Question 1 (a) onsider a wing of finite span with an elliptic circulation distribution: Γ( y) Γo y + b = 1, - s y s where s=b/ denotes the wing semi-span. Use this equation, in conjunction with the Kutta-Joukowsky result for the elementary lift per unit span, to derive an expression for the total lift on the wing. After that, write down this total lift in terms of Γ o and s as well as the free-stream density and speed. [ 1 marks ] (b) An aircraft has a wing loading of 4000 N.m - with wing span s = 6 m and aspect ratio AR = 10.5. Using the wing semi-span s in the corresponding bound vortex calculation, determine the strength Γ of the bound vortex when the aircraft is in steady level flight at a true airspeed of 70 m.s -1 at sea level conditions. [ 8 marks ] Question a) The crash of a new civil-aviation aircraft has led to litigation in a civil court case that alleges the aircraft suddenly became statically unstable before the crash. On behalf of the prosecution, you are called as an expert witness to explain to both the judge and the court the meaning and importance of the following concepts: 1) lift; ) pitching moment; 3) static stability; 4) centre of gravity; 5) static margin; 6) neutral point; 7) stick-fixed stability; 8) stick-free stability. Bear in mind the court members know very little about the engineering jargon of aeronautics and aircraft stability as well as control. Avoiding all reference to involved algebra and mathematical equations, yet using simple diagrams and sketches, write at least 10 clear and concise statements that explain the concepts mentioned above and summarise the evidence you will present to the court. b) The court-case aircraft has the following characteristics: AR w =6, e w =0.9, AR t =4, e t =0.8, d/c = 3, L =0.85, static margin = 8%, i t =1.3634 o. Knowing that the planform wing area is S w =38m, that the wing and tail may be considered made of symmetrical aerofoils, and that the aircraft neutral point is located 0.864 mean aerodynamic chords aft of the wing aerodynamic centre, determine the planform area of the tail and the angle of incidence in degrees α of the wing for trim. In these conditions, would the aircraft be guaranteed to feel natural to the pilot? Page 1 of 7
Question 3 The lift coefficient is given by : L 1 = c TE LE ( ) p, l p, u d x where c is the chord, LE and TE are the leading and trailing edges, and the pressure coefficients on the lower and upper surfaces. Assume that opposite sign to p, u. p, l and p, u are p, l has the An aircraft in steady level flight has a cruising Mach number of M = 0.75 at a pressure altitude of 1600 m. The ambient air temperature is 7 below standard and the ambient density is 0.94 kg.m -3. A static orifice is located on the upper surface of the wing at 40 % chord from the leading edge. The reading from the orifice indicates a pressure coefficient of 0.37. (a) What is the local Mach number and the local speed of sound at this point on the wing? [ 13 marks ] (b) If the average pressure coefficient on the upper surface of the wing equals the value at 40 % chord, and if two-thirds of the total lift is generated by the upper surface, what is the wing lift coefficient? [ 4 marks ] (c) What is the aircraft s wing loading? [ 3 marks ] Page of 7
Question 4 A Learjet is cruising at a pressure altitude of 9000 m at a Mach number of M = 0.60. The ambient temperature is 5 K. The aircraft has the following specifications : gross weight of 6500 kg; wing area is 9 m ; wing span is 14.5 m; the wing is of rectangular planform. Determine : (a) the Reynolds number of the wing; [ 7 marks ] (b) the (flat plate) skin friction drag coefficient and force of the wing; [ 5 marks ] (c) the boundary layer thickness at the trailing edge of the wing; [ marks ] (d) the lift coefficient; [ marks ] (e) the induced drag coefficient and force of the wing (assuming an elliptical lift distribution). [ 4 marks ] Page 3 of 7
Question 5 Discuss the supercritical airfoil. Make reference to the critical Mach number M c, the crest critical Mach number M cc, and the drag divergence Mach number M div. Include the advantages and disadvantages of the supercritical airfoil, its design, as well as a typical pressure coefficient curve. [ 0 marks ] Question 6 a) Draw a schematic yet accurate diagram, with distances, forces and moments, of the main components of an aeroplane that contribute to its static stability. Based on this diagram either derive or state the expression for L,α, for the entire aeroplane, and the equilibrium equations for an aeroplane in steady cruise flight. Also explain the concept of trim and the aerodynamic origin of all terms in the expression for L,α. b) For an aeroplane with AR w =5.5, e w =0.9, AR t =3.5, e t =0.9, S t /S w = 0.3, i t =1.83 o, α=9.531 o, determine the coefficient of lift of the aeroplane. If this information is insufficient to determine whether the aeroplane is in trim, state what additional information may be required. Page 4 of 7
Question 7 With reference to the equations of Question, consider an aeroplane with symmetrical wing and tail and with the following characteristics: AR w =6.5, e w =0.8, AR t =4, e t =0.8, S t /S w = 0.35, d/c =.75, L =1., static margin = 10%. a) Determine in degrees the wing angle of attack α and the tail setting angle i t. b) The tail of this aeroplane has the following characteristics: τ=0.5/rad, b 1 = -0.63/rad, b = -0.97/rad, 3D-effect correction factor = 0.630, tail setting i hs =1 o. Stating whether the elevator is raised or lowered, determine the magnitude of the elevator setting δ e for trim and corresponding coefficient of elevator-hinge moment H. Question 8 The expression for the stick-force gradient A may be stated as W ( b ) xn xg b1 St xn xn A = + ( ) L, α τ 1 εα Lt, α S S d x w t n c free c b Sw c c free τ L, αlt, α Sw c c onsider an aeroplane in steady cruise flight with a trim speed of 60m/s and with the following characteristics, AR w =7, e w =0.8, AR t =4, e t =0.8, S t /S w = 1/3, d/c = 3, static margin = 5%, α=1.059 o, tail setting i hs = o, τ=0.5/rad, b 1 = -0.63/rad, b = -0.97/rad, 3Deffect correction factor = 0.63. For this aeroplane, the total weight is W = 5,000 N, the wing planform area is S w =15 m, the stick elevator gearing is G=1.5 rad/m, the elevator planform area is S e =1.4 m and the elevator average chord is c e =0.3m. a) Based on the results for A, state whether the aeroplane would feel natural to the pilot. After that, determine the stick force at 50m/s and 100m/s and indicate which one is a push and which one is a pull. [ 8 marks ] P 1 =, determine the 1 hs e GSece trim elevator setting for flight at 105m/s at an altitude of 5,400m. [ 1 marks ] b) With reference to the stick force expression ρv ( bα + b δ ) Examiners : Dr. J. Iannelli Dr. A. Irving Brown External examiner : Professor D.I.A. Poll Page 5 of 7
DATA SHEET THE ISA TABLE IS INLUDED TRIGONOMETRI IDENTITY : θ sin θ sin θdθ = + 4 SUTHERLAND S FORMULA : µ = 1.71 10 5 T 73 3 73 T + 110.4 + 110.4 Page 6 of 7
ISA TABLE Page 7 of 7