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Forces Acting on an Airplane


Maintaining a steady flight requires a balance, often described as an equilibrium of all the forces acting upon an airplane. Weight, lift, thrust and drag are the acting forces on an airplane. Assuming a straight and level flight, lift must be equal to weight and drag must be equal to thrust. If this equilibrium is violated, i.e., lift becomes greater than weight, then an acceleration upward will occur. Conversely, if the weight is greater than the lift, an acceleration downward will occur. When the thrust becomes greater than the drag an acceleration forward will occur. However if the drag becomes greater than the thrust a deceleration will occur. This is best explained by using Newton's Second Law of Motion.
The proportion between weight and thrust is determined by the airplane designer depending on the anticipated missions. For example, if by design an airplane must be able to accelerate vertically upwards then the thrust must be greater than the weight and drag combined. In small aircraft the weight/thrust ratio is about. 10:1.

The Four Forces Acting on an Airplane

The presentation of the four forces as shown in (a) illustrates a general view. However, in reality as shown in (b), the weight acts on the Center of Gravity* (CG) and the lift acts at the Center of Pressure; the thrust and drag are paired to reduce the pitching moment which is created by the lift. For convenient reasons, the vectors of the four forces are many times shown as if they all act on a single point.
To maintain an equilibrium of the forces, a coordinated use of controls and power is necessary to compensate for changes in flight situations. The objectives here are to show the the four forces as they apply to straight and level, climbs, glides and turns.

*The Center of Gravity is a point at which the airplane will, if suspended, remain balanced.
Straight and Level

An airplane is in a straight and level flight when it maintains altitude and direction with the wings level while it flies in a constant speed. To maintain an equilibrium the following conditions must be met:

L =W and T = D

The forces during Straight and Level Flight.
The Forces during glide

An airplane is in a glide when it is descending without engine power at a constant speed and rate of descent.
Two sets of forces are considered to show how the equilibrium is maintained. For clarity sake, we shall name the sets as the Gravity Set and the Lift Set. The gravity set is resolved by two components of the weight(W). The vertical component (W') is perpendicular to the horizontal component (W''). In absence of thrust, the horizontal component (W'') is providing a forward force. The lift set is made of the lift (L) and the drag (D) and their resultant (LR). To provide sufficient lift, W" must be equal to the drag (D). This also guarantees a constant speed. To maintain a constant rate of descend, the Lift (L) must be equal to the vertical component of the weight (W').
To maintain equilibrium in glide the following must be met:

W'' = D and W' = L
     The forces during a glide.

The Forces during climb

An airplane is in a climb when an airplane is gaining altitude in a constant speed and rate. To demonstrate how the equilibrium is maintained, once again two sets of forces are considered. Namely, the Gravity Set and the Lift Set. The gravity set consists of the weight of the airplane (W), the vertical component (W') and the horizontal component (W''). The Lift set consists of the lift (L), the drag (D) and the resulting lifting force (LR).
As shown on the right, the thrust (T) must be equal the sum of the drag (D) and the horizontal component of the weight to allow constant speed. The lift (L) must be equal to the vertical component of the weight (W') if a constant rate of climb is sought. To maintain equilibrium in climb the following must be met:

T = (D + W'') and L = W'

The forces during a climb.          
The Forces during a Turn

The understanding of how an airplane turns and how are the forces distributed on a turning airplane requires some knowledge in physics. A simple experiment, as shown in (a) below, the force exerted on a string when a ball is whirled at its end. The tension on the string provides the centripetal force*  that keeps the ball moving in a circle. By releasing the string, the centripetal force ceases to exist and the ball will no longer remain in a circular motion.
When an object moves in a circular motion at a constant speed, the direction of its speed is constantly changing as shown in (b). A change in velocity means acceleration (Newton's Second Law of Motion). Since the object here moves in a circular motion, this force is directed towards the center of the circle.

Centripetal Force

If an airplane is viewed from the front or the rear in a straight and level flight, one could conceptualize two equal forces lift and weight as shown in(a) below. As mentioned earlier lift always acts perpendicular to the wing. By banking an airplane (b). the lift is divided into two components, the vertical and horizontal components. To maintain altitude in a level turn the vertical component of the lift must be equal to the weight of the airplane.    L' = W    The horizontal component of the lift is providing the Centripetal Force that makes the airplane turn.

The forces acting on a airplane in a turn

* Force seeking the center

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Last update May 17, 2005
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