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I haven't read a single instance of that being used in real life. Why? They didn't know ships' lengths! Most of the time either they could not identify what they were shooting at or misidentified it, completely invalidating the use of the method.
There is slightly more justification for using it in U-Boats, as there were scads of nearly identical Liberty Ships all over the Atlantic and the Germans MAY have known what their length was.
Can someone come up with a historical reference to any captain routinely using that method during the war?
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The method was widely used in U-Boats, not in US submarines. In the interwar period, several makes of periscopes (US, british and german) offered models with the fixed line feature, which was actually a different wire, free from the main periscope shaft and coupled to the compass so that when moving the periscope it would stay in the true bearing it had been set (This allows to reduce the effect of own ship speed in the measuring). On surface attacks it was used with the UZO -which only had a vertical line in the crosshair- easily because the U-Boats favoured the dog leg approach, and constantly pointing the bow to the enemy is the best way to use it.
Paragraph 105.e) of the U-Boat commander's Hanbook: "In every submarine attack, whether by day or by night, the attempt must be made to obtain reliable data for aiming (controlling) the torpedo, ... measuring the deflection with the aid of the line ..."
The size of enemy ships was estimated by the commander or IWO, once you have some practice it isn't that difficult and errors of -/+ 15 metres are not much relevant.
I included this method in the tutorial for firing solutions -as well as the aspect ratio- despite both being used in U-Boats because they are by far easier to do in the game and by one single person than plotting -which is what the us submarines crews did to gather target data-. Not coincidentally, because in the U-Boat the captain (Or IWO) worked it all himself out, whereas the US commander had the assitence of the whole tracking party and the TDC operator. Since we are alone when playing, the U-Boat method suits us better IMO.
CHeers