In the script for "The Infinite Vulcan", the typical design of the Swoopers is initially described thus; "It is fifteen feet long with a hinged, segmented body that permits the front end to turn right angles to the back end. It uses this maneuver to change directions in mid-air. The propulsion system is a series of coils that normally encircle the body, but which flatten out behind when it wishes to go forward – like a swimmer with a frog kick. It is this 'flattening out' that is responsible for the flapping sound. The coils serve another purpose as well; they can be used against an enemy to grasp, seize and render inoperable."
Although wings are clearly visible in the Swooper's animated design, the novelization of "The Infinite Vulcan" (as published in Star Trek Log 2) specifically states that the creature had no wings, only the thick coils protruding from its body. The same adaptation also characterizes the Swooper as being "a good twelve feet long."