DRAFT SURVEY: Allowing for Anchor Chain Catenary

CATENARY, in mathematics,?a curve that describes the shape of a flexible hanging chain or cable—the name derives from the Latin catenaria (“chain”). Any freely hanging cable or string assumes this shape, also called a chainette, if the body is of uniform mass per unit of length and is acted upon solely by gravity. (https://www.britannica.com/science/catenary)

When doing a Draft Survey on a ship anchored the weight of the Chain and its Anchor on the bottom is equal to the Anchor plus the weight of the Chain measured from the hause pipe minus the weight of the chain’s catenary between the hause pipe and its point of contact on the bottom.

Deduction for anchor down = (Weight of Anchor and Chain) – (Catenary of the Chain from Hause Pipe to Bottom)

Keeping in mind the chain measured from the hause pipe along its catenary is still supported by the ship.

So the real question is how to determine the length of the Chain’s Catenary based on simple parameters such as the Chain’s Vertical Angle at the Hause Pipe and the Depth from the Hause Pipe to the Harbor’s Bottom or Water Depth plus the Freeboard to the Hause Pipe.

To investigate this, I did some experiments with a simple beaded chain to measure the length of the catenary based on the Depth to the Bottom and the Initial Vertical Chain Angle with both measured at the Hause Pipe. To do this, I set up a simple test. The ship’s chain is affected by gravity the same as my test chain. To Scale there should be no difference except my test was done in air and the ship’s chain is in water. The biggest difference is the buoyant affect of water on the chain. In this case the buoyant force was ignored due to the massive size of a ship’s anchor chain. (There are cases where the buoyancy on the anchoring system is considered but that is a completely different application.)

I do not believe the UN ECE DRAFT SURVEY CODE addresses determining the length of the catenary of an anchor chain to deduct from the length of chain used.

Let’s take a look at what I did.

Figure 1. Vertical angle = 0. Depth = 30. Catenary = 30. Ratio of Catenary to Depth = 1.

Figure 2. Vertical angle = 5. Depth = 30. Catenary = 32.5. Ratio of Catenary to Depth = 1.08

Figure 3. Vertical angle = 10. Depth = 30. Catenary = 34.3. Ratio of Catenary to Depth = 1.14

Figure 4. Vertical angle = 15. Depth = 30. Catenary = 36.5. Ratio of Catenary to Depth = 1.21

Figure 5. Vertical angle = 20. Depth = 30. Catenary = 41.0. Ratio of Catenary to Depth = 1.36

Figure 6. Vertical angle = 25. Depth = 30. Catenary = 44.5. Ratio of Catenary to Depth = 1.48

Figure 7. Vertical angle = 30. Depth = 30. Catenary = 48.0. Ratio of Catenary to Depth = 1.60

Figure 8. Vertical angle = 35. Depth = 30. Catenary = 56. Ratio of Catenary to Depth = 1.86

Figure 9. Vertical angle = 40. Depth = 30. Catenary = 61. Ratio of Catenary to Depth = 2.03

Results from the Figures 1 to 9 are as follows:

TEST #1: Vertical Depth Measured = 30 cm

Vertical Angle in Degrees Length of Catenary Measured Ratio of Catenary / Depth

0 30.0 cm 1.00

5 32.5 cm 1.08

10 34.3 cm 1.14

15 36.5 cm 1.22

20 41.0 cm 1.37

25 44.5 cm 1.48

30 48.0 cm 1.60

35 56.0 cm 1.87

40 61.0 cm 2.03

45 66.0 cm 2.20

The tests were repeated by increasing the Depth to 59 to see that the ratio of Catenary Length to Depth are different. Here are the following results:

TEST #2: Vertical Depth Measured = 59 cm

Vertical Angle in Degrees Length of Catenary Measured Ratio of Catenary / Depth

0 59.0 cm 1.00

5 62.5 cm 1.06

10 70.0 cm 1.18

15 74.0 cm 1.25

20 80.0 cm 1.35

25 86.0 cm 1.45

Note: 30, 35, 40 and 45 degrees were not done due to the size of the test equipment. However This range of initial vertical angles would be extreme for a Draft Survey.

Finally, I averaged the results for both series of test and found the following:

Vertical Angle in Degrees Ratio of Catenary / Depth

0 1.00

5 1.07

10 1.16

15 1.24

20 1.36

25 1.47

30 1.60

35 1.87

40 2.03

45 2.20

Let's try these results out.

Let us assume a Panamax with the following anchor and chain onboard anchoring in Commencement Bay, Tacoma, Washington, USA.

• The ship has two High Holding Type (AC-14) Anchors each weighing 7.425 MT
• The ship has 660 meters of 78 mm diameter Chain (Grade 3) with 330 meters (or 12 shots of chain) stowed in Port and Starboard Chain Lockers. The Weight of Chain per 15 Fathom Shot is 7.98 MT.
• The ship reports that at the Hause Pipe there is 9 shots of chain out plus the weight of the anchor. The total weight of chain and the anchor is:
• 9 x 7.98 MT/shot + 7.425 MT for the Anchor = 79.25 MT
• The Depth from the Hause Pipe to the bottom is 300 feet or 91.46 meters.

What to allow for the catenary of the chain? How much weight to deduct for the anchor and chain on the bottom?

Do you agree or disagree? I would like to hear your comments!The math to calculate the length of the Catenary is complicated, however I chose to attack this from a different approach. We used beaded chains like this in the towing tank for some tests when I was a Graduate Student in Ocean Engineering.

More Information about my Bunker and Draft Survey Course

My?Bunker and Draft Survey Course?is a narrated correspondence course done via email worldwide. Sadly, most Maritime Schools and Academies do not include Draft and Bunker Surveying in their curriculums because it is not included on the License Exams. As a result they do not prepare you to work on this type of ship.

Did you know that a Draft Survey properly done can yield the Total Displacement within 0.5% of the true cargo figure or Displacement if done properly? You can determine a vessel's total cargo weight by reading the drafts and sounding the tanks instead of the cargo manifest which may or may not be correct or verify a Shore Scale Weight. This method works on all vessels as long as they are afloat. You can also use Draft Surveying to independently confirm a vessel's Stability Calculations.

Years ago, I got a great job and a 38 year career, because I knew about SHIPS, STABILITY & TRIM and DRAFT SURVEYING calculations. This Course is a good way to complete your professional education.

To learn about becoming one of my private remote Students or attending an upcoming live event at MITAGS-West, Seattle, Washington, USA.

In November 2022: BEYOND BASIC STABILITY WORKSHOP: Planning a Maximum Load for Restricted Draft Arrivals or Canal Transits.

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