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In 1741 as Rear Admiral of the Blue of British and American colonial army led by Admiral Edward Vernon he led the attack on three forts at Cartagena de Indias (now Colombia) during a disastrous campaign in the War of Jenkins' Ear.
Though this was a major disappointment to Charles II of England, Teddeman's career did not suffer much and he fought, again on the Katherine, the next year as Vice-Admiral of the Blue in the Four Days Battle and as Vice-Admiral of the White in the St James's Day Battle.