AE 451 Aeronautical Engineering Design I Estimation of Critical Performance Parameters. Prof. Dr. Serkan Özgen Dept. Aerospace Engineering Fall 2015

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1 AE 451 Aeronautical Engineering Design I Estimation of Critical Performance Parameters Prof. Dr. Serkan Özgen Dept. Aerospace Engineering Fall 2015

2 Airfoil selection The airfoil effects the cruise speed, takeoff and landing distances, stall speed, handling qualities and overall aerodynamic efficiency during all phases of flight. The airfoil may be separated into: Thickness distribution, influences profile drag, Zero-thickness camber line, influences lift and drag due to lift. Upper surface of an airfoil or wing produces roughly 2/3 of total lift. Zero-lift angle of attack is roughly equal to the percent camber of the airfoil (in deg). 2

3 Design lift coefficient This is the lift coefficient at which the airfoil has the best L/D. The airplane should be designed such that it flies the design mission at or near the design lift coefficient to maximize the aerodynamic efficiency. 3

4 Airfoil geometry 4

5 Stall Some airfoils show a gradual reduction in lift during stall, while others show a violent loss of lift with a rapid change in pitching moment. 5

6 Stall Thick airfoils (round leading edge, t/c>14%) stall starting from the trailing edge. At around α=10 o, the boundary-layer begins to separate starting at the tariling edge and moving forward as the angle of attack is further increased. The loss of lift is gradual, pitching moment does not change significantly. Moderately thick airfoils (6%<t/c<14%) stall from the leading edge. Flow separates over the nose at a very low angle of attack, but immediately reattaches, so the effect is initially small. At some higher α, the flow does not reattach and the airfoil stalls almost immediately. Lift and pitching moment vary violently. 6

7 Stall Thin airfoils (t/c<6%) stall from the leading edge and the flow reattaches immediately. As α is increased, the bubble contnues to stretch towards the trailing edge as the angle of attack is increased. At α where the bubble stretches all the way to the trailing edge, c l,max is reached. Beyond that α, the flow is separated over the entire airfoil, so stall occurs. The loss of lift is smooth, but large changes in pitching moment are observed. Twisting the wing such that the tip airfoils have a reduced angle of attck compared to the root (washout) can cause the wing to stall at the root first. 7

8 Stall Different airfoil sections may be used at the root and the tip, with a tip airfoil that stalls at a higher angle of attack. This produces good flow over the ailerons for roll control (aileron authority) at an angle of attack where the root has stalled. Stall characteristics for thinner airfoils may be improved with leading edge devices like slots, slats, leading edge flaps. Wing stall is directly related to airfoil stall only for high aspect ratio, unswept wings. For low aspect ratio, swept wings, 3-D effects dominate stall characteristics and airfoil stall characteristics can be ignored. Horizontal tail or canard size is directly related to the magnitude of the wing pitching moment to be balanced. 8

9 Thickness ratio Airfoil thickness ratio has a direct effect on drag, maximum lift, stall characteristics and structural weight. A wing with a fairly high AR, moderate sweep, large nose radius provides a higher stall angle and a higher C L,max. For a wing with low AR, swept wings, a sharper leading edge provides greater C L,max due to the formation of vortices behind the leading edge. Wing structural weight ~1/ t/c halving the thickness ratio increases the empty weight of the airplane by 6%. 9

10 Thickness ratio 10

11 Thickness ratio 11

12 Thickness ratio 12

13 Thickness ratio For initial selection of the thickness ratio, historical trends can be used. Supercritical airfoils can be chosen 10% thicker. 13

14 Thickness ratio In subsonic airplanes, the root airfoil can be 20-60% thicker than the tip airfoil without effecting the drag due to fuselage effects. This thicker root should not extend beyond 30% of span. This results in a structural weight reduction as well as more volume for fuel and landing gear. Each airfoil is designed for a certain Reynolds number. Use of an airfoil at greatly different Reynolds numbers produce section characteristics much different than expected. This is especially true for laminar flow airfoils. 14

15 Wing geometry The reference or trapezoidal wing is the basic geometry to begin the layout. The leading edge sweep is important for supersonic flight. In order to reduce drag, it is important to sweep the wing leading edge behind the Mach cone. 15

16 Wing geometry The quarter chord sweep is related to the subsonic flight since the lift produced by a wing is proportional to the component of the freestream velocity vector perpendicular to the quarter chord line. 16

17 Wing geometry For a complete trapezoidal wing, the aerodynamic center is at the quarter chord point of the mean aerodynamic chord. In supersonic flow, the aerodynamic center moves approximately back to 40% of the mean aerodynamic chord. 17

18 Aspect ratio For finite aspect ratio wing, tip vortices lower the pressure difference between the upper and lower surfaces. This reduces the lift near the wingtip. The tip vortices reduce the effective angle of attack of the wing, more so at the wingtips. A high aspect ratio wing has wingtips further apart compared to an equal area wing with low AR. Therefore, the amount of wing effected by the wingtip is less for a high aspect ratio wing and the strength of the wingtip vortex is reduced. loss of lift and induced drag is less for high aspect ratio wing. L/D) max ~ AR W wing ~ AR 18

19 Lift to drag ratio L/D is a measure of overall aerodynamic efficiency. Subsonic speeds: L/D=L/D(wing span,wetted area) Supersonic speeds: L/D=L/D(wing span, wetted area, Mach) Drag components at subsonic speeds: Induced drag or drag due to lift is a function of the wing span Parasite drag or zero lift drag is a function of total surface area exposed to air L/D is a function of wetted aspect ratio =b 2 /S wet 19

20 Wetted aspect ratio 20

21 Aspect ratio Due to reduced effective angle of attack of the wingtips, a low AR wing will stall at a higher angle of attack compared to a high aspect ratio wing. This is why tails have low AR compared to wings. This ensures adequate control even when the wing stalls. 21

22 Aspect ratio 22

23 Wing sweep Wing sweep is used primarily to reduce the adverse effects of transonic and supersonic flow. The leading edge sweep must be such that it is behind the Mach cone. Theoretically, the shock wave formation on a swept wing is determined by the air velocity in a direction perpendicular to the leading edge of the wing. In the transonic flow regime, wing sweep is determined by the requirement for a high critical Mach number, M crit. This requires subsonic airflow over the airfoil measured perpendicular to the leading edge, thus a swept wing. 23

24 Wing sweep 24

25 Wing sweep The exact wing sweep selection depends on the selected airfoil, thickness ratio, taper ratio, etc. 25

26 Wing sweep Wing sweep improves lateral stability (roll). A swept wing has a natural dihedral effect 10 o sweep 1 o dihedral. It may be necessary to use zero or negative dihedral on a swept wing in order to avoid a stiff airplane. The wing sweep and aspect ratio together have a strong effect on the pitch-up characteristics Pitch-up is a highly undesirable tendency of some aircraft near the stall angle to suddenly and uncontrollably increase the angle of attack. 26

27 Wing sweep 27

28 Taper ratio An elliptical wing will produce the lowest induced drag but is difficult and more costly to produce. A tapered wing is almost equally efficient in terms of induced drag. 28

29 Taper ratio There are two competing considerations: Smaller the taper ratio, lighter the wing structure. If λ is less, more lift will be produced at the wingroot center of pressure moves towards the wing root and the moment arm from the wingroot to the center of pressure decreases and the bending moment at the root decreasing the need for heavier structure. Wings with low λ show undesirable stall characteristics. Separation at the root has two advantages: Turbulent flow trailing downstream from the root causes buffeting as it flows over the tail, giving a strong stall warning to the pilot. The wingtips have attached flow so the ailerons will be more efficient. 29

30 Taper ratio Low sweep wing: typically have taper ratios around High sweep wings: have taper ratios around A swept wing will direct the air outward towards the wingtips. This loads up the wingtips creating more lift there compared to an equivalent unswept wing. In order to restore the elliptic lift distribution, it is necessary to reduce the taper ratio. 30

31 Taper ratio 31

32 Twist Wing twist is used to prevent tip stall and to revise the lift distribution to approximate an elliptical one. Typically, wings are twisted between 0 o -5 o. Geometric twist is the actual change in airfoil angle of incidence measured with respect to the root airfoil. A wing with a tip airfoil at a negative angle compared to the root airfoil has «washout». For such a wing, the root will stall before the tip, which improves aileron control at high α and tends to reduce wing rock. If a wing has linear twist, the twist angle changes in proportion to the distance from the wingroot. 32

33 Twist Aerodynamic twist = α L=0,root α L=0,tip Optimizing the lift distribution by twisting the wing will be valid only for one geometric angle of attack. The more twist required to produce an elliptic lift distribution at the design lift coefficient, the worse the wing will perform at other lift coefficients. For this reason, high amounts of twist (>5 o ) should be avoided. Typically, 3 o twist provides adequate stall characteristics. 33

34 Thrust-to-weight ratio and wing loading Thrust-to-weight ratio (T/W) and wing loading (W/S) are the two most important parameters effecting aircraft performance. Optimization of these parameters forms a major part of conceptual design. Wing loading and thrust-to-weight ratio are not independent of each other. Takeoff distance, maximum velocity, rate of climb and maximum load factor are dependent on both T/W and W/S. A good approach would be to guess one parameter and calculate the other to meet various performance characteristics. Most of the time T/W appears as the guessed parameter because statistical norms are more meaningful and scatter is less among airplanes of a given class. 34

35 Thrust-to-weight ratio For propeller-driven airplanes, P/W or W/P (power loading) is a more convenient definition. T W = η p V P W = 550η p V hp W C, For jet-powered airplanes, T W o = am max For propeller-powered airplanes, P W o = a VC max 35

36 Thrust- and power-to weight ratio 36

37 Thrust- and power-to weight ratio 37

38 Thrust-to-weight ratio T/W directly effects the performance of an airplane. An airplane with a high T/W will: Accelerate more quickly, Climb more rapidly, Reach a higher maximum speed, Sustain a higher turn rate, Consume more fuel, which will increase the takeoff gross weight. T/W varies throughout the flight as fuel is consumed. Engine thrust varies with altitude and velocity. T/W usually refers to sea-level static thrust (V = 0), at design takeoff gross weight W o and maximum thrust setting. 38

39 Thrust matching T W cruise = 1 L D max Weight of the airplane at the beginning of the cruise is the takeoff weight minus the fuel burned during takeoff and climb. Thrust during cruise is also different from the takeoff value. For jet aircraft, optimum cruise altitude: ft (best specific fuel consumption), For jet aircraft, optimum thrust setting: % of the continuous non-ab thrust. 39

40 Thrust matching High by-pass ratio turbofans, optimum thrust=20-25% takeoff thrust. Low by-pass ratio turbofans, optimum thrust=40-70% takeoff thrust. 40

41 Thrust matching Piston-powered airplanes, optimum power setting=75% takeoff power. Turboprop powered airplanes, optimum power setting=60-80% takeoff power. 41

42 Wing loading Wing loading effects: Stall speed, Climb rate, Takeoff and landing distances, Maneuvrability, etc. Wing loading and thrustto-weight ratio must be optimized together. 42

43 Wing loading stall speed W = L = 1 2 ρ 2 V stall C L,max S W S = 1 2 ρ 2 V stall C L,max Maximum lift coefficient depends on: Wing geometry, Airfoil shape, Flap geometry and span, Leading edge slat or flap geometry, Reynolds number, texture and interference with other components of the airplane. 43

44 Wing loading stall speed During landing, flaps will be deployed to maximum, During takeoff, they will be partially deployed. C L,max,to 0.8C L,max,landing For AR>5, C L,max 0.9c l,max 44

45 Wing loading takeoff distance 45

46 Wing loading takeoff distance Ground roll: actual distance travelled before the wheels leave the ground, V LO = 1.1V stall. Obstacle clearing distance: distance required from brake release until the airplane has reached some specified altitude, h OB =50 ft (military and small civilian airplanes), h OB =35 ft for civilian transport airplanes. Decision speed: the speed at which the distance to stop after an engine failure exactly equals the distance to continue the takeoff on the remaining engines. Balanced field length: is the distance required to takeoff and clear the specified obstacle when one engine fails exactly at the decision speed. 46

47 Wing loading takeoff distance Factors effecting takeoff distance: T/W and W/S, Aerodynamic drag, Rolling resistance. Takeoff parameter: TOP = σc L,to W/S T W, jet engines, TOP = σc L,to W/S bhp W, propeller engines. Density ratio, σ = ρ, C ρ L,to = C L,max V SL 1.21 LO = 1.1V stall Lift coefficient during takeoff may be limited by the maximum taildown angle. 47

48 Wing loading takeoff distance Jet-powered airplanes: W S = TOP σc L,to T/W Propeller-powered airplanes: W S = TOP σc L,to hp/w 48

49 Wing loading landing distance 49

50 Wing loading landing distance Landing ground roll: actual distance the aircraft travels from the time the wheels touch the runway, to the time the aircraft comes to a complete stop. Landing field length: includes clearing a 50 ft obstacle while the aircraft is still at approach speed. For military aircraft, V app = 1.2V stall, For civilian aircraft, V app = 1.3V stall. s a s g = 80 W S 1 σc L,max, s = s g + s a. =1000 ft (airliners, 3 o glideslope) =600 ft (general aviation, power-off approach) 50

51 Wing loading landing distance If the aircraft is equipped with a thrust reverser or reversible pitch propellers, multiply the ground portion of the distance by For commercial aircraft, multiply total landing distance by 1.67 to provide the required safety margin. For propeller-powered airplanes, W landing =0.85W o, For jet aircraft, W landing =0.85 W o. Military requirements, W landing =W e +W c +W p +0.5W f. 51

52 Wing loading cruise For propeller aircraft, range is maximized when L/D=L/D) max or when induced drag = parasite drag. q SC Do = q SKC L 2 = q S C L 2 πare e: Oswald span efficiency factor is a function of taper ratio and aspect ratio. W = L = 1 2 ρ V 2 C L S C L = W/S q Substituting above yields: W S = q πarec Do 52

53 Wing loading cruise For jet aircraft, range is maximized when L/D=0.866L/D) max or when parasite drag = 3*induced drag. q SC Do = 3q SKC L 2 = 3q S C L 2 πare e: Oswald span efficiency factor is a function of taper ratio and aspect ratio. W = L = 1 2 ρ V 2 C L S C L = W/S q Substituting above yields: W S = q πarec Do 3 53

54 Wing loading loiter For propeller aircraft, endurance is maximized when L/D=0.866L/D) max or when induced drag = 3*parasite drag. 3q SC Do = q SKC L 2 = q S C L 2 πare e: Oswald span efficiency factor is a function of taper ratio and aspect ratio. W = L = 1 2 ρ V 2 C L S C L = W/S q Substituting above yields: W S = q 3πAReC Do 54

55 Wing loading loiter For jet aircraft, endurance is maximized when L/D=L/D) max or when induced drag = parasite drag. q SC Do = q SKC L 2 = q S C L 2 πare e: Oswald span efficiency factor is a function of taper ratio and aspect ratio. W = L = 1 2 ρ V 2 C L S C L = W/S q Substituting above yields: W S = q πarec Do 55

56 Oswald span efficiency factor 56

57 Wing loading - loiter For initial estimates: Piston-props: V loiter = knots Jet airplanes: V loiter = knots Turboprops: V loiter = knots 57

58 Estimation of C Do C Do = S wet S C fe C fe : equivalent skin friction coefficient is a function of the Reynolds number, Re. 58

59 Wing loading instantaneous turn An aircraft designed for air-to-air combat (dogfight) must be capable of high turn rate. An aircraft with a higher turn rate will be able to maneuver behind the other. A turn rate superiority of 2 o /s is significant. 59

60 Wing loading instantaneous turn There are two important turn rates: Sustained turn: turn rate at which the thrust of the aircraft is just sufficient to maintain velocity and altitude in the turn (T=D); thrust available is the limit. For a level turn: ψ = g n2 1 V, n = L W = 1 2 ρ V 2 S W C L Instantaneous turn is limited by the maximum lift, stall or C L,max is the limit. The speed at which the maximum lift is equal to the allowable structural load factor is the «corner speed» and provides the maximum turn rate for a given altitude. Modern fighters have a corner speed around knots. 60

61 Wing loading instantaneous turn n = ψv g Solving for W/S: W S = 1 2 ρ V 2 C L,max n C L,max for a fighter with a simple trailing edge flap, C L,max for a fighter with leading and trailing edge flaps. 61

62 Wing loading sustained turn An aircraft will probably not be able to maintain speed and altitude while turning at the maxium instantaneous turn rate. Sustained turn rate is usually specified in terms of the maximum load factor at a given flight condition that the aircraft can sustain, e.g. 4-5g at M=0.9 at ft. T = D, L = nw n = T L W D Load factor in a sustained turn increases when T/W and L/D increases. 62

63 Wing loading sustained turn Equating thrust available and drag yields: W S = T/W T W 2n KC Do T/W 2 4n 2 C Do K 2n 2 K/q 63

64 R C Wing loading climb and glide = excess power weight = D W = q SC Do + q SC L W Equating the two yields: W S T = T W G 2 T D W R/C V = G = T W G 2 4KC DO 2K/q T D W D W = T W G W G 4KC Do T W G + 4KC Do; T/W must be greater than the climb gradient. 64

65 Wing loading climb and glide Takeoff flap setting, C Do 0.02, e 5% Landing flap setting, C Do 0.07, e 10% Landing gear down, C Do 0.02 The above equation can also be used to obtain the wing loading corresponding to a glide angle, T/W=0 with a negative G. 65

66 Wing loading maximum ceiling The same equation can be used to find the absolute ceiling (G=0), service ceiling (R/C=100 ft/min) or combat ceiling (R/C=500 ft/min). 66

67 Wing loading Remember: For the wing loadings estimated above, choose the lowest one to ensure that the wing is large enough for all flight conditions. Convert all the wing loadings calculated to takeoff conditions. A low wing loading (large wing) will always increase aircraft weight and cost. When W/S is selected, T/W should be rechecked to ensure that all requirements are still met. 67

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