The Three-Vessel Problem

Or: Problems That Don’t Exist

Disclaimer: I am not an attorney of any sort, much less an attorney who specializes in maritime or admiralty law. I am not a representative of the Unites States Coast Guard, the Department of Homeland Security, or any branch of the US government–nor any other government for that matter. These are just my thoughts, put forth for your consideration with all the authority of a disheveled man screaming semi-coherent gibberish from a street corner. With that out of the way…

In physics, there’s thing thing called the three-body problem. While at first glance it doesn’t seem like it should be too difficult to conceptualize how three bodies might interact with one another according to natural laws, coming up with a mathematical solution to such a problem may well prove nontrivial. When gravitational interactions are involved, for instance, it may fall within the scope of chaos theory.

But the so-called (by me) “three-vessel problem” is hardly that.

Application

If you don’t have a copy on hand, follow this link to the official US Coast Guard’s Navigation Rules, aka the COLGREGs, aka The Rules of the Road. From this point on, I’ll refer simply to “the Rules.” For any sea-lawyers reading, I mean specifically the international, vice inland, Rules. Although a similar discussion–with a similar outcome–could be had about the inland Rules, there are some important nuances between the two that I would hate to gloss over, but this post is long enough as it is. So, again, international Rules only from here on out.

Origins

The three-vessel problem, to the extent there is one, is a bit of folklore with its origins, near as I can tell, in Rule 15, which begins:

“When two power-driven vessels are crossing…”

See that? Two power-driven vessels. The problem, then, arises when someone walks up to the whiteboard during wardroom training and draws up something like one of the scenarios below:

Scenario 1
Scenario 2
Scenario 3

Resolution

The precise scenario and the Rules’ alleged deficiencies for arriving at a solution to the problem presented will often depend on how poorly the questioner comprehends the Rules.

Category A

Really doesn’t get it. The questioner may, based on a mistake of memory, have arrived at the erroneous conclusion that Section II of the Rules, Conduct of Vessels in Sight of One Another, applies when two and only two vessels are in sight of one another. But nothing about the Rules or the reality of the maritime domain support that conclusion. First, most obviously, that’s hardly a limitation implied by the section heading: more than two vessels can obviously be in sight of one another. Second, there’s Rule 11, which uses language similar to the section heading: “Rules in this section apply to vessels in sight of one another.” No numbers, no limits, no basis to even infer a limit. On its face, then, Rules 13, 14, and 15 for overtaking situations (any vessel), head-on situations (power-driven vessels), and crossing situations (power-driven vessels) respectively, being within Section II of the Rules, ought to apply when any number of vessels are in sight of one another, unless of course there is something in the individual rules specifically that limits their application.

And you know what? There is one limit I will stipulate to. As noted in the preceding parentheticals, Rules 14 and 15 apply specifically and exclusively to power-driven vessels. But interestingly–and what people often overlook–Rule 13, for overtaking, actually does still apply to all vessels, whatever the type.

But back to the problem at hand. We are presented with someone who insists the Rules must go out the window when the “three-vessel problem” arises. Hopefully after having Rule 11 pointed out to them, they would be persuaded that they are wrong, that the Rules for overtaking, head-on, and crossing situations do still apply when it’s three vessels instead of two, but then they might then be under a new misapprehension. One that has slightly better support under the wording of the Rules. Which leads to…

Category B

Kind of doesn’t get it. This is a matter of quibbling. While the questioner may grant, perhaps always has granted, that Section II in general will apply to any number of vessels in sight of one another, they may yet seize upon the precise wording of Rules 14 and 15 to claim that those two rules specifically are limited in their application by number. Here I quote again, “When two power-driven vessels are…”

The thing about this misapprehension is, it doesn’t hold up. Consider scenario 1 (copied once more below), and the application of the Rules to vessel A:

Scenario 1

With respect to vessel B, is there a crossing situation? Yes. A, one power-drive vessel, is in a crossing situation with B, another power-driven vessel. The two vessels are in sight of one another. The presence of vessel C does not change that. Here, the questioner may note that A, though it is required to keep out of B‘s way, can only do so by appearing to violate Rule 17, action by the stand-on vessel, with respect to vessel C. But is that really the case? Because if vessel A fails to maneuver in a predictable/rational manner with respect to vessel B, then it will never get to the point of having to worry about vessel C: it will collide with B first. Viewed in that light, the clear solution, fully in accordance with all Rules, is to first avoid the collision with vessel B the only way you know how: by taking “early and substantial action to keep well clear,” as required by Rule 16 for action by a give-way vessel (as vessel A is with respect to vessel B). There’s also another blurb in Rule 17(b) that makes clear a stand-on vessel doesn’t have to keep “standing on” if, from any cause, collision can’t be avoided by the give-way vessel alone. And for vessel A, that’s true: vessel A can’t avoid a collision (with vessel B) by vessel C‘s action alone. So of course vessel A can maneuver to avoid collision with vessel B. It is, after all, the give-way vessel with respect to vessel B, even as it may still be considered the stand-on with respect to vessel C.

Provided that the questioner is convinced, whether through an appeal to interpretation (two doesn’t mean only two) or an appeal to intervening causes (can’t have a risk of collision with C if you are due to collide with B first), they may still not be fully convinced. Even if they grant your interpretation of the meaning, they may yet question the applicability of Rules 14 and 15 to a three-vessel problem. So finally it comes to…

Category C

Almost gets it. They may have a photographic recollection of the Rules in their entirety, and as such the three-vessel problem exists in their mind only as a problem of interpretation. This is where effective scenario-based discussions can actually occur. Not just “what Rules apply?” but “how might we apply them?” True, the rules don’t come out and tell you what to do when there are three vessels in sight of one another–but then how could they possibly? And why should they need to? If they did, would that not open up the floor to questions of “what about four?” There are always multiple rules in play, even when there are no vessels in sight of one another. That the Rules are not, in the end, conducive to being learned by rote and regurgitated without thought is a feature, not a bug. It allows them to be condensed own into a single book, letting the interested reader–who presumably doesn’t want to have a collision at sea–think through how to apply them as scenarios arise. With that in mind…

Scenario 1

Scenario 1

To recap, vessels B and C are not presented with anything resembling a three-vessel problem. Vessel A is not presented with simultaneous risks of collisions, but sequential risks of collision. There is nothing in the Rules to prevent it from taking action first with respect to vessel B, and then with respect to vessel C. It’s status as the stand-on vessel with respect to vessel C does not alleviate it of the need to first give way to avoid a collision with vessel B.

Scenario 2

Scenario 2

I would be remiss if I didn’t point out how contrived this scenario is. Here, we are to believe that vessels A, B, and C, are due to arrive at roughly the same point in space at roughly the same point in time, on the open ocean, by sheer coincidence. Any other, less synchronous arrangement would follow the same principles as scenario 1: before there could be three vessels in sight of one another with risk of collision, there would be two, and there is nothing the least bit novel about two vessels in sight of one another maneuvering in accordance with the Rules. But here, just taking it for granted that this highly improbable arrangement of converging ships has occurred, consider:

Rules 6 and 8 (among others) always apply.

Rule 6 will tell you that among the factors to consider in determining a safe speed is traffic density. Here, the traffic density may warrant reducing speed. And as Rule 8 will tell you, “Any alteration of course and/or speed to avoid collision shall, if the circumstances of the case admit, be large enough to be readily apparent to another vessel observing visually or by radar” (emphasis mine). Unless all three ships arrive at the exact same decision at the exact same time, that by itself should remove this scenario from the realm of the three-vessel problem.

Rule 8 will also tell you to take action to avoid collision with ample time and with due regard to the observance of good seamanship and that alteration of course alone may be the most effective action to avoid a close-quarters situation provided that it is made in good time, is substantial, and does not result in another close-quarters situation.

But that begs the question: with or without adjusting speed, and supposing that whatever you do with regard to speed, risk of collision will remain, how should you alter course? Imagine yourself on vessel A.

Here, I quote Rule 15 in full:

“When two power-driven vessels are crossing so as to involve risk of collision, the vessel which has the other on her own starboard side shall keep out of the way and shall, if the circumstances of the case admit, avoid crossing ahead of the other vessel.”

Assuming for a moment that we don’t throw Rule 15 out the window because there are actually three power-driven vessels in a crossing situation, what does this mean?

Well, it means that vessel A, with respect to vessel B (adding up to two power-driven vessels), is the give-way vessel. Conversely, vessel A, with respect to vessel C (also adding up to two power-driven vessels, is the stand-on vessel. Vessel A should give-way for vessel B, so as to avoid crossing ahead of vessel B, but stand-on for vessel C.

Oh, shit… is that a contradiction? Give way for one (and avoid crossing ahead), but stand on for the other? Let’s continue…

Rule 16, action by give-way vessel:

“Every vessel which is directed to keep out of the way of another vessel
shall, so far as possible, take early and substantial action to keep well clear.”

Well, that’s not too threatening. It doesn’t really help resolve this apparent stand-on/give-way paradox that arises if we don’t follow the advice of whoever is telling us that the Rules don’t apply here and we should throw the book out the window, but just because I’m a masochist, how about we read on?

Rule 17, action by stand-on vessel, quoted only in part for brevity:

“(b) When, from any cause, the vessel required to keep her course and
speed finds herself so close that collision cannot be avoided by the action of the give-way vessel alone, she shall take such action as will best aid to avoid collision.”

“(c) A power-driven vessel which takes action in a crossing situation in accordance with subparagraph (a)(ii) of this Rule to avoid collision with another power-driven vessel shall, if the circumstances of the case admit, not alter course to port for a vessel on her own port side.”

Do you see the part in there where it says “…and no matter what, no matter the circumstances, a stand-on vessel shall never ever ever ever alter course and speed”? Yeah, neither do I. What I see instead is, as discussed in scenario 1, that if, “from any cause” the stand-on vessel needs to take action to avoid collision, she “shall” do so. Which is to say that nothing in Rule 17, and by extension Rule 15, locks a stand-on vessel into permanently “standing on.” 17(c) specifically applies if the give-way vessel doesn’t “give.” 17(b) applies if any cause arises that might necessitate maneuver by the stand-on to avoid a collision: including the confounding presence of a third vessel.

Working back to Rule 16, then, for action by the give-way vessel (as each vessel in scenario 3 effectively is, at least with respect to one vessel in the trio), taking into account the general aversion against maneuvering to cross ahead of the stand-on vessel (Rule 15), and the even more explicit aversion against turning to port to avoid a vessel crossing on one’s own port side that has thus far failed to give way, it would seem that the most logical and appropriate action–for all vessels involved in this contrived scenario–would be to come to starboard. That way, no “give-way” vessel crosses ahead of its own stand-on–whether or not that stand-on maneuvers itself, provided they don’t make a completely inexplicable turn to port–and no “stand-on vessel” turns to port to avoid the vessel on its starboard side (hence what I just said about a completely inexplicable turn to port). This is entirely within the bounds of Rule 15 and indeed all applicable rules (and, again, a Rule 6 safe speed evaluation is always appropriate). No need to throw the book out the window: just learn what it really means to be the stand-on or the give-way vessel. If the latter, you really must give way. If the former… it turns out the Rules are not a suicide pact: you can still maneuver–indeed, are required to–to avoid collision.

Scenario 3

Scenario 3

Scenario 3 is almost too easy. Here, vessel A has a head-on situation with respect to vessel C, and vessel C has the added burden of being overtaken by vessel B, in addition to its reciprocal head-on situation with vessel A.

First, sea-lawyer it all you want, but vessel A should clearly comply with Rule 14, seeing itself as one of two power-driven vessels in a head-on situation, and alter course to starboard. Even the most ardent and misguided of the “Rules go out the window when there’s three or more vessels in sight of one another” crowd must grant this.

Then there’s vessel B. Also easy. It is, based on the speed vectors I have in my own mind but which I neglected to include in my diagrams, overtaking vessel C. Rule 13 doesn’t even have that problematic–to some–language about “two power-driven vessels.” As I noted up-page, there is no mentions of the number of vessels involved or even if the vessels are power-driven: the mere fact that vessel B is overtaking vessel C means that it “shall keep out of the way” of vessel C. That includes leaving sufficient room for vessel C to maneuver to avoid collision with other vessels as needed.

But what if it doesn’t? What if vessel B has gone from riding vessel C‘s ass, to now passing within a hair’s breadth of vessel C, such that vessel C has no room to maneuver to starboard? Well, that right there is your first problem if you’re standing on the deck of vessel C. How did you let that happen? Sure, vessel B is supposed to “keep out of the way,” but if they haven’t–if they really haven’t, to the point they are inside your turning radius and the density of traffic is such that you are unable to comply with the rules–it seems like you ought to do something about it. And then there’s vessel A, off your bow, on a nearly reciprocal course and appearing just as clueless as vessel B.

So I guess you turn to port, right? Just this once?

WRONG!

First, re-evaluate your safe speed. If you need to slow down to buy time with A and also let B slip by, then do it. It should have happened as soon as you realized B was overtaking you and cutting it too close. If you’d recognized this prior to the head on situation with vessel A, too, you might plausibly have altered course to port and opened things up a bit more between you and B before A even appeared on the horizon, and then had all the freedom to maneuver you needed. But as it stands: slow down, and come to starboard when you can. It might be tempting to come to port, but if you do that and whoever has the deck on A suddenly wakes up and does what the Rules tell them to do (belatedly) at the same time, then they’ll come to starboard and you’ll turn right into each other. Which, by the way, is pretty close to what happened when USS Fitzgerald collided with ACX Crystal, albeit with a crossing, vice head-on, situation. Fitzgerald turned port (the wrong move), ACX Crystal turned starboard (technically the right move, but taken too late, given Fitzgerald‘s failure to act sooner), and seven men died in the pitch black.

So don’t turn to port in a head-on situation, and don’t let yourself get into a situation in which turning to port is your only option should a head-on situation arise. Also, five short blasts of the whistle is always an option. If you find yourself in a situation like scenario 3, being overtaken by another vessel inside your turning radius, that might be a good time to do it, in addition to whatever speed and course alterations you might make. Flashing light, too. Especially for the vessel out ahead of you on a reciprocal course. It’s a shitty situation if you allow yourself to get into it, but the Rules never go out the window. You just have to think a little harder about how to apply them.

Caveat, all that stuff in Rule 2 about “the ordinary practice of seamen.” There are, of course, some circumstances in which this kind of close-quarters overtaking and meeting might well be “the ordinary practice of seamen,” such as in a narrow channel (Rule 9) or a traffic separation scheme (Rule 10). In that kind of a situation, continuing along track (down one side the channel or scheme) as much as can be allowed, and accepting that vessels will be passing close down either side might make perfect sense, and suddenly dropping speed might actually be the worst idea imaginable. Which isn’t to say that anything goes or that the rest of the Rules go out the window in a narrow channel or traffic separation scheme (far from it), only that you must consider the totality of circumstances when determining how best to comply with the Rules as they apply.

Rule 14: Three-vessel Head-on Situation

I will note that it would be extraordinarily difficult, but not technically impossible, for more than two power-driven vessels to be in a head on situation. I say “not technically” because of course two power-driven vessels could be on nearly or precisely parallel courses, with some amount of lateral separation between them, and both heading towards a third vessel on a “nearly reciprocal” course. This would in fact present that third vessel with a scenario in which they have two vessels approaching them head-on relative to their own position and movement. Imagine something like Scenario 3, but with B and C on more nearly, even if not quite, parallel courses. Even the most ardent sea-lawyer would, I hope, still agree that vessel A‘s most appropriate course of action would be to alter course to starboard such that vessels B and C will both pass down her port side. Thus, without even quibbling over the meaning of “When two power-driven vessels are…” we’ve arrived at the precise solution prescribed by the Rules, as if there were no confounding factors.

Closing Thoughts

I think the existence of the three-vessel “problem” stems from a misunderstanding, by some, of the Rules that comes from learning them by rote. If, for instance, one’s understanding of Rules 15, 16, and 17 reduces down to “turn to starboard for a vessel crossing on your starboard, maintain course and speed for a vessel crossing on your port, and never ever ever turn to port” and nothing more, then it’s easy to see how one might end up in a logic loop like the ones in bad or intentionally ironic Sci-Fi stories where a super intelligent computer is defeated by getting it to adopt self-contradictory positions and then explode from the effort. But, as I think I’ve pretty well laid out by now, that’s not actually what Rule 15 says. While it’s true that Rules 15, 16, and 17 really do only apply to vessels in sight of one another (Rule 11), there’s no limit based on the number of ships on the horizon. If there’s one point to take away from this reading it’s this: the Rules are not to be learned by rote, they must be understood, with a full appreciation for how they interrelate.

The truth about the the three-vessel problem is, there is no “three-vessel problem.”

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