Miscellaneous                                                                    
Anchor Chain Snubber Design
1998

Shortly, I will be building snubbers for the all-chain rode of my soon to arrive (“end of
Dec”) Krogen 39, so I started looking into design specifications.  Finding no
specifications, I then started thinking about design criteria and analysis.  I don’t
remember ever reading anything anywhere about the specifics of snubber design or
analysis, (has anyone else on the list?), so I started down that road.  

STRETCH
First off, I found out that premium three-stranded nylon New England Ropes line
stretches 16% at its safe working load, SWL, and the SWL is 15% of its average
breaking strength, ABS.  The latter is rather remarkable; I didn’t realize that it was so
low. Anyway, the first question is, How much stretch do we need at the SWL limit?  I
have no idea but consider the following table:  (L = S / 0.16)  
Stretch (ft) at
the SWL
Length (ft) of
Line Needed
1
6.25
2
12.50
3
18.75
4
25.00
5
31.25
6
37.50
7
43.75
8
50.00
10
62.50
15
93.75
20
125.00
30
187.50
40
250.00
4 feet and 8 feet of stretch jump out at me based on the nice round number of the length
of line needed. It tickles my fancy. I think I will go with 4 feet of stretch with 25 feet of
line.  That feels right to me.  What do you think?  
(ps: If the SWL is exceeded, the line length will be permanently increased and its
stretchability will be decreased.)

LINE SIZE
Now, what size line do we need?  Well that depends on the wind strength.  If you want 4
feet of stretch at the high end of each line's wind range, then you have to have a
number of snubber lines in order to cover the entire set of wind ranges.   This will
become more clear later.  Consider the next table:
Line Size (in)
ABS (#)
SWL (#)
Wind strength (kn) @ SWL
1/4
2000
300
15.0
5/16
3000
450
18.4
3/8
4400
660
22.4
7/16
5900
885
25.8
1/2
7500
1125
29.0
9/16
9400
1410
32.5
5/8
12200
1830
37.0
3/4
16700
2504
43.3
1
29400
4410
57.5
  32000
4800
60.0
  50000
7500
75.0
The wind strengths needed to generate the SWL-limit forces were calculated using V =
(SWL/1.333)^0.5 which was derived from the ABYC anchor load tables for a 40 foot
powerboat.  Yes, I know the ABYC numbers are conservative, but so am I.

Son of a gun, that’s a lot of possible snubbers. I wonder what my all chain catenary will
do for me; maybe it can eliminate some of the smaller snubbers.  Then probably 3/4
(43kn), 9/16 (32 kn.), and 7/16 (26 kn.) will do it.  This choice results in a loss of 2 (an
arbitrary choice) of the 4 feet of desired stretch, at the low end of the usable wind range
of the snubber.  For example, if 3/4" line were used in 43.3 kn. of wind, the snubber
would stretch out the full 4 feet.  However, if the wind were to drop to 32.5 kn, it would
stretch only 2 feet.  In order to have 4 feet of stretch in a 32.5 knot wind, the snubber
would have to be 9/16".   

I could use 2 ea. 3/4’s for 60 knots and 3 ea. for 75 knots.  Or maybe just one 3/4 as it
has a breaking strength much higher than the wind forces.  That way if I ever encounter
a 60 or more knot wind, I could use the 3/4 snubber and then throw it away afterwards
and get a new one.

One thing you should note is that in order to ensure that the SWL of the snubber is not
exceeded, the length of the stretch has to be limited.  This can be done by adjusting the
length of the chain, from the chain hook to the bow, so that it is not longer than 29 feet,
ie the 25’ length of the snubber plus the allowed 4 feet of stretch.  However, limiting the
stretch defeats the purpose of the snubber.

CHAIN
I determined that the boat will move horizontally X feet from the position it had with no
wind nor current, i.e. from where the chain was hanging straight down, to the position it
will have when the chain is bar tight.  The equation is:

X = ((S^2 - 1)^.5 - (S-1))*(D+B)
S is the scope as defined by:
Length of chain L = S*(D+B)
D = depth of water
B is the height of the bow (about 7’ for my K39).  

For example, for a 7:1 scope in 30’ of water the boat will move 34’, almost a boat length.

Next comes the catenary.  It has a little more math to it, but what the heck, if you are still
reading this then I suppose you want the math.  So here it is such as it is.  

Being a little lazy, I made a simplifying assumption, namely that the weight of the chain
will be a point mass in the middle of the span, in order to make the math easier.  I then
took the sum of the X axis components and the sum of the Y axis forces and ended up
with two equations in five unknowns.  From this I solved for T1, the force acting on the
bow.  The results are as follows:

T1 = W/(sin b - (cos b * tan a))
W = the weight of the chain
W = w*L = w*S*(D+B)
w = the unit weight of the chain; 1.5 #/ft for 3/8 hi test
S = L/(D + B) = scope
L, D, and B as described previously
b = phi + d
a = phi - d
phi = the angle of the chain to the horizontal when bar tight
phi = arc sin 1/S
d = the number of degrees the middle of the chain is from being bar tight.
F = T1 cos b = the horizontal force of the wind and waves on the boat.
kn. = the wind strength that produces F.

Since there are 5 unknowns, I selected the value of 3 and solved for the other two.  I
selected the depth to be 15 feet and the scope to be 5:1, a somewhat typical situation.
Then I selected several values of d and solved for the corresponding values of T1, the
force on the bow.  The results are as follows:
d
T1
F
kn
2
2346
2281
40
4
1175
1132
29
6
740
753
23
8
591
563
20
10
442
448
18
11.5
422
389
17
Drawing conclusions from this one condition of depth and scope, and from equations that
were derived from a simplified model, is fraught with dangers but I am going to do it
anyway.  Its either that or 4 more tables to define the extremes: shallow water and short
scope, shallow water and long scope, deep water and short scope, and deep water and
long scope.  Or worse yet, ditch the assumption, redo the analysis and then do the 4
extreme conditions.  So here goes with conclusion leaping.

It looks like the chain catenary will provide adequate snubbing for my boat in winds up to
about 20 knots.  After that the forces needed to straighten the chain any more get
progressively higher in a hurry, i.e. the boat has moved back almost all the way at 20
knots.  This can be seen by plotting the data of the above table.  I would be greatly
interested in hearing from anyone who has had contrary experiences with similar
hardware and conditions.

SUMMARY AND CONCLUSIONS
1. Stretch is a function of line length, line size and the force applied. The amount of
stretch required to do a good job of snubbing is the big gaping hole in this analysis.  But
you can choose length based on experience and what feels right.  I will go with 4 feet of
stretch.  Maybe more is needed for the higher wind ranges, I don’t know.  Does anyone
else have a handle on this?
2. One snubber does not fit all.  Three or more snubbers are needed.  I will use 1/2" line
for (expected) gusts of wind from 15 to 29 knots, 5/8” to 37 kn, 3/4"  to 43 kn, and two
3/4" lines for over 43 kn gusts.
3. If the SWL is not to be exceeded, then the amount of stretch needs to be physically
restrained by a loop of chain of the appropriate length.  
4. I think that if the expected wind is higher than 43 kn., I will use two 3/4 inch snubbers
and leave extra length in the chain of the snubber loop, ie not let it bottom out.
5. I think I will also use rubber snubbers like Falcon Line-Master Compensators (p574 of
the West Marine catalog).  This is intended to enhance the snubbing effect in the lower
end of the snubber’s wind range.
6. A boat will move back about one boat length max when all of the slack of the chain is
taken out by wind, current, or wave forces.
7. The chain alone should provide sufficient snubbing in winds up to 20 kn., if you have a
K39 and 3/8” high test chain or the equal.  (Experience has shown that 15 to 18 knots is
a better number.)
8. If you need more snubbing in winds less than 20 kn., let out more chain.


p.s.:  Experience has shown that I can use the 5/8" line over 95% of the time, from 15 to
37 knots of wind.  And I only need to use about 6 to 10 feet of the line.  The rest I use to
secure the loose loop of chain so it won't rub against the boat.  However, if I ever have to
anchor off of a lee shore in a blow, I will use the full 25 feet of the snubber.  NK  1-27-07
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