FLIGHT MECHANICS - STABILITY

INTRODUCTION : 

INTRODUCTION SUB:FLIGHT MECHANICS – II CLASS:III B.Tech II Sem DISCIPLINE:AERONAUTICAL ENGINEERING UNIT I

CONTENTS : 

CONTENTS DEGREES OF FREEDOM OF A SYSTEM STATIC STABILITY DYNAMIC STABILITY NEED FOR STABILITY IN AIRPLANES PURPOSE OF CONTROLS INHERENTLY AND MARGINALLY STABLE AIRPLANES

1.DEGREES OF FREEDOM : 

1.DEGREES OF FREEDOM The In mechanics, degrees of freedom (DOF) are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation of the body or system. A rigid body moving in 3–D space system has six degrees of freedom – 3 translational and 3 rotational. In general, a rigid body in d dimension space system has d(d + 1)/2 degrees of freedom (d translations and d(d −1)/2 rotations).

Degrees of freedom – EXAMPLEGIMBAL LOCK : 

Degrees of freedom – EXAMPLEGIMBAL LOCK A gimbal is a ring that is suspended so it can rotate about an axis. Gimbals are typically nested one within another to accommodate rotation about multiple axes.

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd : 

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd ROTATING GIMBAL

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd : 

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd Gimbal lock is the loss of one degree of freedom that occurs when the axes of two of the three gimbals are driven into the same place and cannot compensate for rotations around one axis in three dimensional space. GIMBAL NO LOCK GIMBAL LOCK – LOSS OF ONE D O F

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd : 

Degrees of freedom – EXAMPLEGIMBAL LOCK-contd Note – In a gimbal lock no gimbal is restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbal axes there is no axis available to accommodate rotation along one axis. This results in loss of one degree of freedom.

Degrees of freedom – EXAMPLEAIRPLANE : 

Degrees of freedom – EXAMPLEAIRPLANE The airplane axis system is shown below. It is a right hand axes system with the positive X and Z axes in the plane of symmetry and Y axis perpendicular to the plane of symmetry

Degrees of freedom – EXAMPLEAIRPLANE-contd : 

Degrees of freedom – EXAMPLEAIRPLANE-contd The airplane is in a kind of gimbal lock when it is in the plane of symmetry when two planes coincide with each other.

Degrees of freedom – EXAMPLEAIRPLANE-contd : 

Degrees of freedom – EXAMPLEAIRPLANE-contd The components of forces and moments acting on the airplane and the components of airplane motion reffered to this axis system are as follows

Degrees of freedom – EXAMPLEAIRPLANE : 

Degrees of freedom – EXAMPLEAIRPLANE The motion of an airplane can be completely defined only if the six velocity components are given, the airplane is considered to be a dynamic system in six degrees of freedom The equation of statics must be applied to each degree of freedom to check the equilibrium conditions viz., ΣFX =0 ; ΣFY=0 ; ΣFZ =0 ; & ΣL=0 ; ΣM=0 ; ΣN=0

Degrees of freedom – EXAMPLEAIRPLANE-contd : 

Degrees of freedom – EXAMPLEAIRPLANE-contd In three dimensions, the six DOFs of a rigid body (airplane) are described using the following nautical names: Moving up and down (heaving); Moving left and right (swaying); Moving forward and backward (surging); Tilting forward and backward (pitching); Turning left and right (yawing); Tilting side to side (rolling).

2. STATIC STABILITY : 

2. STATIC STABILITY As any vehicle moves it will be subjected to minor changes in the forces that act on it, and in its speed. If the change causes further changes that tend to restore the vehicle to its original speed and orientation, without human or machine input, the vehicle is said to be statically stable. The aircraft has positive stability. If the change causes further changes that tend to drive the vehicle away from its original speed and orientation, the vehicle is said to be statically unstable. The aircraft has negative stability. If the change causes no tendency for the vehicle to be restored to its original speed and orientation, and no tendency for the vehicle to be driven away from its original speed and orientation, the vehicle is said to be neutrally stable. The aircraft has zero stability.

STATIC STABILITY - contd : 

STATIC STABILITY - contd LONGITUDINAL STABILITY – It is the stability of an aircraft in the longitudinal, or pitching, plane during static (established) conditions. This characteristic is important in determining whether an aircraft will be able to fly as intended. The longitudinal stability of an aircraft refers to the aircraft's stability in the pitching plane – i.e., the plane which describes the position of the aircraft's nose in relation to its tail and the horizon.

STATIC STABILTY – contd LONGITUDINAL STATIC STABILITY : 

STATIC STABILTY – contd LONGITUDINAL STATIC STABILITY If an aircraft is longitudinally stable, a small increase in angle of attack will cause the pitching moment on the aircraft to change so that the angle of attack decreases. Similarly, a small decrease in angle of attack will cause the pitching moment to change so that the angle of attack increases.

STATIC STABILITY - contd : 

STATIC STABILITY - contd DIRECTIONAL STABILITY – It is the stability of a moving body or vehicle about a vertical axis. If a vehicle is directionally stable, a yawing moment is produced which is in a direction opposite to the rotational disturbance. This "pushes" the vehicle (in rotation) so as to return it to the original orientation, thus tending to keep the vehicle oriented in the original direction.

STATIC STABILITY - contd : 

STATIC STABILITY - contd LATERAL STABILTY – An airplane is said to possess lateral static stability if after undergoing a disturbance that rolls it to some bank angle ø, it generates forces and moments that tend to reduce the bank angle and restore the equilibrium flight condition.

STATIC STABILITY - contd : 

STATIC STABILITY - contd Lateral and directional stability are interrelated. The motions of an airplane are such that a roll motion causes a yaw motion and a yaw motion causes a roll motion. Thus, cross-coupling exists between the directional static stability and lateral static stability and gives rise to the three important dynamic motions observed: directional divergence, spiral divergence, and Dutch roll.

STATIC STABILITY : 

STATIC STABILITY

Slide 20: 

Time = 0.0 Time = 1.0 Time = 2.0 Aircraft encounters gust Nose pitches up cg Tail Force Airflow Direction Longitudinal Static Stability Tail Force Tail Force Resulting Motion

Slide 21: 

Lateral Static Stability Resulting Motion Weight Dihedral Angle Lift Vectors Weight Aircraft rolls slightly to the right View Downstream Time = 0.0 Time = 1.0 Time = 2.0 Dihedral Angle Lift Vectors Weight

LATERAL CONTROL : 

LATERAL CONTROL

STATIC DIRECTIONAL STABILITY : 

STATIC DIRECTIONAL STABILITY a) STATICALLY STABLE AIRPLANE b) RESTORING MOMENT in yaw direction

ANGLE OF ATTACK vs PITCHING MOMENT : 

ANGLE OF ATTACK vs PITCHING MOMENT

3.DYNAMIC STABILITY : 

3.DYNAMIC STABILITY It deals with the time history of aircraft motion after the aircraft is disturbed from an equilibrium or trim condition. If the aircraft goes to its original condition as the time goes to infinity, it is said to have positive dynamic stability. If the aircraft neither returns to trim nor diverges further from the disturbed condition, it is said to have neutral dynamic stability. If the aircraft diverges from the trim condition and the disturbed condition as time goes to infinity, it si said to have dynamic instability

DYNAMIC STABILITY – Contd. : 

DYNAMIC STABILITY – Contd. The study of dynamic stability is important to understand aircraft handling qualities and design features that make an airplane fly or not as well while performing specific mission tasks.

DYNAMIC STABILITY : 

DYNAMIC STABILITY

DYNAMIC STABILITY – Contd. : 

DYNAMIC STABILITY – Contd. LONGITUDINAL DYNAMIC STABILITY Deals with statically stable airplane Two types of oscillations Phugoid mode of oscillation – long & slow Short period variation with angle of attack

Phugoid and short period oscillations : 

Phugoid and short period oscillations

LONGITUDINAL DYNAMIC STABILITY : 

LONGITUDINAL DYNAMIC STABILITY PHUGOID MODE LONGITUDINAL OSCILLATION is a long-period, slow oscillation of the airplane's flight path. The pilot generally can control this oscillation himself

LONGITUDINAL DYNAMIC STABILITY : 

LONGITUDINAL DYNAMIC STABILITY SHORT PERIOD VARIATION WITH ANGLE OF ATTACK this oscillation decreases very quickly with no pilot effort. But, with its natural short period, the oscillation may worsen if a pilot attempts to lessen it by use of a control because of the pilot's slow reaction time where he may get "out of phase" with the oscillation, and thus induce dynamical instability that may eventually lead to destructive forces.

LONGITUDINAL DYNAMIC STABILITYSHORT PERIOD VARIATION WITH ANGLE OF ATTACK : 

LONGITUDINAL DYNAMIC STABILITYSHORT PERIOD VARIATION WITH ANGLE OF ATTACK occurs if the elevators are left free. This is called the "porpoising" mode, and is influenced by the elevator balance. The main effect is vertical accelerations of the airplane that may get out of hand if a coupling between the free elevator and airplane occur. Proper design is essential to avoid this type of instability.

Slide 33: 

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