Authentic method of getting firing solution?

[Tom]

Ok, this is the first thread I start... so sorry if I'm asking something that's already been discussed here.

I've recently started doing my targetting manually with no map updates, using watch officer estimates for target range when overhauling and periscope range finding when closing in, and plotting the solutions on the navigation map. What I would like to know is the authentic method used by the germans to turn target range/bearing/time information into target AOB/speed. (The Submarine Commander's Handbook calls for "estimation of range and position at regular intervals of time", but doesn't (or I just somehow missed it) explain the preferred method of calculating AOB/speed from these.)

They obviously didn't have a navigation map displaying the exact location of the submarine at all times, but they could have plotted the submarine's movement based on course and speed, together with the target bearings/ranges/times, and use this information to plot the course and speed of the target much like I do it on the navigation map now. But is this how it was done?

Furthermore, how did they estimate the firing solution in cases where observations over a longer time weren't available? (Bad weather, target changed course moments before attack, etc.)

Using search I found several threads explaining working methods for manual targeting, but couldn't find out which was the actual method used. If I just missed the information, could someone please point me to the thread?