jhpatton is spot on. The submarine has a limited speed at which it can approach (say 10 knots). The target is travelling at say 20 knots. Obviously, if the sub is astern, it can never catch up to reach a firing range. If it is right ahead, it only has to sit and wait. As its start position moves further towards either beam of the target, the sub has to approach at faster and faster speeds in order to reach a firing range (the torpedo danger zone) where the target speed and torpedo speed will result in the torpedo successsfully hitting the target. There is a point on either beam where the submarine must approach at 10 knots to just make it into the TDZ to fire at the last moment before the target passes (called point target). The limiting lines of submerged approach are (as patton says) the limits where the sub at 10 knots (or other speed limit) can steer a course to reach point target. If it starts outside these lines, it is physically impossible to reach a firing position without going faster than 1o knots (and the risk of detection, depleted battery etc). If the target becomes aware of the submarine's position, a simple alteration of course to place it outside the LLSuA will prevent it from ever reaching a firing position.