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Exeter was one torpedo hit away from sinking. She was down in the bow ; flooding ; listing and burning from end to end with all main guns destroyed or out of action and limping away at 12 knots. It's unfortunate Langsdorff lost his cool and ran away from the fight, since this doomed him. His best chance was to use the second half of his ammo to run down the Exeter and sink her. This would force the balance of Harwood's force to attack and get battered until they were crippled too. Only at that point could AGS escape before the rest of the RN fleet arrived a couple of days later.
Since AGS had been at sea for months her hull was fouled so she could only make 24 knots....but had enough fuel to run for 16 days at that speed. The British Cruisers could only manage that speed for a few days before they would fall out due to lack of fuel and return to port.
He obviously felt that escape in AGS's current condition was impossible, so attempting to sortie could likely doom most of the 1,000 man crewGiven the choice of running or death, it would be a worthwhile risk.
Maybe Langsdorff was too good a man for such dirty work. We often see Germans as evil Nazis. But Langsdorff was a true hero in my book. And was respected as a decent honourable man.
An interesting point about the battle is how history seems almost to repeat itself. In WW1, the German Armored Cruisers, Scharnhorst and Gneisenau along with lighter ships had decimated a British force at the Battle of Coronel. The commander of the German force was Von Spee. That force was going to raid the base in the Falkland Islands only to find a British force there including two BCs, Invincible and Inflexible. The German armored cruisers were outgunned and were too slow and were sunk. Now in the same vicinity, in a ship named after Von Spee and commanded by a man, Langsdorff, who was in the same mold as the officers of the Kaiser's navy another German raider could have been confronted by a British BC , faster and more heavily gunned. I wonder if Harwood ever revealed what his tactics were going to be if the Spee had come out to do battle with the RN cruisers?
The situation Langsdorff faced at the Plate would make an excellent plot for an alternative history.