Free body diagram of an airplane (engineering notes)

[David Lewis]

Gravitational force acts on every part of an airplane but it's often just as well to replace all the individual forces and moments with a single resultant force located where the moment vanishes. The magnitude of the resultant is called the "weight" and point of application is called the center of gravity (CG) or balance point. The CG symbol looks a bit like a BMW logo.

The vertical plane at x=0 is the reference datum. You can arbitrarily locate the datum anywhere that's convenient for you.

[David Lewis]

When an airplane is in unaccelerated flight (dynamic equilibrium), that means it is:
1. Not rotating, turning, or changing direction
2. Not speeding up
3. Not slowing down

In power-off gliding flight, we can idealize an airplane as a free-body being acted upon by the following forces:
1. Aerodynamic force generated by the wing (wing force)
2. Aerodynamic force generated by the stabilizer (stab force)
3. The force of gravity (weight)

freebody.gif

Referring to diagram (a), since the lift-to-drag ratio of the stabilizer is less than the lift-to-drag ratio of the wing, the stabilizer and wing force vectors are not perfectly vertical. Stab force vector is swept back slightly, and wing force is swept forward. Referring to diagram (b), when you add the wing force and stab force together, the total resultant aerodynamic force of the whole airplane is perfectly vertical. Note in diagram (a) that the force generated by the wing (and hence the wing load) is greater than the weight of the airplane. The wing has to counteract the force of gravity in addition to download from the stabilizer.

Consequently, when selecting an airfoil, you can't just pay attention to lift coefficient. You also need to take into account section moment. The lower the section moment, the higher the maximum lift coefficient of the airplane, all other things equal.

Diagram (b) sums all the aerodynamic forces into one resultant force. The diagram is too simplified for wing load calculations, but adequate for analyzing the flight path and understanding flight behavior. Note the sum of moments is zero, and the aerodynamic force is equal and opposite to the force of gravity.

[David Lewis]

airfoil1.gif

When calculating flying surface loads, it can be more accurate to use the total aerodynamic force instead of lift.

SUMMARY
* When an airplane is in unaccelerated flight (i.e. the airplane is moving in a straight line at constant speed), the airplane is said to be in dynamic equilibrium. When a body is in equilibrium, the sum of all FORCES and MOMENTS OF FORCES acting on the body is zero (Galileo's Law of Motion).
* You will often see the claim that in order for an airplane to fly, lift must be greater than the weight (Aristotle's Law of Motion). Now we know better.
* You will often see it said that lift generated by the wing in straight and level flight equals the weight of the airplane. However, that's only true when the stabilizer is not producing lift. (The distinction between lift produced by the WING and lift produced by the AIRPLANE -- a.k.a. total lift -- needs to be carefully kept in mind.)
* The distinction between LIFT and AERODYNAMIC FORCE needs to be carefully kept in mind. (Aerodynamic force is the vector sum of lift and drag forces.)