Article: Calculating the catenary and sag of a towline

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In this week’s Tuesday article update, we’re publishing an article on Calculating the Catenary and Sag of a Towline. The article presents a detailed look at how to use the catenary equations to calculate the configuration and sag of a towline. This is helpful in situations of shallow water depth when the catenary runs the risk of fouling by dragging on sea-bed due to high sag.

To read more, click on the link below:

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That equation would be much more complicated and impractical than a simple sniff test.

If the information was thought to be useful calculations could be made assuming the relevant parameters and the results put into table form.

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I see a problem with your calculation method and catenary curve. It assumes the towing gear is the same weight, bouyancy, and surface area, per foot along its entire length. That would be a rare condition.

Typically, there are towing bridles and some type of surge gear that are heavier than the tow wire.

Often there are very heavy: chain bridles, a chain “pigtail”, and chain surge gear. This moves the point of maximum catenary draft much closer to the towed vessel. The shorter the tow wire is, the closer the point of maximum draft will be to the barge.

Conversely, light wire or synthetic bridles and nylon surge gear would move the point of maximum catenary closer to a tug using a tow wire.

It also assumes that there is a tow wire tension meter. While a tension meter might be fitted on large European tugs, or AHTSs, the vast majority of tugs go not have tension meters.


Many thanks for your feedback. Yes, the case described in the article simplifies the scenario a lot, and definitely heavy towing gear will lead to an asymmetric catenary. These inputs are well taken, and will be used to refine the article with more research


This information would have been great for the disastrous AIVIQ tow.

I am pretty sure dragging their gear through the rocks south of Kodiak probably their towline and maybe their jewelry.

“…reading the USCG report which stated that the tension meter on the winch exceeded the safe working loads of the tow wire many times for hours repeatedly settled off alarms which were ignored.”

They were not ignored. The “buffoons” as you so eloquently put it had no idea what those alarms were. If you listen to the bridge tape you can distinctly hear the mate yelling, “What is that bleeping noise?” That tells me he had NO IDEA what he was hearing, not ignoring it.

I would have figured out what it was AND THEN blindly destroyed my career and any future chance of drilling in US Arctic waters in my lifetime, thank you very much.

I my be wrong, but the limited pictures I saw did not reflect much catenary in that tow before it broke.

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Chafing gear is important.

I have an Excel spreadsheet that does all the math and calculates the catenary.

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With one of the factors being the tension on the tow wire? Does the tension come from a tension meter? Or is it assumed to be the bollard pull of the tug?

I think they had the opposite problem: tow wire too short and little or no catenary to prevent shock loading.

IIRC the CG was investigating possible misconduct on the part of the bridge crew.

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However the person inputting the numbers wants to come up with the tension. I’m sure that a decent approximation can be made based on the RPM you’re running.

I will defer to you Sir.

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Unfortunately, the USCG really has no experience on tows of this kind and will defer to industry so this does not disrupt commerce or create more regulations.

It will be viewed as a “onetime deal” and they will expect industry to police itself until it happens again. The only way the USCG will get involved in situations like this is if three requirements are met:

  1. Loss of life and apparently 35 people incinerated or two people blown apart do not fulfill this requirement.
  2. Bad publicity. The USCG hates bad publicity unless it is covering up for an important shareholder in industry or Congress.
  3. Someone holds a gun to their head and their is so much evidence, they have not choice. Witness the MARINE ELECTRIC.

NURSE! My drink is empty.

Normally, one expects to see the tow wire always leading down from the stern roller. (In a big following sea the wire may come up off the roller at times due to pitching).

They were not using tow pins or a hold down. Both of which are universal on the West Coast.

Often a “shoe” is put on the wire to prevent chaffing. Without tow pins and a hold down, the typical shoe will not work. Alternatively, the wire can be paid out a foot or two periodically to prevent chaffing in one spot. There are other types of chaffing gear.

As I recall, AIIVIQ has a Rolls Royce towing machine capable of dynamically paying out wire at peak load and paying in again as the strain comes off. With this, no chaffing gear is required. But they were not using that dynamic towing feature. It was set on a hard brake.

They parted the shackle (200 ton?) at the KULLUK end, not the tow wire itself, so chaffing was not a factor.

It appeared to me that AIIVIQ’s officers lacked basic towing skills.


Watching the bridles is a needed visual among quite a few other things…The boat will let you know if it is straining and if adjustments to speed , course, and or length of cable are needed.


I think they had basic towing skills for the GOM. A deckhand has basic towing skills.

The Pacific is a totally different animal.

However, I do not want to area Towing Endorsements and correct me if I am wrong, there is no Towing Endorsement required by the USCG for towing drilling rigs. I believe some pressure (bakshish: Government officials sell out for bargain prices) was applied in the appropriate and they are exempt in the US.

In situations like this the company should be fined heavily for not providing proper personnel and the Master and Mates should lose their endorsements and re-qualify from scratch.

It’s not what you’re towing, it’s what vessel is doing the towing. The Aiviq is a towing vessel and towing endorsements are/were required.