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Navigation problem

7K views 42 replies 21 participants last post by  SailNet Archive 
#1 ·
Are there any navigators here? What is the procedure for plotting an intercept course, as in meeting another boat that is approaching from a different direction. For example, if my friend is on a steady course of 036T and travelling at 5K and I am 84NM away on a bearing of 096T and I make 7K, how do I plot a new course to intersect him so we arrive at the same spot at the same time?(assume a constant track and speed) Anyone? Thanks, John Davidson
 
#27 ·
On a paper chart, plot your friend's DR track out past the time you want to meet, then set a compass to the distance you can make during that same period. Set the compass point on your current position, and strike an arc through your friend's DR track; this is point where and when the meeting will take place, if you steer the course between your current position and there. If the arc does not intersect your friends track, one of your assumptions is unrealistic (speed, etc.). You can adjust for set and drift as you near each other. That's the way I did it thirty years ago, in the Navy, on the bridge.
 
#28 ·
tmhdgpth,

That's a useful technique, but doesn't respond directly to the problem as stated.

This is because there is no fixed time (time desired) for meeting. Rather, the desired meeting time is the EARLIEST time possible, given the relative positions of the vessels, the (fixed) course of one of them, and their respective speeds.

It's a classic intersect problem used in war gaming and targeting, as well as air and maritime navigation. Maneuvering Boards were the classic way to solve the problem, and a few brave souls used trig, but now calculators and computers make it easy.

Regards,

Bill
 
#29 ·
I'm impressed with all the effort that has gone into solving this. I apologize for the ambiguity in my original post. I meant the relative bearing TO the other boat (friend)was 096T, but did not make that clear. The actual USCG question uses different courses, I was looking for the method, not an answer, and if I understood trig better (at all?) I think you guys have done it. The testing is multiple choice with four possible answers given. The answers only vary by 2-3 degrees each so you have to be right on. In the actual test nothing except a simple calculator, plotter, parallel rule, dividers and a pencil are allowed. By the way, the CG has a data bank of 14,000 total questions, (Navigation General, Rules of the Road, Deck General, Navigation problems) and I am working my way through all of them(lot's of duplicates). Thanks again for all the help and ideas. If I come across something else that stumps me I'll post it. Now, back to how many round turns to put on a bitt before figure eights using nylon line:)) John
 
#31 · (Edited)
btrayfors said:
Capt Hand,

Yeah, easy, but I believe confusing on several counts.

First, the friends boat (Vessel #1) is on a COURSE of 036T, not a BEARING.
Oops, my bad, thanks for catching that. I've edited the post to correct it.

As for the question of the initial bearing from one boat to the other, I responded to the post the way it was asked. This was explained several posts back and a link to a diagram of the vectors was included.

If the bearing of the intial positions is interpreted in the conventional way, from your boat to the friend's boat, then the internal angle between the initial bearing to the friends boat and his course will be 120 deg. The solution is to head on a course of 57.8 deg. The boats will intercept in 28 hours.

Is this horse dead?
 
#32 ·
Okay guys, I have a really easy fix to this problem with the least amount of errors that could occur.

One guy heaves-to and reports their position

the other guy sails to his position.

Done!


Take drift and current into account of the other boat, and it's flawless!
 
#33 · (Edited)
To the best of my knowledge, you are allowed to use manoeuvering board sheets in the USCG exam and, as previously mentioned, they come complete with the directions on them. It really is the easiest, most fool-proof way to do the problem. They can also be used for small area plotting sheet construction used in celestial navigation. A word to the wise on USCG exam questions (I've passed four, not counting renewals). The multiple choice answers have accounted for the, "oh good, it's multiple choice if I'm close the answer will be right there" factor. The incorrect answers are the result of the most common errors made in answering the question and, as such, will be exactly wrong. Clever people those CGs. Good luck and remember to read the question. I taught the navigation portion of the license prep course at the USMMA and one of the most common complaints was, "oh, I thought they meant something different". The wording must be read and interpreted exactly as written and not as to what you "think" it's trying to say. (I know that doesn't make sense to those who haven't been there-just think in terms of a double trick question!) If you are in doubt about the accuracy of the wording of the question, you can protest it in writing, but the protest writing comes out of your exam time. Don't waste time asking the proctor for an explanation of the question, he is generally a petty officer with little or no knowledge of the exam itself-he's just there to pass out the papers and monitor.

Just nit-picking, but relative bearings are not marked True, Magnetic, Compass or otherwise. Relative bearings are only related to where the bow is and the bow doesn't change regardless of what choose to call the course you are on.

As btrayfors said, it is of utmost importance to use these navigational terms with rigorous exactitude. Mis-speaking can lead to mis-construing, and that can ruin your day at sea. As Robert Ganier, who has also taught navigation, will tell you-the devil is in the details. Small math mistakes ruin the other 99% done correctly. A "passing" grade on the navigation portion of the exam is 90% on the principle that the correct answer is right where the ship is located and an incorrect answer is, well.....aground.

Allowing for set and drift does not detract from the relevance of the question. We always have to factor that in, usually as we go, and it doesn't change the fact that we do have to set an initial course. I suppose one could intercept Bishop Rock starting with even a westerly heading, but something in the northeastern quadrant might be less time consuming.
 
#42 ·
how about this one?

two guys want to meet at sea soon as possible.
what course they have to set respectively to minimize intercept time?


Easy, they progress directly toward each other at that instant since they are in identical boats with the same wind drag (in essence they are mere mathematical points). Cam's redhead's snout is pointing at the boat with the acorns, and she really likes it when the sea gets sloppy. :D
 
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