What is the control surface located on either side of the tail called?

The control surface located on either side of the tail is referred to as the stabilator. A stabilator is a combination of a horizontal stabilizer and an elevator; it moves as a single unit, allowing for pitch control of the aircraft. Unlike traditional elevators, which are separate from the stabilizer, the stabilator's design can provide more effective control in certain flight regimes, offering a more responsive handling characteristic.

The stabilator's integration of both surfaces reduces drag, leading to better performance and efficiency. It is often used on high-performance aircraft where enhanced maneuverability and reduced weight are essential. This capability to control both pitch and, to some extent, stability quickly makes the stabilator a critical component in the dynamics of tail design.

In contrast, the rudder, elevators, and ailerons are separate control surfaces that manage other aspects of aircraft maneuverability: the rudder controls yaw, the elevators control pitch but are separate from the stabilizer, and the ailerons manage roll. Each of these surfaces plays a distinct role in aircraft control, but the stabilator specifically refers to the combined control surface on the tail.