Static directional stability

� Static directional stability is a measure of

the aircraft's resistance to slipping. The greater

the static directional stability the quicker the

aircraft will turn into a relative wind which is

not aligned with the longitudinal axis.

� In an equilibrium condition (figure (a)), an

airplane flies so that the yaw angle is zero. To

have static directional stability, the appropriate

positive or negative yawing moment should be

generated to compensate for a negative or

positive sideslip angleexcursion

Directional (Weathercock) stability

� The main contributor to the static directional stability is the fin. Both the size and arm

of the fin determine the directional stability of the aircraft. The further the vertical fin is

behind the center of gravity the more static directional stability the aircraft will have.

(This is often called the weather veining effect, because it works the same way as a

weather vein.)

� As mentioned previously all rotational motions of the aircraft occur around the center

of gravity. Directional stability refers to motions around the normal axis

Stable/unstable aircraft

This figure shows the variation of yawing-moment coefficient with sideslip angle.

This positively sloping line indicates a directionally stable case.

Wing contribution to directional stability

A wing produces two effects that give a yawing moment with sideslip. The important one

is due to sweep-back angle, and the other minor effect is due to geometric dihedral.

(Both effects are stabilizing)

The second effect,

due to dihedral,

results from a tilt of

the lift vector

with sideslip.Directional and lateral effects of wing sweep due to sideslip

Lateral Effects

� Wing Dihedral

– Dihedral effects due to sideslip

– Sideslip produces two important effects

other than those mentioned directional

effects:

• rolling moment

• side force

� Wing Sweep

� Fuselage

Contribution to directional stability

Fuselage and engine nacelles (in general are destabilizing)

Wing-body interference factor

Reynolds number

correction factor

Vertical tail contribution

Sidewash due to wing vortices

Moment produced by a side force

Vertical tail volume ratio

Dynamic pressure ratio

USAF Stability and Control Datcom:

Some comments

� The moment associated with yawing and rolling are cross-coupled, i.e., the angular

velocity in yaw produces rolling moments and vice versa. If a pilot steps on a rudder pedal

causing the aircraft to yaw one wing will advance and the other will retreat. The faster

moving wing produce more lift than the other which will cause a roll in the same direction

as the yaw. This will be exaggerated by wing dihedral.

� At a normal flight, i.e., steady rectilinear symmetric motion, all the lateral motion and

force variables are zeroes.

� There is no fundamental trimming problem: control surfaces (ailerons and rudder)

would normally undeflected.

� Lateral control provides secondary trimming functions in the case of asymmetry.

� Effects of CG movement are negligible on lateral and directional stability

� Due to cross-coupling effect, (e.g., the rolling motion will cause sideslip), we investigate

the directional and lateral effects of sideslip.

Directional Control

� Rudder

Positive rudder deflection,

produces a positive side force,

that will produce a negative

yawing moment

Rudder control effectiveness

Requirements for Directional Control

� Adverse yaw

� Crosswind landings

� Asymmetric power condition

� Spin recovery

Adverse Yaw

�Roll-Yaw Coupling

� Asymmetric aileron

deployment produces

asymmetric drag

Asymmetric drag

produces adverse yaw

� Rudders required for

coordinated turn

Static Roll Stability

The roll moment created on an airplane when it start to slip depend on:

– Wing dihedral angle G

– Wing sweep L

– Position of wing on the fuselage

– Vertical tail

Dihedral Effect

Figure (a) shows a head-on view of

an airplane that has dihedral where

the wings are turned up at some

dihedral angle to the horizontal. If a

disturbance causes one wing to

drop relative to the other

(figure(b)), the lift vector rotates

and there is a component of the

weight acting inward which causes

the airplane to move sideways in

this direction. When wings have

dihedral, the wing toward the free-

stream velocity, hence the lower

wing, will experience a greater

angle of attack than the raised wing

and hence greater lift. There results

a net force and moment tending to

reduce the bank angle (figure (c)).

Approximation

for the sideslip

Down-moving wing

Up-moving wing

Effect of wing placement on lateral stability

Fuselage contribution to dihedral effect

Wing sweep effect on roll stability

�The windward wing (less effective sweep) will experience more lift than the trailing wing.

The result is that the sweepback adds to the dihedral effect

� On the other hand, sweep forward will decrease the effective dihedral effect

Roll moment due to vertical tail

Roll Control

� By differential deflection of ailerons or by spoilers

� By differential deflection of ailerons or by spoilers

Tapered wing

Control power