[jason210]

Given that the convoy is ahead of you, ie within a 180 degree arc around the bow of the sub...

1. There's usually a warship in front of and behind the convoy so ignore those and turn the dial to where the "big sound" of the convoy either starts or ends and use that point. Track it for a while, taking bearings periodically - for example every 10 minutes. (Ideally the Uboat should be still for this, but so long as it is moving very slowly and not turning it will be ok).

2. Note which way round the dial the sound appears to be moving, this will tell you whether the point where the big sound starts is the front or back of the convoy.

3. If the convoy is moving away, the angle detected on the Hydrophone will be successively decreasing with each periodic measurement; if it's approaching, the angle will be successively increasing with each peridoic measurement.

These simple steps tells us whether the convoy is getting closer and gives us an idea of its bearing.

Range
The range is related to the size of the angles between the periodic measurements. If the angles are very small, then the target is a long way off. Another thing you can use is the size of the angle occupied by the "big noise". Again, if this is small angle, the convoy is far way; a large angle, the convoy is close. This gives you a basic idea of the situation.

For more detail, you need to know the speed of the convoy. This is vital, but unfortunately without intel we can only guess that. Most convoys move pretty slowly, so you could perhaps go for 12 kts. But the success of any calculation using passive sonar depends on this.

Now for math:

a) How many metres will a ship in that convoy travel in 10 minutes, moving at 12 kts?

Answer:

First convert to metres per minute using 0.032:
12/0.032 = 375 metres

In ten minutes:
375 x 10 = 3750 metres


b) Now to work out range using using distance as represented by the angle on the hydrophone. You need to use trigonmetry for that, and it gets messy if the target is not perpendicular to your course. But if you use 3750/sin (5) you'll get a reasonable estimate, ie 43 KM. The more the ship is turned away from a perpeniducular course to yours, the less accurate this result will be.

This is as much as I am prepared to do manually, but in order to get a good estimate on the convoy's bearing, more work is needed. And it get's messy just using pure forumulae. The best way to approach this is to draw geometric diagrams on paper. Also, if you have access to any of the Sonalyst Sub Simulators like Sub Command, Dangerous waters etc, then there's a good geometric representation within that simulator that shows you periodic plots of sound contacts and proposed solutions that you can move about.