Those patches are round, white fabric background with yellow merrow border. Dominant colors: Blue and gold. Thirteen stars symbolizing the colonies of the United States. The crest with the American Bald Eagle is the symbol of US. The year 1947 written in Roman numerals format. Department of the Air Force was established in 1947.
The designs used on the small shield located below the eagle is taken from mythological thunderbolt.
You can read more about those symbols and the history of it here.