After doing a little bit of mathematical mulling over the 90 degree Dick O'Kane attack, I figured out an equation that can be used to calculate the attack angle required.
Y = lead angle in degrees
X = target speed in knots
Z = torpedo speed in knots
Y = arctan(X/Z) * 57.3
Before you go and run away because this has trigonometry in it, the arctan operation does the same thing that we do when we connect our torp & target speed vectors tip to tail and measure the angle with a protractor. Arctan (or inverse tangent, they're two names for the exact same thing) spits out the angle measure (in radians, hence the multiplication by 57.3) of the angle that is opposite from leg X, and adjacent to leg Z.
Of course, using this equation without a calculator or trig sheet would be quite impractical, but I'd imagine that submariners back in the day had access to trig sheets.
In any case, this equation isn't terribly useful unless you are greater than about 2,500 yards from the target, where getting hits requires closing down on uncertainty as much as possible. For a closer in attack, RR's rules of thumb (10 degrees for slower than 15 kts, 20 degrees for greater than 15 kts) more then well enough do the job.
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