AOB can be calculated by comparing the true angular length with the observed angular length. With true angular length I mean the angular length of the target at an AOB of 90 degrees. At this aspect the observed angular length reaches it's maximum. To calculate the AOB divide the observed angular length with the true (maximum) angular length. Now calculate the inverse sine of this number to get the AOB angle. Note that if the target is heading towards you the calculated angle is the AOB. If the target is heading away from you the AOB is 180 degrees minus the calculated angle. See first photo.
I will show how to do this calculation with an example, see second photo.
We observe a large steamer (I think) through the atack periscope and measure an angular height of about 76 mrad and an angular length of about 236 mrad. Actual mastheight is 26.2m and actual length is 141m. To calculate the AOB find the angular height (76 mrad) on the D scale and mark it with the hairline. Now find the actual mastheight (26.2m) on the C scale and slide it under the hairline (see third photo).
Now find the actual length (141m) on the C scale and mark it with the hairline (see fourth photo).
On the D scale you can now find the true angular length (408 mrad). This is the angular length you would measure with an AOB of 90 degrees. Now slide the 1 on the C scale under the hairline. On the S scale we now read 90 degrees. See fifth photo.
(this might be a bit confusing as there is a line directly above 90 which appears to indicate 90 degrees. This line however is the 80 degrees mark, the next small line is 85 and the line after that (1 on the C scale) is the 90 degree mark. The numbers are bunched together here which makes it a bit chaotic. If you don't know why the numbers are bunched together here just take a look at a sine curve).
Finally we find the observed angular length (236 mrad) on the D scale and we can read the AOB on the S scale (black numbers). The target is heading towards us so AOB = calculated angle. AOB in this example is 35.25 degrees. See sixth photo.
