And as to the why:
The idea behind intercepting is you want to meet the target at a certain place in the future. But ideally, the sooner the better. This calls for butting your head with the other skipper. You are going for a near-collision course. By the time you detect the target you change your approach to overtake him, or whatever else you feel like. The point is: you want to merge. But where to go?
Merging means closing the distance (only). You don't want to move around him, or he around you. That can be left to the final stage. You want all your energy spent to be focussed on distance. So let's head directly towards him.
1a: plot a line between you and the target.
Oh dear, he's not playing dead, or even comming directly towards you. He is moving at a course, with some angle to the bearing of step 1a.
1b: plot a (long) line representing his course.
(or 1a+1b: plot a protractor/angle thingy: from you, to the target, to his heading)
He having a course not in-line with the bearing means that going directly towards him isn't going to help us. He is stepping sideways, so you need to do that too. Not the same angle mind you. But the same steps for his side steps. Or else you and him will end up doing a swirl around each other. Let's see how much he moves sideways from the bearing line.
2a: Plot a line along the target course, ....
Do you actually know how quickly he moves? Do you need to make a guesstimate of it? Or are you relatively sure, because the convoy speed was given. Oh well. At worst slow contacts move 8 knots when slow, and 12 when medium. (Secret: actually, it's 7.5 and 11.5 due to rounding numbers)
Hmm?... , he moves to the interception point in the same time as you do. Does time then really matter? If you move sideways just the same amount as much as he does, does it matter at all? No! So time, or the actual units of measure used for the length do not matter. Let's imagine we are going to start a drawing that represents a shortended version of the intercept. A period where target moves 6 km at 6 nautical miles per hour (6 knots) (if you insist, it's 32.5 minutes)
2b: Make the length of the line along the target course equal to the target speed. From the starting (or current) position.
Erhm, how quick can you go anyway? Are your engines in fit shape? Are you still required to charge up the batteries? Are the weather-gods favouring you? Whatever the case. Choose a speed that you can maintain all throughout.
Ok, in the same time you also move your last kilometers, at your speed. So you would need to draw a line of your own. Let's say 16km, because your moving at 16 nautical mile per hour (knots).
But you don't yet know where it has to start. It can't be your current position, because we are creating a make-believe drawing first. You don't even know in which direction to pull the endpoint. Just that it must be 16 km (units) of length. And that it ends where the target will be. Ok, so you need to consider all possible directions.
3: Draw a circle around the target endpoint, with a radius of 16 km. It doesn't matter where the arrow is pointing too.
Now you have the collection of all possible starting locations that gets you to end up at the meeting point. All you need to do is choose which one (or two
) it is going to be.
Well, for starters, you currently are on the bearing line. And that is also the shortest path to the target. So, could there be 1 or 2 places that meet those conditions?
Well, yeah. Or, .... probably. It depends. If he is not doing a marathon like a taskforce gone wild. If you are faster than he is, you can bet on there being exactly 1 point on the circle and bearing line. It doesn't matter where he goes, he's toast sooner or later. (Assuming he doesn't change course) If you are slower than he is, then you might get 2 points on the circle and bearing. If he is then also moving away (with more than 90 degrees AOB) then there isn't going to be a point matching the circle and bearing line. And he's a lost cause.
Either way, if there are 2 points on the circle that cross the bearing line, then take the closest one to your current position. The far one will work, but it leads to the the slower, rather than the quickest direction to close the distance. Let's not go there, will you.
4a: Locate the closest intersection of the circle and the bearing line. (from your real position) If there is any. If none, then speed up, or forget him.
Ok, so now you know where you would need to start from. In order to move 16km at 16 knots, while the target is moving his 6 km at 6 knots. And you both whould be meeting each other at the CENTER of the action. (from step 3)
Cool, now you know the direction. To go from the intersection, to the center of the circle. You could also consider this to be the angle you have to steer away from the bearing line, to be meeting the target in the face.
4b: Draw a protractor (angle thingy) from the center of the circle, to the nearest intersection point, to along the bearing line.
Now you know how much you need to lead the target with your bow.
"Any other information I can glean from this triangle?" You sure do, smart cookie!
Measure the length between the intersection point, and the current target location. That length is the rate at which the distance is shortening. Closure rate. The value is in knots, because all the other speeds are in knots too. But you wouldn't have to bug your navigator about calculating it. Oh wait, you are the navigator. Oh well, remember that closure rate! Convert it to km/hour by multiplying it by 1.852. Or use the nomograph.
"Homo... , say what?"
See the vertical scales on that colorful map drawing!
Wiki hint!
"Ok, whatever! But remember this was only make-belief. I'm way much further away than that. I'm never going to meet him in 32 minutes, ... and a bit."
Correct, but do you remember that you only had to steer exactly so many degrees (as step 4b) away from the bearing line? Yes? Then do that.
5: Draw another protractor/angle thingy: from the target, all the way to you. And then match the angle in the corner to step 4b. Drag it out until it crosses the target course.
"Got it!"
Good! Now, what's keeping ya. Set sail. Drop a waypoint on the new meetingpoint. And keep an eye out on that (true) bearing. If you did your speed guessing right, someone is going to be lingering on it. At least you'll know where to start looking.
Godspeed friend. I hope that is step by step enough.