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Static margin

## Summary

If an aircraft in flight suffers a disturbance in pitch that causes an increase (or decrease) in angle of attack, it is desirable that the aerodynamic forces on the aircraft cause a decrease (or increase) in angle of attack so that the disturbance does not cause a continuous increase (or decrease) in angle of attack. This is longitudinal static stability.

Static margin is a concept used to characterize the static longitudinal stability and controllability of aircraft and missiles.

In aircraft analysis, static margin is defined as the distance between the center of gravity and the neutral point of the aircraft, expressed as a percentage of the mean aerodynamic chord of the wing. The greater this distance and the narrower the wing, the more stable the aircraft. Conventionally, the neutral point is aft of the c.g., although in rare cases (computer controlled fighter aircraft) it may be forward of the c.g., i.e. slightly unstable, to obtain quickness of response in combat. Too great longitudinal stability makes the aircraft "stiff" in pitch, resulting in such undesirable features as difficulty in obtaining the necessary stalled nose-up pitch when landing.

The position of the neutral point is found by taking the algebraic net moment of all horizontal surfaces, measured from the nose of the aircraft, in the same manner as the c.g. is determined, i.e. the sum of all such moments divided by their total area. The stabilizer and elevator dominate this result, but it is necessary to account for all surfaces such as fuselage, landing gear, prop-normal, etc. It is also necessary to take account of the center of pressure of the wing, which can move a good deal fore and aft as angle of attack of a flat-bottom wing section (Clark Y) changes, or not at all in the case of self-stabilizing sections such as the M6.

The neutral point in conventional aircraft is a short distance behind the c.g. ("The feathers of the arrow must be at the back"); but in unconventional aircraft such as canards and those with dual-wings, such as the Quickie, this will not be so. The overall rule stated above must hold, i.e. the neutral point must be aft of the c.g., wherever that may be.

The position of the center of gravity is determined by factors such as the positions of loads, e.g. passengers, fuel, weapons, etc.; whether such loads can vary, e.g. presence or absence of luggage, ammunition, etc.; and how fuel is consumed during flight. Additional information regarding the usual position of the neutral point aft of the center of gravity is at longitudinal static stability.[1] (For an aircraft this may be described as positive static margin.) The response of an aircraft or missile to an angular disturbance such as a pitch disturbance is determined by its static margin.

In missile analysis, static margin is defined as the distance between the center of gravity and the center of pressure. Missiles are symmetric vehicles and if they have airfoils they too are symmetric.

For missiles, positive static margin implies that the complete vehicle makes a restoring moment for any angle of attack from the trim position. If the center of pressure is behind the center of gravity then the moment will be restoring. For missiles with symmetric airfoils, the neutral point and the center of pressure are coincident and the term neutral point is not used.

## Relationship to aircraft and missile stability and control

• If the center of gravity (CG) of an aircraft is forward of the neutral point, or the CG of a missile is forward of the center of pressure, the vehicle will respond to a disturbance by producing an aerodynamic moment that returns the angle of attack of the vehicle towards the angle that existed prior to the disturbance.
• If the CG of an aircraft is behind the neutral point, or the CG of a missile is behind the center of pressure, the vehicle will respond to a disturbance by producing an aerodynamic moment that continues to drive the angle of attack of the vehicle further away from the starting position.

The first condition above is positive static stability. In missile analysis this is described as positive static margin. (In aircraft analysis it may be described as negative static margin.)
The second condition above is negative static stability. In missile analysis this is defined as negative static margin. (In aircraft analysis it may be described as positive static margin.)

Depending on the static margin, humans may not be able to use control inputs to the elevators to control the pitch of the vehicle. Typically, computer based autopilots are required to control the vehicle when it has negative static stability - usually described as negative static margin.

The purpose of the reduced stability (low static margin) is to make an aircraft more responsive to pilot inputs. An aircraft with a large static margin will be very stable and slow to respond to the pilot inputs. The amount of static margin is an important factor in determining the handling qualities of an aircraft. For an unguided rocket, the vehicle must have a large positive static margin so the rocket shows minimum tendency to diverge from the direction of flight given to it at launch. In contrast, guided missiles usually have a negative static margin for increased maneuverability.

## References

1. ^ Effect of CG on handling of swept-wing airplanes