On February 16, 1964, his light plane crashed in the sea. He ran into bad weather near Cuba and then out of gas while flying to the United States. Burns shrugged off his shirt and slacks, put on his "Mae West" life jacket, and checked that his waterproof watch was still working. He was particularly concerned because at 43 years of age and 222 pounds, he wasn't the most athletic of men and certainly not a good swimmer. Fighting off sharks, he had to swim for 28 hours before reaching Guana Key where a Cuban navy patrol boat picked him up.