Method for manufacturing carbon fibers and fiber joining method

A joining method, comprising:

• joining a first target fiber bundle and a second target fiber bundle with a joining fiber bundle to obtain joined fiber bundles, the first target fiber bundle being configured to be carbonized when being fed through one or more carbonization furnaces and yet to be carbonized, the second target fiber bundle being configured to be carbonized when being fed through the one or more carbonization furnaces and yet to be carbonized,
• the joining the first target fiber bundle and the second target fiber bundle including forming an overlap between a first end of the joining fiber bundle and a second end of the first target fiber bundle and jetting a fluid to the overlap in a state where both ends of the overlap are clamped at a relaxation ratio of 0.03 to 2% to form a first entangled portion, and forming an overlap between a second end of the joining fiber bundle and a first end of the second target fiber bundle and jetting a fluid to the overlap in a state where both ends of the overlap are clamped at a relaxation ratio of 0.03 to 2% to form a second entangled portion,
• the entangled portions are formed such that each of the first entangled portion and the second entangled portion has two or more entangling points N1 each having a tensile force F1 not less than 400 N, so as to satisfy the relationship defined by inequality (1):
• 40>{L2/(L2−A)}×(S+13) (1)
• wherein L2 is a length in mm of an elongation section inside a first carbonization furnace most upstream in a direction in which the fiber bundles are fed, A is a maximum distance in mm between an entangling point in the first entangled portion and an entangling point in the second entangled portion, and S is an elongation in percentage of the joined fiber bundles being fed through the carbonization furnace.