[RingoCalamity]

I was thinking about how to do this simply yesterday and I think I've developed a method for mounting an attack - or at the very least generating accurate heading/speed/range data for a target. I had some success with it last night tracking a target in a custom mission but didn't have time to launch a fish or try it out in the wild.

I apologize if much of this is old news - I can't be the first one to have tried something like this but my searches didn't find much. I'm probably reinventing the wheel here but it's been a fun challenge anyway.

I'll explain what I've done here on pencil and paper and try to explain the issues I'm having with it as well as I get to them.

The example assumes a fairly close range target just because I've already done the time/distance conversions for it on this scale. Some of the measurements will be in metric as that's the way I worked it out. This will probably be clearer if you follow along on paper.

This is a long post but it's not complicated. I've summarized the steps just below. I just worked it out with a pen and ruler and calculator for the distance conversions.

A summary of the process:

-take 3 timed measurements
-determine target course
-plot future timed bearings
-move and take new timed bearing
-determine actual speed and range

The first two steps above would probably have to be repeated a few times to move your boat into a suitable attack position.

PART I

First, we start with the boat, presumably stationary and submerged, and a passive sonar contact. We mark the bearing and draw a line from our boat on that bearing. We start our stopwatch and plot a second bearing 3 minutes later.

Why three minutes? At the ranges we're talking about (medium to short-ish - 5 km and under) it should usually give us a good separation on our headings, if our target isn't heading right for us or directly away. For longer range targets, you'd want to use more time, it's a call you'd have to make in the moment depending on the quality of the data you're getting.

Three minutes after our second timed bearing, we take a third bearing on our target. We'll want to keep the clock running for the duration of the attack (probably a good reason to have a real-life stopwatch if the ticking of the one in game drives you crazy).

We now have three timed bearings on our target.

PART II

What can we learn from these bearings? I think I've found a few things, provided we make a few assumptions:

1. Our target is moving at a constant speed

This means that he covered the same amount of distance between bearings one and two, and between bearings two and three.

2. Our target is moving in a straight line

We can already tell whether the target is moving towards us or away from us - if the distance or angle between the first two bearings is greater than the distance between the second two bearings, he's moving away from us - as the target grows more distant, his relative bearing to us will change more slowly if his speed remains the same.

Likewise, if the distance or angle between the second pair of bearings is greater than the first pair, the target is closing with us - his relative bearing will change more quickly the close he gets.

If the angles and distance between the two sets of bearings (one and two, and two and three) are the same, he is passing directly past us but will soon be moving away.

I've read that you can use the rate of bearing change to calculate either speed or range or both. I don't know how to do that. However, we can get a heading.

This is the part that's easy on paper and more difficult with the in-game interface. Our target has traveled the same distance between bearings one and two, and bearings two and three. So, we're going to throw our first estimate out there and use that get his estimated distance (for his estimated speed) and his actual heading.

PART III

We'll estimate a speed of 11 knots. This translates to 1017.72 metres every 3 minutes, as per our timed measurements above. With the pen and paper, I've been working in a scale where 1cm = 500m.

With this example, I'm assuming that the bearings we've taken will have a total spread of about 45 degrees, which would give an 11 knot range of about 3km. Initial contact is likely to be much more distant and, as mentioned previously, require longer duration timed bearings. At that range, however, good estimates will be good, enough, as we'll just want to close on the target, at that point we don't need data good enough to shoot with.

So, pencil and ruler time. This is the biggest problem with this method as it stands - there isn't an easy way to do this in game and I can't express it in math. Yet, it's really simple just by eyeballing it.

Taking our ruler, we need to find the 4cm long line - this is the 2035 metres the target traversed over the course of our timed bearings, if his speed was 11 knots - that fits on our three bearing lines. All 3 points must be on a bearing line, and there is, as far as I can tell, only one position where the 0cm, 2cm, and 4cm marks all fit perfectly on the bearing lines we've drawn.

To make this as clear as possible - with our ruler, 0 cm is where the target was when we shot our first bearing. 2 cm is where he was when we shot our second. 4 cm is where he was when we took our third. His path is right there on the ruler. We have to fit those three points onto the bearings we took.

That one spot where the line fits gives us the target's course, as well as his estimated range given his estimated 11 knot speed.

There's got to be some kind of way of using math/trig to find that point where the line fits, but I don't know it and I haven't been able to work it out. As well, the tools for doing so in the game are clumsy and inaccurate. The best option seems to be taking the two angles to the bearings from our boat and the measurement from game data, plotting them on paper, and using your ruler to find the course, then sticking it back in the game. Some of the other measurements would be easier on paper but can be done in game.

That's all I have time to post right now, I'll come back to this in a bit. So far, we've developed our target's course. Next, I'll look at determing range and speed. Sorry this is so long, if this idea turns out to have any merit, I'll do up some diagrams to make it clearer.