Collision Avoidance, Cones of Uncertainty, and Appropriate CPA

[Lodesman]

Originally Posted by Exile

Not your question I realize, but it seems odd that an exception for agreement via radio would be explicitly included in US Inland Rule 14 (head-on), but not the inland rules for overtaking (13) or crossing (15). As you say, maybe it is implied.

I think it may be to cover the 14(d) situation which is unique to the Inland rules; the vessel with the current may out of necessity want a GtG, and can propose that with whistle signals as well.

[Exile]

Originally Posted by Lodesman

I think it may be to cover the 14(d) situation which is unique to the Inland rules; the vessel with the current may out of necessity want a GtG, and can propose that with whistle signals as well.

Seems like this may be the only logical explanation since 14(d) is the only rule I could find which explicitly allows the exception. And thus far I haven't found anywhere in the Rules where the manner of "agreement" is not through use of signals. Is the use of the radio ever mentioned? Maybe both "agreement" and use of the radio to accomplish it are both "intentionally implied" as you say because the Rules do not want to encourage it. Or maybe anachronisms??

You're right that 2(b) is expressly contingent on "special circumstances" and so should probably not be relied on in routine cases. There is the "ordinary practice of seaman" clause in 2(a) which could be construed as a way to support more modern practices, but that has more to do with cases of neglect and not the proactive circumstances we're discussing here.

Don't have an answer for your query about GtG, etc. in other countries, but I am surprised to learn that routine exceptions to the basic crossing rules based on mutual agreement/use of the radio don't seem to be codified. Or maybe I missed something here too.

[David M]

Trying to quantify the Rules down to specific numbers and specific situations is an exercise in futility.

The Rules are written in both a quantitative and qualitative way so that good seamanship and common sense can be used as well. The Rules often need to be flexible in order to avoid a collision and to keep people safe.

The Rules are not written to get super specific for all situations. It is why the Rules quite often use qualitative words like "close" rather than 500 meters for example. There are many other qualitative words written into the Rules as well....and that is a good thing.

[David M]

You guys got it. You can use the radiotelephone to make passing arrangements outside of what is stated in the Colregs. You are not breaking the Colregs by doing this. As I said, I hear pilots all the time making passing arrangements that do not meet the letter of what is stated for passing definitions in the Rules.

This is common sense and you are still sticking to the Rules.....agree with another vessel how you want to pass by radio and then stick to it. I do starboard to starboard passings all the time from a distance where it is not apparent yet how we are going to pass should we hold course. In those situations I get on the VHF and come to an agreement on how we are going to pass. If I cannot contact the other vessel then I make a course change, usually to starboard, so that it is very apparent how I want to pass. I would never make a starboard to starboard passing if it is not clearly apparent from a good distance (early and apparent action) and I have not made contact with the other vessel.....because that would be a violation of the Rules and dangerous.

[StuM]

Originally Posted by ramblinrod

I don't know where you are getting this from but it is incorrect. If I am crossing at 90 degrees, to be 180 ft off (nearest distance) his port transom corner, at any time before reaching this point, I am further away from him.

OK, so you are not trying to pass 50 metres astern of the lead ship. You are passing with a minimum distance of 50 metres from his port transom corner. That's a bit different.

If you are 50 metres away as his port transom crosses your path, it will take you 20 seconds to be in line with his port transom - at which time he will be 200 metres away from you.

Let's assume he is 200 metres long. (small for today's container ships).
10 seconds before CPA, you will be pointing at the middle of his hull and be 75 meters away from him. 20 seconds before CPA, you will be 100 metres away from his bow and pointing directly at it.

Again - do you consider this prudent seamanship?

[TJ D]

Originally Posted by StuM

OK, so you are not trying to pass 50 metres astern of the lead ship. You are passing with a minimum distance of 50 metres from his port transom corner. That's a bit different.

If you are 50 metres away as his port transom crosses your path, it will take you 20 seconds to be in line with his port transom - at which time he will be 200 metres away from you.

Let's assume he is 200 metres long. (small for today's container ships).
10 seconds before CPA, you will be pointing at the middle of his hull and be 75 meters away from him. 20 seconds before CPA, you will be 100 metres away from his bow and pointing directly at it.

Again - do you consider this prudent seamanship?

Would anyone think this was prudent? Here's the view from my bridge this afternoon. Who would want to be 180 feet from one of these things? This picture is taken from 2 miles.

[TJ D]

And, here's the next guy in line, taking my stern at .7nm. He's making 21 knots, I'm making 11. This is a pretty close crossing in the professional world. This is 2 ships, making consistent speed, holding very steady courses, and .7's close. This is an open sea crossing.

Now, introduce all the variations of speed an course that we have on our little toy boats, and it's easy to see how tight quarters maneuvers like are being suggested are just simply not the way to go.

i can say with great certainty that if I had a guy set up to cross 180' from my stern, I would be seriously unhappy with that skipper. In most cases, I wouldn't allow it to happen. I would view it as a rule 2 situation in open waters.

If a guy did it to me while navigating in a TSS, i would undoubtedly be inclined to report the pleasure boat operator to the local marine authority for reckless operation.

But, the question remains- why would anybody get so close to one of these ships in the first place? It's nuts.

[Juho]

Originally Posted by Dockhead

OK, but how would you get there? Can you draw it for us?

Ramblinrod discussed the ideal angle to meet a queue of ships. It is 90° minus a small correction. If my calculations are correct, the correction is atan(1/sqrt(k^2-1)), where k is the speed difference factor. In the discussed example the speeds are 20 knots and 5 knots, and thereby k = 20/5 = 4. With these speeds the correction would be 14.48°.

If he wants to implement the 180' CPA exactly, maybe he would approach the shipping lane in the ideal angle (i.e. no last minute turns) and continuously monitor his CPA counting device (I'm not sure if there are devices that could do this). He would keep his speed below 5 knots until (when TCPA ≈ 1 min) he needs all the 5 knots to maintain the planned 180' CPA. The CPA counting device must be sophisticated enough and we must have sufficient information of the ship to calculate CPA to the nearest corner of the transom of the ship. When he reaches the CPA his bow will point directly to the nearest corner of the transom of the ship (this is a property of the ideal angle).

When his bow reaches the track of the nearest corner of the transom, distance to the corner will be 720' (=4*180'). When his aft (32' behind the bow) reaches the track of the other corner of the transom (ship beam = 100'), distance from the aft to the other transom corner will be 1231.2' (=720'+4*132'/cos(a)-132'*tan(a)) (a = angle_correction = 14.48°). The beam of the sailboat was not taken into account in the calculations.

Note that crossing the track of the ship (centre) 180' behind the ship is not possible since even if the bow of the sailboat touches the nearest corner of the transom (CPA(corner) = 0') (the aft of the ship is square), the ship will be already 193.6' away (=4*50'/cos(a)-50'*tan(a)) when the bow reaches the track.

Note that in the last formula 50'/cos(a) refers to the longer distance (more than 50') that the sailboat has to travel due to changing the angle. Formula 50'*tan(a) refers to the distance that the sailboat won by "approaching" the ship, thanks to changing the angle.

I hope I got the numbers right. I'm tired now. Don't trust these unless someone else confirms the calculations.

[TJ D]

I'm heartened to see that good ol' fashioned geometry is still being practiced here and there. it's easy to let all the gizmos do your thinking for you. I'm certainly guilty of it. Reminds me to break out the traditional methods more often.

[Dockhead]

Originally Posted by Juho

Ramblinrod discussed the ideal angle to meet a queue of ships. It is 90° minus a small correction. If my calculations are correct, the correction is atan(1/sqrt(k^2-1)), where k is the speed difference factor. In the discussed example the speeds are 20 knots and 5 knots, and thereby k = 20/5 = 4. With these speeds the correction would be 14.48°.

If he wants to implement the 180' CPA exactly, maybe he would approach the shipping lane in the ideal angle (i.e. no last minute turns) and continuously monitor his CPA counting device (I'm not sure if there are devices that could do this). He would keep his speed below 5 knots until (when TCPA ≈ 1 min) he needs all the 5 knots to maintain the planned 180' CPA. The CPA counting device must be sophisticated enough and we must have sufficient information of the ship to calculate CPA to the nearest corner of the transom of the ship. When he reaches the CPA his bow will point directly to the nearest corner of the transom of the ship (this is a property of the ideal angle).

When his bow reaches the track of the nearest corner of the transom, distance to the corner will be 720' (=4*180'). When his aft (32' behind the bow) reaches the track of the other corner of the transom (ship beam = 100'), distance from the aft to the other transom corner will be 1231.2' (=720'+4*132'/cos(a)-132'*tan(a)) (a = angle_correction = 14.48°). The beam of the sailboat was not taken into account in the calculations.

Note that crossing the track of the ship (centre) 180' behind the ship is not possible since even if the bow of the sailboat touches the nearest corner of the transom (CPA(corner) = 0') (the aft of the ship is square), the ship will be already 193.6' away (=4*50'/cos(a)-50'*tan(a)) when the bow reaches the track.

Note that in the last formula 50'/cos(a) refers to the longer distance (more than 50') that the sailboat has to travel due to changing the angle. Formula 50'*tan(a) refers to the distance that the sailboat won by "approaching" the ship, thanks to changing the angle.

I hope I got the numbers right. I'm tired now. Don't trust these unless someone else confirms the calculations.

Great stuff!

So if he manages (and I say it's impossible, but let's suspend disbelief for a moment) to pass through a point which is 180' from his quarter, so achieving the 50 meter CPA, then on an exactly perpendicular course, and assuming the ship is running on rails (also a fantasy, but stay with me), CPA will occur when the transom of the ship has cleared a line extending along the side of your boat by 43.5'. It means that at CPA, you will have been able to see daylight across his transom for 1.29 seconds (OK, 1.44 seconds if he's standing 5 feet from the rail). So he would have to sail right at the side of the ship and will still be sailing right at him, until only 1.44 second before CPA.

Does anyone here think he can judge that? By eyeball or any other means? And that is the IDEAL crossing, where the speed vector across his path is equal to boat speed. At more acute crossing angles, it's worse.

As to your "CPA calculating device" -- such a thing does not exist. AIS gives most precise data, but it treats the ship as a mathematical point, and our devices don't have access to data about location of the GPS antenna.

So you need to figure in this and the various other uncertainties. Once you do that, you will see that you can't get anywhere near 180 feet away from the ship, while he's making 20 knots in open water, without great risk of being run down -- basically flipping a coin with your life -- because you don't know within +/- 180 feet even where he is or will be.

I think Rod had in mind making a run at the side of the ship, and then turning off to run down his side, then turn again across his transom. This would be easier than trying to hit that magical point off his quarter which we were analyzing, because you only need to get to 180 feet off anywhere along his side (or 180 feet plus enough extra to account for the time it takes to turn and displacement during your turn). But taking account of the cumulative effects of all of the uncertainties, you still cannot judge it anywhere near that close. At 5 knots, he can only move 50 meters (!) in the time it takes the ship to pass him by, if the ship is 200 meters long. So he must already be within 100 meters of a line extending along the side of the ship, by the time the bow of the ship passes him, in order to barely get to 50 meters from his quarter as it flashes by.

So it means to have any time for running along the side of the ship on a reciprocal course, he will have to get closer than 100 meters to a line extending from his side, BEFORE he's cleared his bow. You cannot judge that at all -- that would be like hitting a period mark on a newspaper at 50 meters with a dart. You can't even see what you're trying to hit. Nor do you know or can you know where this magical point is -- it's not drawn on the sea.

You could do this if the ship were anchored, or if it's moving at 5 to 8 knots, but not at 20 knots.



The key, as I keep saying, is the difference in speeds. At 20 and 5 knots, the speed vector triangle looks like this:



Note the very fine angle at the left, 14 degrees. That's how much control you have, in a slow boat meeting a fast ship. That will be your bearing, as seen from his bow, when you are on an exact collision course. That's what a sitting duck looks like.

[evm1024]

As dockhead said above and as has been shown for the math of a crossing. The sailboat needs to be on a collision course to shave it so close.

We have been looking at this from the aspect of the sailboat. The sailboat skipper says pucker factor, what pucker factor just watch me shave the tail of this ship.

Now view it from the bridge of the ship. In our calculation of geometry we have placed the ship on rails. But the reality is that the officer of the watch is urgently worried about not hitting the sailboat. To him it looks like they are going to run over the boat.

We are ignoring occupation, stand-on, give-way and such in this discussion. Assuming that the ship does not attempt any corrective action.

The sailboat is just a ship length ahead and "fine" off the bow heading into the ships path. If the Captain is not on the bridge already then he is on his way quickly.

5 blasts of the horn are sounding over and over again. Heck, a sense of doom is in the air.

And in reality no ship would allow such a crossing to develop in the real world in open water. And if it did the ship would be taking corrective action. They could be attempting to slow or changing course. And then all bets are off.

For the ship a CPA of 180' is the same as zero.

[Dockhead]

Let me illustrate the point using the logical technique called reductio ad absurdum.

Let's suppose you are trying to cross not with a 20 knot box ship, but one of the Condor Ferries, say the Condor Liberation, which is about 100 meters long, beam about 30 meters, and has service speed of 35 knots.

How are you going to have a crossing with this vessel with a 180 foot CPA?

You can obviously forget about lining up to pass 180 feet behind. Can we at least approach within 180 feet and run down the side?

Here's the speed vector triangle:



So in order to reach any spot which is 180 feet from his side, or 100 meters, or whatever, you have to first get to a place which is on a line which is 8.13 degrees from there. Let's say you want to get to a place which is 100 meters from his side but in line with his bow, so you can then turn off to a reciprocal course before darting in behind him to cross behind.

So at one mile out, you are 102 seconds from reaching this spot, and you are able to travel only 1.42 cables in this time, sailing flat out at 5 knots.

But you don't know where that spot is, so you can't aim for it. If you are on an exact collision course with the point of his bow, then his bow is bearing 8.13 degrees ahead of directly abeam of you. You can't really see the difference between directly abeam and 8 degrees from there, with your bare eyes. You can just about see this with a HBC, but not with your bare eyes.
So he will seem to be approaching from directly abeam. At night, you will see both sidelights.

If you are heading towards not a collision, but the desired spot 100 meters from his side and in line with his bow, then you will be 115 meters further back. His bow will now be bearing 3.5 degrees further ahead -- so 11.5 degrees instead of 8 degrees. Can you see the difference? 102 seconds from impact?

But what is much worse is that he doesn't run on rails. His course varies by a degree or two plus or minus naturally -- and that assumes he is trying to hold a steady course, rather than making some corrections of his own for whatever reason. 2 degrees of difference in his course makes SEVEN TIMES the difference, in where he will be at CPA, than 2 degrees of your own course change. In 102 seconds, every degree of inaccuracy in course keeping (or your data about his course) will put him 35 meters away from where you expected him. Every knot of difference in his speed will add to this uncertainty.

I hope it's obvious to everyone how extremely dangerous it is to be sailing 2 cables from the course line of a ship a mile off and travelling at 35 knots -- where you would have to be, to do Rod's maneuver. You are well inside the "killing zone" in front of him, and you are basically a sitting duck -- you can only move 1.42 cables in the time it will take him to run you down, so you have basically zero control over the crossing. You can't tell, even with AIS, whether you are passing ahead or behind, so you wouldn't even know which way to turn.

The key is that the difference in speed determines the geometry of the crossing -- what will be the relative bearing in order to reach some spot close to him. The greater the difference in speed, the closer you have to be to his course line, and at a certain point, you have to be inside the cone of uncertainty about his position, which means you have no way of knowing whether you are about to be run down or not.

Suppose you magically end up in this spot, 100 meters from his side and even with his bow. Can you then do Rod's maneuver? Well, no. 35 knots is 17m/s, so he will flash by and by GONE, in less than 6 seconds. You can only move 15 meters in that amount of time. So you can't correct your distance from his side, once you're already there.

The key to visualizing this is to focus on the ANGLE -- whatever point in relation to a vessel travelling 35 knots, will be only 8.13 degrees from dead abeam of you.

OK, but that's the extreme case -- what about the ship travelling at 20 knots?

Well, it's somewhat easier, but the whole situation is very similar. Instead of 8 degrees ahead of the beam, the spot you are going to run into is 14 degrees, so you will likely still see both his sidelights at night. TCPA at one mile off is 175 seconds instead of 102 seconds. You still can't get within 180 feet of him, without getting nearly under his bows.

The extreme case, I hope, makes it easier to visualize this.

[Dockhead]

Originally Posted by evm1024

. . . .For the ship a CPA of 180' is the same as zero.

Exactly. That pretty much sums it up.

[evm1024]

I'm a bit strong headed at times. Of course I mean well but - more often in my youth than now - sometimes I would just assert something that was just not true or reasonable or wise and then defend that position all the while digging a deeper hole.

In moments of lucidity I would realize how absurd my position was and then admit the same. It was very hard at least for me to admit that I was wrong or promoting something ridiculous.

But I did notice that when I did this the people around me had a greater respect for me...

Just speaking for myself.

[Exile]

Originally Posted by evm1024

I'm a bit strong headed at times. Of course I mean well but - more often in my youth than now - sometimes I would just assert something that was just not true or reasonable or wise and then defend that position all the while digging a deeper hole.

In moments of lucidity I would realize how absurd my position was and then admit the same. It was very hard at least for me to admit that I was wrong or promoting something ridiculous.

But I did notice that when I did this the people around me had a greater respect for me...

Just speaking for myself.

For me, and having to learn so many different technical, previously unknown-to-me boat-related subjects a bit later in life than many, I've found it far more rewarding to acknowledge being wrong (or just not knowing) than trying to appear smarter or more knowledgeable. In the first instance I usually become far better educated; in the latter I just remain . . . well . . . sorta dumb uninformed. But to each his own, it is the internet after all. The upside is that, personalities aside, CF has always been the best resource for me for just about everything pertaining to my boat, as this thread amply illustrates.