Theory and Definitions
In steady-level flight, an aircraft is in equilibrium; that is, the lift, L, equals the aircraft weight, W, and the thrust, T, equals drag, D. During conceptual design, when generating the preliminary aircraft configuration, it is understood that the wing produces all the lift with a spanwise distribution (see Section 3.14).
In equation form, for steady-level flight:
Figure 5.1. Equilibrium flight
5.5.1 Load Factor, n
Newton’s law states that change from an equilibrium state requires an additional applied force; this is associated with some form of acceleration, a. When applied in the pitch plane, the force appears as an increment in lift, AL, and it would overcome the weight, W, to an increased altitude initiated by rotation of the aircraft (Figure 5.1).
From Newton’s law:
AL = centrifugal acceleration x mass = a x W/g (5.2)
The resultant force equilibrium gives:
L + AL = W + a x W/g = W(1 + a/g) (5.3)
where L is the steady-state lift equaling weight, W load factor, n, is defined as:
n = (1 + a/g) = L/ W + A L/ W = 1 + AL/ W (5.4)
The load factor, n, indicates the increase in force contributed by the centrifugal acceleration, a. The load factor, n = 2, indicates a twofold increase in weight; that is, a 90-kg person would experience a 180-kg weight. The load factor, n, is loosely termed as the g-load; in this example, it is the 2-g-load.
A high g-load damages the human body, with the human limits of the instantaneous g-load higher than for continuous g-loads. For a fighter pilot, the limit (i. e., continuous) is taken as 9 g; for the civil aerobatic category, it is 6 g. Negative g-loads are taken as half of the positive g-loads. Fighter pilots use pressure suits to control blood flow (i. e., delay blood starvation) to the brain to prevent “blackouts.” A more inclined pilot seating position reduces the height of the carotid arteries to the brain, providing an additional margin on the g-load that causes a blackout.
Because they are associated with pitch-plane maneuvers, pitch changes are related to changes in the angle of attack, a, and the velocity, V. Hence, there is variation in CL, up to its limit of CLmax, in both the positive and negative sides of the wing incidence to airflow. The relationship is represented in a V-n diagram, as shown in Figure 5.2. Atmospheric disturbances are natural causes that appear as a gust load from any direction. Aircraft must be designed to withstand this unavoidable situation up to a statistically determined point that would encompass almost all-weather flights except extremely stormy conditions. Based on the sudden excess in loading that can occur, margins are built in, as explained in the next section.
Aircraft speed V)