P1 OTA/XYZ P2 ABC c11 BLBK308/Swatton August 12, 2010 20 46 Printer Name Yet to Come 11 Static Stability 11 1 Static Stability According to Newton’s first law a body remains in a state of rest or unif[.]
P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton 11 11.1 August 12, 2010 20:46 Printer Name: Yet to Come Static Stability Static Stability According to Newton’s first law a body remains in a state of rest or uniform motion unless acted on by an external force Stability is the reaction of an aeroplane after an external disturbing force to its equilibrium ceases or is removed The ability of an aeroplane to return to its original state following an undemanded disturbance is a measure of its stability Too much stability is undesirable because the aeroplane is slow to respond to control inputs and is sluggish in manoeuvring Too much instability is also undesirable because the attitude of the aeroplane requires continual correction There are two main types of stability; they are static stability and dynamic stability: a The static stability of an aeroplane is the immediate short-term response of the aeroplane to a disturbance and b The dynamic stability is the subsequent long-term response of an aeroplane to a disturbance to its equilibrium It is a measure of its reaction to damp out any unwanted oscillations, which depends on how fast or slow the aeroplane responds to a disturbance The dynamic stability of an aeroplane is dependent on the design of the aeroplane, its speed and the height at which it is being flown A statically (short-term) stable aeroplane can be dynamically (long-term) stable, neutral or unstable However, a statically neutral or statically unstable aeroplane can never be dynamically stable The reaction of an aeroplane to a disturbance is conditioned by its original state of equilibrium For instance, in straight and level flight an aeroplane is in equilibrium because the four forces are balanced and the resultant sum of these forces and their moments is zero and this will determine its reaction to a disturbance There are three degrees of stability – positive, neutral and negative a Positive stability An aeroplane that returns to its predisturbed attitude without assistance, once an external disturbing force ceases, is considered to be stable and to have positive stability b Neutral stability An aeroplane that remains in the attitude that it attains when an external disturbing force ceases is neutrally stable c Negative stability An aeroplane that continues to diverge from its predisturbed attitude after an external disturbing force ceases is an unstable aeroplane and has negative stability The Principles of Flight for Pilots C 2011 John Wiley & Sons, Ltd P J Swatton 233 P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come STATIC STABILITY 234 NEGATIVE SLOPE UNSTABLE AREA NEUTRAL STATIC STABILITY DISTURBANCE ESTABLISHED POSITIVE SLOPE STABLE AREA DISTURBANCE CEASES DISPLACEMENT TIME Figure 11.1 Degrees of Stability The degree of stability is depicted graphically in Figure 11.1 it shows the magnitude of the displacement by the vertical axis and the time period over which the disturbance was applied and the reaction to it is shown by the horizontal axis The graph in Figure 11.1 also indicates the point at which a disturbance is applied or established and the point at which the disturbance is removed or ceases It shows: a A horizontal straight line commencing at the point where the disturbance ceases indicates neutral static stability b Any reactive force in the area beneath the neutral static stability horizontal line is a positive force and indicates that the aeroplane is stable The angle of the graph line down from the disturbance cessation point indicates the degree of static stability The steeper the line the greater is the stability of the aeroplane c Similarly, any reactive force in the area above the horizontal neutral static stability line is a negative force and indicates that the aeroplane is unstable The angle of the graph line up from the disturbance cessation point indicates the degree of instability The steeper the line the greater is the instability of the aeroplane The reaction of an aeroplane to a disturbance can be resolved into components around the three axes of the aeroplane that pass through the CG and are shown in Table 11.1 The motion is an angular velocity and the reaction to the disturbance is an angular displacement If the total moment of the aeroplane is not zero it will rotate about the CG Table 11.1 The Resolution of Reactive Motion Axis Control Surface Motion (about the axis) Positive Motion Stability Longitudinal (x) Aileron Roll (p) Right Lateral Lateral (y) Elevator Pitch (q) Nose-up Longitudinal Normal (z) Rudder Yaw (r) Right Directional (Weathercock) P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come THE DIRECTIONAL RESTORING MOMENT 11.2 235 The Effect of the Variables on Static Stability The following variable factors increase the static stability of an aeroplane: a Decreased altitude – stability is proportional to dynamic pressure and inversely proportional to TAS therefore it is greatest at low altitude b Increased IAS increases the dynamic pressure without the necessity of decreasing the altitude Therefore, the static stability is directly proportional to the IAS c Increased air density increases the dynamic pressure without having to increase the IAS Static stability is therefore increased with decreased ambient temperature d Decreased aeroplane mass increases the responsiveness of the aeroplane to the correcting forces e Forward CG position increases the moment arm from the aerofoil surfaces CPs, thus increasing the moment of the correcting forces 11.3 Directional Static Stability The rotation of an aircraft about its normal, or vertical, axis is a yaw If this movement is the result of an undemanded disturbance then the ability of the aeroplane to return to its original heading without the assistance of any control-surface movement is a measure of its directional static stability It is a measure of the aircraft’s ability to realign itself with the relative airflow In a skid the aeroplane has a tendency to recover without the use of rudder It is known as ‘weathercocking’ stability, alluding to the movement of a weathercock when wind is blowing 11.4 Yaw and Sideslip A yaw is positive to the right and negative to the left The yawing moment, N, is calculated by using the formula: N = Cn1/2V2 Sb Where Cn the yawing moment coefficient; = air density; V = airspeed; S = wing area and b = the wingspan The yaw angle is the displacement angle of the aeroplane’s longitudinal axis in azimuth from a specified reference datum It is negative when the longitudinal axis is to the left of the reference datum See Figure 11.2(a) Sideslip is the displacement angle of the aeroplane’s longitudinal axis in azimuth from the relative airflow It is positive when the relative airflow is to the right of the longitudinal axis and negative when the relative airflow is left of the longitudinal axis See Figure 11.2(b) An aeroplane has directional static stability if, when in a sideslip with the airflow coming from the left initially the nose tends to yaw left An aeroplane that has excessive directional static stability compared to its lateral static stability is more prone to spiral dive 11.5 The Directional Restoring Moment Having experienced a disturbance to its equilibrium by an outside force an aeroplane requires a restoring moment to return to its original attitude The strength of that restoring moment is dependent on two factors, the design area of the fin and rudder and the distance of the tailplane from the CG When these two defining factors are multiplied together the result is the fin volume, which determines the directional stability of an aeroplane P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come STATIC STABILITY 236 (a) YAW ANGLE YAW ANGLE AZIMUTHAL REFERENCE DATUM (b) SIDESLIP ANGLE SIDESLIP ANGLE RELATIVE AIRFLOW NEGATIVE YAWING MOMENT Figure 11.2 Yaw and Sideslip Angles P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come THE DIRECTIONAL RESTORING MOMENT 237 11.5.1 Fin and Rudder Design The fin, which is the vertical stabilising symmetrical aerofoil mounted on top of the fuselage at the rear, creates the correcting movement or restoring moment The manner in which it achieves this is that the disturbing force moves the aeroplane about its normal axis causing the fin to have an angle of attack to the relative airflow When it has a positive angle of attack to the airflow the fin produces an aerodynamic correcting force, which is lift in a sideways direction In a sideslip the fin has a positive angle of attack that will produce a force proportional to both the ‘lift coefficient’ and the area of the fin The magnitude of the force, the sideways lift, is proportional to the area of the fin, its aspect ratio and its sweepback To decrease the likelihood of the fin stalling (in a sideways direction) at high sideslip angles, the aeroplane design team include either a large degree of sweepback on a fin of low aspect ratio or multiple low aspect ratio fins in the design of the tailplane Not only is the magnitude of the sideways force proportional to the size of the fin and rudder, it is also proportional the length of the moment arm This arm will rotate the aeroplane around its centre of gravity in the opposite direction to the disturbance The amount of lift and the size of the restoring moment diminishes as the aeroplane returns to the direction opposite to that of the relative airflow and vanishes altogether when it is pointing exactly into the relative airflow See Figure 11.3 11.5.2 The Dorsal Fin A dorsal fin is an additional fillet inserted on the top of the fuselage and forward of but joined to the fin There are three main reasons for including a dorsal fin in an aeroplane design they are to: a Increase the effective surface area of the fin, thus enhancing the yawing moment and augmenting the static directional stability and the weathercocking effect b Decrease the aspect ratio of the fin, therefore enlarging the sideways stalling angle of attack, which ensures that the fin continues to be effective at increased sideslip angles c Maintain directional static stability when the aeroplane has a large sideslip angle 11.5.3 The Ventral Fin To assist the directional static stability of an aeroplane in normal flight, some aeroplanes are fitted with strakes or ventral fins These are flat plates or strips positioned under the fuselage of the aeroplane aft of the CG and form a keel running parallel to the fore and aft axis of the aeroplane As an alternative to this, large transport aeroplanes are often fitted with small additional fins added to the tailplane All of these factors increase the directional static stability of the aeroplane 11.5.4 The Moment Arm The position of the CG affects the length of the moment arm of the fin, which directly influences the ability of the fin to achieve its purpose The distance of the CP of the fin from the CG fixes the length of the moment arm A large restoring moment is generated by a large fin situated a considerable distance from the CG A small restoring moment is the result of a small fin positioned close to the CG The combination selected by the aeroplane design team is normally determined by other factors Any movement of the CG will change the length of the arm of the restoring moment and either increase or decrease its effectiveness A forward movement of the CG will lengthen the moment arm and increase the directional static stability of the aeroplane and an aft movement of the CG will shorten the moment arm and decrease the directional static stability of the aeroplane (See Figure 11.3) P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come STATIC STABILITY 238 G URBIN DIST CE FOR ORING REST ENT M O M IVE LAT RE FLOW AIR ARM ANGLE OF ATTACK SIDEWAYS LIFT FORCE FIN CP Figure 11.3 Directional Restoring Moment 11.6 Aeroplane Design Features Affecting Directional Static Stability 11.6.1 Fuselage When the centre of pressure (CP) of the fuselage of a normal aeroplane is well forward of the CG it causes the fuselage to be a destabilising influence on the directional static stability of the aeroplane If such is the location of the CP relative to the CG, then in a sideslip the relative airflow exerts a larger yawing moment forward of the CG than it does aft of the CG In other words, the length of the fuselage ahead of the CG has an unstable static direction influence, whereas the fuselage length behind the CG has a stabilising influence This effect is particularly noticeable at high angles of attack when the disturbed airflow around the fuselage causes the fin to stall and the aeroplane to become directionally unstable To counteract the unstable influence of the fuselage an aeroplane requires a high vertical fin or stabiliser to produce positive directional static stability to move the CP of the fuselage to a position aft of the CG 11.6.2 Wing The two design characteristics that directly affect directional static stability are dihedral and sweepback P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come AEROPLANE DESIGN FEATURES AFFECTING DIRECTIONAL STATIC STABILITY 11.6.2.1 239 Dihedral Compared with sweepback, the effect of dihedral is insignificant; it decreases the directional static stability because the lift produced by the sloping wings (the dihedral) contributes to the yawing moment due to their inclination 11.6.3 Sweepback The drag of a swept wing is less than that of an unswept wing The advantage of this type of wing at high speeds is gained at the expense of its poor performance at low speed The drag experienced with a swept wing is the component of the relative airflow at 90◦ to the line joining the aerodynamic centres of the wing, which if the wing has parallel leading and trailing edges will be the normal to the leading edge of the wing In Figure 11.4 the normal component of the relative airflow is greater on the port wing than the normal component on the starboard wing The drag on the leading wing, the port wing, in Figure 11.4 is of greater magnitude than that of the trailing starboard wing because of its decreased effective sweep angle It is therefore a stabilising influence Positive sweepback has a stabilising effect on directional stability because the CP is further aft and the stalling angle is increased The significance and magnitude of this effect on directional static stability is directly proportional to the angle of sweepback RELATIVE AIRFLOW SIDESLIP ANGLE NORMAL COMPONENT LEADING WING Figure 11.4 The Effect of Sweepback (on Directional Static Stability) NORMAL COMPONENT TRAILING WING P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come STATIC STABILITY 240 11.7 Propeller Slipstream The effect caused by the slipstream of a single-engined propeller-driven aeroplane is dependent on the direction of rotation of the propeller The corkscrew airstream produced by the propeller will strike one side of the fin more than the other To counteract this effect the fin and rudder have to balance the asymmetric airflow to prevent sideslip, which for a single-engined aeroplane is more likely in one direction than the other To assist in this task the fin is mounted slightly offset from the fore and aft axis into the corkscrew airstream, thus decreasing the asymmetric influence See Figure 16.7 11.8 Neutral Directional Static Stability POSITIVE YAWING MOMENT COEFFICIENT The effect that each major component has on the overall directional static stability of an aeroplane can be plotted graphically Cn is the yawing moment coefficient and is shown on the left vertical axis of Figure 11.5 The sideslip angle is shown along the horizontal axis The highest point of each curve is the stalling sideslip angle and is the point of neutral directional static stability; to the left of this point the aeroplane has positive directional static stability and to the right of this point the aeroplane has directional static instability NEUTRAL STABILITY STALL LY F IN ON FIN AL RS O +D LE O WH AE NE LA P RO SIDESLIP ANGLE Figure 11.5 Directional Static Stability 11.9 Lateral Static Stability The lateral static stability is a measure of the aeroplane’s tendency to return to the wings-level attitude after a disturbance has caused the aeroplane to be disturbed in the rolling plane Positive lateral static P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come LATERAL STATIC STABILITY (a) SIDESLIP ANGLE 241 V SIDESLIP COMPONENT OF RELATIVE AIRFLOW SIDESLIP ANGLE LIFT (b) SIDESLIP FORCES RESULTANT SIDESLIP FORCE V SIDESLIP VELOCITY MASS Figure 11.6 Sideslipping (a) Sideslip Angle P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 2010 20:46 Printer Name: Yet to Come 242 STATIC STABILITY stability is the tendency of the aeroplane to roll to the left with a positive sideslip angle, nose to the left Its ability to recover is dependent on the effect of sideslip A disturbance in the rolling plane causes the angle of attack of the upgoing wing to decrease and the angle of attack of the downgoing wing to increase Provided the aeroplane is not flying close to the stalling speed, then the upgoing wing produces less lift than it did before the disturbance and the downgoing wing will produce more lift than it did Together, these changes result in a rolling moment in opposition to the initial disturbance and have a ‘roll-damping’ effect When the roll damping exactly matches the aileron torque the aeroplane has a steady rate of roll A sideslip is defined as the angle between the speed vector and the plane of symmetry It not only produces a rolling moment but also a yawing moment, the strength of which is dependent on the magnitude of the directional static stability When considering lateral static stability it is only necessary to account for the relationship between the sideslip and rolling moments The ‘roll-damping’ effect is proportional to the rate of roll and therefore cannot bring the aeroplane back to the wings-level attitude and is unaffected by an increase of altitude Because of this then, the aeroplane will remain with the wings banked and as such will have neutral lateral static stability with respect to a bank-angle disturbance However, after a lateral disturbance an aeroplane experiences a sideslipping motion, caused by the inclined lift vector, as well as the rolling motion See Figure 11.6 An aeroplane with greater lateral static stability than directional static stability is prone to developing ‘Dutch’ roll, which is exacerbated by any rearward movement of the CG 11.10 Aeroplane Design Features Affecting Lateral Static Stability 11.10.1 Increased Lateral Static Stability The aeroplane design features that increase the lateral static stability are: a b c d e f dihedral; sweepback; high-wing mounting; increased effective dihedral; large, high vertical fin; low CG 11.10.2 Decreased Lateral Static Stability The aeroplane design features that decrease the lateral static stability are: a b c d e anhedral; forward-swept wings; ventral fin; low-wing mounting; extending inboard flaps As a result, of the sideslip, different parts of the aeroplane produce forces that together create a correcting rolling moment, which tends to restore the aeroplane to its original wings-level attitude The lateral static stability reacts to the sideslip velocity ‘v’ or the displacement in yaw shown in Figure 11.6 This effect considerably modifies the long-term response, the lateral dynamic stability of the aeroplane An aeroplane in a sideslip at a constant speed and constant sideslip angle increases the geometric dihedral of the wing, which requires an increased lateral control force or increased stick force ... stability of the aeroplane 11.5.4 The Moment Arm The position of the CG affects the length of the moment arm of the fin, which directly influences the ability of the fin to achieve its purpose The. .. is the location of the CP relative to the CG, then in a sideslip the relative airflow exerts a larger yawing moment forward of the CG than it does aft of the CG In other words, the length of the. .. by the relative positions of the CP and the CG The greater the distance the CP is aft of the CG the larger is the nose-down pitching P1: OTA/XYZ P2: ABC c11 BLBK308/Swatton August 12, 20 10 20 :46