Elastic anchoring

During the ADAGIO design phase one of my top priority projects was Ground Tackle. This seemed to be the area that brought more cruising yachts to grief than any other. Over time I found a number of technical sources that were very generous in sharing what they had learned from empirical work and theory: Chuck Hawley at West Marine, Earl Hinz, author of The Complete Book Of Anchoring And Mooring, and William G. Van Dorn, author of Oceanography And Seamanship, Second Edition.

I learned a lot about anchor testing, about the design of elastic anchoring schemes. And I just realized that the results of all that effort did not make the transfer to our new website. So this post is intended to restore some of that research. I’ll do more when I have the time.

For several years we had a vigorous discussion on the old Compuserve Sailing Forum — one of the predecessors of the modern Internet. That means it is a silo, so the content is no longer available. For laughs I just Googled for “compuserve sailing forum”. The second result was my little paper on Anchoring Theory which still exists in the old Adagio Marine website. I have just uploaded Anchoring Theory.PDF to this website. The anchor testing analysis is dated, as the new generation of anchor designs either did not exist or had not been tested. But the principals remain sound, especially the methodology for evaluating anchor performance relative to weight (often neglected in anchor tests).

I’ve found a copy of one of my last bits of correspondence with Dr. Van Dorn — his reply to my queries on the physics described in Oceanography And Seamanship, Second Edition.

Research Oceanographer Emeritus, Scripps Institution
of Oceanography, University of California, San Diego
April 28, 1997

Dr. Stephen Darden
Te Wahapu Road
Bay of Islands, NZ

Dear Dr. Darden:

Sorry about the delay; your problem caught me at a busy time, and it has taken me two weeks to go back to my files of 30 years ago and find out how I did the early calculations. Now I think I am up to speed and find that the corrections are relatively minor–albeit important. I thank you for bringing the problems my attention. I am sending an errata page to the publisher and this longer discussion to you.

It might be best to first clear up the errors in my book (O&S) before responding to your questions about elastic anchoring:

p.276 change coefficient of equation from 0,004 to 0.0034. This changes Hinz’s 0.00238 from feet/sec to knots; viz. 0.00238*1.69^2*(l/2) =0.0034

p.388 Eq.(3) should read: lo+O.8lc=5.8h; an overlooked typo that verifies the scope of 7.2 for an all-chain rode on p.389.

p.390 Eq.(4) should read: Fh = 0.18*V^2*W^(2/3).

This equation is a special case of the general wind force equation on p.276, whose solutions can be found graphically from Figs. 114 & 115 on pp275 &276. Eq.4 is derived in the attached spreadsheet labeled ANCHORS, for the special case of an anchored sailboat at a swinging angle: A(30)= 30 degrees, a wind gust factor, Fg=1.5 (see p88), and a yawed drag coefficient, Cd=1.0, corresponding to a displacement/length ratio D/L=28.6/(.01*60)^3=277 (see below). Eq-4 now correctly gives wind force and rode size from fig. 155 and functions of displacement, subject to the conjecture at the bottom of the spread sheet.

Eq.(4), combined with Eq.(5) p392, yields the revised Eq.(6): w/W=V^3*.079/Ca^1.5, as shown in the spreadsheet, which also gives the computed table from which Fig. 156 was plotted.

At this point, I began to worry whether scaling wind drag areas in terms of W^(2/3) was really appropriate in view of recent changes in yacht design; viz., the table on p291. The latter half of the ANCHORS spreadsheet compares the influence of drag coefficient and D/L ratio on w/W, from which I conclude that their product is roughly constant and about 30 percent lower than predicted by Eq. (6). I believe that this result is safe enough, considering that the wind force equation includes a gust factor Fg^2=2.25, which can be taken to represent the surge factor invoked by Hinz.

The same argument applies to the wind force equation, which includes both W^(2/3) and Cd. Here we must take the 2/3 power of 0.70 = 0.79% of the calculated wind force. For your 30,000 lb (13.3 ton) cat, this would yield a force of 3100*.79=2450 lbs, which is rather close to Hinz’s figure, and still includes the 2.25 surge factor and the 30-degree swinging allowance.

Re your question about Example 2, p393, you are right. The chart says you would need a 96-lb COR. But, if you believe the above caveat, you could reduce it to 96-30% = 67 lbs. This seems consistent with Hinz’s account (His pl 76) of holding a 10-ton Morgan in coral sand at Fanning. However, having dragged miles of CQR-tracks through coral sand in Pacific atolls, including Fanning, I would carry a 40-lb Danforth–just in case. Coral sand is light and has very low cohesion. It is produced by fish chewing the reef. However, it tends to re-cement in brackish water. So it can have a highly variable texture.

My personal experience with Bruce and COR anchors is that they are much the same, except for the tendency of Bruces to ball-up in sticky clay and having to be hauled up and washed clean before resetting. I like Danforths in sand, coral sand, and all lo-cohesion sediments. I have never tried a Delta.

Your Table B is quite interesting. However I must admit my table of anchor coefficients involves a lot of surmise and conjecture–and I have found no reliable data on coral sand. As with all anchoring problems, there is lots of room for improvement, and I believe you have made a considerable contribution by your analysis. Please let me know if you find further errors in O&S. The page of errata I am sending to the publisher will be sent out to future buyers, until they can be incorporated in the next printing.

With regard to your question about how much nylon to use as an all-chain snubber, I would approach it as follows. From the design wind force, find rode size from Fig.155. From wind speed and anchoring depth, find the anticipated max height from Fig. 153, p389. Take four times the wave height as the max stretch required. Divide by 0.38 to get the length of nylon required. Of course, you need to have enough chain slack to accommodate four wave-heights of stretch. I do hope you aren’t planning an all-chain rode for your cat.

With alI best and thanks for your interest,
William G. Van Dorn, Phd

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