Mailport September 2013 Issue

Mailport: September 2013

Catenary Equation

This letter is in response to the “Sizing Ground Tackle” and “Anchor Bending” letters and your replies in the July 2013 Practical Sailor. In my opinion, the element missing from the discussion is the relationship between water depth and recommended scope. Scope is normally defined as anchor-line length deployed divided by water depth. Most discussions of anchoring treat scope as independent of water depth (which it is for a rope rode) but for an all-chain rode, water depth has a large impact on the required scope. In 40 feet of water, a 3:1 scope is probably all you need. In 10 feet of water, 10:1 scope may not be enough. 

Charles Springett opines that added scope matters more than we think. He relies on the catenary of heavy 3/8-inch chain to help his Bristol 433, Ariel, stay put in a blow.

Your answer to Richard Lewis cites Beth Leonard’s rule of thumb for sizing chain and while I respect her superior experience in all things cruising, I would add that there are two reasons for choosing an all-chain rode: It eliminates the potential for abrasive failure of a rope rode on the bottom, and it reduces the overall length of rode length required in any situation. It reduces the length requirement because of its weight. So while 5/16-inch chain is strong enough to restrain my 41-foot boat, I prefer to use 3/8-inch chain because it provides an increased safety factor as well as a reduction in the required scope.

In your answer to Richard Paden, you state: “Because you are in shallow water, you lose most of the advantage of chain catenary in absorbing shock loads.” That statement is true, if you stick with the conventional 7:1 scope ratio. If you increase the ratio to say 15:1, then the performance of the system comes closer to the performance of the same system in 40 feet of water with its attendant shock-absorbing properties.

The explanation for this lies in the properties of a chain rode. An anchor’s performance is compromised once the anchor line starts to exert an upward force on the anchor shank. An upward force cannot be exerted on the anchor shank until all of the anchor chain is suspended off the bottom. In order to suspend all of the anchor chain off the bottom the vertical component of anchor chain tension at the bow roller must equal the suspended weight of the chain (in water). If the angle of the rode to horizontal at the bow roller is 5 degrees when you have 150 feet of 3/8-inch chain out in 10 feet of water and the bow roller is 4 feet above water level then the horizontal force required to start anchor uplift is approximately 2,300 pounds. With only 70 feet of chain out, the horizontal force will be approximately 520 pounds. (Angle at the bow roller is 11 degrees.)

The above numbers are approximate, but they are good enough to develop an appreciation of what is actually happening. In 10 feet of water with an approaching storm, putting out 150 feet of chain rather than 70 feet will increase your resistance to uplift on your anchor by a factor of four. The choice of anchor has far less effect on the result than the amount of chain out. As you point out, there are many other factors that should be evaluated when sizing and deploying an anchor; however, I would argue not enough weight is given to the relationship between recommended scope and water depth for an all-chain rode.

Charles Springett
Ariel, Bristol 433,
White Stone, Va.

Chain is our preferred rode in most situations, including shallow water. What you lose in catenary, you gain in friction through bottom contact. The downside is that you can snag on a rock, causing the links to flatten, or even break, under load. In mud, the uptick in holding power can be significant. There’s also a yaw-dampening effect that can be a big plus.

Next: Snubber Specs

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