Collision Avoidance, Cones of Uncertainty, and Appropriate CPA

[Dockhead]

Originally Posted by Lodesman

. . . This might cause more problems, because large helm orders cause an incipient yaw in the opposite direction - ie. the stern would swing closer before it started to go the other way. I can't stress enough how dangerous crossing this close would be.

Indeed!

I think actually that if you get into an extreme close quarters situation like that -- 180 feet -- you are better off if the ship just doesn't see you, and doesn't do anything with the rudder.

Because of displacement, you could be facing a towering wall of steel coming at you at 20 knots, and you with absolutely nothing you can do, other than plead with God for forgiveness for your stupidity.

We little boat sailors sometimes don't realize what kind of rates of turn, big ships moving at sea speed are capable of. Your Neopanamax vessel may have more than a cable (!) of ship behind its pivot point:



That's nearly 200 meters, or 600 feet (!) of ship, swinging around in front of you, in case he puts the rudder over thinking to avoid you. If there are 600 feet behind his pivot point, then he only needs to change course by 17 degrees -- AWAY from you -- to whack you with his stern, if you are running down his side, 180 feet away.

[Juho]

Originally Posted by Juho

Earlier I claimed that the ideal crossing angle (deviation from 90° towards the direction of the traffic) when crossing a unidirectional shipping lane, and knowing the speed of the first approaching ship (v1) and our own speed (v2), is atan(1/sqrt(k^2-1)), where k = v1/v2.

That works when v1>v2. In the case that v2>v1 we can use a simpler formula asin(k). We do have more freedom here (to use also other angles) since now our fast vessel can get away from any situation if needed. With this formula I could slip between two ships that are only 10 m from each others (aft to bow) with my sailboat (assuming that it is fast, powerful, nimble and stable enough) .

But what if v1=v2? What is the ideal crossing angle then? If someone wants to give me an opinion on that, I'll delay my own answer to that question until tomorrow .

Back to the question. What is the ideal crossing angle when v1=v2? The first function approaches 90° when v1 approaches v2. The second function gives 90° when v1=v2. The ideal crossing angle is then, according to the formulae, 0° (you deviate 90° from the perpendicular crossing).

The only problem is that with this angle you will never reach the other side of the shipping lane. You have to cheat a bit. You should merge with the traffic by joining it with the same speed, and then slowly shift to the other side of the lane, and exit when you have reached the other side.

Meanwhile I learned a bit more about trigonometry. I noticed that atan(1/sqrt(k^2-1)) = asin(1/k). This means that as the description of the function that calculates the ideal crossing angle can be made simpler. It is asin(v1/v2), where v1 is the slower speed and v2 is the faster speed. This formula applies both when the crossing vessel is slower than traffic on the unidirectional shipping lane, and when the crossing vessel is faster. V1 and v2 change places, if needed, so that v2 is always larger. The function is symmetric in the sense that it gives me the same angle when the ships are x times faster than me, or n times slower than me.

Lodesman gave polar coordinate based diagrams for calculating the movements of crossing vessels. You can calculate also the ideal crossing angle using a similar approach. See the first picture below. There you have the speed of the slower vessel on the y-axis, and the speed of the faster vessel on the x-axis. I used speed 1 for the slower vessel. This way the x-axis gives directly the proportion of the speeds.

If you follow the arc from point 4 on the x-axis towards the horizontal line (that cuts y-axis at 1), you can see that the ideal angle is about 14.5° (deviation from the perpendicular crossing line). This corresponds to speeds 5 knots and 20 knots. On paper you can use a pair of compasses if it is otherwise difficult to see.

Note that if you compare the ideal angle to the speed vector triangle of post #535, the difference is that when calculating the ideal angle, the higher speed is on the hypotenuse (instead of on the longer one of the other sides). I drew another picture to show that the difference between the sharp angle of that triangle and the ideal crossing angle is very small when the difference between v1 and v2 is large (see two triangles in the picture, sharing the same base at the y-axis). They deviate more from each others when the difference between v1 and v2 gets smaller. In the second picture you can see the two triangles for k=4. The difference is less than 0.5° (14.036° vs. 14.478°).

I'm already quite far from the colregs, but let's try to jump back. The colregs say that "Ships must cross traffic lanes steering a course "as nearly as practicable" at right angles to the direction of traffic. This reduces confusion and enables that vessel to cross the lane as quickly as possible.".

That means that you should actually forget everything that we have discussed about the ideal angles to follow the passing ships, and always cross the traffic lanes perpendicularly.

Colregs say that to cross the traffic lane as quickly as possible, you should cross it at right angle. That is true, but that approach may not be the approach that causes least harm to the traffic. The ideal angle would be less harmful. But on the other hand, if we add to the equation the risks that recreational sailors may cause to the traffic (with all their (possibly erroneously) calculated ideal angles etc.), maybe it is better to keep it simple and tell them to cross the traffic lanes always at right angle. The colregs say "reduces confusion". Obviously the fathers of colregs understood that recreational sailors (and others too) might cause problems with their tricks .

When I checked the traffic in the English Channel (in Marinetraffic), I noticed that one ship did not follow the colregs when it crossed the lane in about 45° angle. It was a fast passenger ferry. I don't remember its exact speed, but it is quite probable that it followed the ideal crossing angle approach, instead of following the colregs. If your speed is sqrt(2) times that of the ships on the traffic lane, your ideal angle is 45°. Should we thank the captain for his good seamanship, or report a breach of colregs? Maybe we can allow some privileges to experienced captains that sail that route daily. I will probably stick to the (almost) perpendicular crossings. That is, at least on busy traffic lanes. On less busy places, when ships are far away, I have been more relaxed and taken some liberties when sailing across the lanes .

[ramblinrod]

Originally Posted by Dockhead

That's the whole point! Not just a change of course, but a slight variation in course.

You can't set it up at all. AIS is not precise enough.

Yet, another in a plethora of strawman arguments.

As everyone wholeheartedly agrees, one cannot rely on AIS for close quarters maneuvers; it is simply not accurate enough, and the AIS antenna location most likely does not represent the nearest portion of the ship.

So lets throw this one out with the bathwater shall we?

Again, everyone needs to get their heads out of the electronics now and again.

Once one has determined that they are going to exercise a close quarters maneuver, they need to stick their head out the window and watch, with their eye, as Colregs dictates.

So, to clear something up, I did make an error previously, describing a crossing situation. Keeping a 180 ft minimum distance from the ship, and greatest distance from the following ship...

On the approach to the lead ship, on a 90 degree course, the give way sailboat would be 180 ft from the ships port transom corner.

Claiming that this is not possible is ridiculous. All the sailboat has to do to be in this exact spot is make course adjustments to compensate for variations in speed, (as one does in every crossing when they have their eyes on the vessel instead of into the screen).

The instant the sailboat reaches this point, proximity to the lead ship will be every expanding and distance from the following ship will be every diminishing.

This is why it is so important to be close to the lead ship for the crossing.

If one doesn't feel comfy with the 180ft minimum, they can choose something greater. If one is comfy being a bit closer, they can do that to.

Of course large, possibly heavily laiden ships, at speed, are not on rails, but as has been described so much in this thread, they have a lot of momentum, and it takes a whole helluva lot to get one to suddenly jump sideways at you.

Any professional mariner who would needlessly turn to starboard to maintain minimum arbitrary CPA, kicking the stern toward the sailboat, should have their ticket revoked.

In my experience, they would stand on as they are required under Colregs, and trust the giveway sailboat is going to avoid colliding with them, as required by Colregs, if there is no other underlying reason to alter course (which the sailboat should have considered, before deciding to make this kind of close quarters maneuver).

If one maintains a minimum 2.5 cables (1500 ft) from the lead ship they will be crossing the bow of the following ship more closely, which is a more dangerous maneuver, than a 180 ft minimum distance, under these circumstances.

[Dockhead]

Originally Posted by Juho

Back to the question. What is the ideal crossing angle when v1=v2? The first function approaches 90° when v1 approaches v2. The second function gives 90° when v1=v2. The ideal crossing angle is then, according to the formulae, 0° (you deviate 90° from the perpendicular crossing).

The only problem is that with this angle you will never reach the other side of the shipping lane. You have to cheat a bit. You should merge with the traffic by joining it with the same speed, and then slowly shift to the other side of the lane, and exit when you have reached the other side.

Meanwhile I learned a bit more about trigonometry. I noticed that atan(1/sqrt(k^2-1)) = asin(1/k). This means that as the description of the function that calculates the ideal crossing angle can be made simpler. It is asin(v1/v2), where v1 is the slower speed and v2 is the faster speed. This formula applies both when the crossing vessel is slower than traffic on the unidirectional shipping lane, and when the crossing vessel is faster. V1 and v2 change places, if needed, so that v2 is always larger. The function is symmetric in the sense that it gives me the same angle when the ships are x times faster than me, or n times slower than me.

Lodesman gave polar coordinate based diagrams for calculating the movements of crossing vessels. You can calculate also the ideal crossing angle using a similar approach. See the first picture below. There you have the speed of the slower vessel on the y-axis, and the speed of the faster vessel on the x-axis. I used speed 1 for the slower vessel. This way the x-axis gives directly the proportion of the speeds.

If you follow the arc from point 4 on the x-axis towards the horizontal line (that cuts y-axis at 1), you can see that the ideal angle is about 14.5° (deviation from the perpendicular crossing line). This corresponds to speeds 5 knots and 20 knots. On paper you can use a pair of compasses if it is otherwise difficult to see.

Note that if you compare the ideal angle to the speed vector triangle of post #535, the difference is that when calculating the ideal angle, the higher speed is on the hypotenuse (instead of on the longer one of the other sides). I drew another picture to show that the difference between the sharp angle of that triangle and the ideal crossing angle is very small when the difference between v1 and v2 is large (see two triangles in the picture, sharing the same base at the y-axis). They deviate more from each others when the difference between v1 and v2 gets smaller. In the second picture you can see the two triangles for k=4. The difference is less than 0.5° (14.036° vs. 14.478°).

I'm already quite far from the colregs, but let's try to jump back. The colregs say that "Ships must cross traffic lanes steering a course "as nearly as practicable" at right angles to the direction of traffic. This reduces confusion and enables that vessel to cross the lane as quickly as possible.".

That means that you should actually forget everything that we have discussed about the ideal angles to follow the passing ships, and always cross the traffic lanes perpendicularly.

Colregs say that to cross the traffic lane as quickly as possible, you should cross it at right angle. That is true, but that approach may not be the approach that causes least harm to the traffic. The ideal angle would be less harmful. But on the other hand, if we add to the equation the risks that recreational sailors may cause to the traffic (with all their (possibly erroneously) calculated ideal angles etc.), maybe it is better to keep it simple and tell them to cross the traffic lanes always at right angle. The colregs say "reduces confusion". Obviously the fathers of colregs understood that recreational sailors (and others too) might cause problems with their tricks .

When I checked the traffic in the English Channel (in Marinetraffic), I noticed that one ship did not follow the colregs when it crossed the lane in about 45° angle. It was a fast passenger ferry. I don't remember its exact speed, but it is quite probable that it followed the ideal crossing angle approach, instead of following the colregs. If your speed is sqrt(2) times that of the ships on the traffic lane, your ideal angle is 45°. Should we thank the captain for his good seamanship, or report a breach of colregs? Maybe we can allow some privileges to experienced captains that sail that route daily. I will probably stick to the (almost) perpendicular crossings. That is, at least on busy traffic lanes. On less busy places, when ships are far away, I have been more relaxed and taken some liberties when sailing across the lanes .

Just remember that most traffic lanes are NOT TSS's. You can cross any angle you want as long as you're doing it safely, outside of a TSS. In my opinion, perpendicular crossings are much easier to see and judge, and you get across faster (if there are no tides -- see below), so if you are trying to get through a dense line of ships, then I think you would normally want to do it perpendicular to the flow if you can.

Just to throw another complication into it -- when you DO cross TSS's, you are obligated to hold your HEADING perpendicular to the lane -- not your COG.

If you are used to sailing in the tideless Baltic, you will find this bizarre. But it's true -- a perpendicular heading gets you across the fastest, but you're course over ground will be bent by the tide which, in the Channel, rips at 4 or 5 knots or more at springs. It means in a little slow boat, if you are trying to get to C-bourg from the Needles on 180, and you are holding a 180 heading as you cross the lanes, your COG might be up to 45 degrees off of that in either direction.


I'm glad we have someone on here who's good at math. Keep up the fascinating analyses.

[Dockhead]

Originally Posted by ramblinrod

Yet, another in a plethora of strawman arguments.

As everyone wholeheartedly agrees, one cannot rely on AIS for close quarters maneuvers; it is simply not accurate enough, and the AIS antenna location most likely does not represent the nearest portion of the ship.

So lets throw this one out with the bathwater shall we?

Again, everyone needs to get their heads out of the electronics now and again.

Once one has determined that they are going to exercise a close quarters maneuver, they need to stick their head out the window and watch, with their eye, as Colregs dictates.

So, to clear something up, I did make an error previously, describing a crossing situation. Keeping a 180 ft minimum distance from the ship, and greatest distance from the following ship...

On the approach to the lead ship, on a 90 degree course, the give way sailboat would be 180 ft from the ships port transom corner.

Claiming that this is not possible is ridiculous. All the sailboat has to do to be in this exact spot is make course adjustments to compensate for variations in speed, (as one does in every crossing when they have their eyes on the vessel instead of into the screen).

The instant the sailboat reaches this point, proximity to the lead ship will be every expanding and distance from the following ship will be every diminishing.

This is why it is so important to be close to the lead ship for the crossing.

If one doesn't feel comfy with the 180ft minimum, they can choose something greater. If one is comfy being a bit closer, they can do that to.

Of course large, possibly heavily laiden ships, at speed, are not on rails, but as has been described so much in this thread, they have a lot of momentum, and it takes a whole helluva lot to get one to suddenly jump sideways at you.

Any professional mariner who would needlessly turn to starboard to maintain minimum arbitrary CPA, kicking the stern toward the sailboat, should have their ticket revoked.

In my experience, they would stand on as they are required under Colregs, and trust the giveway sailboat is going to avoid colliding with them, as required by Colregs, if there is no other underlying reason to alter course (which the sailboat should have considered, before deciding to make this kind of close quarters maneuver).

If one maintains a minimum 2.5 cables (1500 ft) from the lead ship they will be crossing the bow of the following ship more closely, which is a more dangerous maneuver, than a 180 ft minimum distance, under these circumstances.

Rod, instead of squirming around trying to defend the indefensible, you should read and try to absorb some of the many trenchant things which have been written about this in this thread. You would benefit greatly from it, I assure you.

You were invited to draw how you plan to get to 180 feet from his quarter, but you declined the invitation. But in subsequent posts, others analyzed it quite deeply. Lodesman, a professional, even did a maneuvering board on it. His comment was "I can't stress enough how dangerous crossing this close would be."

And here is what he drew, showing where you would be, trying to get to 180 feet from his quarter:



And now you suggest ignoring the AIS the doing it by eye? Look at that maneuvering board, and tell me how that's going to look by eye!

I have to admire your persistence -- and by hammering away at this, you've done us all a great favor, forcing us to think this through deeply. Otherwise we would just never find someone willing to argue that there's no such thing as a safe CPA -- it's purely subjective -- and that it's possible (not to speak of safe) to cross 180 feet behind a large ship moving at 4 times your speed. Normally everyone would just take for granted that these ideas are simply nuts, and we wouldn't have anything to talk about, and we wouldn't question or analyze why we know what we know, so thanks. That is completely sincere and without any irony.

[longjonsilver]

this thread started out well, but now has dissolved into bickering. Unless i am convinced otherwise, i'm out.
jon

[Juho]

Originally Posted by Dockhead

Just to throw another complication into it -- when you DO cross TSS's, you are obligated to hold your HEADING perpendicular to the lane -- not your COG.

That makes a lot of sense (especially for slow vessels), but do the actual words of colregs support taking this approach? In the text that I used above, colregs referred to "steering a course". That could refer either to the direction where you steer the bow, or to the resulting COG. Anyway, colregs seem to understand that we may have problems and may need to take into account other factors (like tides) when they say "as nearly as practicable".

[Suijin]

Originally Posted by Dockhead

But it's a whole different thing if you're making 5 knots and he's making 20 -- the case we've been discussing. In that case, on perpendicular courses, he will bear 14 degrees ahead of your beam. Even worse -- if his course is 14 degrees off perpendicular, then you will see him right on your beam. It's very hard to perceive such a small different of his course. Is he passing ahead? Behind? You can't tell. You can't tell from AIS, either, to better than a ship's length and probably several. Maybe you're passing slightly ahead, in which case stopping might put you on a collision course.

That's why it's so dangerous to sail into a crossing with a fast moving vessel with a small CPA. It's why good seamanship demands passing at a safe distance (not measured in feet ), and taking action in good time. That's required by the Rules, too.

In my experience in these situations I rely on an eyesight bearing. If it does not change over a reasonable period, I take proactive, early action to avoid any question of the outcome. Same with radar targets. I’ve had too many encounters with big ships offshore that were completely unresponsive to hails to trust them to take any action at all much less know I’m even there.

Busy shipping lanes and channels are a different animal and have so many different inputs and variables such that any strict formula for action is likely to be more dangerous than on the spot analysis and solution finding.

[Dockhead]

Originally Posted by Juho

That makes a lot of sense (especially for slow vessels), but do the actual words of colregs support taking this approach? In the text that I used above, colregs referred to "steering a course". That could refer either to the direction where you steer the bow, or to the resulting COG. Anyway, colregs seem to understand that we may have problems and may need to take into account other factors (like tides) when they say "as nearly as practicable".

Yes, it specifically means heading, and it is not controversial that you let your COG do what it will.

And yes -- as usual, COLREGS are not dogmatically precise, so allowances can be made for the particular situation, and there is always Rule 2 -- always do the seamanlike and safe thing.

It is a hell of a thing crossing the Dover TSS at springs -- we do this every time we're going out into the North Sea or coming back, and if we are going up the European coast. The tide rips intensely there because it is funneled through the narrow straight, and if you get the timing wrong, you can be carried many miles in the wrong direction. I do fudge the heading a bit as necessary, and provided it's safe to do so, in order to get to a more favorable spot on the other side.

But besides the very intense transit traffic, you also have fast ferry traffic crossing. You can get into a lot of trouble with this traffic if you are going much slower, and so your COG might bring you into conflict with ferries whose COG is closer to their heading. This is one place where Rule 2 may kick in and demand that you steer differently.

[Dockhead]

Originally Posted by Suijin

In my experience in these situations I rely on an eyesight bearing. If it does not change over a reasonable period, I take proactive, early action to avoid any question of the outcome. Same with radar targets. I’ve had too many encounters with big ships offshore that were completely unresponsive to hails to trust them to take any action at all much less know I’m even there.

Busy shipping lanes and channels are a different animal and have so many different inputs and variables such that any strict formula for action is likely to be more dangerous than on the spot analysis and solution finding.

If you are able to do every crossing so that you achieve a bearing change which you can see with the naked eye from several miles off -- then you are doing fine. That will keep you a mile or more away from everything. You may need better information than naked eye stuff in denser traffic.

Concerning "on the spot analysis and solution finding" -- as long as you are doing that from a safe distance, then OK. But collision avoidance, like landing planes, and other things like that, are usually safer and work more smoothly with a methodical, systematic approach, the way the pros do it. Not "on the spot". A "methodical, systematic" approach doesn't mean necessarily a "strict formula". And you're right about strict formulas -- they are hard to apply, because different crossings can be so different from one another.

But the methodical, systematic, disciplined approach puts into muscle memory all your accumulated knowledge about what is safe and what is not, what to do in this situation or that situation, rather than just relying in inspiration at the last moment. That's generally smoother and safer. As was said earlier -- if you're puckering, you're doing it wrong.

[evm1024]

Rod, Dockhead is not acting as a moderator in this thread. Other moderators are deleting your posts for cause because of what you have written.

You should not be citing fallacies of logic when your arguments are rife with them.

As for the high road.... I wish you would take it and refrain from personal attacks.

[ramblinrod]

Originally Posted by Dockhead

Nothing disparaging was intended.
.

Sorry, but I simply don't believe this statement at all.

Someone who didn't intend to offend, simply would not post that.

[Dockhead]

Originally Posted by ramblinrod

Sorry, but I simply don't believe this statement at all.

Someone who didn't intend to offend, simply would not post that.

Well, then I'm really sorry. I really didn't intend to offend you or anyone. I was simply arguing the point with analogies.

[Exile]

Originally Posted by ramblinrod

Sorry, but I simply don't believe this statement at all.

Someone who didn't intend to offend, simply would not post that.

It really doesn't matter what the intent was Rod, since it's 100% in your control to decide if you want to feel offended or not. Would be much more persuasive to just demonstrate why someone you presumably don't know or have never met out in cyberspace is simply wrong on the merits of the issue. Failing that, just acknowledge that the error is yours, or simply move on. That's entirely in your control too, but questioning intentions or motives will get you nowhere. It's an internet forum with a lot of knowledgeable, experienced posters weighing in, and I've always found that if one doesn't have their ducks in a row they'll likely be challenged. I view this not only as a positive generally, but what has made me a better sailor and even a reasonably competent onboard technician on occasion. In other words, it's for educational purposes only and is not some sort of competition. Nobody's "keeping score."

[ramblinrod]

Originally Posted by Dockhead

--------------------------------------

(Personal attack removed.)

And now you suggest ignoring the AIS the doing it by eye?

No, you would be foolish to ignore AIS and that would violate Colregs (if it is available). I did not suggest ignoring AIS (yet another strawman).

Rule 5, mandates that "Every vessel shall at all times maintain a proper look-out by sight and hearing..." In this case, "sight" is very important, hence my recommendation to get ones eyes off the screen. AIS could (and should if available) be used for the approach, but in close quarters, nothing is better than eyeballs.

-----------------------------------------

(Personal attack removed.)

The scenario that I prepared has a degree of risk associated, no matter how one attempts to cross.

The safest approach would be to avoid the crossing.

Any attempt to cross, certainly involves some "Pucker Factor".

In my opinion, your proposal to maintain a minimum 1/4 nm CPA via AIS from the lead vessel is patently unsafe.

Even if the AIS based positions were accurate, the 1/4 nm distance from the port stern quarter would place your vessel dangerously closer to the following ship, needlessly.

Therefore, I believe passing closer to the stern of the lead ship may be safer, than your proposed 1/4 nm CPA, which my proposed solution would keep you further ahead of the bows of the following ship you are crossing.

If the lead ship has standing orders for 1nm CPA min, they are already going to be concerned with your approach, so it makes more sense to stay closer to their stern, and further ahead of the following ship.

So you can post all of the personal attacks, rhetoric, and strawman arguments you wish, but this will not change the fact that your approach to this crossing scenario, IMHO, is patently wrong.