Collision Avoidance, Cones of Uncertainty, and Appropriate CPA

[Dockhead]

Originally Posted by evm1024

Just for fun I ran some calculations describing a crossing at 90 degrees between a ship and boat. There are lots of assumptions like the boat is pencil thin and the ship has a square bow. Also keep in mind that we start with the boat directly in front of the ship and end with the ship directly astern of the boat. There are no waves speed variations and the like. This does not give the CPA. It is only calculated for the ship being directly astern of the boat by a given distance. CPA will be less than this distance.

OK, the boat is doing 7 kts and is 50 feet long. The ship has a beam of 110 feet and is doing 15 kts. (for sake of understanding say the boat is on 090 true and the ship is on 000 true)

So if we want the boat to just miss being hit by the ship the boat needs to be 171 feet ahead of the ship when it crosses the ships bow. The ship will just miss the boat after 6.77 seconds. (hey, this is a good crossing! Just my pucker factor is less obvious than yours)

If we want to have 180 feet between the ship and the boat when the ship is directly astern of the boat the boat needs to be 557 feet ahead of the ship when crossing the bow. It will take 22 seconds for the ship to move to the place where the boat was when the boat was directly ahead. (great crossing, 22 seconds is a long time - I'm listening on headphones, I don't hear anything)

If we want a quarter of a mile between us then we need to be 3426 feet ahead of the ship when we cross her bow and it will take the ship 2.2 minutes to get to where we crossed her bow. (Easy peasy - what pucker factor)

If we want a half mile between us then we need to be 6681 feet (a nm) ahead of the ship when crossing her bow. The ship will take 4.4 minutes to get to the crossing point. (I have no clue why he keeps sounding his horn)

Lastly if we want 1 nm between us then we need to be 2.17 nm ahead of the ship when crossing her bow. The ship will take 8.7 minutes to reach the point of crossing.

If we take the last crossing and expand it to become a full crossing rather than just an escape we start with our boat 1 nw away from crossing the ships path. Still doing the same speeds and a 90 degree crossing aspect we get a CPA of 0.9 nm 15.4 minutes later. This crossing starts with the ship 4.45 nm away from us 77 degrees off our bow. We will be directly ahead of the ship in 8.7 minutes.....

Hey, this is really great stuff

I'm glad someone else is thinking about the actual geometry, because this is REALLY important, and it can be TOTALLY different from how you imagine one of these crossings in your mind. I have also been plotting some crossings, and I'll post something over the weekend.

Why don't you continue with that? Just, don't assume the ship is pencil thin, because of course, it's not. Also, take account of uncertainties of his course keeping and position of his GPS antenna. Draw a "cone of uncertainty" to cover what we can't know about where he will be, and one concerning our position.

Also, collision avoidance becomes harder with bigger differences in speed. We have been using 5 knots and 20 knots. If you also use them, the problems will become more obvious.

See what kind of maneuvers it takes, at what distance, to disconnect these cones. Wherever they intersect, we are either (a) having a collision; or (b) not having a collision just by pure luck. We can only control the crossing within the limitations of what we can know. That's where a safe CPA comes from -- it gives enough space to account for all those things, which we cannot know.

Like in so many things -- knowing what you do not know, is the essence of wisdom. That hasn't changed since Aristotle said it thousands of years ago.

[evm1024]

Thanks - The boat (sailboat) is pencil thin and the ships beam is taken into consideration.

I just tossed these out so as to show what we are talking about when speaking of less than a 1 nm CPA. It is easy to forget that Ships look freeking huge 1/4 nm away in open water.


I might get around to doing a few with cones of uncertainty....

I should do a geometry to show what crossing astern with a 180 foot CPA looks like....

[Dockhead]

Originally Posted by evm1024

Thanks - The boat (sailboat) is pencil thin and the ships beam is taken into consideration.

I just tossed these out so as to show what we are talking about when speaking of less than a 1 nm CPA. It is easy to forget that Ships look freeking huge 1/4 nm away in open water.


I might get around to doing a few with cones of uncertainty....

I should do a geometry to show what crossing astern with a 180 foot CPA looks like....

Yes --

You'll find that crossing astern with 180 foot CPA simply can't be done, because you can't know enough about his position to set it up.

Let's just suspend disbelief for a moment and imagine we have God's knowledge of where we both are, to the cm. You have to run right at him, and it will look for all the world, from your cockpit, like you're going to T-bone him. 20 knots is 10 meters per second, so 180 feet will be covered in about 5 (!) seconds. Yet, you are moving at only 2.5 meters per second. So the side of the ship will still be dead ahead of you just a few seconds from what would otherwise be impact.

Talk about "pucker factor"! From your cockpit, it would look like you are sailing right into a T-bone situation, and then his stern just flashes by at the last second. You cannot set that up, without God's knowledge, which we mortals with our limited human senses, and weak electronic aids, do not possess.

[dano098]

From basic air intercepts, but a useful and much slower, collision analysis is assisted by examining relative relative motion of the target. If your hypothetical freighter is staying on the same point of reference on your boat, then you have attained collision geometry. If you alter course so the apparent motion of your "target" is moving toward your bow you will pass behind. Converse to pass in front. Obviously there is the parallel or reciprocal case when the apparent size isn't changing, would indicate parallel tracks. (If reciprocal the target would be getting smaller.)

Fair warning, my sailing experience is dated and I'm not currently sailing. I offer this notion as food for thought. It easy to "chair fly" though.

[Lodesman]

Originally Posted by David M

I hear ship pilots agreeing frequently to pass starboard to starboard in narrow channels...by VHF.

They are not breaking the COLREG"s.

Way to take something out of context - I was specifically talking about the application of rule 2. In my subsequent post (#449) I illustrated the very point you are now making. Do keep up.

[evm1024]

Originally Posted by Dockhead

Yes --

You'll find that crossing astern with 180 foot CPA simply can't be done, because you can't know enough about his position to set it up.

SNIP!

Yes, pucker factor in the true meaning of the phrase.

Just some quick back of the napkin calculations.

Same sailboat doing 7 kts and a 500' long, 110' beam ship doing 15 kts. Assume that the superstructure is 80' above the water. Assume a 90 degree crossing.

Let's assume that a CPA of 180' is achieved when you are 45 degrees off the aft corner of the ships stern. This would put your stem 127 feet aft of the ship and 127 feet from the path of the side of the ship.

So 45 seconds from your 180' CPA you will be 658' from the path of the side of the ship and the bow of the ship will be 511' before your path. The ship will be bearing 52 degrees off your bow.

40 seconds from the CPA you will be 599' from the path of the side of the ship and the ships bow will be 385' off your path. The bearing is 33 degrees off your bow.

35 seconds from CPA you will be 540' from the ships path and the ships bow will be 258' from your path. The bearing is 26 degrees off your bow.

30 seconds from your CPA you will be 481' from the ships path with the ships bow 132 ' from your path. The bearing is now 15 degrees.

25 seconds from your CPA you will be 422' from the ships path and the ships bow is 5' off your path. The bearing is 1 degree (dead ahead!).

From now on you are pointing at the ship. Your 1st mate is signing divorce papers.

20 seconds form your CPA you will be 363' from the ship with the ships stern 379' from your path. The top of the ship appears 12 degrees above the horizon.

15 seconds from CPA you will be 304' from the side of the ship with the ships stern 252' from your path. The ship rises up at a 15 degree angle.

10 seconds from CPA you will be 245' from the side of the ship with the ships stern 126' from your path. The ship rises up 18 degrees.

5 seconds from your CPA you will be 186' from the side of the ship. The ships stern has just crossed your bow. The ship rises 26 degrees above you.

0 seconds from CPA you will be 127 feet from the path of the side of the ship and an actual distance of 180' from the aft corner of the ship. the ships aft corner is not 127' past your path. The ship towers above you at 32 degrees.



I'm told that it is safe to pass like this....

[Dockhead]

Originally Posted by evm1024

. . . I'm told that it is safe to pass like this....

ROTFLMAO.

And this is 7 vs 15 knots.

Why don't you run this at 5 vs 20? "Pucker" is not the word!

[evm1024]

In the above passing astern with a CPA of 180' we assume that the ship is on rails and does not alter course at all. A change of course for any reason could quickly lead to a collision.

It does not take much helm to cause a ship to shift its stern 180' in the 2 ship lengths that the calculations describe.

The calculations also assume that the sailboat and ship are crossing an 90 degrees to each other. This is very hard to judge by eye. If by chance the actual crossing were less than 90 degrees then the CPA would be much closer - possibly leading to a collision

These and many other factors are what lead to the uncertainty of position at any given time. And when you project those uncertainties over time give us the cones of uncertainty.

If you were to attempt to cross like this and there was a collision I feel certain that you would be found negligent at least and most likely grossly negligent. With the full responsibility resting on your shoulders.

When I can't get away to the San Juans and Canada I boat on the Columbia river. The river has a lot of ship traffic that is bound to the channel. When crossing behind a ship it often looks like the CPA is 180' but in reality the actual crossing CPA is more like 300'. It just looks damn close. Perhaps 180' is a mis statement based on how it looks.

And further - no way in hell would I pull a 180 CPA in open water. Far too close, far too unpredictable, far too risky and just not smart. I try no never let my gonads tell me what risks to take.

[evm1024]

Originally Posted by Dockhead

ROTFLMAO.

And this is 7 vs 15 knots.

Why don't you run this at 5 vs 20? "Pucker" is not the word!

I'll leave that as an exercise for the reader. I'm actually at work letting this distract me.

But it is important to get across the reality of the numbers and to drive home that there are cones of uncertainty that will bite you if you ignore them.

I should write a program to calculate this rather than doing it by hand.

Back to work, back to work, back to work.

[Dockhead]

Originally Posted by evm1024

In the above passing astern with a CPA of 180' we assume that the ship is on rails and does not alter course at all. A change of course for any reason could quickly lead to a collision.

. . .

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. Subjectively it would be like making a dead run at the side of the ship, looking for all the world like you're going to T-bone him. Then his stern just flashes by at the last second. If either vessel's course or speed varies slightly in the wrong direction, then you're dead. All of this is why there is such a thing as a safe CPA, and why there is such a thing as an inadequate one, and the difference does not depend on anyone's sphincters.

[carstenb]

Originally Posted by evm1024

Yes, pucker factor in the true meaning of the phrase.

Just some quick back of the napkin calculations.

Same sailboat doing 7 kts and a 500' long, 110' beam ship doing 15 kts. Assume that the superstructure is 80' above the water. Assume a 90 degree crossing.

Let's assume that a CPA of 180' is achieved when you are 45 degrees off the aft corner of the ships stern. This would put your stem 127 feet aft of the ship and 127 feet from the path of the side of the ship.

So 45 seconds from your 180' CPA you will be 658' from the path of the side of the ship and the bow of the ship will be 511' before your path. The ship will be bearing 52 degrees off your bow.

40 seconds from the CPA you will be 599' from the path of the side of the ship and the ships bow will be 385' off your path. The bearing is 33 degrees off your bow.

35 seconds from CPA you will be 540' from the ships path and the ships bow will be 258' from your path. The bearing is 26 degrees off your bow.

30 seconds from your CPA you will be 481' from the ships path with the ships bow 132 ' from your path. The bearing is now 15 degrees.

25 seconds from your CPA you will be 422' from the ships path and the ships bow is 5' off your path. The bearing is 1 degree (dead ahead!).

From now on you are pointing at the ship. Your 1st mate is signing divorce papers.

20 seconds form your CPA you will be 363' from the ship with the ships stern 379' from your path. The top of the ship appears 12 degrees above the horizon.

15 seconds from CPA you will be 304' from the side of the ship with the ships stern 252' from your path. The ship rises up at a 15 degree angle.

10 seconds from CPA you will be 245' from the side of the ship with the ships stern 126' from your path. The ship rises up 18 degrees.

5 seconds from your CPA you will be 186' from the side of the ship. The ships stern has just crossed your bow. The ship rises 26 degrees above you.

0 seconds from CPA you will be 127 feet from the path of the side of the ship and an actual distance of 180' from the aft corner of the ship. the ships aft corner is not 127' past your path. The ship towers above you at 32 degrees.



I'm told that it is safe to pass like this....

Well heck,

180 feet is 1/4 of a cable - lots of room - someone with real "pucker factor" woujld scoff a this and do it with only 90 feet

I mean - how hard can it be?

[Dockhead]

Originally Posted by evm1024

I'll leave that as an exercise for the reader. I'm actually at work letting this distract me.

But it is important to get across the reality of the numbers and to drive home that there are cones of uncertainty that will bite you if you ignore them.

I should write a program to calculate this rather than doing it by hand.

Back to work, back to work, back to work.

Wouldn't it be cool if there were a simulator? Commercial guys train on them to learn collision avoidance -- why don't we? I figure it would not be a big challenge for a game developer -- all the vector math and modelling is pretty basic.

I think a lot of people would be really surprised to see, what this or that crossing really looks like, and training on the simulator would be immensely valuable.

[Dockhead]

Originally Posted by carstenb

Well heck,

180 feet is 1/4 of a cable - lots of room - someone with real "pucker factor" woujld scoff a this and do it with only 90 feet

I mean - how hard can it be?

Heh, heh.

[StuM]

Originally Posted by ramblinrod

That there is human decision involved at the time the "Safe Distance"
decision is made is clearly subjective. I'm not saying that I would pass
The transom within 180 ft, but I guarantee that as I approach the crossing, I will subjectively determine the minimum safe distance I need to give the lead boat transom port corner, and if that distance is determined to be 180 ft by me, that s how close I will come. I will also turn to port as soon as I clear that corner, by the degree required to get no closer to the lead boat, and maintain maximum distance from the following boat, until I am the hell out of its path.

To me, in this example, that is the "safe distance" and it s
completely subjective. Handle it.

Have you ever actually sailed close to a large ship travelling at speed?

Even if you turn 90° to port when you clear the port transom corner, you will get no closer to the lead boat if you are doing 5 knots and it is doing 20 knots!

So with a ship bearing down on you at 20 knots and you doing 5 knots, you turn so that you are in his path for a longer period? Madness!

[ramblinrod]

Originally Posted by Dockhead

What is an acceptable RISK is an individual decision.

Exactly my point, that many has been rejecting.

Thank you for acknowledging.

This is the Pucker Factor.

To me, cutting close (maybe to 180' from the transom, if I believe I can safely do so) behind the lead ship, to maintain max distance from the crossing the bows of the following ship, WILL BE acceptable RISK to me.

If I screw up, and cause a collision, OF COURSE I AM AT FAULT, the same as if I screw up and cause collision under any circumstance.

But if I don't screw up, and come within 180 ft of the lead boat transom as planned, and stay as far as possible out of the way of the following boat, I have maintained a "safe distance" UNDER THOSE CIRCUMSTANCES, according to Colregs.