Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
Recreational sailors frequently have a fundamental misunderstanding of how to cross safely with ships. They don't understand the critical decision point in a crossing, misjudging it by miles, and don't understand what safe passing distances are. We recently had this discussion in another thread:
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The poster believes that a mile CPA is "preposterously" much for crossing with a ship  "180 feet" is plenty. Five miles is way too far away to get worried. He has expressed these common misconceptions very well, and I hope he'll let me use some of his posts in the book I'm working on. I gave him a clue, which he unfortunately did not take up. I suggested that he just do the math, but he is so sure in his visualization of how he crosses with ships that wouldn't bother. The math is not at all complicated (Trigonometry 101), and I did it myself in about 5 minutes. I hope that other boaters who suffer from the same misconceptions will learn something useful. The popular misconception runs something like this – “My boat is highly maneuverable; I don’t need no math; all I have to do is keep a good lookout and dart out of the way if I see something scary. 5 miles is a long, long way, plenty of time to deal with it, and a one degree course change at that distance will easily get me well out of danger. 180 feet is plenty of room. 5 miles away is hull down on the horizon – we hardly even notice ships at that distance; surely a ship can’t already be dangerous so far away.” Every sentence of this is completely wrong, and reflects a potentially fatal misconception. Let’s say we encounter a large container ship moving at 24 knots (the latest box boats are usually somewhat slower than this, but plenty of passenger ferries travel at this and higher speeds) and having 60 meters of beam. It is 5 miles away and we are on course for a headon collision. We are travelling at 6 knots and our boat has 4 meters of beam. We are keeping a fantastic watch, and recognize the problem and work out and execute our maneuver in two minutes. We make a one degree correction to “get me well out of danger.” What happens? Combined speed is 30 knots, so if no one alters course, we will get run down and crushed to smithereens in 10 minutes, during which the ship will travel four miles and we will travel one mile. The place of our death will be one mile from our starting position. But what about our onedegree course correction? Trig tells us that an instantaneous onedegree course correction (we generously assume that our nimble little sailboat has an infinite ROT), executed two minutes after we spot the ship, will change our position 8 minutes and 8 cables later, by 0.0175 miles or 32 meters. So if the ship continues perfectly along its course, we will not move more than half his beam plus half of our own beam, and so we will be crushed. RIP, Rod. OK, well, how about 10 degrees? Surely that will do it? An instantaneous 10 degree course change will move your position at the moment of potential collision by 0.14 miles or 261 meters. So we’re safe, right? Not so fast! IF we had perfect information, IF the ship’s GPS is exactly on the centerline, IF the ship (and we) perfectly hold course and speed as we approach each other – then yes – we will pass a little less than one cable from his side – a very close call, but not a collision. But none of those “IF’s” is realistic – not one of them. The ship’s position at the point of potential collision is subject to a socalled cone of error – defined by adding up all of the potential errors and projecting them over time. Do we know where his GPS is? It’s included in the static AIS data, but not even displayed by recreational plotters. So the GPS receiver might be anywhere – and he has a 60 meter (200 foot) beam. So there’s plus or minus 30 meters right there. What’s the position error of his GPS? The new ones are better, but a position error of 10 meters is not unusual even with a modern set. How accurate is our data on his course? Surely not better than plus or minus a couple of degrees. A couple of degrees in the given scenario will change his position (since he is travelling four times faster than we are) by more than a cable in either direction – 0.11 miles or 207 meters. And how well is he keeping his course? Very often fastmoving ships will wander a bit, just like we do. Even one degree plus or minus of error in course keeping will add another error of plus or minus 103 meters. These are not all of the possible errors in our prediction of his position! But add just these up, and we have plus or minus 340 meters, which is nearly two cables. Your 10 degree course correction will simply enter you in a lottery, where the stakes are your life – how will the compounded errors add up? Do you feel lucky? OK, so what if we turn 90 degrees and high tail it out of his way? This maneuver, of course, provides the best chance of a happy outcome, provided of course you are absolutely sure you are turning the right way (you will need the AIS for that, and you might need some time to discern the change of bearing – most recreational AIS displays do not tell you which way you are crossing). At 6 knots, you will get 8 cables – likely to get you out of trouble IF he doesn’t change course himself and IF you are sharp enough to realize the problem while the ship is still hull down and execute your maneuver in two minutes. I rarely meet sailors who are that sharp. And the “I don’t need no math; collision avoidance is easy” type of sailor doesn’t even notice ships that far away. On top of all of that  can you assume that he will not change course? What if he is avoiding another vessel? What if he is trying to avoid you, and turns the same way you do? What if he has a turn? What if he doesn’t see you? THIS is why competent sailors set up their passes in open water to stay at least a mile, and if the waters are not congested, two miles away from passing ships, and to be reasonably safe, you need to do that, too. And why good sailors stay alert to course changes and changes in CPA, during encounters with ships, until they are safely past. Concerning the myth of sailboats’ supposed greater maneuverability – let’s lay it to rest once and for all. It is true that our small boats have a higher rate of turn (ROT) than big ships. So we can just “dart out of the way”, right? Well, no. If you are headed towards a collision, and you want to maneuver to get yourself into a place other than where that collision would happen, your power to do so depends not only on ROT, but speed. At very short distances (like in bays and harbors) ROT may be relatively more important, but in open water, dealing with fast ships traveling at sea speed, speed is the key factor and ROT is relatively meaningless. That is because even a fully loaded VLCC can change its course by 10 degrees in less than two shiplengths, and two shiplengths even of a VLCC is nothing at 5 miles out  it's just a few seconds. With respect to the fast box ship in the scenario above, the effect of his course change is radically different than the effect of ours, and at four miles out, will result in: 1 degree Ship 129 meters Yacht 26 meters 10 degrees Ship 1 306 meters Yacht 261 meters So who is more maneuverable? It’s not us – and it is a gigantic misconception to think so. When encountering fast ships in open water, our slow boats are almost like sitting ducks, and more and more so, the greater the difference in speed. We can’t just “dart out of the way” at all  that's a fantasy. So on the contrary, we have to detect potential collisions from far away and take early action. If we get in trouble, we have much less power to deal with it, than a fastmoving ship. And they don’t always see us. Many recreational sailors feel confident in their ability to avoid collisions because they have never actually found themselves on a collision course with a ship, and so don’t think it could ever happen to them. But that is usually because ships maneuver far earlier than we typically do, and have usually maneuvered to avoid us before we are even aware that they are there. Commercial mariners usually follow the principle that all targets must be analyzed by 10 miles out, and when they see WAFIs like us, they typically take early action, because they know they can’t rely on us to know what to do. They like to give us such a wide berth that no stupid thing we could do, could cause a collision. And so your typical recreational sailor thinks collision avoidance is no big deal – because it’s been done for him all his life. Do you want to continue to depend on ships avoiding you? Or do you want to play a meaningful role yourself in avoiding collisions? It's up to you. Like many recreational sailors, the poster above thinks that 180 feet is plenty of space, and 5 miles out is way too soon to get worried. They need to get acquainted with the math, and understand what is a "cone of uncertainty" concerning the ship's position at the point of impact. It could save lives. 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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When I mentioned, the 1 degree course change, it was with respect to a situation that was not dire, where this is all that is necessary to get out of a collision situation. Of course if circumstances demand a sharper turn, a sharper turn is required. To put this in proper context, it was in repsonse to those suggesting it be necessary to stay more than 1nm away at all times. I was responding to how that is nonsense and not even possible in lots of cases. If a 1 degree course change 5 nm or more away, gets you to a standon position, that is all that is required. You do not have to make a 30 degree course change (for example) to get clear by a mile. 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
I'd hate to face you in Court Dockhead [emoji4]
Well done! 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
Dockhead,
Trig may be basic math to you, but I never had anything beyond high school algebra. Now, my guess is that many, maybe even most of the men here have that knowledge, but unless you propose a Trig for Dummies class here on CF, can you show us maths ignoramuses another way to do this, please? I do know about closing speeds, and I do know to make large course changes, which have worked so far ;), both in terms of crowded (SF Bay) and uncrowded (shipping lanes in Oz), but for the arithmetically or mathematically challenged, is there a short cut? Thanks. Ann 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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These will give you all three angles and all three sides of any triangle, if you give any three. So for any problem such as this  make a right triangle with one defined angle 90 degrees, the other defined angle whatever variable you have  like your 1 degree or 10 degree course change. Define one side as the distance to the collision point. Then the solver will give you the two missing sides  how far away you got from the collision point being the shorter of the two new sides. 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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Only thing that's ever hit me was a French yacht.. they hate Brits. :biggrin: 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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Some here seem to be taking themselves way too seriously. If one is crossing shipping lanes in a small boat, all that is required, is a changing angels to pass astern, and it most certainly doesn't have to be by a mile. In fact, if there is only 2 miles between ships in the lane, 1 mile astern the first is not desireable at all. 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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I appreciate your method for its dead simplicity. Even exhausted, you could make it work. I probably couldn't add 2 + 2 when I'm really exhausted. :wink: Ann 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
My takeaway is that some leisure craft sailors should start using their sails.
A sailing boat is supposedly the one with the right of way (over a steamer). Most of the time. Be seen (AIS). Be heard (vhf). Sail. Imho 1 Nm is a close encounter and when the CPA prediction gets down to 0.5 I get itchy all over. But it may be just me. Maybe other sailors are happy with a cable or so. Cheers, b. 
Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
Not only recreational but navy watchmen also!
The basic rule: "if a boat's bearing to your boat doesn't change as you move along... you are on a collision course..." 
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Re: Collision Avoidance, Cones of Uncertainty, and Appropriate CPA
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Rule 7  Risk of Collision ...such risk shall be deemed to exist if the compass bearing of an approaching vessel does not appreciably change 
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