layman's language then find a good teacher to help you develop a lesson plan. And if you use a good Socratic approach, even the weakest students will learn.
If you're not sure how to present this in layman's language then find a good teacher to help you develop a lesson plan. And if you use a good Socratic approach, even the weakest students will learn.
Would get the jock's attention for sure.
Back when I was teaching as a fill in for a number of years, I would have posted this picture and said "think about it ya little fu _ _ ers" and you'll see why scope matters.
While a little course for a public school setting, Ralph is on the right track.
Start with a simple question, "You've found a nice cove to stop and have lunch in. How do you keep from drifting out to sea or drifting on to the rocks?" Some brilliant students will answer, "drop an anchor, of course." Great answer, now how does the anchor keep the boat from drifting. Collect a bunch of answers, some will be close, some will be way off base. Build on that, with a very low tech explanation that it is combination of weight and anchor shape. Going through step by step, adding a little guidance and informative illustrations like Ralphs. Eventually you will get to the part about scope, all they need to know is horizontal pull is more important than vertical pull and to get the horizontal pull you need a scope of 5:1. And if someone wants to know why, tell them the math is beyond the scope of this course and lesson and practical experience by thousands of sailors have found this to be a good rule of thumb. Limited math, no fancy language, no right angles and trigonometric functions or calculus.
KG,
Maine Sail did a wonderful explanation of this years ago, I don't know if it's still up on his marinehowto.com website. He took long pieces of string and stretched them out like in Ralph's diagram, and his point was that beyond 5:1 or 7:1 one was NOT gaining much in the angle between the chain and the anchor / bottom.
But recognize that this is a completely different issue than scope, although directly related, even proportionally mathematically.
Maine Sail did a wonderful explanation of this years ago, I don't know if it's still up on his marinehowto.com website. He took long pieces of string and stretched them out like in Ralph's diagram, and his point was that beyond 5:1 or 7:1 one was NOT gaining much in the angle between the chain and the anchor / bottom.
But recognize that this is a completely different issue than scope, although directly related, even proportionally mathematically.
In questions of definition, the first step is always to consult a dictionary. If it's nautical, the OED is the base reference. In technical committees, you always look to the dictionary first, only creating a different definition if no suitable definition exists or if it is in conflict to what you mean. The OED definition is suitable and includes historical use references.
I also really like Ralph's image!
Scope:
Note that the distance along the bottom does not figure in, only the length of the cable. Therefore 1:1 is straight up and down. Going farther down the rabbit hole (although there is no reason to), if 1:1 meant a 45 degree angle, then straight up and down would be zero scope (0:1)?
11. Nautical. The length of cable at which a ship rides when at anchor. Also riding-scope.
1841
1868
1885
1893
I also really like Ralph's image!
Scope:
Note that the distance along the bottom does not figure in, only the length of the cable. Therefore 1:1 is straight up and down. Going farther down the rabbit hole (although there is no reason to), if 1:1 meant a 45 degree angle, then straight up and down would be zero scope (0:1)?
11. Nautical. The length of cable at which a ship rides when at anchor. Also riding-scope.
- 1697
W. Dampier, New Voyage around World xv. 437
G. Shelvocke, Voyage round World vii. 265
1841
R. H. Dana, Seaman's Manual 84
1868
Nat. Encyclopedia vol. I. 691
1885
Law Times Reports vol. 53 53/2
1893
W. C. Russell, Ida Noble 98
Lots of answers here - some correct and some, less so. As some have noted, 1:1 scope means you are in 20 feet of water and let out 20 feet of rode. In other words, the anchor is hanging straight down until it just touches the bottom. Contrary to some answers, triangles do figure into this discussion. It is a simple matter of Pythagorean theorem: a2 + b2 = c2 (a squared + b squared = c squared). In this case, "a" is the depth, and "c" is the rode paid out. If we solve for "b", we know what the maximum swing could be.
Now, in the case of 1:1 scope the math is pretty simple:
a = 1
c = 1
b = ?
... therefore ...
a2 = 1
c2 = 1
... therefore ...
1 + b2 = 1
... therefore ...
b2 = 0 and b 0
Therefore, with a 1:1 scope, there appears to be no swing. This is actually illustrative and not just pointless math. This is because, if it were possible to hang an anchor off of your bow and have it hold while your boat swings in a full circle, we know that the radius of the circle is not zero. It is the length of your boat.
This is important because it is often overlooked when we start looking at more practical scopes such as 5:1 or more. My boat is a 32-footer. So, no matter what I do, I will swing through at least a 64-foot circle.
At a 5:1 scope (pretty much the minimum for most cases) in ... say ... 20 feet of depth, let's repeat the math:
a = 20
c = 100
b = ?
... so ...
a2 = 400
c2 = 10000
... so ...
400 + b2 = 10000
b2 = 9600
b = 98 (rounded)
This makes it seem that I would swing through a circle with a radius of 98 feet (196 ft diameter). But, I actually would swing through 130-ft radius or a circle with a 260-ft diameter. That is a significant difference but one that is sometimes ignored.
Now, for me, the difference is pretty academic because I am not going to drop an anchor within 200-300 feet of anything I don't want my boat to touch. But, if you cut things a bit closer, you should not ignore the length of the boat in making those calculations.
As a tangent, it boggles my mind how close people anchor to each other. Many people place a lot of confidence in the mistaken notion that all boats will swing in harmony and unison. To my mind, no part of one boat's circle should overlap any part of another boat's circle. This is because, around here, currents can be going several knots one direction, with winds blowing in a different direction. And, as we move into shallow waters close to shore, we see currents doing one thing in one place, and something completely different just a few feet away. When I see a power boat drop anchor a few feet from a sailboat, it just about defies comprehension.
I know that many places find this sort of packing "necessary" and it is certainly the norm at some locations. And, in fact, if currents are not a factor and winds are pretty consistent, there isn't much risk to it. But, around here, it is not uncommon to find some boats facing one way and other boats facing a different way (possibly 180 degrees), with varying bearings from their anchors. I truly cannot comprehend why there aren't more issues. Or, maybe there are and I just don't see them because I just don't allow myself to get caught up in that.
But, I swear, if one more powerboater drops an anchor within swinging distance of a mooring buoy, I am going to lose my mind. (Yes, for some reason, it is always a powerboater.)
Now, in the case of 1:1 scope the math is pretty simple:
a = 1
c = 1
b = ?
... therefore ...
a2 = 1
c2 = 1
... therefore ...
1 + b2 = 1
... therefore ...
b2 = 0 and b 0
Therefore, with a 1:1 scope, there appears to be no swing. This is actually illustrative and not just pointless math. This is because, if it were possible to hang an anchor off of your bow and have it hold while your boat swings in a full circle, we know that the radius of the circle is not zero. It is the length of your boat.
This is important because it is often overlooked when we start looking at more practical scopes such as 5:1 or more. My boat is a 32-footer. So, no matter what I do, I will swing through at least a 64-foot circle.
At a 5:1 scope (pretty much the minimum for most cases) in ... say ... 20 feet of depth, let's repeat the math:
a = 20
c = 100
b = ?
... so ...
a2 = 400
c2 = 10000
... so ...
400 + b2 = 10000
b2 = 9600
b = 98 (rounded)
This makes it seem that I would swing through a circle with a radius of 98 feet (196 ft diameter). But, I actually would swing through 130-ft radius or a circle with a 260-ft diameter. That is a significant difference but one that is sometimes ignored.
Now, for me, the difference is pretty academic because I am not going to drop an anchor within 200-300 feet of anything I don't want my boat to touch. But, if you cut things a bit closer, you should not ignore the length of the boat in making those calculations.
As a tangent, it boggles my mind how close people anchor to each other. Many people place a lot of confidence in the mistaken notion that all boats will swing in harmony and unison. To my mind, no part of one boat's circle should overlap any part of another boat's circle. This is because, around here, currents can be going several knots one direction, with winds blowing in a different direction. And, as we move into shallow waters close to shore, we see currents doing one thing in one place, and something completely different just a few feet away. When I see a power boat drop anchor a few feet from a sailboat, it just about defies comprehension.
I know that many places find this sort of packing "necessary" and it is certainly the norm at some locations. And, in fact, if currents are not a factor and winds are pretty consistent, there isn't much risk to it. But, around here, it is not uncommon to find some boats facing one way and other boats facing a different way (possibly 180 degrees), with varying bearings from their anchors. I truly cannot comprehend why there aren't more issues. Or, maybe there are and I just don't see them because I just don't allow myself to get caught up in that.
But, I swear, if one more powerboater drops an anchor within swinging distance of a mooring buoy, I am going to lose my mind. (Yes, for some reason, it is always a powerboater.)
My experience was not power boaters, but catamarans - rentals. But then, how they used them seems powerboat might apply....
dj
@thinwater do you have a link or complete reference to the OED? I've not heard of it. I'd love to get a copy or link.
dj
Oh, i have that - never realized it was applicable for nautical terms... Good to know.
dj
I entered Clifton harbor and it was chock a block. So full the big charter cats were 2 and 3 to a mooring on New Year's Eve day. After quite a few runs through the harbor looking for a spot to anchor and clear customs. I finally found d a spot to park Skipping Stone (53') and we dropped the anchor. For some reason the chain picked that moment to foul itself (it had never done so before) and there we were in 50' of water with about 70' of chain out and surrounded with million dollar mobile hotel rooms, in about 2q0 knots of wind. Nik hurried below to clear the problem and I stood dumbfounded on the foredeck looking around, wondering how much damage we were going to do, before heading for the fenders secured around the base of the mast. As I began to move aft I was nearly knocked off my feet as that reliable old Rocna bit into Union Island. &0' feet of chain in 50' of water and we were anchored it seemed. Whew...1.5:1. Nik came up and we continued to let out as much scope as I thought we'd need for an hour's stay.
Quite often the Rocna would be so well set that I'd bring in the chain until we were 1:1 and have to wait 15" or so for it to work its way free. So it might be possible to hang on less than 3:1, if one set the anchor first and then shortened up, though I doubt I could relax @ less than 3:1, my normal scope.
Quite often the Rocna would be so well set that I'd bring in the chain until we were 1:1 and have to wait 15" or so for it to work its way free. So it might be possible to hang on less than 3:1, if one set the anchor first and then shortened up, though I doubt I could relax @ less than 3:1, my normal scope.
You're both wrong and right.
Right about the math.
Wrong about the fact that the question was about scope, NOT swing.
Good analysis, thanks.
Swing is directly related to scope. It is one of the two main factors in determining the appropriate scope for a given scenario. (The other obvious one being anchor effectiveness.) Granted, it is a bit of a tangent to the original 1:1 question, but the only answer that isn't a tangent to the original question would be, "Yes".