Aircraft Design Lecture 9: Stability and Control G. Dimitriadis Introduction to Aircraft Design Stability and Control H Aircraft stability deals with the ability to keep an aircraft in the air in the chosen flight attitude. H Aircraft control deals with the ability to change the flight direction and attitude of an aircraft. H Both these issues must be investigated during the preliminary design process. Introduction to Aircraft Design Design criteria? H Stability and control are not design criteria H In other words, civil aircraft are not designed specifically for stability and control H They are designed for performance. H Once a preliminary design that meets the performance criteria is created, then its stability is assessed and its control is designed. Introduction to Aircraft Design Flight Mechanics H Stability and control are collectively referred to as flight mechanics H The study of the mechanics and dynamics of flight is the means by which : – We can design an airplane to accomplish efficiently a specific task – We can make the task of the pilot easier by ensuring good handling qualities – We can avoid unwanted or unexpected phenomena that can be encountered in flight Introduction to Aircraft Design Aircraft description Flight Control Pilot System Airplane Response Task The pilot has direct control only of the Flight Control System. However, he can tailor his inputs to the FCS by observing the airplane’s response while always keeping an eye on the task at hand. Introduction to Aircraft Design Control Surfaces H Aircraft control is accomplished through control surfaces and power – Ailerons – Elevators – Rudder – Throttle H Control deflections were first developed by the Wright brothers from watching birds Introduction to Aircraft Design Modern control surfaces Rudder Elevator Aileron Rudderon (rudder+aileron) Elevon Introduction to Aircraft Design (elevator+aileron) Other devices Flaps Airbreak Spoilers H Combinations of control surfaces and other devices: flaperons, spoilerons, decelerons (aileron and airbrake) H VectoredIntroduction to Aircraftthrust Design Aircraft degrees of freedom Six degrees of freedom: 3 displacements x: horizontal motion y: side motion ω z: vertical motion v cg 3 rotations x x: roll y y: pitch z z: yaw v: resultant linear velocity, cg: centre of gravity Introductionω: resultant to Aircraft Designangular velocity Airplane geometry c s = b/2 c(y) y c /4 cg c /4 lT lt c Introduction to Aircraft Design Airplane references (1) H Standard mean chord (smc) s s c = ∫ c(y)dy / ∫ dy −s −s H Mean aerodynamics s chord (mac) c = ∫ c 2(y)dy / ∫ c(y)dy −s −s H Wing area S = bc H Aspect Ratio AR = b2 /S Introduction to Aircraft Design Airplane references (2) H Centre of gravity (cg) H Tailplane area (ST) H Tail moment arm (lT) H Tail volume ratio: A measure of the aerodynamic effectiveness of the tailplane S l V = T T T Sc Introduction to Aircraft Design Airplane references (3) c /4 cg c /4 lF lf H Fin moment arm (lF) SF lF H Fin volume ratio VF = Sc Introduction to Aircraft Design Aerodynamic Reference Centres H Centre of pressure (cp): The point at which the resultant aerodynamic force F acts. There is no aerodynamic moment around the cp. H Half-chord: The point at which the aerodynamic force due to camber, Fc, acts H Quarter-chord (or aerodynamic centre): The point at which the aerodynamic force due to angle of attack, Fa, acts. The aerodynamic moment around the quarter-chord, M0, is constant with angle of attack Introduction to Aircraft Design Airfoil with centres By placing all of the lift and drag L L a on the Lc Camber line aerodynamic F F F a centre we move c cp ac the lift and drag Da D Dc due to camber V0 from the half- L chord to the M quarter chord. D 0 This is c /2 hnc c /4 balanced by the c moment M0 Introduction to Aircraft Design Static Stability H Most aircraft (apart from high performance fighters) are statically stable H Static stability implies: – All the forces and moments around the aircraft’s cg at a fixed flight condition and attitude are balanced – After any small perturbation in flight attitude the aircraft returns to its equilibrium position H The equilibrium position is usually called the trim position and is adjusted using the trim tabs Introduction to Aircraft Design Pitching moment equation LT Lw ac cg MT M0 l T mg hc h denotes the cg c position h0c Introduction to Aircraft Design Equilibrium equations H Steady level flight is assumed H Thrust balances drag and they both pass by the cg H Force equilibrium: Lw + LT − mg = 0 H Pitching moment around cg equilibrium: M = M0 + Lw (h − h0 )c − LT lT + MT = 0 (nose up moment is taken to be positive) Introduction to Aircraft Design Stable or Unstable? H An equilibrium point can be stable, unstable or neutrally stable H A stable equilibrium point is characterized by dM M = 0 and < 0 dα H A more general condition (takes into account compressibility effects) is dM dCm M = 0 and < 0 or Cm = 0 and < 0 dL dCL Introduction to Aircraft Design Degree of stability Cm 1 2 3 α Trim point 4 1: Very stable 2: Stable 3: Neutrally stable 4: Unstable Introduction to Aircraft Design Pitching moment stability (1) H The pitching moment equation can be written as = + − − = Cm Cm0 CLw (h h0 ) CLT VT 0 H Where M L L = = w = T Cm , CLw , CLT 1 2 1 2 1 2 ρV0 Sc ρV0 S ρV0 ST 2 2 2 H And the tailplane is assumed to be symmetric so that MT=0 Introduction to Aircraft Design Pitching moment stability (2) H For static stability dC m / d C L < 0 or, approximately, dCm /dCL w < 0 H Then = − − dCm /dCLw (h h0) VT dCLT /dCLw H Since M0 is a constant. H Unfortunately, the derivative of the tail lift with respect to the wing lift is unknown Introduction to Aircraft Design Wing-tail flow geometry H The downwash effect of the wing deflects the free stream flow seen by the tailplane by an angle ε. H Total angle of attack of tail: αT=α-ε+ηT Wing Tailplane ηT αT α α V0 η Elevator ε V0 Trim tab βη H The total lift on the tailplane is given by: = α + α + η + β CLT 0 a1 T a2 a3 η Introduction to Aircraft Design Pitching moment stability (3) H For small disturbances the downwash angle is a linear function of wing incidence α: ε ε = d α dα H Wing lift is also a linear function of α: = α α = CLw a or CLw /a H So that CL % dε ( α = w '1 − * + η T a & dα ) T Introduction to Aircraft Design Pitching moment stability (4) H The tail lift coefficient can then be written as % ( a1 dε C = C '1 − * + aη + a η + a βη LT Lw a & dα ) 1 T 2 3 H And the derivative of the pitching moment coefficient becomes % ( dC a % dε ( dη dβη m = (h − h ) −V ' 1 '1 − * + a + a * 0 T ' & α ) 2 3 * dCLw & a d dCLw dCLw ) H since ηT is a constant Introduction to Aircraft Design Controls fixed stability H Assume that the aircraft has reached trim position and the controls are locked H What will happen if there is a small perturbation to the aircraft’s position (due to a gust, say)? H The pitching moment equation becomes dC a % dε ( m = (h − h ) −V 1 '1 − * 0 T & α ) dCLw a d Introduction to Aircraft Design Stability margin H Define the controls fixed stability margin as dCm Kn = − dCLw H And the controls fixed neutral point as % ( a1 dε Kn = hn − h, so that hn = h0 + VT '1 − * a & dα ) H A stable aircraft has positive stability margin. The more positive, the more stable. H If the cg position (h) is ahead of the neutral point (hn) the aircraft will by definition be stable H Too much stability can be a bad thing! Introduction to Aircraft Design Stability margin H Certification authorities specify that Kn ≥ 0.05 at all times H Of course, the stability margin can change: – If fuel is used up – If payload is released: H Bombs H Missiles H External fuel tanks H Paratroopers H Anything else you can dump from a plane Introduction to Aircraft Design Controls Free Stability H Pilots don’t want to hold the controls throughout the flight. H The trim tab can be adjusted such that, if the elevator is allowed to float freely, it will at an angle corresponding to the desired trim condition. H This is sometimes called a hands-off trim condition. H Therefore the pilot can take his hands off the elevator control and the aircraft will remain in trim. Introduction to Aircraft Design Controls Free Stability Margin H This is an expression for η that can be substituted into the pitching moment equation. H Differentiating the latter with respect to wing lift coefficient gives dC a % dε (% a b ( m = (h − h ) −V 1 '1 − *' 1 − 2 1 * 0 T & α ) dCLw a d & a1b2 ) H Where b1, b2 and b3 define the elevator hinge moment coefficient Tailplane Elevator hinge H ηT C = bα + b η + b βη αΤ H 1 T 2 3 α V0 η Elevator ε Trim tab Introduction to Aircraft Design βη Controls Free Neutral Point H Define the Controls Free Stability Margin, K'n, such that dCm Kn! = − = hn! − h dCLw H The controls free neutral point is then & )& ) a1 dε a2b1 h n" = h0 + VT (1 − +( 1 − + a ' dα *' a1b2 * a b & dε ( " = h − V 2 1 − or h n n T '1 ) ab2 dα Introduction to Aircraft Design Discussion H As with the controls fixed stability margin, the controls free stability margin is positive when the aircraft is stable.