Lateral and Directional stability

Dihedral effect - Lateral control - Coupling between rolling and yawing moments - Adverse yaw effects -

Aileron reversal - Static directional stability - Weather cocking effect - Rudder requirements - One engine

inoperative condition - Rudder lock

Damped oscillation Divergent oscillation

Undamped oscillation Subsidance

Divergence Neutral stability

Case Statically stable Dynamically stable

Damped oscillation Yes Yes

Divergent oscillation Yes No

Undamped oscillation Yes No

Subsidence Yes Yes

Divergence No No

Neutral Stability No No

Where do we stand?

Lateral Stability

• Stability in Roll• w/o Directional stability

Slip

• Forward slip – The forward slip will change the heading of the

aircraft away from the down wing, while retaining the original flight path of the aircraft

• Sideslip– The airplane's longitudinal axis remains parallel to

the original flightpath, but the airplane no longer flies straight along its original track. Now, the horizontal component of lift forces the airplane to move sideways.

Sideslip

• Phenomenon due to unbalanced sideforce• Flying in a slip is aerodynamically inefficient• In a slip much more drag is created• However if a cross wind is present an

appropriate side slip may be necessary at touchdown.

• A sideslip is also one of the methods used by pilots to execute a crosswind landing while the other two are Crab and De-crab

Angle of Sideslip(β)[ITF θ]

Dihedral angle

• Dihedral angle is the upward angle from horizontal of the wings or tail plane of a fixed-wing aircraft.

Dihedral

Dihedral effect

• Dihedral effect is the amount of roll moment produced per degree (or radian) of sideslip.

• Dihedral effect of an aircraft is a rolling moment resulting from the vehicle having a non-zero angle of sideslip. Increasing the dihedral angle of an aircraft increases the dihedral effect on it.

• Hence Dihedral effect α Dihedral angle

Other Aircraft Parameters Affecting Dihedral effect

• Wing sweep• Vertical location of center of gravity • The height and size of anything on an aircraft

that changes its sidewards force as sideslip changes.

Keel effect• Keel effect is the result of the sideforce-generating surfaces being above or below the

center of gravity in any aircraft.• Examples of such surfaces are the vertical stabilizer, rudder, and parts of the fuselage.

When an aircraft is in a sideslip, these surfaces generate sidewards lift forces. If the surface is above or below the center of gravity, the sidewards lift forces generate a rolling moment. This "rolling moment caused by sideslip" is "dihedral effect". Keel effect is the contribution of these side forces to rolling moment (as sideslip increases), i.e. keel effect is the contribution of the side forces to dihedral effect. Sideforce producing surfaces above the center of gravity will increase dihedral effect, while sideforce producing surfaces below the center of gravity will decrease dihedral effect.

• Increased dihedral effect (helped or hindered by keel effect) results in a greater tendency for the aircraft to return to level flight when the aircraft is put into a bank. Or, reduces the tendency to diverge to a greater bank angle when the aircraft starts wings-level.

• Keel effect is also called "Pendulum Effect" because a lower center of gravity increases the effect of sideways forces (above the center of gravity) in producing a rolling moment. This is because the moment arm is longer, not because of gravitational forces. A low center of gravity is like a pendulum (which has a very low center of gravity).

Coordinated Flight

• Coordinated flight of an aircraft is flight without sideslip.

• When an aircraft is flying with zero sideslip a turn and bank indicator installed on the aircraft’s instrument panel usually shows the ball in the center of the spirit level. There is no lateral acceleration of the aircraft and occupants perceive their weight to be acting straight downwards into their seats.

• Particular care to maintain coordinated flight is required by the pilot when entering and leaving turns

Turn and Bank indicator

Turn and Bank Indicator with zero slip

Advantages of Coordinated Flight

• It is more comfortable for the occupants• It minimizes the drag force on the aircraft• It causes fuel to be drawn equally from tanks

in both wings• It minimizes the risk of entering a spin

Coordinating the turn• If the pilot were to use only the rudder to initiate a turn in the

air, the airplane would tend to "skid" to the outside of the turn. • If the pilot were to use only the ailerons to initiate a turn in the

air, the airplane would tend to "slip" towards the lower wing.• If the pilot were to fail to use the elevator to increase the angle

of attack throughout the turn, the airplane would also tend to slip towards the lower wing

• However, if the pilot makes appropriate use of the rudder, ailerons and elevator to enter and leave the turn such that sideslip and lateral acceleration are zero the airplane will be in coordinated flight.

Adverse Yaw

• Adverse yaw is a yaw aircraft movement opposite to the direction change initiated by a roll movement. It is a secondary effect of the application of the ailerons in aircraft. Its cause and effect can be explained as follows:

• As the outer turn wing moves up, its induced drag increases; as the opposite inner turn wing descends, its induced drag decreases. There is a differential moment drag opposite to the turn.

• There is an additional adverse yaw contribution from a profile drag imbalance between the upgoing and the downgoing wing.

• The net effect is a tendency to yaw the aircraft in the wrong direction for the turn.

• According to the diagram, when the control column of an aircraft is moved to the right, the right aileron is deflected upwards, and the left aileron is deflected downwards, causing the aircraft to roll to the right. As the right wing descends, its lift vector, which is perpendicular to the relative motion, tilts forward and therefore has a forward component. Conversely, as the left wing moves up, its lift vector tilts back and therefore has an aft force component. The fore/aft lift force components on the right and left wings constitute the adverse yaw moment.

Minimizing the adverse yawAdverse yaw is countered by using the aircraft's rudder to perform a coordinated turn,

however an aircraft designer can reduce the amount of correction required by careful design of the aircraft. Some methods are common:

General characteristics• As the induced drag is the major cause to adverse yaw, an important parameter is

the lift coefficient. Lower wing loading and higher minimal speed lead to less adverse yaw.

Yaw stability• A strong directional stability is the first way to reduce adverse yaw . That means

important vertical tail moment (area and lever arm about gravity center).Roll spoilers• On large aircraft where rudder use is inappropriate at high speeds or ailerons are

too small at low speeds, roll spoilers can be used to minimise adverse yaw or increase roll moment. To function as a lateral control, the spoiler is raised on the down-going wing (up aileron) and remains retracted on the other wing. The raised spoiler increases the drag, and so the yaw is in the same direction as the roll.

Differential deflection ailerons

• Because downwards deflection of an aileron typically causes more profile drag and induced drag than an upwards deflection, a simple way of mitigating adverse yaw would be to rely solely on the upward deflection of the opposite aileron to cause the aircraft to roll. However, this would lead to a slow roll rate - and therefore a better solution is to make a compromise between adverse yaw and roll rate. This is what occurs in Differential ailerons.

• The down-going aileron moves through a smaller angle than the up-going aileron, reducing the amount of aileron drag, and thus reducing the effect of adverse yaw.

Differential deflection ailerons

Frise ailerons• Frise ailerons are designed so that when up aileron is applied, some

of the forward edge of the aileron will protrude downward into the airflow, causing increased drag on this (down-going) wing. This will counter the drag produced by the other aileron, thus reducing adverse yaw.

• Unfortunately, as well as reducing adverse yaw, Frise ailerons will increase the overall drag of the aircraft much more than applying rudder correction. Therefore they are less popular in aircraft where minimizing drag is important

• Note : Frise ailerons are primarily designed to reduce roll control forces. Contrary to the illustration, the aileron leading edge has to be rounded to prevent flow separation and flutter at negative deflections. That prevents important differential drag forces.

Frise aileron

Static Directional Stability

• Stability in the direction of travel• Categorized into– Weathercock stability– Spiral stability

Angle of Yaw and Sideslip

Weather cocking effect

• Application of the static stability principle to rotation about the z axis suggests that a stable airplane should have "weathercock stability

• If an aeroplane is yawed due to a gust of wind, it’s ability to automatically return to it’s previous heading depends on the area behind it’s centre of gravity to produce a restoring force. The fuselage ahead of the centre of gravity will tend to produce a force to destabilize the aircraft.

Spiral stability

• Spiral stability is the airplane's resistance to spiraling or going into a turn that gets tighter and tighter A large rudder or vertical fin and a lack of dihedral can mean the aircraft is pushed into a turn.

Rudder requirements• There are two sections covering tail surface to reflect the fact that there is

an aerodynamic side and a structural side to sizing.• The size of the tail surfaces depends on the force they have to generate.

This in turn depends on their distance from the centre of gravity and their area.

• In general, the surfaces have to be large enough to control the airplane but they must not be too large to produce excessive amounts of drag. This means balancing their size with the length of the tail boom.

• A relatively simple approach will be taken with some “rules of thumbs” taken from other aircrafts, the idea we shall use is “tail volume coefficient”, that is a length times an area (a volume) divided by a length times an area (another volume) to give a non-dimensional number.

• Regard the results as a starting point.Increase the area or the tail boom length as a result of flight tests.

• The rudder is used to control the direction of flight as well as keep the aircraft flying straight if side gusts are encountered.

• A value suggested for the vertical tail coefficient VV is 0.035

• The value suggested for the elevator tail volume is 0.5

• The elevator has to balance drag with weight, a large elevator with a short tail boom will result in a large amount of drag, making the tail boom longer will reduce the elevator area but the weight of the tail boom will start to be a problem.

• A good starting point is a tail boom length about 1/5

th the wing span

Remarks

• Highly Maneuverable = Poor Stability• Highly Stable = Poor Maneuverability

Longitudinal dihedral

• Longitudinal dihedral is the difference between the angle of incidence of the wing and angle of incidence of the horizontal tail.

• Longitudinal dihedral can be meaningfully identified as the angle between the zero lift axis of the two surfaces instead of, between the root chords of the two surfaces i.e. the wing and the horizontal tail.

Dorsal Fin

Any queries?