Figure 6.3 Two Aircraft With Unusual Control Surfaces

When the sum of the moments about an aircraft’s center of gravity is zero, the aircraft is said to be trimmed. The act of adjusting the control surfaces of an aircraft so they generate just enough force to make the sum of the moments zero is called trimming the aircraft. The trim condition is an equilibrium condition in terms of moments. Strictly speaking, the sum of the forces acting on an aircraft does not have to be zero for it to be trimmed. For instance, an aircraft in a steady, level turn would be considered trimmed if the sum of the moments acting on it is zero, even though the sum of the forces is not.

Stability is the tendency of a system, when disturbed from an equilibrium condition, to return to that condition. There are two types of stability which must be achieved in order to consider a system stable. The first is static stability, the initial tendency or response of a system when it is disturbed from equilibrium. If the initial response of the system when disturbed is to move back toward equilibrium, then the system is said to have positive static stability. Figure 6.4(a) illustrates this situation for a simple system. When the ball is displaced from the bottom of the depression, forces resulting from the ball’s weight and the sloped sides of the depression tend to move the ball back toward its initial condition. The system is described as statically stable.

Figure 6.4 (b) illustrates the reverse situation. When centered on the dome, the ball is in equilibrium. However, if it is disturbed from the equilibrium condition, the slope of the dome causes the ball to continue rolling away from its initial position. This is called negative static stability, because the system’s initial response to a disturbance from equilibrium is away from equilibrium. The system is described as statically unstable.

The second type of stability which a stable system must have is dynamic stability. Dynamic stability refers to the response of the system over time. Figure 6.5 (a) shows the time history of a system which has positive dynamic stability. Note that the system also has positive static stability, because its initial tendency when displaced from the zero displacement or equilibrium axis is to move back toward that axis. As the system reaches equilibrium, the forces and/or moments which move it there also generate momentum which causes it to overshoot or go beyond the equilibrium condition. This in turn generates forces which, because the system is statically stable, tend to return it to equilibrium again. These restoring forces overcome the momentum of the overshoot and generate momentum toward equilibrium, which causes another overshoot when equilibrium is reached, and so on. This process of moving toward equilibrium, overshooting, then moving toward equilibrium again is called an oscillation. If the time history of the oscillation is such that the magnitude of each successive overshoot of equilibrium is smaller, as in Figure 6.5 (a), so that over time the system gets closer to equilibrium, then the system is said to have positive dynamic stability. Note that the second graph in Figure 6.5 (a) shows a system which has such strong dynamic stability that it does not oscillate but just moves slowly but surely to equilibrium.

Lightly Damped Highly Damped

(c) Negative Dynamic Stability