## Wednesday, April 21, 2010

### Sample Calculations for Jackline Stress and Energy Absorption

Rev.3-27-2012

Introduction

Climbing ropes are not rated in terms of strength; rather they are rated by the number of falls they can withstand. These "falls" are defined by a UIAA test procedure (converted to US units):

• 176-pound weight, simulating climber (but without the harness and soft tissue give a real person would add).
• 8.2-foot rope length. This is anchored 6 inches below a small radius edge, simulating a carabiner. As a result, the roe always fails where it passes over this edge, resulting in a breaking point below that of the rope alone. In climbing this is realistic; in sailing, this is probably a conservative approach, though there will be similar strength losses in knots, there can be sharp edges on deck, and a highly loaded rope cuts very easily. I will accept this as a reasonable model for impact loading.
• 15.8-foot fall, plus rope stretch (typically another 2.8 feet).
• Elongation. To avoid bungee ropes that would bounce a climber dangerously by stretching too far, the rope may not stretch more than 10% under a 176-pound weight. It would also be difficult to climb or descend a stretchy rope. There is no stretch limit under impact forces.
Watch the video: UIAA Rope Testing
A rope must survive 5 falls without the fall impact force exceeding 2,245 pounds. Most climbing ropes survive 7-12 falls with impact forces remaining below 1,950 pounds. Elongation is typically 7-8% under 176-pound weight. The rope will retain some of this stretch after each fall and is thus allowed to "rest" for several minutes between falls. Note that there is no strength requirement; it is all about energy absorption. A stronger rope or a steel cable would have too much impact force.

This is an incredibly severe test of energy absorption. The test wiegh reaches about 32 feet/second. The falling mass gains about (15.8' + 2.8') x 176# = 3,274 ft-pounds of energy, and the rope must absorb this within about 2.8 feet of stretch. 3,274 ft-pounds = 2.8' x 1950# x 0.6. If the rope were a perfect spring, the 0.6 "factor" would be 0.5, but the rope is non-linear and this factor gives a better fit. Basically, a climbing rope must absorb about 400 ft-pounds of energy per foot, because a climber gains 176 ft-pounds of energy for every foot he falls, he can fall twice the length of the rope in a worst-case fall, and a safety factor is needed. This is a true worst case fall, it is VERY unusual in actual practice, and it is impossible to match the forces unless the climber is quite large. In practice, no UIAA approved climbing rope failures have been documented since the 1960s that did not involve cutting over an edge or chemical damage to the rope.

For jacklines, the math is related, but every boat size will give different answers. We will be using more "gentle" assumptions more reflective of actual conditions possible during a wave strike.

Assumptions

• 40-foot boat with 30-foot jacklines (start 2' from the bow and end 8' forward of the stern).
• "Fall" in this case is a man moving 20ft/sec across the deck, ignoring the force of the wave and falling. That is about as fast as any breaker could be expected to throw a crewman.We will then double this result, to allow for the force of the wave and the weight of the sailor sliding down a wet and sharply heeled deck.
• ISAF approved jacklines must have the same strength as 3/16-inch 316 stainless cable, or about 3,700 pounds. 1-inch nylon climbing webbing meets this requirment when dry, but not when wet, when it will fail at about 3,250 pounds. ORC requires a 6,000-pound rating and we will base or calculations on this higher value. 17% elongation at failure is typical of 1-inch tubular webbing; I am assuming that the 6,000-pound webbing exhibits the same elongation at failure.
• Webbing is weakened 12% when wet. Nylon fiber is weakened about 10%, rope about 20%, and webbing about 12%. We will use 5,200 pounds as breaking strength, since jackline systems are only tested to their limits in wet conditions. However, the elongation to failure increases to about 20%, so the energy absorption to failure is little effected by moisture. This result seems to be supported by the observation that climbing ropes do not fail when wet. US Sailing requires 4,500-pound test webbing or SS wire. 1-inch climbing webbing is 4,000- to 4,200-pound test. 1-inch rigging webbing tests at 6,000 pounds.
• Person with gear weighs 200 pounds.

The applicable ISO specification, for harnesses and tethers on small sailing boats:
ISO 12401

We are assuming one man per jack line. Clearly, there can be more, but they should not both fall in the same worst-case manner at the same instant, so perhaps a 160% multiplier would make sense for 2 men. Yes, it is not unlikely that the same wave would sweep 2 men, but they would not hit the end of their tethers at the same moment and they would not both be at the mid-point of the jackline.

UV deterioration. Webbing: several sources suggest that tubular webbing of the types used loose about 15-20% of their strength each year on temperate latitudes, and energy absorption ability may deteriorate faster. Rope: UV does not penetrate as deeply, so deterioration rates of 5-10% are expected. This has not been considered in the calculations.

Knotting vs. Sewing. Sewn jacklines will be effectively 100% strength. Knotted webbing jacklines will be about 85% strength if waterknots are used. A rope jackline will be about 85% strength if a figure-8 is used. A cleated end will be about 95% strength. This has been considered in the calculations, as described in the drop test procedure above.

Calculations

Fall energy =  2*1/2 MV^2 = 2*1/2 x (200/32) x 20^2 = 2,500 ft-pounds

(note: ISO and OSR standards specify 1,430 ft-pounds fall energy; I have used a higher value because multihulls typically use longer tethers. However, if we use 1,430 ft-pounds of fall energy, all of the stress results will be 43% lower and the ISAF 3,700-pound webbing and cable will be suficient.)

We have assumed 30 feet of jackline, so we need to absorb only 83 ft-pounds per foot. However, webbing is not so good as rope at absorbing energy. With only 20% elongation to break and a 2.8X safety factor (the same ratio of ultimate strength to impact strength used for climbing ropes), energy absorption capacity = 5,200#/2.8 x 20% x 0.6 = 223 ft-pounds per foot (1-inch climbing webbing will absorb 156 ft-pounds/foot). This is far less energy than a climbing rope can absorb, but it's enough and it has the lower stretch characteristics we desire; we want to keep people on deck. 223 x 30 feet of webbing = 6,690 ft-pounds of energy absorption capacity (4,680 ft-pouhnds for 1-inch webbing). If 2 men fall, as discussed above, we are appraoching the limit of the ORC webbing and we are at the limit of the US Sailing/ISAF webbing. We have applied no safety factor to the strength of the webbing, but we have modeled a more severe fall than ORC standards. We have not allowed for wear and UV exposure in use.

How quickly will this stop the sailor and what with the force on the tether be? We would like to keep harness forces below 900 pounds to reduce the risk broken ribs and reduce anchor stress, based on climber and OSHA experience (OHSA tethers absorb energy at 900 pounds, climbing tethers at 550 pounds).

Assuming 8% stretch and using Pythagoras (remember?) the jackline will deflect about 2.6 feet to the side at the center, plus 0.1 foot tether stretch . The maximum force based upon energy absorption, at that angle would be about 3.4 x less than the jackline stress = (42/89) x 5,200 pounds/3.4 = 722 pounds. A good hit, and probably less than this because you will hit the harness at an angle. It's going to hurt later, but not break ribs if the harness is properly fitted high on the chest. How about the energy absorption on the crewman's end of the tether - does it match? 2x(2.6'+0.1') x 722 pounds x 0.6 = 2,340 ft-pounds; a good match to the 2,500 ft-pounds the jackline absorbed.

What If We Clip Dirrectly To A U-Bolt?

The forces become much greater because of the abrupt stop. There have been instances of tethers breaking. Generally there is no body to examine for injuries.

We will adjust our assumption, since the sailor is now in the cockpit and not exposed on the bow. It turns out that that a 6-foot fall and a lesser wave strike are not all that different: A falling body accelerates at 32 ft/sec^2; if you fall for 0.38 seconds you reach 12 ft/second and cover 6 feet in that time. This the same 1,430 ft-pound energy fall ISO and OSR standards specify.  It's not hard to imagine that a sailor could be thrown across the cockpit at 12 ft/second by a breaking wave, or even faster. Add the force of the wave, the tether can easily break and the sailor is never found. In each case I read (more than the two I copied below) the sailor was attached to a fixed u-bolt and not a jackline (the jackline would have absorbed energy through sliding and stretch). Without the jackline stretch, the sailor is stopped in about 6 inches and subjected to a peak deceleration of about 24 gavities. In independent testing many harness and tethers fail and all show evidense of trama, since the impact force is 2,500-4,500 pounds. A person cannot survive this without serious spine or rib injury. It seems clear that fixed-point anchors are the hazard.

• "A lesson in harness and tether construction can be learned from Tami Ashcraft, who along with a sailor friend was making a sailboat delivery to Hawaii when they ran into a powerful storm. Ashcraft was knocked unconscious. When she came to more than 24 hours later, she climbed to the cockpit where a single tether dangled over the side. The D-ring had snapped where it was connected to her friend's PFD. He was gone. Ashcraft was convinced a round ring might have held, like those on Mustang vests." Ashcroft, in my opinion, was wrong in her conclusions.

• 1998 Sydney-Hobart Race Accident. Glyn Charles was never found, after his tether parted. But the force of dragging his body through the water could not have generated that kind of force, only a sudden impact. The inquest stated that he was attached to a "fixed point" and thus would not have benefited from jack line shock absorption. The lanyard may have also been defective, though I can't locate the information. http://www.parliament.nsw.gov.au/Prod/parlment/hansart.nsf/V3Key/LA20010307027.
http://www.telegraph.co.uk/sport/othersports/snooker/2994528/Yachting-Charles-died-after-safety-harness-failed.html.

I don't think the tethers failed due to bad construction; I think they were simply stressed past 4500 pounds and broke. Making them strong wouln't help, as they would simply break the sailor in half. We need to make them softer.
These expereinces lead to a clear and very interesting conclusion: cockpit u-bolts require shock absorption in order to provide suvivable security in a worst-case wave strike. Fortunatly, Yates Gear Inc. manufactures the solution; a compact shock absorber designed to absorb the energy of climbing falls. This is the original, since addaped to construction, rescue, and military application. While this adds a little cockpit clutter, it could save lives for cheap! In practice, the mere presence of shock absorbers on construction lanyards has been credited with safer work practices, as it reminds the workers of the incredible forces involved. Perhaps the presence of Screamers in the cockpit might encourage sailors to shorten their tethers.

Well, at least that's one possible answer, something very simple that would only need be deployed in extreme conditions. ISAF now requires an over-strain indicating flag instead--a half measure which only warns that you nearly died, instead of doing something about by absorbing shock. This is much how climbers originally use Screamers; other applications came later.

Conclusions

We've taken a stroll through the numbers. What have we learned?
• A 40-foot boat the 6,000 pound webbing required for off-shore racing is a good engineering fit. In fact, it matches well proven OSHA and climbing equipment engineering practice. However, if your boat is longer than 55 feet, you may need stiffer and stronger jacklines to control stretch, particularly if multiple crewman are on the same jackline.
• Smaller boats would be well served in many cases by lines with more stretch, particularly catamarans, with wider decks (longer falls) and shorter jacklines. 1-inch webbing or a rope with more stretch will do well.
• Keep your tether VERY short if attached to a fixed point or risk serious injury from the quick stop.
• Cockpit u-bolt anchors MUST have shock absorption added or the impact forces will break tethers and people in worst-case wave strikes. The Yates Sceamer is the most reasonable canidate, at ~ \$18.00. Tethers made from 8-10 mm dynamic climbing rope--even nylon double braid in a pinch--will also reduce the shock to acceptable levels.

A longer post on jacklines can be found here: Climbing Gear for Sailors. This post is more specific to my boat, my ideas, and the way I sail. Some comments will not apply to a more general audience.

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References
Additional information on climbing gear, deterioration over time, and failure modes can be found at UIAA Safety Page

ISO harness and tether standards (referenced by ISAF)
ISO 12401 2009

Yates Gear Inc. manufactures many intersting tether products for climbers, industry, rescue, and the military. I expect to see them entering the marine market very soon. Many of their products are useable as-is and will not require adaptation.
http://www.yatesgear.com/climbing/screamer/index.htm

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1. Nice analysis. I appreciate your engineering approach to boats and sailing.

bob
s/v Eolian
Seattle

2. I found as a rock climber that once I understood the rope and anchor systems I could use them better, climb safer, and relax. When I began ice climbing, this became even more important to my peace of mind.

Boats are like that too; when we understand we don't fear unnecessarily. But they can be so difficult to understand.

3. (this comment relocated from the "Gulf Spill" thread)

Anonymous said...

Hi Drew
I have read a lot of your blog, I find it very interesting. I am in agreement with a lot of your jackline and tether info. I am making tethers, and I am sourcing my supplies from a rock climbing supply company. I have seen you refer to "proper sewing" when suggesting that one could sew one's own tethers, and I wonder if you would elaborate. I have sewn some tubular webbing up into test pieces, and had my stitches ripped out by a local rigging and supply company, to try and quantify the strength of my stitches. Up to now, I have sewn box stitches and partial box stitches to reach a stitch that will "give" at 500 lbs. This is for a flag that will give the user an idea of the stress the tether has been subjected to....
For making the major loops that secure the spinny shackle and two locking gate clips, I have been using a series of rows of bar stitches. If you have a better and stronger stitch type suggestion, I'd like to hear of it...
I am also doubtful about the use of the quick release shackle, as a way of releasing the harness from the tether, WHEN UNDER THE PRESSURE OF THE WEIGHT OF THE PERSON WHO FALLS OVERBOARD. Two things: such an unfortunate person would need to temporarily unload the weight on the shackle to get it to release. Secondly, the key ring type of connector between the spinny shackle and the row of beads one is supposed to pulltto release, might very well pull out and leave the overboard person with a handfull of beads and his tether still attached to the boat! I am currently eliminating the ring ding and running a loop of 1/16 inch SS stranded wire through 4 beads and through the stem of the spinny shackle pin, so you will either pull the pin or not have enough strength, one will not normally be able to break the SS wire. There is actually more to the tether story, as I have been in contact with the international offshore group, and their requirements for tethers are not well thought out either. Also, If you need some stitching done, I'd be glad to help out. John Spurlock Inland Sail Boise Idaho
May 18, 2010 12:49 PM

4. Yes, bar tacks are a good way to do that.

If you use climbing locking biners, keep some water-proof grease in them. I froze a few up over the years before learning that. Wire gates are fine.

I assume when you created a "flag" it is a loop who's failure will not effect the strength of the tether.

By the way, there is nothing wrong strength-wise with a water knot on tethers, though there is some increased tendency to catch.

Yes, the quick-release tether bit is controversial; I am certain that if you asked any climber to connect to the rope with one, for even a short time, you would be polity directed to "get stuffed." Yes, the boat could roll, but I would consider it the less probable risk, compared to simply becoming unhooked. My opinion.