Quote:
Originally Posted by SailRN
I'd love to see how to do this!
Thank you.
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[The first time I posted this, I found some errors. Here's attempt #2.]
In the attached image, I've used a maneuvering board. But you can use a plotting sheet, graph paper or even blank paper. You just need a way to measure angles, such as a protractor or
compass rose, and a way to measure distances, such as a ruler or chart scale and dividers.
Let's say there's another vessel at a bearing of 140° at a distance of 3 NM. We've determined* that its true course and speed is 280° @ 5 kts., and we'd like to intercept it. We've found that we can also make 5 kts. in a southerly direction, so we'll use that speed†.
First, we plot the other ship's position relative to us (the red square in the image). Then, we decide what
relative motion we'd like the other ship to make. Since we want to intercept it, we want it to move on the reciprocal of its bearing from us, 320°, so that it will appear to move straight toward us.
Next, we plot the other vessel's true speed and course as a line extending from the center of the plot (the "top" of the triangle in the image). This is a relative motion plot and is completely separate from the plot of the ship's position. Any convenient scale can be used for both plots and they don't have to be the same.
Then, we draw a circle centered on the plot and with a radius equal to our desired speed, 5 kts. We then draw a line in the direction of the desired relative motion, 320°, which ends at the end of the other ship's true motion vector (the "left side" of the triangle in the image). We draw this line long enough that it also intersects the speed circle we drew earlier.
Finally, from the point where the relative motion line intersects the speed circle, we draw a line back to the center of the plot (the "right side" of the triangle in the image). This is our true course to make good to intercept the other vessel at a speed of 5 kts., about 189° in this case.
If we measure the length of the relative motion line, we see that the other ship will appear to close on us at 7.1 kts. At a distance of 3 NM, this means that our CPA (closest point of approach) will occur in about 25 minutes and - if we do nothing else - will be a
collision.
As others have written: there are instructions on how to find this and many other solutions online. I recommend the
Radar Navigation and Maneuvering Board Manual, Chapter 6. Also as stated: there are apps that can do all of these calculations for you. But, as I wrote, it can quickly and easily be done on a sheet of paper, too.
* There are ways to determine true course and speed of another vessel using this method. See manual linked above.
† One can also find the course to make good and speed to use for the fastest intercept time if speed is not limited. However, speed limitations can often prevent a direct intercept. In that case the distance, bearing and time of the closest possible approach can still be determined.