Conference unifix::sailing

I have solved (correctly I hope) the equations that give the tension in 
a jackline for a given sideways load. The tension depends on:

  the distance between the jackline attachment points

  the elasticity of the jackline

  and of course the load.

The less elastic the jackline, the higher the tension in the jackline 
for a given load. The solution appears to be nonanalytic due to the 
elasticity of the jackline and must be calculated numerically (ie, 
guessing at the solution). I'm still verifying the correctness of my 
solution and the computer program that calculates the tension. It 
appears that the tension in a 60" long 3/16" wire jackline can exceed 
3000 pounds for a 700 pound load. (Again, the typical breaking strength 
of new 3/16" wire lifeline fittings is about 2200 pounds.) It should of 
course be noted that the loads are shock loads which are, I think, more 
likely to cause failure than a slowly applied load. Also, the lower 
jackline tension with a (more) elastic jackline argues in favor of a 
rope jackline.

Once I get the solution into a neat form, I'll post it here.

Alan

    Here is another possible approach to solving the problem, using
    vector diagrams.
    
    I can't seem to draw one here with the angle that I'd like so try
    it on paper.  Imagine a jackline stretched between two points A
    and B.  Apply a force to AB in the middle, called D, in the direction
    C which is perpendicular to AB.  Now there is a triangle ACB, with
    the angle ACB obtuse.  Now for some vectors.  At the point A draw a 
    vector towards B and then a second vertical vector from A and parallel
    to DC, AE.  The contention is that AE and the equivalent at BE'
    when added equal the force at DC.
    
    So, the result is a formula for the force that must be applied to
    the jackline to break it. I use a couple of hypothetical angles

    BAC = 30 degrees : sin 30 = (1/2 DC)/4700 or sin(30)*4700*2 = DC
    	where 4700 = breaking strength of 3/16 wire = 9287 pounds
    
    BAC = 45 degrees : sin 44 = (1/2 DC)/4700 = 7998 pounds
    
    It seems that the steeper the angle the less force need be applied
    to break the line.  I believe that rope, with a greater capability
    to stretch, will therefore break sooner and rope doesn't provide
    the equivalent breaking strength per diameter in the first place.
    
    I do believe that the stretchiness of rope will be better at absorbing
    the shock and thus could possibly prevent serious injury.  But I
    can't imagine surviving the force required to break the jackline
    in the first place so what does it really matter that we solve this
    at all????
    

re .2:

You have chosen the one case that is easy to solve analytically. 
However, your conclusions are wrong. The force W required to break the 
jackline (perpendicular load applied at the center) is:

	W = 2*B*sin(A)

where B is the breaking strength of the jackline and A is the angle
between the line connecting the jackline attachment points and the
stretched jackline. As the elasticity of the jackline decreases, A
decreases, and the force required to break the jackline decreases. If
the jackline had zero elasticity, zero force would break it. 

Analytically, the tension in the jackline is (for a perpendicular load
at applied at the center) 

	T = W*(1+F*T)/2*SQRT((1+F*T)*(1+F*T)-1)

where W is the load applied (in pounds), T is the jackline tension (in 
pounds), and F is the elasticity of the jackline. If the length of the
jackline is L with no tension, its length is L*(1+F*T) with tension. For
3/16" wire, F is about .01/940 (ie, it stretches about 1% with a load
equal to 20% of its breaking strength -- roughly). Notice that the above
equation has the jackline tension on both sides, which makes solving it
messy. However, for a 700 pound load, the tension in the jackline is
1809 pounds. For a jackline twice as elastic (2% strecth at a load of
20% of its breaking strength -- ie, dacron rope), the tension in the
jackline decreases to 1444 pounds (assuming I got it right). 

The usual safety factor for standing rigging is that the rigging load 
should not exceed 40% of the breaking strength of the rigging 
components. Using this criterion for a 3/16" wire jackline, the breaking 
strength of the wire should be 1809/0.40 = 4522 pounds, which is very 
close to the actual breaking strength of 4700 pounds. For a 1000 pound 
load (which is possible) the 3/16" wire will certainly break. 

Alan (MS Physics, University of Pennsylvania)

The BASIC program below can be used to calculate the tensions in a 
jackline for a perpendicular load applied anywhere along a jackline. The 
results are interesting. 

First, the maximum tension in a jackline (or lifeline for that matter)
occurs when the load is applied midway between the jackline attachment
points (not intuitively obvious to me). 

Second, the maximum tension is independent of the length of the 
jackline (obvious after seeing the results).

Third, the maximum tension increases significantly and rapidly as the
elasticity of the jackline decreases (see table below). 

Fourth, the maximum deflection of the jackline under load increases with 
increasing jackline elasticity (to be expected). The greater the 
deflection of the jackline, the lower the shock load on the person going 
over the side. I think that this reduction in shock load is very 
important. 

Fifth, the maximum tension decreases more slowly than decreasing load 
(ie, halving the load less than halves the maximum tension). 

In the table below, I  assumed a 700 pound load and the following 
elasticities for various jacklines:

The elasticity of 3/16" 1x19 wire is .0025/1175 and the elasticity of 
1/4" 1x19 wire is .0025/2050 (derived from data in a Navtec brochure). 

The elasticity of 3/8" New England Ropes Sta_Set dacron rope is .02/490 
and the elasticity of 1/2" New England Ropes Sta-Set dacron rope is 
.02/850 (derived from data in the current West Marine catalog).

The elasticity of 1/2" New England Ropes nylon braid is .065/1245 and the 
elasticity of 1/2" New England Ropes three-strand nylon is .165/1125 
(derived from data in the current West Marine catalog).

700 pound load        maximum tension   maximum tension        maximum 
                      in jackline       divided by breaking    deflection
                      (pounds)          strength (%)           (inches)

3/16" 1x19 wire         3074               63                    3.4
1/4" 1x19 wire          3696               43                    2.9
3/8" dacron braid       1172               24                    9.4
1/2" dacron braid       1398               16                    7.8
1/2" nylon braid        1084               13                   10.2
1/2" 3-strand nylon      789               11                   14.8

Note that reducing the load to 350 pounds (certainly a reasonable load
for a moderate size person falling overboard) reduces the maximum
tension in a 3/16" 1x19 wire jackline to 1932 pounds (41% of breaking
strength). As I have said before, the standard hand crimped lifeline
fittings have a breaking strength of only 2200 pounds (when new). These
calculations lead me to believe that a 3/16" 1/19 wire jackline, even
with standing rigging fittings, is too weak to be safe. 

Note that the elastic limit of 1x19 wire is about 40% of its breaking 
strength. That is, if the wire is loaded beyond its elastic limit, it is 
permanently deformed. I chose a 700 pound load as that is somewhat 
higher than the load actually measured when a test subject fell 
overboard at 11 knots (surfing downwind in a gale). Moreover, Navy 
safety harnesses must include a shock absorbering mechanism when the 
load exceeds 700 pounds.

Please make your own assumptions and decisions about what you think is 
safe. The opinions stated here are my own. Your conclusions may vary. I 
of course welcome comments, questions, and constructive criticism 
(including showing that I am wrong). 

Alan

The Program:

100 INPUT "DISTANCE BETWEEN ATTACHMENT POINTS"; S
110 ! PERPENDICULAR LOAD
120 INPUT "LOAD"; W
130 ! DISTANCE FROM ATTACHMENT POINT LOAD APPLIED
140 INPUT "DISTANCE FROM ATTACHMENT POINT LOAD APPLIED"; S10
150 S20 = S - S10
160 PRINT

170 ! ELASTICITY 3/16" 1X19 WIRE
180 F = .0025/1175
190 ! ELASTICITY 1/4" 1/19 WIRE
200 ! F = .0025/2050
210 ! ELASTICITY 3/8" NE ROPES STA-SET DACRON ROPE 2% ELONGATION AT A
220 ! LOAD OF 10% OF THE BREAKING STRENGTH
230 ! F = .02/490
240 ! ELASTICITY 1/2" DACRON ROPE 2% AT 10% BREAKING STRENGTH
250 ! F = .02/850
260 ! ELASTICITY 1/2" NYLON BRAID 6.5% AT 15% BREAKING STRENGTH
270 ! F = .065/1245
280 ! ELASTICITY 1/2" THREE STRAND NYLON 16.5% AT 15% BREAKING STRENGTH
290 ! F = .165/1125
300 ! THE SOLUTION HAS BEEN FOUND WHEN THE ASSUMED TENSION IN THE
310 ! JACKLINE IS SUCH THAT THE SUM OF THE VERTICAL LOADS (CALCULATED FROM
320 ! ELASTICITY AND STATIC EQUILIBRIUM) EQUAL THE APPLIED LOAD

330 INPUT "ASSUMED TENSION IN JACKLINE"; T1
340 D=1
350 S1 = S10*(1+F*T1)
360 L1 = SQRT(S1*S1-D*D)
370 L2 = S - L1
380 S2 = SQRT(L2*L2+D*D)
390 T2E = ((S2/S20)-1)/F
400 T2S = (S2*W*L1)/(D*S)
410 V1 = D*T1/S1
420 V2E = D*T2E/S2
430 V2S = D*T2S/S2
440 D = D+.001
450 IF T2E < T2S THEN GOTO 350

460 ! T2E AND T2S MUST BE EQUAL
470 PRINT "TENSION COMPUTED FROM ELASTICITY OF JACKLINE"; T2E
480 PRINT "TENSION COMPUTED FROM STATIC EQUILIBRIUM    "; T2S

490 ! VERTICAL LOADS MUST EQUAL W
500 PRINT "VERTICAL LOADS FROM ELASTICITY CALCULATON   "; V1+V2E
510 PRINT "VERTICAL LOADS FROM STATIC EQUILIBRIUM      "; V1+V2S

520 PRINT "DEFLECTION OF JACKLINE                      "; D
530 PRINT

540 GOTO 330

    Your analysis makes sense to me and it stimulated some random
    recollections of data.  Unfortunately, I couldn't find the references,
    so here goes with what might be approximately correct.
    
    I think the Fastnet inquiry resulted in changes to harness
    requirements,i.e. that they meet a national standard & I think that
    they are required to withstand forces in the thousands of pounds,
    eg 2500 lbs.  Therefore, why make the jacklines the weakest link?
    Seems to me that a design goal might be 4-5000 lb or a safety factor
    of two.
    
    As a point of reference, climbing ropes are designed to absorb the
    energy of a fall.  Specs I have, for ropes to contain a 5 meter
    fall, show ropes with a breaking strength of 2200 kg (about 4500
    lbs) and an "impact force" of 880 kp.  (I don't know what kp's are.)
    
    So, back to Physics 101.  What is the force generated in arresting
    a fall?  Some playing with formulas yields:
    
             F = w*h/x  where  w is weight in lbs
                               h is fall height in feet
                               x is arresting distance in feet.
    
    assuming constant acceleration (ok for a fall = g), and constant
    decceleration (which is obviously not true, since the initial
    deflection of the jackline requires zero force).
    
    How far can you fall on a sailboat?  1. at least the length of the
    harness tether eg 6 ft.  2. maybe twice the tether length, if for
    instance one is tied to the mast and falls high side to low side.
    Of course the tether helps if made of nylon (aren't they all?) since
    it will stretch.  If attached to a padeye, only the tether does
    the work, so maybe we get 6" of stretch, so F for a 200 lb body
    falling 8 ft is 3200 lb!  No wonder so many harnesses and attachment
    points failed in the Fastnet disaster. 
    
    Assuming Alan's calculations are correct (the analysis makes sense
    to me) a wire jackline looks like a bad way to go because it creates
    unneccesarily high forces, even high enough to self destruct.  I've
    always used 7/16 or 1/2 inch nylon tied to mooring cleats forward
    and aft, and think I'll stay with this approach.
    
    Thanks Alan for helping quantify once again what seat of the pants
    felt right.  And I also make no recommendations as to how others
    should rig their boats.
    

    re .-1  I think I'll be renewing my recently purchased safety
    harnesses! Even though they are to some standard (BSIxxxx), I know
    they are only supposed to withstand some 2000 lbs - which seemed
    perfectly adequate to me.
    
    Thinking further, there is an additional force induced if you actually
    go overboard and hit the water - say your yacht is doing 8 knots
    and you fall just in time to hit a nice big wave! I know some decent
    waves that actually stop my boat dead in the water because I hit
    one the other night at the wrong angle.  Anyone got any further
    inputs on the attachment points? My lines run fore and aft between
    the base of the pushpit aft and a U-bolt with backing plate for'ard
    of the anchor locker. I attached a large bag of chain to the forward
    point and threw it overboard (when the boat was on dry land) and
    it held OK, but it was hardly scientific!
    
    Hints?	Brian not_sure_he's_as_safe_as_he_thought_he_was!!

    
      Excellant articles in the May issue of Sailing World on the Sydney
    Hobart race and the captain who got washed off of MEM, a J35. His jack
    line parted. He spent 4.5 hours in the ocean in a major storm before 
    they found him. Excellant reading. Makes you appreciate the
    conservative nature of the calcualations above.
    
       He also mentioned the 3 crew next to him were ok. Above, the weight
    is based on 1 person and not the crew though the shock is unlikely to
    be exactly at the same time.
    
     John
    
      
    ps  Attaching new lifelines to my boat yesterday, I found one of the 
    previous owners had used cheap cotter pins rather than stainless Steel
    ones for the turnbuckles. the ends popped right off. If you didn't put
    them on, you may wish to pull that rigging tape and have a peek.

I am in the early stages of installing jacklines on my new pride and joy.  So I
thought I would open the discussion on various approaches to jacklines and 
safety harnesses.

As rough physical limitation, I am not too worried about the strength of 
material.  From rock climbing I learned that the human body can handle
something like  2500 lbs, so 6,000 tinsile in webbing is nice but hardly
critical.

The big impetus comes in the form of a 2 1/2 year old daughter.  In a Womanship
sailing course that Amy recently completed, the suggestion was to basically have
Jessica on a harness.  This would b=give her freedom of the deck and allow us
to briefly be distracted by other things (eg, tacking, sail change).  Of course
it is not a bad thing for us either.

The bottom line is that I am going to purchase three harnesses, one for each of
us.  I no longer have the copy of the Practical Sailor which reviewed harnesses,
but I recall Lirakis being well thought of.  We will purchase the harnesses
through probably Boat US, E&B, or West Marine.  Comments on other harnesses are
welcome.  I am especially interested in brand name remarks and any feed back on
which harnesses work best for rug rats.  Since Jessica will be wearing hers
alot, and Amy and I often, comfort counts.  This implies combination harness and
floatation is probably out.  How important is the wider webbing for comfort, and
where?  

Two differnt questions on jacklines.  I am currently thinking of using flat 
webbing.  Unlike line, cable, or tubluar webbing, it is not as likely to roll
underfoot.  I want it to be a good day night contrast color to a teak deck. 
Flouresent colors may wash out to an unaccpetable grey in poor light (eg orange
and teak have similar grey scales).  The two best choise currently appear to 
be black/dark blue or white.  

The second issue is mounting locations.  I have an anchor bit in the foredeck. 
This is under no use when sailing.  It looks like a good choice for the forward
anchor.  There are some left over anchors for the lifelines at the stern.  This
would bring the jacklines further aft than needed, but who cares?  The life
lines have a differnt anchor located at the chain plates for the mizen.  The
basic question is, should I run the differntly (ie. along the grab rail of the
trunk to just the mast ect.)?

Doug Claflin

    Doug,
    
    We purchased the SOS combination harness and automatically inflating
    jackets and use them with flat webbing jacklines like you are
    describing. We are very pleased with the results. We run ours from the
    boom gallows (which is at the forward end of our cockpit) to the
    bowsprit. They lay on the cabintop, not the deck. We actually have two 
    sets of Jacklines. One Yellow for us and one dark green that we connect 
    our dogs to. They wore their harnesses too when offshore. Two sets
    allowed us to go forward, regardless where the dogs were located on
    their jacklines. They were always on their lines when offshore if they
    were out of the cockpit.
    
    We purchased the webbing at an Army/Navy surplus store. The webbing was
    new and at a bargain price. We set them up where they wrap around the
    bowsprit and use caribiners at the aft end connected to the boom
    gallows. This arrangement works well - allows us to walk on the
    jacklines should we need to without slipping and had sufficient
    strength to hold us when required.
    
    We chose to purchase the inflatable vest/harness combo for the safety
    of having them (i.e. somehow getting washed overboard due to stupidity)
    and their comfort. They are amazingly comfortable and thus far haven't
    accidently gone off, even when soaked by rain and waves. We did jump in
    the water with one to test it. It took between 2-3 seconds max to go
    off and inflate. 
    
    Hope this helps.
    Regards,
    Robert

re .8:

We use 1/2" low stretch dacron rope for jacklines and have in several 
years not had a problem with it rolling when stepped on, but then our 
jacklines are stretched fairly tight. Besides, in rough weather we crawl 
along the deck, not walk.

I also have three concerns about using flat webbing:

First is the need for sewing at the ends if shackles (or whatever) are
used. Safety harness makers, etc, have the right industrial strength
sewing machines to do the sewing right. Thin thread is quite prone to UV 
degradation. I can do quite good eyesplices myself. 

Second, flat webbing has more surface area than round rope and thus will
be more prone to UV degradation. Flat webbing jacklines should probably
be unrigged when not sailing, which is a bother.

Third, flat webbing is hard to hold onto with your hands. We have a flat 
webbing lead to an overhead trolley wire for our dog. One night the dog 
dashed off abruptly, pulling the thin edge of the webbing along the web 
of Julie's hand between her thumb and forefinger. The resulting gash 
required eight stitches at the local emergency room and several weeks to 
heal (plus an unpleasantly large medical bill soon came in the mail). If
your hand slides along a wet flat webbing jackline, the same thing could
happen. Just another consideration.

We have Switlik safety harnesses and like them. Survival Technology in 
Florida makes good harnesses, too. Many of the ones in the West, etc, 
catalogs aren't too good. 

Alan

re .8

When our son was a toddler, we always had him wear a harness when on deck. We
didn't have jack lines, and we didn't permit him to go forward most of the time.
We clipped him to stanchion bases in the cockpit. If he did go forward, we'd
just move his clip to stanchion bases forward, or to the mast step.

We wear harnesses whenever recovery might be troublesome, e.g. in rough seas or
at night. We don't have jacklines on our current boat, and I consider the need
to manually move the harness clip to be an acceptable risk for coastal cruising.
As mentioned in previous notes, a jackline is itself a hazard, and it is a
hazard at all times, not just in bad weather. Whether the jackline is flat or
round, it has the potential to trip a person walking on deck.

I use the basic cheap $30 harnesses from Boat US. I find them to be quite
comfortable. I've used them on trips to Bermuda where we wore harnesses whenever
we were on one-man watch, and they were just as comfortable as a light jacket.
In my opinion they are well designed for the task. On those trips, we had 1/2"
round jacklines, laying on the deck. They worked OK, and I don't recall any
incidents where they rolled underfoot.

--RS

    
    	While I also have (blue) flat webbing, I mostly concur with Alan.
    The only thing I would count on for fulltime jacklines is steel cable,
    like another (continuous) lifeline. However, the webbing's replaceable
    and the child will grow. All materials can be tripped over, so can
    sheets, vangs, cunninghams, etc. etc.
    
    	As a climber, you already know the best knots for webbing, I'd bet.
    A bit of sailtwine to sieze up the end, and I'd trust it more than
    line.
    
    	Lirakis: a bit overpriced, IMO, but if you're the type that
    believes in absolute quality, go for it. 
    
    	Finally, good for you, making the boat enjoyable for all ages.
    
    	Scott.
    

re .8

We have a system very much like that mentioned, i.e., Lirakis harnesses (adult
and child) and webbing jacklines.  This summer will be the third with the
setup.  The motivation for installing it was our son, who will be 4 this
summer.  When underway, he's either below or in the harness.  (The summer he
turned 2 we also used car seat strapped in the cockpit.  Last year he
consistently opted for the harness over the seat, so we probably won't bother
with it again.)  While we've used this arrangement consistently, it's never
been put to the test (fortunately), so I can't comment from experience, for
example, on how the shock absorption or strength of webbing compares with
other choices.

I choose webbing because I was concerned about rope rolling underfoot.  On our
boat the line lies in a spot which is generally stepped on when moving out of
the cockpit to go forward.  I bought the webbing from REI - sky blue with a
dark tracer on one side.  It's sort of like a small flattened fire hose, i.e.,
there are 2 distinct layers.  It's usually used for climbing harnesses, etc. 
They looked at me a little funny when I bought 60'; I guess their usual sale
is considerably smaller.  The webbing expands when wet, so I found it
difficult to keep it stretched tight.  After a while I just got used to it
being a bit slack.  I've never had a problem tripping over it.

The line runs on each side from an eye on the deck where the running backstays
attach, forward to a shackle through the toerail near the bow.  (Our toerail
is aluminum with periodic holes.)  I agree with Alan's comments about trying
to stitch this stuff myself, so I tied it.  This particular webbing is soft
enough to hold a bowline without coming untied.  (Any comments on a better
knot for webbing?)  We leave the lines installed all season.  I have replaced
them every year because I was concerned about uv exposure, though I've never
seen any observable effects.  (Cutting up the old ones makes lots of nice sail
ties.)  In the cockpit we also have an eye installed specifically for clipping
into (through bolted, etc.).  Hooked on there I can move around most of the
cockpit.

I've found the Lirakis adult harness reasonably comfortable to wear.  Getting
it on can be a little confusing the first few times.  It's pretty easy to put
it on upside down and it's not very comfortable like that.  The child's
harness is adjustable.  (Be careful to get the buckle on correctly after
adjusting it though.)  I expect it to last until our son is large enough to
wear a small adult harness.

/Dan Jackson

    My jacklines are massive things, PVC coated 1/4" 7x19 wire with wichard
    shackles on each end.  I have backed padeyes mounted on the cockpit
    coaming just forward of primary winches and another just behind the bow
    cleat.  The jacklines run from forward in the cockpit, along the inside
    edge of the 12ft genoa track, inside the shrouds and straight up to the
    forward padeye.  Each end is double swaged and left open (not taped)
    for inspectability.
    
    I built these to meet requirements for the single handed trans-Erie
    race in 1990.  I am lucky that the genoa track is mounted within 3-4"
    of the cabin house so that the lines lie in the "gutter" so created
    where you cannot step on them.  Of course, once forward of the mast it
    is a different story.  
    
    But then working on the bow is a different story too.
    

Below is an improved version of the program in an earlier reply (787.4). 
I'm moderately confident that the mathematics/physics/mechanics/whatever 
are correct (but absolutely no guarantees -- use at your own
discretion). The results are both enlightening and sobering -- the
tensions in jacklines and lifelines can be really quite high. With not
unrealistic assumptions about applied loads there is a very small safety
factor (as low as 2) in many designs. It is important to note that the
tension loads in the jackline or lifeline increase quite significantly
as the elasticity of the jackline/lifeline decreases. In other words,
wire seems to be not the best choice. (This another reason we use 1/2"
dacron rope for jacklines instead of wire. The rope tension load is
about half the 1/4" 7x7 wire tension load for the same applied load. The
load on the rope is a much smaller percentage of the rope's breaking
strength than for wire.) 

The results given by this program convinced us to spend almost $900 to
replace our old lifelines with 1/4" 7x7 wire lifelines using standing
rigging turnbuckles and other heavy, strong components. My estimate is 
that the breaking strength of the new system is as much as 6000 pounds 
(though realistically it is likely somewhat less). I'd be surprised if
the breaking strength of the old system was much over 2000 pounds. 
Unfortunately, sometimes safety is expensive.

Another thought: knots significantly reduce the breaking strength of 
rope -- 25 to 50% or more depending on the knot. I'd assume that the
same is true for knotting flat webbing. If I were to use webbing, I'd
have it sewn as in safety harness tethers. 

Alan

================================================================================

100 ! JACKLINE.BAS

    ! Written by Alan Berens, April 1988, extensively modified February 1994

    ! THE SOLUTION HAS BEEN FOUND WHEN THE TENSIONS IN THE JACKLINE
    ! ARE SUCH THAT THE SUM OF THE VERTICAL LOADS (CALCULATED FROM
    ! ELASTICITY AND STATIC EQUILIBRIUM) EQUALS THE APPLIED LOAD.
    ! THE TENSION IN THE JACKLINE TO THE LEFT OF THE APPLIED LOAD IS, IN
    ! GENERAL, NOT THE SAME AS THE TENSION TO THE RIGHT. THEY ARE THE
    ! SAME ONLY WHEN THE LOAD IS APPLIED IN THE CENTER.

    ! SOLUTION IS FOUND BY ASSUMING (GUESSING) A TENSION IN THE JACKLINE
    ! TO THE LEFT OF THE LOAD AND THEN CALCULATING WHAT THE TENSION TO
    ! THE RIGHT MUST BE FOR THE TENSION CALCULATED BY EQUILIBRIUM TO
    ! EQUAL THE TENSION CALCULATED BY ELASTICITY. THIS PROCESS IS
    ! REPEATED UNTIL THE VARIOUS TENSIONS SATISFY THE VARIOUS CRITERIA.

    ! IT IS ASSUMED THAT THE JACKLINE IS STRETCH TAUT BETWEEN TWO POINTS
    ! AND THAT THE LOAD IS APPLIED PERPENDICULAR TO THE JACKLINE. WORST
    ! CASE IS WHEN THE LOAD IS APPLIED MIDWAY BETWEEN THE END POINTS.

    ! THE ANALYSIS AND RESULTS ARE BELIEVED TO BE MODERATELY ACCURATE, 
    ! BUT NO GUARANTEES. USE AT YOUR OWN DISCRETION.

    DECLARE DOUBLE S, S1, S10, S2, S20, W, F, L1, L2, T, T2E, T2S
    DECLARE DOUBLE D, DINC, V2E, V2S, ELASTICITY_DATA(20), B_S, B_S(20)

    ! ELASTICITY OF WIRE FROM BRIAN TOSS, "THE RIGGER'S APPRENTICE",
    ! 2ND EDITION, p72 and p182

    ! ELASTICITY 3/16" 1X19 WIRE
    B_S(1) = 4700
    ELASTICITY_DATA(1) = 0.00260/1175

    ! ELASTICITY 3/16" 7X7 WIRE
    B_S(2) = 3700
    ELASTICITY_DATA(2) = 0.00316/975

    ! ELASTICITY 1/4" 1/19 WIRE
    B_S(3) = 8200
    ELASTICITY_DATA(3) = 0.00256/2050

    ! ELASTICITY 1/4" 7X7 WIRE
    B_S(4) = 6100
    ELASTICITY_DATA(4) = 0.00293/1525

    ! ELASTICITY 3/8" NE ROPES STA-SET DACRON ROPE 2.4% ELONGATION AT A
    ! LOAD OF 15% OF THE BREAKING STRENGTH
    B_S(5) = 4900
    ELASTICITY_DATA(5) = 0.024/(0.15*4900)

    ! ELASTICITY 1/2" NE ROPES STA-SET DACRON ROPE 2.4% ELONGATION AT
    ! 15% OF BREAKING STRENGTH
    B_S(6) = 8500
    ELASTICITY_DATA(6) = 0.024/(0.15*8500)

    ! ELASTICITY 1/2" NE ROPES NYLON BRAID 6.5% ELONGATION AT 15% OF
    ! BREAKING STRENGTH
    B_S(7) = 8300
    ELASTICITY_DATA(7) = 0.065/(0.15*8300)

    ! ELASTICITY 1/2" NE ROPES THREE-STRAND CAPROLAN NYLON
    ! 16.5% ELONGATION AT 15% OF BREAKING STRENGTH
    B_S(8) = 7500
    ELASTICITY_DATA(8) = 0.165/(0.15*7500)

    ! ELASTICITY 7/16" NE ROPES STA-SET X YACHT BRAID
    ! 1.6% ELONGATION AT 15% OF BREAKING STRENGTH
    B_S(9) = 6600
    ELASTICITY_DATA(9) = 0.016/(0.15*6600)

    ! ELASTICITY 3/8" NE ROPES STA-SET K-900
    ! 0.8% ELONGATION AT 15% OF BREAKING STRENGTH
    B_S(10) = 8700
    ELASTICITY_DATA(10) = 0.008/(0.15*8700)

110 PRINT
    PRINT '(1)   3/16" 1x19 WIRE'
    PRINT '(2)   3/16" 7X7 WIRE'
    PRINT '(3)   1/4"  1x19 WIRE'
    PRINT '(4)   1/4"  7X7 WIRE'
    PRINT '(5)   3/8" NE ROPES STA-SET DACRON BRAID ROPE'
    PRINT '(6)   1/2" NE ROPES STA-SET DACRON BRAID ROPE'
    PRINT '(7)   1/2" NYLON BRAID'
    PRINT '(8)   1/2" THREE-STRAND NYLON'
    PRINT '(9)   7/16" NE ROPES STA-SET X YACHT BRAID'
    PRINT '(10)  3/8" NE ROPES STA-SET K-900'
    PRINT '(11)  OTHER'
    PRINT

    INPUT 'JACKLINE TYPE   '; K
    PRINT

    GOTO 120 IF K<11

    INPUT 'BREAKING STRENGTH               '; B_S
    INPUT 'TEST LOAD (% OF BREAK STRENGTH  '; TL
    INPUT '% ELONGATION AT TEST LOAD       '; ETL
    PRINT
    F = (ETL/100)/(TL*B_S/100)
    GOTO 125

120 F = ELASTICITY_DATA(K)
    B_S = B_S(K)

125 INPUT "DISTANCE BETWEEN ATTACHMENT POINTS          "; S

    ! DISTANCE FROM ATTACHMENT POINT LOAD APPLIED

130 INPUT "DISTANCE FROM ATTACHMENT POINT LOAD APPLIED "; S10

    ! PERPENDICULAR LOAD

    INPUT "LOAD                                        "; W
    PRINT

    INC = 100
    D = 0.1
    DINC = 0.1

    S20 = S - S10


140 T1 = W

    ! D IS THE DEFLECTION OF THE JACKLINE UNDER THE APPLIED LOAD

150 S1 = S10*(1+F*T1)
    L1 = SQRT(S1*S1-D*D)
    L2 = S - L1
    S2 = SQRT(L2*L2+D*D)
    T2E = ((S2/S20)-1)/F
    T2S = (S2*W*L1)/(D*S)
    V1 = D*T1/S1
    V2E = D*T2E/S2
    V2S = D*T2S/S2
160 IF T2E < T2S THEN D = D + DINC
    GOTO 150
170 D = D - DINC
    DINC = DINC/10
    IF D <= 0 THEN D = DINC
180 IF DINC > .0001 THEN GOTO 150

190 X = V1+(V2E+V2S)/2
	! PRINT USING "###.#### ####.### ####.###, ####.### ##.### .####", &
        ! INC, T1, T2E, T2S, D, DINC
200 IF X > W THEN GOTO 230
210 T1 = T1+INC
    D = 0.1
    DINC = 0.1
220 GOTO 150

230 T1 = T1-INC
    INC = INC/10
    IF INC < .0001 THEN GOTO 250
240 D = 0.1
    DINC = 0.1
    GOTO 150

    ! T2E AND T2S MUST BE EQUAL

250 PRINT "TENSION LEFT (ASSUMED)                   "; T1; &
	"("; 100*T1/B_S; "% OF BREAK STRENGTH)"
    PRINT "TENSION RIGHT (ELASTICITY)               "; T2E; &
	"("; 100*T2E/B_S; "% OF BREAK STRENGTH)"
    PRINT "TENSION RIGHT (STATIC EQUILIBRIUM)       "; T2S; &
	"("; 100*T2S/B_S; "% OF BREAK STRENGTH)"
    PRINT

    ! VERTICAL LOADS MUST EQUAL W

260 PRINT "VERTICAL LOAD LEFT                       "; V1
    PRINT "VERTICAL LOAD RIGHT (ELASTICITY)         "; V2E
    PRINT "VERTICAL LOAD RIGHT (STATIC EQUILIBRIUM  "; V2S
    PRINT "TOTAL VERTICAL LOAD                      "; V1+(V2E+V2S)/2
    PRINT
    PRINT "DEFLECTION OF JACKLINE                   "; D
    PRINT

270 GOTO 130

    oooppps....meant 7x7 not 7x19, but you knew that..  :>)
    
    IN that case, might not nylon actually be even better?
    
    

re .16:

Well, as in most problems there are tradeoffs. Dacron braid is 
marginally stronger than nylon braid or three-strand nylon, but not 
enough to matter. There is a point of diminishing returns. For 60" 
between the end points and a 600 pound load applied in the middle:

                        deflection   tension    %breaking strength
                         (inches)   (pounds)

3/16" 7x7 wire              3.8       2413          65
1/4" 7x7 wire               3.2       2869          47
1/2" dacron braid           6.8       1354          16
1/2" nylon braid            9.7        975          12
1/2" nylon three-strand    14.0        708           9

Dacron braid comes in white and colors, nylon rope comes in black and white.
The usual 3/16" lifeline fittings break around 2200 pounds (when new).

    
    	The math would boggle the mind, if not the PC! I'd most like to see
    the stresses from a 300lb. man falling over the (flexing) lifelines, 6'
    of line on his harness, an untensioned, semirigid jackline on say, a 40
    footer. Substantially less boat would yaw under his weight. I bet we'd
    put bigger backing plates on the connection points!! Still, logic and
    gut tell me a system designed to take 2000lb. static would cut the
    mustard.
     $900? Eeek. Well worth it, tho, if it was ME being dragged thru the
    water at midnite while alone on watch! I hope construction details from
    the Whitbread dribble down.
    	CheapScott.

From what I have read, I don't think the maximum load is necessarily that of the
man's weight itself. It is much more the loadings generated by the sudden
acceleration of the body to boat speed (having been effectively brought to rest
in the water) aggravated by the drag of the body in the water. This is quite
possibly greater than the force due to the dead weight (unfortunate choice of
phrase!) of the body itself. I say this from the comments I have seen about the
difficulty of puling oneself along a lifeline when dragged behind a moving boat.
Assuming that a reasonably fit man could support his own weight by his arms when
climbing a rope, and maybe even lift himself a little, then how much greater the
force on that person must be if he cannot pull himself along a horizontal rope
when just resisting moving water pressure. Reports from some survivors say just
that, and those are probably people who are fitter than average.

So, do not base your calculations on, say, 300lb (large man with lots of
foul-weather gear?). My gut feel suggests that the force exerted on the man
after hitting the water and then being brought up by his lifeline may be around
2g - giving a lifeline loading of maybe 500-600lb? Of course, if the jackline or
its mountings have not given way, this peak loading will probably fall to a
lower steady-state value. There's something to look forward to as you go over
the side :-)

- Brian

It's generally dangerous to apply substantial lateral force to a taut line,
because of the tremendous mechanical advantage that it has against the
line itself and its end fittings. The mechanical advantage drops off
rapidly as the line deflects. A good rule of thumb for this type of
application is to use a line that permits a high % of stretch before failure,
since the line will tend to deflect to reduce its tension, rather than simply
parting. Clearly, wire rope is not the optimal material, from this point of view.
On the other hand, if the wire rope is strong enough, it will provide the least
deflection.

Note also that the deflection of the line will provide a controlled deceleration
when you are slammed against the end of your rope by that nasty wave. This will
also reduce the applied load against the jackline, in turn reducing the tension
on the jackline itself. Alan's program does not attempt to compute the actual
shock load on the jackline. If this were incorporated, it would show an even
stronger advantage for nylon rope vs. wire rope.

--RS

re last three replies:

Right, I didn't try to calculate shock loading -- much too difficult. 
But .... from note 782.15:

  ..... Second, in a published test of safety harness three different 
  men were unable to release the harness tether while being towed behind 
  a boat at less than 5 knots. This test found that the impact loads of 
  falling overboard at 11 knots (surfing downwind in a gale) reached 
  615 pounds .....

The impact (shock) loads were measured using a dummy and a load cell in 
the harness tether. This data is why I have been using a 600 pound 
applied load in my calculations.

Yup, $900 for new lifelines is quite expensive, and we've procrastinated 
about spending the money for several years. The additional cost for 
complete replacement using 1/4" wire was very roughly $200 more than 
complete replacement using 3/16" wire, and since we'd decided to replace  
everything anyway ..... On the bright side, installing a jackline for 
our 13 pound cat will be inexpensive.

Alan

Note .19 wanted to know a ball park figure on a 300 pound man on a 6' tether.

I have played foot loose and fancy free on the math, but it clearly shows why
instant changes in velocity (spatting onto cement comes to mind) are not good.
This also explains why there is not truely anything like a static belay in 
climbing.  Indeed climbing ropes are built with intentional stretch to absorb
shock.  Other lines (eg. Blue Water, Spectra) are built with low stretch to 
aid in climbing out of a cave, or keeping sails taut.

The basic approach is to solve for the time in the fall, and then calculate the 
resulting momentum.  Reducing this momentum to 0 in 0 time is the instantaneous
force needed.  Extend the time of decceleration even a small amount and the
force required drops quickly, (actually it is a quadradic relationship which
is asymptotic with the force of the man at rest).  Boy now isn't that a bunch of
fancy malarkey.

With a tether of 6' the maximum fall is 12' and the boat is on its beam ends.
Clearly this would be a worst case.

D = 1/2 * a * t**2 + v0 * t + d0 * t

does everyone remeber their linear physics from 20 years ago?

12 ft = 1/2 * (32 ft/(sec **2 ))* t **2 + 0 + 0

24 ft = 32 ft /(sec **2 )* t **2

24 ft / (32 ft/ (sec **2) = t**2

~.75 sec **2 = t**2

(.75 sec **2)**1/2 = (t**2)**1/2

.25 sec ~= t

so a 12 foot fall lasts a little over 1/4th second.

P = m*v

P = 300 pounds * V ft/sec

  = 300 pounds * a ft/(sec**2)* t sec

  = 300 pounds * 32 ft/(sec**2) * .25 sec

  = 9600 pounds/ (sec**2) * .25 sec

  ~= 2600 pounds of force

In practical terms, you will see far less than that.  Boats seldom have truely
verticle falls.  In climbing where verticle falls happen ( I can personally 
attest to the adreniline rush when 300 feet up), the loading feels to be a
couple of g's.  The difference is in the stretch of lines, scrapping on the rock
face, and of course mental levitation.  Even so, the load is 600 pounds.  This
is probably a good working number for boats.  This is basically supported in the
two previous replys.

When new, everything should be OK.  When you through in strength loss as the
result of knots, sloppy installation, sun, dirt etc, you may want something a
bit heaftier.  Incidently the tubular webbing sold at REI is for climbers.  It
is a nylon braid designed to be stretchy.  Tinsile strength from my foggy memory
is something like 2600 pounds after stretching 60%.  Pretty tough stuff.

re .22:

Ah, yes, units for measurements. If you use feet and seconds in your
calculations, you are implicitly using the English systems of units. In
this system, mass is measured by the unit slugs. Pounds is a unit of
force. When you step on a bathroom scale, your are measuring your weight 
in pounds of force. Your mass in slugs is your weight in pounds-force 
divided by the local acceleration of gravity (about 32 ft per sec at sea 
level). Yup, confusing, which is one reason the metric system was 
invented.

I'm not going to slog through the math. As you point out, falls on a 
boat are not free, vertical falls. There are so many variables that I 
suspect that all one can say is that the load on a lifeline or jackline 
or whatever is probably usually less than some number.

Another consideration is that at some load, your body will break (your back 
probably if you are wearing a safety harness), so that there is little 
to be gained by massively strong safety harnesses, etc.

As I've said cynically before, falling overboard is all too likely a 
non-survivable accident, especially in rough weather.

Alan

    Alan notes:
    >>As I've said cynically before, falling overboard is all too likely a 
    >>non-survivable accident, especially in rough weather.
    
    I suggest everyone that has not tried to recover someone from overboard
    do so at the first warm oportunity. It is amazing how difficult it is,
    even in quiet water, with the person in the water fully alert and
    helping. 
    
    In rough weather, at night, and a person at least scared as hell, maybe
    injured, you really  ought to think of your fancy harness and jackline
    as a simple trolling rig for sharks. The chances you and a small army
    of helpers can drag the body back aboard are real slim.
    
    I have one story that I dont tell often- About 25 years ago, I was
    racing the Bayview Overnight race- a 24 hr race in Folkboats, up across
    Lake St. Clair and back. We carried our chute out of the river and into
    the lake for a couple hours. About 10PM we decided the chute was to
    much and went to get it off. I went forward, tripped the pole guy and
    the chute went off. The cockpit crew had the wrong end of the sheet and
    lost it, so I started down the low side deck hauling the chute down.
    
    Next thing I knew I was hung up in the main sheet, which was dragging
    flat across the water at our great angle of heel. The helmsman reached
    out, grabbed the back of my pants and rolled me into the boat. Since we
    were rail down and in a low freeboard boat there was no lift, just a
    roll. 
    
    By sheer luck I was scooped in by the main sheet. We were 8-10 miles
    offshore, 10PM on a moonless night, in 25+mph winds, broad reaching,
    rail down with a chute out of control. Coming about and finding a
    swimmer would have been tough. 
    
    The race rules required a harness, which I had borrowed for the race,
    but had it carefully stowed in my duffel. 
    
    After the race I bought my own harness.
    

re .22

Your arithmetic appears to be incorrect, judging by the difference in units at
the beginning amd end of your second calculation.

I think P = m*v is a power calculation, not force.

Assuming the first calculation is correct...

You will be falling at 8ft/sec after .25 seconds of acceleration.
You will decelerate from 8ft/sec to 0 when you hit the end of the rope. Let's
say the deceleration takes 0.1 seconds. (It will be far less if the jackline is
wire rope!) Then you will decelerate at an average rate of (8ft/sec)/0.1sec
= 80 ft/sec = 2.5 G's. For comparison, let's guess that the wire rope will stop
you in 1/3 the time, i.e. .03 seconds. That would decelerate you at an average
rate of 7.5 G's. This will put 1500 lbs of load on your tether, and several
times that much on your jackline. The 7.5 G's may be a bit rough on your body
as well.

Now that covers a free fall to the end of the rope. Getting dragged through the
water is bad also. You may also be swept off the deck by a wave going perhaps
15 MPH. One might be able to extrapolate the force of this from the Practical
Sailor data.  

I've dragged behind our boat at 3-4 knots just for fun. At that speed, it's
difficult to pull yourself along the line back to the boat. At 6 knots, you
won't be able to get back to the boat unassisted.

You will probably need to use a winch to recover a MOB in bad weather. The
person in the water will be of little help, and may be too exhausted to even
drag himself over the lifeline once he's out of the water.

--RS

    If you've read about the Smeetons, when Tzu Hang went over the first
    time, Beryl had a rope tide around her when she was thrown over. 
    Although she never admitted to it (she was too tough) subsequent x-rays
    showed compression fractures of a number of ribs from the shock, plus
    the rope broke !

    Easy for me.....my open transom is 4" above water line at rest.  Just
    hop on.  do it all the time in full scuba gear.  The next step up to
    the rudder post is 15" inboard and up another 12"  
    
    One neat feature of the Soverel 33.
    
    I know, I know.....following seas right?  Well ULBD tend to surf down
    those pretty well.
    
    Yes its not a blue water cruiser, but it does have its points.

>>    Easy for me.....my open transom is 4" above water line at rest.

I don't believe that I would be able to board your boat's 4" transom while the
boat is moving at 5-6 knots in rough seas, after spending a few minutes being
dragged through cold water. If the transom has two well-placed handholds, then
it might be possible. I'm not even certain that I could board my own boat that
has a boarding ladder off the stern, extending into the water.

For planning purposes, it's prudent to assume that your MOB is unconscious,
since the person may have been injured during the fall overboard.

--RS

    You are probably right.  But the stern pulpit rails arc down to that
    step and are of great assistance.