Good summary Stoianm, but if I can add a few additional pointers:
As you point out, this method is only really accurate if the target is at an AOB of around 90 degrees to your sub. The rest of the time, it will not give you an accurate speed reading.
Another method which is independent of AOB is the map plot method, namely:
1) determine Range, Bearing, plot on TAI/NAV map(Mark #1);
2) run chrono for a fixed time period;
3) determine Range, Bearing, plot on TAI/NAV map(Mark #2);
4) draw a line from Mark #1 to Mark #2, measure distance with ruler.
You can then determine speed with the following formula:
-distance measured on map x (factor to convert to distance travelled over an hour, for example if you ran chrono for 1 min, you would multiply by 60) divided by 1852;or
-if you run the chrono for 3min 15 seconds, you can just drop the last 2 digits from the distance measured to get the speed in knots.
I know this method ( i think i readed in Wazoo's Manual ploting). You are right there are not related to AOB but with the one that i described i had an area of wron calculation aroun 0.5 knot when the AOB was far away from 90 degree - so, not so big deal (with the one that you described i had almoust the same area of wrong calculation) - i use this one because is fastes.
If you have one of the realistic periscope mods (I use Arclight's mod), you can also measure range by eye as follows:
1) identify target and determine mast height;
2) measure mast height in number of Horizontal Bars on the scope;
you can then measure the range based on a formula, for example with Arclight's MRP, the formula is:
1.5x - MastHeight x 100 / horizontal bars = Range
6x - MastHeight x 400 / horizontal bars = Range
for example, a Liberty Ship has a mast height of 27.1 meters, if the measured height is 4 bars at 6x, the range would be 2,710 meters.
i.e. 27.1 x 400= 10,840 divided by 4= 2,710 meters.
This thread can also be of interest. The 1st post by Hitman links to a document of German U-boat periscopes.
http://www.subsim.com/radioroom/showthread.php?t=166280
I know ,,manual targeting by Hitaman''.
We use now the ,,manos scope'' (tested also the arlight scope - manos had more acurate readings). Almoust the same thing like you find in Hitmans posts you can find in Trevally tutorials but he use the real RAOFB - very good tutorial.
if you using the map plot method, you will also have the accurate course of the target on the map. You can then easily determine the AOB by using the protactor to measure it.
You now have Range, Bearing, Speed and AOB which can plug into the TDC. Best of all, you just need the scope, map and a calculator.