There seems to be a bit a bit if confusion about what the Normal Approach Course is, and what it is for. here's the plate of diagrams in the Torpedo Fire Control Manual. We are interested in Figure 1.
what armistead seems to describe is the normal course, not the normal approach course. The normal course is perpendicular to the target track. the normal approach course is perpendicular to the bearing to target.
If you are on the surface, or surfacing is an easy option, you can go generally go faster than your target. If you can go faster than your target then you can end around any target (land and ports and enemy warships/planes not withstanding). It's just a matter of time.
If you need to remain submerged then most targets travel faster than you.
In cases where you know the target range, speed and course, you can calculate an intercept course and point with some precision, and optimised to meet at the earliest opportunity.
In cases where you do not know the target details, it can be mathematically proven that the normal approach course will successfully intercept the greatest possible range of target speeds and courses.
If your angle of approach is anything other than 90, then more possible combinations of target aob and speed will escape your intercept attempt.