There's no reason to have the periscope up.
Assume that a destroyer is approaching you and you calculate its speed as 24 knots. You are initially on the surface at 18 knots and heading away from the destroyer, but once you realize that the destroyer is gaining on you, you sensibly dive. Let's say you go to 20 meters.
Now I don't know what depth you can fire torpedoes at, but I believe you can be somewhat deeper than periscope depth and still fire. Now let's say that you know or believe that the destroyer in question is some 4,000 meters from you. Your new differential of speed is around 17 knots because you are making 7 knots underwater whereas the destroyer is still coming at you at a rate of 24 knots. Start the timer.
The destroyer will then cover 1700 meters of relative distance every 3:14.4 seconds. In other words after 6:29 he will be 600 meters from you (slightly less because he may zigzag or you may temporarily be going slightly faster than 7 knots as your boat, which was originally going at 18 knots, slows to its final 7 knot figure).
So set your firing solution, directly aft, 0 speed, 0 angle on bow, magnetic, correct depth, and fire scope down when the clock reads 6:20 and immediately dive. There are really only three possibilities:
A) The destroyer swerves to avoid the torpedo giving you enough time to reach a safe depth.
B) The destroyer is blown out of the water by the torpedo.
C) The torpedo is a dud or goes to deep, in which case you'd better swerve to avoid the depth charges.
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