Aside from using the actual trigonometry to setup the entire firing solution, which is not hard mind you, one easy method to calculate the speed is by making an intelligent guess (as discussed before with bow-wave or half of the listed reference speed) and entering this data into the position keeper. If your range and AOB estimates are reasonably good, then you can compare the relative bearing of your locked periscope as it tracks the target to the relative bearing your position keeper is telling you the target should be based on the speed, range, and AOB you entered. Let's say the PK says the target is at 55 deg, when your locked periscope clearly sees the ship at 52 degrees. If the target was travelling such that the relative bearing should be increasing (i.e. 0-->90) then this would be an indication that your PK has him travelling too fast, and you should dial down the speed estimate and try again. Once you can make a couple of successive checks where the periscope relative bearing matches what the PK bearing is predicting, you know you have a decent solution and should feel comfortable expending one of your torpedoes.
As mentioned earlier, the actual trigonometry that the chronometer feature would be using (if it woked properly) is not hard to derive and calculate, and can be used for more exact initial guesses. Regardless of the situation, it is always a good idea to compare your firing solution via the PK with actual target observations from the periscope and hydrophone before engaging. The PK was a huge advantage for US subs and I rely on it quite heavily on my patrols.
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