2.D : Principles of Flight

This is the initial tendency displayed by the aircraft when equilibrium is disturbed.

While static stability refers to the initial response to an upset of equilibrium, dynamic stability refers to how the system responds over time. It describes whether the system returns to equilibrium over time, and the degree of stability is described in terms of how quickly it returns to equilibrium (assuming it does).

Dynamic stability can also be divided into oscillatory and non-oscillatory modes. Oscillatory describes the motion of a marble in the bottom of a smooth bowl where if it is disturbed it eventually returns to rest back at the bottom of the bowl. This describes a system that exhibits both positive static stability and oscillatory positive dynamic stability. The longer the oscillations in time, the easier the aircraft is to control Neutral or divergent short oscillation is dangerous as structural failure can result. Non-oscillatory can be described by replacing the marble with a cotton ball, and the system returns to rest with no oscillations.

The image above shows the flight path of an aircraft with various combinations of static and dynamic stability.

Longitudinal stability describes the stability around the pitch axis. A plane that is longitudinaly unstable tends to dive and climb progressively steeper making it difficult (or dangerous) to fly. To achieve this stability it must be the case that if disturbed the wing moments and tail moments will change so their forces provide a restoring moment bringing the nose back into the proper attitude again.

Static longitudinal stability is dependent upon three factors: the location of the wing in relation to the center of gravity, the location of the horizontal tail with respect to the center of gravity, and the area/size of the tail surface.

The wing is usually behind the center of lift, which results in a nose down pitch force. This nose heaviness is balanced by a downward force generated by the tail. This is due to the fact that the tail is designed with negative AOA to create a natural tail-down force. This creates a situation which resembles a lever where the tail lifts the nose pivoting around the CG. The stronger force is at the CG and the tail force is weaker, but has a longer lever arm.

If the nose is pitched up airspeed will decrease, and therefore the down force on the tail will decrease. This allows the nose to pitch back down. If the nose goes down the speed increases and the down force on the tail increases, raising the nose again. If left untouched this oscillation will continue dampening out with each cycle until the aircraft reaches equilibrium again.

The center of gravity impacts stability because of it’s relation to the horizontal tail surface. If the plane is loaded with the CG forward, more tail down force is needed to balance which adds to longitudinal stability. If the reverse loading is the case then the CG goes back, the force on the tail is lightened. In extreme cases where the CG is moved behind the CL, it will create a situation where a pitch up will cause less airflow over the tail, causing the nose to pitch further, and ultimately causes the plane to be uncontrollable.

Lateral stability describes the stability around the roll axis. Stability around this axis is impacted by dihedral, sweepback angles, keel effect, and weight distribution.

Dihedral is the angle at which the wings are slanted upward from the root to the tip of the wing. This angled arrangement causes the wings to be at a different angle of attack when the plane rolls, with the low wing being at the greater AOA. This increased AOA causes the low wing to generate more lift, thus rolling the plane back upright, returning to straight-and-level flight.

Sweepback is the angle at which the wing are slanted to the rear of the aircraft from the root to the tip. This has a similar affect to dihedral, but the effect is rather less pronounced.

Keel effect is the action of the relative wind on the side of the plane. If the greater portion of the "keel" is above and behind the CG then the relative wind’s pressure on the keel has a tendency to roll the aircraft back to a level attitude. In short, keel effect forces the plane to parallel the relative wind.

Weight distribution impacts lateral stability by the simple expedient of where the weight is placed. If it is placed to one side, it can cause the aircraft to have a tendency to roll to that side.

Directional stability is affected by the area of the vertical fin and the sides of the fuselage fat of the CG. These components make the aircraft behave as if it were a weather vane, pointing the nose into the relative wind.

Of course, for a weather vane to work the side surface must be greater aft of the pivot point (in the case of the plane, this is the CG). In addition to this weather vane effect the vertical stabilizer acts like a feather on an arrow. The further aft the fin is place the greater stabilizing force will be exerted due to the longer lever arm.

Newton’s third law says that for every action there is an equal and opposite reaction. Therefore as the propeller rotates one way, it creates a force in the opposite direction. When airborne this force acts around the longitudinal axis resulting in a left rolling tendency. On the ground during takeoff the left side is being forced down resulting in more ground friction, causing a turn to the left (and the higher the power setting, the more force is exerted).

Torque is countered by various methods. The engine can be offset somewhat. The ailerons and rudder can have trim tabs. But any force not designed out with these tools must be offset with appropriate rudder and aileron inputs.

The high-speed rotation of the propeller sends the air backward along the aircraft in a corkscrewing manner. As this happens the air strikes the side of the vertical stabilizer pushing the nose of the aircraft left.

At high prop speeds and low forward speeds this rotation is very compact which exerts a strong sidewards force on the vertical stabilizer. There is also some rolling force imparted as well, which is to the right and which may counter some of the left turning tendency. As speed increases the spiral elongates reducing its effectiveness. These forces are also countered with coordinated rudder and aileron inputs.

Gyroscopes are based on two fundamental principles: rigidity in space (not a key factor in the current discussion) and precession. Precession is the resultant action of a spinning rotor when force is applied to it’s rim. If a force is applied it takes effect 90 degrees ahead of, and in the direction of, the spin.

In the case of an aircraft this can cause either a pitch or yaw moment (or a combination of the two) depending upon where the force is applied. This is most apparent in a tailwheel aircraft when the tail is raised, and the prop disk is therefore pitched upright. The change in pitch (lifting the tail) has the same effect as applying a forward force to the top of the propeller. This force is felt 90 degrees clockwise (when viewed from inside the cockpit), which has the force taking effect on the right side of the propeller, imparting a left turning force.

This also means that any pitching around the lateral axis will result in a yawing moment, and a yawing around the vertical axis will create a pitching moment.

The term p-factor refers to the asymmetric loading of a propeller when operating at high angle of attacks. This has the net effect of moving the center of thrust to the right of the propeller disc, and is due to the "bite" of the down-going blade being greater than the "bite" of the up-going blade.

Looking at the image above you can see that when the propeller is straight upright the forces are equal all around. However, as the angle of attack increases the pitch of the blades with respect to the relative wind changes, with the down-going blade having a greater angle of attack. This generates more force, thus shifting the center of the aggregate force toward the side with the higher angle of attack.