Mathematical probability of collision with a ship?

I agree with tourbo on part 1 but slightly different on part 2.

pt 2 I reckon it takes 10 secs for the yacht to cross the bows of the big boat ( (25+10)*(60^2)/(2000*6) ) and in that time the big boat travels 87.5 metres. In toher words it has to be more than 87.5 meters away when the small boat starts crossing so the chances are 87.5/2000 or 4.4%

co combined probability of being sunk is about 10%

probably wrong but I've got to the stage of life where the brain only works in the mornings and then only after a good nights sleep.


/forums/images/graemlins/frown.gif
 
ZERO!

Your initial post indicates a presumed TSS (not mentioned) of 0m (zero metres) width.

What you could have said was how many zillions of wine runners on the UK/Cherbourg/UK tax avoidance wine run have been run down?

None known ....
 
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co combined probability of being sunk is about 10%

[/ QUOTE ] Why are we adding the probabilities together? Mathematically it's an either/or situation (the bows or the side impact). If it's an either/or, then it's the mean of the two, not the sum of the two.
 
Re: ZERO!

[ QUOTE ]
Your initial post indicates a presumed TSS (not mentioned) of 0m (zero metres) width.

What you could have said was how many zillions of wine runners on the UK/Cherbourg/UK tax avoidance wine run have been run down?

None known ....

[/ QUOTE ]

TSS is irrelevant, as I said before. There isn't one between Casquets and the Dover Straights, anyway.

I only know one boat be run down in the shipping lanes in the past 6 years - Wahkuna - who unfortunately got themselves a little confused and turned round back in the ship's path. Fortunately all lived to tell the tale, except the brand new boat.

There was also the Ouzo who suffered the loss of boat and three fine chaps, but they werent crossing the lanes at the time.

Anyway, the wine in France won't be worth fetching at 1Euro to the pound! /forums/images/graemlins/frown.gif
 
[ QUOTE ]
[ QUOTE ]
co combined probability of being sunk is about 10%

[/ QUOTE ] Why are we adding the probabilities together? Mathematically it's an either/or situation (the bows or the side impact). If it's an either/or, then it's the mean of the two, not the sum of the two.

[/ QUOTE ]

It isnt an either / or - there are three possibilities and the chances of all three add up to 1.

Clearly if the yot doesnt hit the side of a biggie there is still a 4% or thereabouts chance he will get impaled by the bows. So I dont see how a 4% or so chance of hitting the biggie amidships and a 4% chance of being hit if he escapes the former can add up to a 4% chance of a problem in total. The total risk has to be greater
 
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The answer has nothing to do with maths. If you fall asleep it is certain that you will wake up to find a ship within 1/2 mile on a collision course, even if the horizon was totally clear 10 minutes ago.

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I can vouch for that! My nearest collision was rounding Cape wrath in the dark. The only boat we saw in 50 miles was a ferry coming westwards on our port side on a non collision course. I was not asleep, but was helming on a nice course eastwards just at the point of Cape Wrath.

OOps.. silly "skipper of the day"- of course the ferry was turning south once clearing Cape Wrath. Unfortunately that's where we were. The sailing school "real" skipper was indeed asleep....

YIKES...... flashing lights and VHF saved the day.

Crossing a TSS seemed a doddle after that.
 
Ladies & Gents,

Returning to the original question, you'll notice that the question master has only given us the average LOA and beam of the enemy. There is obviously some variability in the ships' dimensions. How does this affect the possibility of an involuntary swim?

Madame has added a supplementary for Nick le Grand. What is the age of the skipper?
 
I remember an instructor pointing out to me that for a collision to occur, two boats must be occupying the same bit of water.

If one of 'em isn't there, then a collision just isn't going to happen. /forums/images/graemlins/ooo.gif

I think he was the bloke that asked an unobservent helm if they had heard of pantomime ships :
"No, what are they?"
<points astern at closing coaster>
"It's behind you!"
 
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Ladies & Gents,

Returning to the original question, you'll notice that the question master has only given us the average LOA and beam of the enemy. There is obviously some variability in the ships' dimensions. How does this affect the possibility of an involuntary swim?

Madame has added a supplementary for Nick le Grand. What is the age of the skipper?

[/ QUOTE ]

err..... what is the age of the skipper??? you mean I'm a doddery old fool (or just an old bird?)
 
Reminds me of a comment by Niall Ferguson on 'The Ascent of Money' referring to The Quants......

"They knew a lot of mathematics, but nothing about history."

Me, I'd just keep clear for a while, until they'd passed, then the stats would would be highly favourable. /forums/images/graemlins/grin.gif
 
I wish you a Very Merry Christmas and Happy New Year ...

In answer to your question - impossible - too many variants ! cause it's not so simple ....
Read the rubbish on previous threads about similar !! /forums/images/graemlins/wink.gif
 
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Madame has added a supplementary for Nick le Grand. What is the age of the skipper?

[/ QUOTE ]Tell Madame that the skipper is not as old as the person who asked that question! /forums/images/graemlins/blush.gif

Alternatively, the answer is that the skipper won't get much older if he/she happens to fall asleep on a singlehanded channel crossing!
 
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My nearest collision was rounding Cape wrath in the dark. The only boat we saw in 50 miles was a ferry coming westwards on our port side on a non collision course. I was not asleep, but was helming on a nice course eastwards just at the point of Cape Wrath.

OOps.. silly "skipper of the day"- of course the ferry was turning south once clearing Cape Wrath. Unfortunately that's where we were.

[/ QUOTE ]

This is probably a quibble, but AFAIK no ferries round Cape Wrath. Might have been a cruise ship. (This is a quibble, isn't it... /forums/images/graemlins/blush.gif)
 
What's the answer, then?

And is it true you're better off in a fast MOBO ? /forums/images/graemlins/shocked.gif

And worse off in a cat ? /forums/images/graemlins/shocked.gif /forums/images/graemlins/shocked.gif


Andy /forums/images/graemlins/smile.gif
 
Ive no idea what the real answer is, that's why I asked the question!!

Bearing in mind that ships are not all the same size, or travelling in one straight line at the same speed, and looking at the sums in this thread, a 10% chance seems about right. This also stacks up with how often we seem to have to alter course in the E Channel, although JJ seems to be blessed with more luck.

Bottom line is - if you are single handed, don't go to sleep when you are approaching the shipping lanes !!
 
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Ive no idea what the real answer is, that's why I asked the question!!

Bearing in mind that ships are not all the same size, or travelling in one straight line at the same speed, and looking at the sums in this thread, a 10% chance seems about right. This also stacks up with how often we seem to have to alter course in the E Channel, although JJ seems to be blessed with more luck.

Bottom line is - if you are single handed, don't go to sleep when you are approaching the shipping lanes !!

[/ QUOTE ]

Cor blimey - if we hadn't had the question and discussion I'd never have thought of that! Thanks.
/forums/images/graemlins/smile.gif
 
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A yachtsman is sailing his 10metre boat at 6 knots on his own with the autohelm in control, when he falls asleep at the chart table. He is approaching a shipping lane at right angles, where the vessels are travelling in a single file at 15knots, 1nm apart. The average beam of the vessels is 25m, and length 100m.

What is the chance of the yacht being hit by the bow of one of the ships? Similarly, what is the chance of the yacht sailing into the side of one of the ships?

Please show all workings.

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Well, I don't think that anyone has the right answer yet.

Hitting the side of the ship is fairly easily covered. The bigger problem is the bow, because we don't know how it's shaped. But let's make an approximation, and think of the ship as a big rectangular box. Come to think of it, that's what most of them look like nowadays, anyway.

For side-on impacts, the critical line is the one running along the near-side of the ship. When the bows of the yacht arrive at that line it is already occupied by the ship, then there will be a side-on impact. That is to say that the boat's stem has to cross a specific 100m within the inter-ship distance of 1 mile, or 1852m. The probability of side-on collision is therefore 100/1852, or 0.054 (1 in 18.52).

For impact with the ship's bow, the yacht's bow must have passed this critical line before the ship arrives. But if the yacht is well ahead of the ship, then she will clear the bow anyway. Let's neglect the beam of the yacht, and think of her just as a line. To prevent collision, the stern of the line must have cleared the far side of the ship. To do that, the yacht must travel her own length (10m) plus the beam of the ship (25m), a total of 35m. While she is doing this, the ship will move forward. Because the ship is doing 15 knots to the yacht's 6, the ship will move forward by 35x15/6 = 62.5m. So if the yacht's bow crosses the ship's bow within 62.5m of the ship, there will be a bow-on collision. The probability of bow-on collision is therefore 62.5/1852, or 0.034 (1 in 29.6).

For any collision to occur, the yacht's bow must cross that line anywhere from 62.5m ahead ahead of the ship right back to the ship's stern, a total length of 162.5m. The total probability of collision is therefore 162.5/1852, or 0.088 (1 in 11.4).

Of course, this assumes that the OP meant one ship per mile in his question specification. He could have meant that the spaces between the ships were a mile, in which case the 1852 of the working above would have to be changed to 1952, giving a total probability of 0.0832 (1 in 12).

I've neglected the effects of the ship's wash and of the peculiarities of the shapes of the two vessels. But those are my answers.

Why don't we get more collisions? Partly, I think, because there aren't that many ships, but mainly because not all yachtsmen go to sleep on the job!
 
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