TAIL SIZING

Tail configurations:

Conventional:Pros

Adequate stability at lightest weight Efficient Simple in design

Cons

Horizontal and Vertical tails in the region of wing wake.

T-tailPros

Horizontal tail is out of regions of wing wake, wing downwash, hence higher efficiency

Smaller tail area (both horizontal and vertical tails (due to end plate effect.

Cons Heavier vertical tail structure Deep stall Horizontal tail contribution to longitudinal stability is largely

reduced

CruciformReduces the disadvantages and advantages of T-tail and conventional tail.

Pros Lighter than T-tail Tail out of wake region of wing and fuselage

Cons Heavier than conventional tail] Proper positioning of horizontal tail needed to avoid deep

stall

H-tailComprises of one horizontal in between the two vertical tailsPros

At high angle of attack the vertical tail is not influenced by the turbulent flow coming from the fuselage

Vertical tail end-plate effect improves the aerodynamic performance of the horizontal tail

Allows twin vertical tails to be shorter. Lateral control of aircraft will be improved due to shorter

vertical tail span Allows fuselage to be shorter, since h-tail an be installed on a

boom

Cons H-tail is heavier than the conventional and T-tail Design of H-tail is more tedious

V-TailPros

Reduction in tail area Performs the longitudinal and directional trim control

satisfactorily

Cons Deficient in maintaining directional and lateral stability More susceptible to Dutch roll tendencies Induce undesirable phenomenon of adverse roll-yaw

coupling

Y-tailExtension to v-tail; extra surface located under the aft fuselage

Pros Complexity is much lower than that of the y-tail Tail out of wing wake regions at high angles of attack Reduction in tail area as compared to conventional

Cons Lower section limits the performance of the aircraft as during

take off and landing the tail hitting the ground must be avoided

Not a very popular configuration

Twin vertical tail

Pros

Largely improves the directional controllability of the aircraft Two short span vertical tails have smaller mass moment of

inertia about x-axis

Less negative effect on roll control. Both rudders are almost out of fuselage wake region, since

they are not located on the fuselage center-line

Cons Slightly heavier than conventional

Boom-mounted

Pros Greater efficiency than any tail configuration when in a prop-

driven aircraft engine is installed at the aft fuselage Reduction in tail area Satisfactorily performs longitudinal and directional trim

requirements Reduction in fuselage length as tail can be installed using

booms

Cons Deficient in performing lateral and directional stability

requirements

AIRCRAFT TRIM REQUIREMENTS

(Assumed that thrust line is along the axis of fuselage)Moments due to wing drag, landing gear drag and engine thrust will be included in the actual design process)

(EQUATION -1)(EQUATION -2)

VHT = Volume Tail Coefficient for horizontal tail= (lSh)/CSVolume tail coefficient is an indication of handling quality in longitudinal stability and longitudinal control.

As VHT increases the aircraft tends to be more longitudinally stable and less longitudinally controllable and vice- versa.

If is in ballpark number we are 90% sure that the longitudinal stability requirements are satisfied.

(EQUATION -3)

If the wing has been designed prior to the design of the horizontal tail and aircraft c.g. has been decided then EQ-3 has only two unknowns.In fact the design of the wing and location of the c.g. are not independent of tail design. Hence tail design is an iterative process.

Due to the effect of the wing and fuselage on the on horizontal tail, a new parameter is added i.e. nh efficiency of the tail

nh=Vh2/ V2

Vh=speed of air at horizontal tail region

V= aircraft speed

Hence equation 3 becomes EQUATION -4Equation 4 is the most important equation in the design of the horizontal tail.

Now in Equation 4, We need to first select a value for VHT depending upon our need of longitudinal stability and control. This is just the initial value of VHT and will be revised in the later design process.From equation 4 now CLH can be calculated.

OPTIMUM TAIL ARM

While calculating optimum tail arm the main intention is to reduce the wetted area and hence reduce the zero lift drag.

EQUATION -5 EQUATION -6

Hence if horizontal tail is located at lopt then the wetted area of the aft fuselage is minimum so the drag of the aft part will be minimized.

In all flight conditions EQUATION-7EQUATION-8 Must hold

TAIL INCIDENCE

The tail setting angle (it) primary requirement is to nullify pitching moment about c.g. at the cruising flight.

It is determined to satisfy trim requirements when no control surface is deflected.

Initially the tail angle of attack is determined by following equation EQUATION 9In the next step a mat-lab file is used to calculate with angle of attack as calculated from equation 9If it does not satisfy the required CLH as obtained from equation 4 then we use hit and trail method to calculate the angle for which desired CLH is obtained.

After finding out the value of initial tail setting angle, the downwash is taken into account for calculating actual tail setting angle.

EQUATION-10EQUATION-11EQUATION-12

Then actual tail setting angle is calculated byEQUATION-13

LONGITUDINAL DIHEDRAL

Longitudinal dihedral is invented by tail designers to transfer the technical meaning of wing dihedral from y-z plane similar angle to x-z plane.Longitudinal stability is improved by geometry referred to as the aircraft longitudinal dihedral angle.When the tail horizontal chord and the wing chord line can form a v-shape, it is said to have longitudinal dihedral.

Technical interpretations of longitudinal dihedral:When the wing effective angle of attack is higher than that of the horizontal tail the aircraft is said to have longitudinal dihedral.

TAIL GEOMETRIES Now as tail volume coefficient and optimum tail arm has been calculated the Planform area for horizontal tail can be calculated by

EQUATION -14EQUATION -15

ASPECT RATIO: Aspect ratio of tail has direct effect on the lift curve slope, and thus

influences tail incidence angle. In a single engine prop-driven aircraft, it recommended to have aspect ratio such

that the tail span is longer than the prop diameter.

Hence taking all this into account the initial value of aspect ratio for horizontal tail is taken to be 2/3 to that of the wing.

TAPER RATIO: To lower tail weight Influences lateral tail stability and control performance, tail aerodynamic

efficiency, aircraft weight and center of gravity.It is initially taken equal to that of the wing.

EQUATION-16EQUATION-17EQUATION-18

TAIL VERTICAL LOCATION

An aircraft computational fluid dynamics model allows the designer to find the best location in order to increase the effectiveness of the tail.There are few components that are sources of interference with tail effectiveness.They include downwash due to wing and fuselage.

The following equations are recommended for initial approximation of horizontal tail vertical heightEQUATION -19EQUATION -20

STABILITY CHECK

When all tail parameters have been decided the stability can be checked by using the following stability derivative.

EQUATION -21It should be less than zero for the plane to be statically longitudinally stable, i.e. the aircraft neutral point is behind the aircraft c.g.

A dynamic longitudinal stability analysis is performed after all components are designed and the roots of the longitudinal equation are calculated.

A general form of longitudinal characteristic equation is EQUATION-22

An aircraft is dynamically longitudinally stable if real parts of all roots of the equation are negative.

Another way to analyse dynamic longitudinal stability is to make sure that the longitudinal mode (i.e. short period and long period phugoids are damped)

VERTICAL TAIL DESIGN

Vertical tail tends to have two primary functions: Directional trim Directional stability

The summation of all forces along the y-axis and the summation of all moments about the z-axis must be zero.

Initially a typical value of the tail volume coefficient for vertical tail is selected.Typical value of tail volume coefficient for vertical tail is 0.02-0.12

EQUATION-23

VERTICAL TAIL MOMENT ARM

The vertical tail moment arm must be long enough to satisfy directional stability, control and trim requirements.

Increasing value of tail moment arm increases the value of directional derivatives Cnb and Cnr and thus makes it longitudinally more stable.

EQUATION -24Kf has a typical value of 0.7Clav is determined byEQUATION-25

Initially vertical tail moment arm is taken equal to horizontal tail moment arm.When spin occurs all that is mainly required is a sufficient yaw rate while the aircraft is stalled. If the vertical tail is in horizontal tail wake region it will lose its effectiveness. Therefore vertical tail moment arm needs to be determined such that it provides a wake free region for vertical tail.As a rough estimate at least 50% of the tail planform area must be out of wake region of horizontal tail and at least one third of the rudder must be out of wake region of wing and fuselageFIGURE -1

PLANFORM AREA

Vertical tail area must be large enough to satisfy lateral-directional stability control and trim requirements.

Increasing value of tail area increases the values if the derivatives Cnb and Cnr and thus makes the aircraft laterally more stable. But it should not be too stable, otherwise control requirements not satisfied. Hence a middle value must be selected.

Typical value for ratio between vertical tail area and wing area is 0.1-0.15.

Planform area is calculated using EQUATION 26AIRFOIL SECTION

The airfoil must be able to generate the required lift with minimum drag coefficient. To ensure the symmetricity about the x-z plane the vertical airfoil section must be symmetric.

Another requirement that the airfoil selected must be clean of compressibility effect. This objective is realized by selecting a vertical tail airfoil section thinner than the wing airfoil section.

Third desire is high value of lift slope, since Cnb is directly a function of Clav.

VERTICAL TAIL SETTING ANGLEIn a prop driven aircraft with single engine the lateral trim is disturbed by the revolution of propeller and the engine shaft about the x-axis.To nullify this yawing moment, the vertical tail in most prop driven aircraft have about 1-2 degrees of incidence to ensure prevention of aircraft roll in reaction to prop revolution.Exact value for this setting angle can be calculated by calculating rolling due to prop revolution.

ASPECT RATIO

ADVANTAGES OF HIGH ASPECT RATIO (>1.5)

Higher directional control High aspect ratio vertical tail is aerodynamically more efficient (has higher L/D

than vertical tail with lower aspect ratio. The reason is tail tip effect. If the aircraft has T-tail configuration the horizontal tail location and efficiency

are functions of vertical tail aspect ratio. Thus is deep stall is a major concern then the vertical tail aspect ratio must be large enough to keep the horizontal out of wing wake when wing stalls.

Directional stability is improved due to longer due to increase in tail moment arm.

DISADVANTAGES OF HIGH ASPECT RATIO Bending moment and bending stress at vertical tail root increases which causes aft

portion to be heavy. High aspect ratio tail are more prone to fatigue and failure.

Longitudinally destabilizing as drag generates nose-up pitching moment Induced drag increases when aspect ratio increases.

TAPER RATIO

ADVANTAGES OF LOW TAPER RATIO.

To reduce the bending stress on vertical tail root To allow vertical tail to have a sweep angle.

DISADVNTAGES OF LOW TAPER RATIO

Taper ratio application adds complexity to manufacturing process As taper ratio is increased the yawing moment am is reduced which reduces the

directional control Reduces the lateral stability of the aircraft.

SWEEP ANGLE Improves directional control and weakens directional stability since mass moment

of inertia about z-axis in increased. Decreases wave drag for subsonic and supersonic flight regime. If the aircraft has T-configuration a increase in the vertical tail sweep angle

increases the horizontal tail arm which improves longitudinal stability and control.

VERTICAL TAIL GEOMETRIES

For vertical tail:EQUATION-16EQUATION-17

EQUATION-18

STABILITY CHECK

The stability derivative Cnb must be positive to satisfy static stability directional requirements. Cnb is calculated using the following equationEQUATION -24The Cnr be negative to satisfy dynamic directional requirements. Two major contributors in to the value of these stability derivatives are vertical tail area and vertical tail moment arm. If vertical tail moment arm is long enough and vertical tail area is large enough the stability requirements are easily satisfied. The directional stability requirements could easily be satisfied. EQUATION -27

IN ALL CONDITIONS SUMMATION OF ALL FORCES ALONG THE Y-AXIS AND SUMMATION OF ALL MOMENTS ABOUT THE Z-AXIS IS ZERO.

ELEVATOR DESIGN

FACTORS AFFECTING THE DESIGN OF THE ELEVATOR ARE: Elevator effectiveness Elevator aerodynamic and mass balancing

Elevator effectiveness is a measure of how effective the elevator deflection is in producing desired pitching moment.

Prior to design of the elevator the wing and horizontal tail must be designed as well as the most aft and most forward c.g. must be known.

In elevator design process the following parameters must be determined: Elevator chord to tail chord ratio Elevator span to tail span ratio Maximum up-deflection Maximum down-deflection Aerodynamic balance and mass balance of the elevator

When elevator is deflected more than 20-25 degrees, flow separation over the tail tends to occur. Thus the elevator will lose its effectiveness.

ELEVATOR EFFECTIVENESS

The primary function of the elevator is an aircraft pitching moment to control pitch rate. Longitudinal control power derivative is the rate of change of aircraft pitching moment w.r.t. elevator deflectionEQUATION -28

Rate of change of lift coefficient w.r.t. elevator deflection and is defined as followsEQUATION-29 Contribution of elevator to tail liftEQUATION-30

The most significant elevator design requirement is the take-off rotation requirement. This design requirement is a function of aircraft mission and landing gear configuration.

In a conventional aircraft, the takeoff rotation when c.g. is at its most forward location, requires the most negative elevator deflection The longitudinal trim when aircraft c.g. is at its most aft location and aircraft has most positive elevator deflection.

TAKE-OFF ROTATION REQUIREMENT

The take-off rotation requires the elevator design to be such that pitch angular acceleration is greater than a desired valueThere are three governing equations of motion that govern the aircraft equilibrium at the instant of rotationEQUATION -31

EQUATION -32EQUATION -33EQUATION -34EQUATION -35EQUATION -36

The contributing pitching moments in take-off rotation control are aircraft weight moment(MW), aircraft drag (MD) engine thrust moment (MT), wing-fuselage lift moment(MLwf), wing fuselage aerodynamic pitching moment (Mowf), horizontal tail lift moment(MLh) and the linear acceleration moment(Ma)

EQUATION -37EQUATION -38

The horizontal tail lift thus obtained is such that it can satisfy the take off rotation requirement.EQUATION-39EQUATION-40EQUATION-41

After calculating Te from the above equation tail chord to elevator chord can be calculated.

LONGITUDINAL TRIM REQUIREMENT

Summation of all forces about the z-axis is zero.Summation of all forces about the x-axis is zero.Summation of all moments about the c.g. is zero.Which would yield:

EQUATION -42EQAUTION -43EQUATION -44EQUATION-45EQUATION-46

Here there are two unknowns Aircraft angle of attack Elevator deflection

Hence EQUATION -47EQUATION -48

There is constraint on the elevator design which must be considered and checked. The elevator deflection must not cause the horizontal tail to stall. The elevator deflection decreases the tail stall angle. The elevator designer must check whether tail stall occurs when maximum elevator deflection is employed and fuselage is lifted up. The recommendation is to keep the tail within 2 degrees of its stall angle of attack.EQUATION -49

When elevator is designed the generated horizontal tail lift coefficient needs to be calculated and compared with the desired lift coefficient.Tools such as computational fluid dynamics or lifting line theory may be utilized to such calculation

RUDDER DESIGN

In the design of the rudder, four parameters must be determined:Rudder areaRudder chord

Rudder spanMaximum rudder deflection

The aircraft side force is primarily a function of dynamic pressure, vertical tail area and in the direction of vertical tail lift

EQUATION -50EQUATION -51EQUATION -52EQUATION -53

FUNDAMENTALS OF RUDDER DESIGN Rudder plays different roles for different phases of flight in various aircraft

Crosswind landing Turn coordination Spin recovery Adverse yaw

CROSSWIND LANDINGIf when a crosswind blows during landing operations and if the pilot does not react the aircraft will exit out of the runway.The approach under crosswind conditions may be consulted in the following wayWith the wings level (applying drift correction in order to track the runway centerline. This type of approach is called crabbing.

Consider an aircraft, which is approaching with a forward speed of U1 along the runway. There is a crosswind of Vw from the right that is creating positive sideslip angle.

EQUATION -54

The sideslip angle generates a yawing moment (NA) and an aerodynamic side force by the aircraft.

EQUATON -55

In order to keep the aircraft landing along the runway, the rudder is employed to counteract the yawing moment created by the wind. The rudder produces a vertical tail lift along the y-axis (LV) which consequently contributes to the aircraft yawing moment and aerodynamic side force.The rudder must be powerful to create the crab angle i.e. the angle between the fuselage centerline and the runway.Summation of all forces about the c.g. is zeroEQUATION -56EQUATION -57

EQUATION -58EQUATION -59EQUATION -60

SPIN RECOVERY Spin is a high angle of attack situation. Spin has two particular specifications:

Fast rotation about the vertical axis Fully stalled