Another historical method also explained in the same thread mentioned in below post #5.
In this method you measure the change in bearing over a period of 1 minute. You take the bearing of the target (b1) and start the stopwatch.
At this time you also estimate the range (R) to target. Exactly 1 minute later you take a second bearing (b2).
The change in bearing (Δb) will allow you to calculate the correct speed input for the TDC with below formulae.
1.) V(col) = V(own) x SIN(b2)
This represents the speed input for the TDC IF WE WERE ON A COLLISION COURSE.
We are not – the bearing is changing and thus we need to apply a correction (c):
2.) c = R x 3.2967 x SIN(Δb)
Remember to convert your range (R) to hectometers by dividing by 100! The 3.2967 factor is to correct from metric to nautical miles since the correction (c) is in knots.
3.) V(input) = V(col) +/- c
Speed to input into the TDC. If sub and target bow go in the same direction and the bearing change shows the target pulling ahead, you will ADD correction (c) to V(col). SUBTRACT if sub and target bows are going the opposite directions, or if you are gaining on target (bows in same direction).
We can do these calculations quickly with the slide rule as demonstrated in below example.
We are stalking a target submerged (own speed 1.5 knots) and take a bearing of 313 degrees and start the stopwatch. Estimated range is 1800 meters.
One minute later we take the second bearing and it is 317 degrees. This is a relative bearing of 43 degrees. We can now calculate the TDC speed input.
1.) V(col) = V(own) x SIN(b2) = 1.5 x SIN(43)
Point the 1 on the C scale to 1.5 on the D scale. (All numbers on the D scale are now multiplied by 1.5 on the C scale).
Find 43 degrees on the S scale and put the hairline on it. On the C scale we find that the sine of 43 degrees equals 0.682.
We find on the D scale that 0.682 multiplied by 1.5 equals 1.02. So V(col) equals 1.02 knots. See first photo.
2.) c = R x 3.2967 x SIN(Δb)
Point the 1 on the C scale to 3.2967. (All numbers on the D scale are now multiplied by 3.2967 on the C scale).
Find 4 degrees on the ST scale (small angle less than 6 degrees so we use the ST scale instead of the S scale) and put the hairline on it.
On the D scale we find that 3.2967 x SIN(4) equals 0.23. Now we need to multiply this with the range (1.8 hectometer).
To do this simply slide the 1 on the C scale under the hairline. (it is now pointing to our answer (0.23) and all numbers on the D scale are now multiplied by 0.23 on the C scale). Now point the hairline on 1.8 on the C scale and we find that 0.23 x 1.8 equals 0.414. See photo's 2,3 and 4.
3.) V(input) = V(col) +/- c
The target bow is coming towards us so we must add the correction to the speed.
So the final speed in put for the TDC is 1.02 + 0.41 = 1.4 knots.
Calculation like this are very simple to make using the slide rule and might even be quicker than using a calculator and the accuracy is more than enough.