Estabilidad y Control Detallado Derivadas Estabilidad Longitudinal Tema 14.2

Transcription

1 Cálculo de Aeronaves Sergio Esteban Roncero, 1 Estabilidad y Control Detallado Derivadas Estabilidad Longitudinal Tema 14.2 Sergio Esteban Roncero Departamento de Ingeniería Aeroespacial Y Mecánica de Fluidos

2 Cálculo de Aeronaves Sergio Esteban Roncero, 2 Derivadas, Angle of Attack Derivatives

3 Estimación Derivadas Contribución Contribución Ala Canard/horizontal/V-tail Fuselaje Contribución Ala Canard/horizontal/V-tail Fuselaje Derivadas en 1/rad si no se indica lo contrario Si las derivadas no están en 1/rad hay que convertirlas Cálculo de Aeronaves Sergio Esteban Roncero, 3

4 Cálculo de Aeronaves Sergio Esteban Roncero, 4 C D Estimación Asumiendo modelo polar no compensada Coeficiente de resistencia inducida Coeficiente de Oswald (dept. aerodinámica)

5 of the entire Airplane Efectividad de las Superficies de control representa la pendiente de sustentación del conjunto ala-fuselaje En 1ª hipótesis sólo las superficies aerodinámicas generan sustentación En 2ª hipótesis se puede estimar la contribución del fuselaje - Mediante métodos experimentales : análisis software XFLR5 - Mediante métodos empíricos: ecuaciones analíticas función de geometría Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 5

6 Cálculo de Aeronaves Sergio Esteban Roncero, 6 C L,w,C L,t and C L,c Cálculo de para cualquier superficie aerodinámica Se emplean los métodos ya descritos en Aerodinámica - Métodos experimentales (XFLR5) - Métodos analíticos Fig A1 Fig A2 Fig A3

7 Fig A1 Cálculo de Aeronaves Sergio Esteban Roncero, 7

8 Fig A2 Cálculo de Aeronaves Sergio Esteban Roncero, 8

9 Fig A3 Cálculo de Aeronaves Sergio Esteban Roncero, 9

10 Cálculo de Aeronaves Sergio Esteban Roncero, 10 2 / Fig A5 is the apparent mass constant which is a function of fineness ratio (length/maximum thickness) = total body volume = cross sectional area at.. = body station where flow ceases to be potential, this is a function of, the body station where the parameter / first reaches its minimum value. (This station where the change in area with respect to x first reaches its lowest value can be estimated from a sketch of the body.) = body cross sectional area at any body station = body length. Fig A6

11 Cálculo de Aeronaves Sergio Esteban Roncero, 11 Fig A5 Reduced Mass Factor

12 Cálculo de Aeronaves Sergio Esteban Roncero, 12 Fig A6 = body station where flow ceases to be potential, = the body station where the parameter / first reaches its minimum value. Body station where flow becomes viscous

13 Cálculo de Aeronaves Sergio Esteban Roncero, 13 Wing-Fuselage Contribution Estimation of lift-curve slope. The lift-curve slope of the combined wingbody is given by Ratio of nose lift ratio Ratio of the wing lift in presence of the body Ratio of body lift in presence of the wing to wing-alone lift, lift-curve slope of the isolated nose,, lift-curve slope of the exposed wing 1ª aproximación, exposed wing area, reference (wing) area. 2, is the apparent mass constant, is the maximum cross-sectional area of the fuselage

14 Cálculo de Aeronaves Sergio Esteban Roncero, 14 Wing-Fuselage Contribution Estimation of lift-curve slope. The lift-curve slope of the combined wingbody is given by

15 Cálculo de Aeronaves Sergio Esteban Roncero, 15 Wing-Fuselage Contribution maximum width of the fuselage wing span. Fig A4

16 Fig A4 Cálculo de Aeronaves Sergio Esteban Roncero, 16

17 of the entire Airplane Momento cabeceo planta propulsora Asumir inicialmente =0 representa la pendiente de sustentación del conjunto ala-fuselaje En 1ª hipótesis sólo las superficies aerodinámicas generan sustentación En 2ª hipótesis se puede estimar la contribución del fuselaje - Mediante métodos experimentales : análisis software XFLR5 - Mediante métodos empíricos: ecuaciones analíticas función de geometría Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 17

18 Cálculo de Aeronaves Sergio Esteban Roncero, 18 for cambered fuselages such as those with leading-edge droop or aft upsweep, is the apparent mass constant, is the wing zero-lift angle relative to the fuselage reference line, is the incidence angle of the fuselage camberline relative to the fuselage reference line. The parameter, is assumed to be negative for nose droop or aft upsweep Fig A5 Fig A6 y A7

19 Fig A6 Cálculo de Aeronaves Sergio Esteban Roncero, 19

20 Fig A7 Cálculo de Aeronaves Sergio Esteban Roncero, 20

21 Cálculo de Aeronaves Sergio Esteban Roncero, 21 Estimación para fuselajes o nacelles Método 1 = empirical factor Fig A8 = maximum width of the fuselage or nacelle = length of fuselage or nacelle Fig A8

22 Cálculo de Aeronaves Sergio Esteban Roncero, 22 Fig A8 = empirical factor for fuselage or nacelle contribution to,

23 Cálculo de Aeronaves Sergio Esteban Roncero, 23 Method 2: Multhopp modified Munk s theory Método más complejo local width/diameter, fuselage length, reference (wing) area lreference length (wing mean aerodynamic chord). Se analiza la contribución del fuselaje en 3 zonas 1. Zona alejada de la influencia up-wash (segmentos 1-5 ejemplo) 2. Zona bajo influencia up-wash (segmento 6 ejemplo) 3. Zona bajo influencia down-wash (segmentos 7-14 ejemplo)

24 Cálculo de Aeronaves Sergio Esteban Roncero, Zona alejada de la influencia up-wash (segmentos 1-5 ejemplo) La distancia se mide desde el borde de ataque Al punto medio de cada sección 2. Zona bajo influencia up-wash (segmento 6 ejemplo) Fig A10

25 Cálculo de Aeronaves Sergio Esteban Roncero, 3 - Zona bajo influencia down-wash (segmentos 7-14 ejemplo) 25 is the distance (measured parallel to the root chord) between the trailing edge of the root chord and the horizontal tail aerodynamic center. Here,, and are wing aspect ratio, wing taper ratio, and horizontal tail location factors distance measured parallel to the wing root chord, between wing mac quarter chord point and the quarter chord point of the mac of horizontal tail height of the horizontal tail mac above or below the plane of wing root chord, measured in the plane of symmetry and normal to the extended wing root chord and positive for horizontal tail mac above the plane of the wing root chord taper ratio, Aspect Ratio

26 Cálculo de Aeronaves Sergio Esteban Roncero,

27 Fig A9 Cálculo de Aeronaves Sergio Esteban Roncero, 27

28 Fig A10 Cálculo de Aeronaves Sergio Esteban Roncero, 28

29 Cálculo de Aeronaves Sergio Esteban Roncero, 29 of the Airplane, / / = empirical factor Fig A8 = maximum width of the fuselage or nacelle = length of fuselage or nacelle ,, width of the fuselage at the wing 2 3 leading esge, mid chord, and trailing edge

30 Cálculo de Aeronaves Sergio Esteban Roncero, 30 of the Airplane

31 Cálculo de Aeronaves Sergio Esteban Roncero, 31 Derivadas, Speed Derivatives

32 Cálculo de Aeronaves Sergio Esteban Roncero, 32 Estimación Derivadas Contribución Contribución Contribución Derivadas en 1/rad si no se indica lo contrario Si las derivadas no están en 1/rad hay que convertirlas

33 Cálculo de Aeronaves Sergio Esteban Roncero, 33 Estimación At low subsonic speeds (M <0.5), the drag coefficient is practically constant 0 As the flight Mach number approaches the critical Mach number the drag coefficient starts rising It assumes a peak value in the transonic Mach number range and starts decreasing as Mach number becomes supersonic. It tends to assume a steady value at high supersonic or hypersonic Mach numbers. Therefore, if the flight Mach number exceeds 0.5, the derivative should not be ignored

34 Cálculo de Aeronaves Sergio Esteban Roncero, 34 Estimación At low subsonic speeds (M <0.5), the lift curve slope is practically constant 0 For C L of the form then

35 Estimación At low subsonic speeds (M <0.5), the drag coefficient is practically constant Or equivalenty with therefore variación del centro aerodinámico con cambio de Mach 0para 0.5, hay que tenerla en cuenta para 0.5 Cálculo de Aeronaves Sergio Esteban Roncero, 35

36 Cálculo de Aeronaves Sergio Esteban Roncero, 36 Derivadas, Pitch Rate Derivatives

37 Estimación Derivadas Contribución Contribución Wing Horizontal/V-tail/canard Contribución Wing Horizontal/V-tail/canard Derivadas en 1/rad si no se indica lo contrario Si las derivadas no están en 1/rad hay que convertirlas Cálculo de Aeronaves Sergio Esteban Roncero, 37

38 Cálculo de Aeronaves Sergio Esteban Roncero, 38 Pitch Rate Derivatives The airplane drag-coefficient-due-to-pitch-rate derivative is negligible

39 Cálculo de Aeronaves Sergio Esteban Roncero, 39 Pitch Rate Derivatives The airplane lift-coefficient-due-to-pitch-rate derivative is wing V-tail horizontal canard

40 Wing contribution Contribución Ala Método 1 wing aspect ratio compressibility sweep correction factor Λ / is the wing quarter chord angle. wing contribution to airplane lift-coefficient-due-to-pitch-rate derivative at Mach equals zero 1ª Aproximación Δ 0 Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 40

41 Contribución Ala The contribution of the wing-body combination Método 2 mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wing and contributions of the exposed wing and isolated body Velocidades subsónicas distance of exposed wing aerodynamic center from the leading edge of the root chord distance of the center of gravity from the leading edge of the exposed wing root chord. and are measured parallel to the exposed wing root chord. The parameter will be positive if the aerodynamic center of the exposed wing is aft of the center of gravity Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 41

42 Cálculo de Aeronaves Sergio Esteban Roncero, 42 Wing-Fuselage Contribution Método 2 maximum width of the fuselage wing span. Fig A4

43 Cálculo de Aeronaves Sergio Esteban Roncero, 43 Fig A4 Método 2

44 Contribución Ala The contribution of the wing-body combination Método 2 mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wing and contributions of the exposed wing and isolated body Velocidades subsónicas distance of exposed wing aerodynamic center from the leading edge of the root chord distance of the center of gravity from the leading edge of the exposed wing root chord. and are measured parallel to the exposed wing root chord. The parameter will be positive if the aerodynamic center of the exposed wing is aft of the center of gravity Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 44

45 Cálculo de Aeronaves Sergio Esteban Roncero, 45 Contribución Ala The body contribution Método 2 is the apparent mass constant, is the maximum cross-sectional area of the fuselage, total length of the fuselage volume of the fuselage. 4 1 Fig A5

46 Cálculo de Aeronaves Sergio Esteban Roncero, 46 Contribución Horizontal Tail contribution horizontal tail lift curve slope. horizontal tail dynamic pressure ratio. horizontal tail volume coefficient. X-location of horizontal tail aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. horizontal tail area. wing area.

47 Cálculo de Aeronaves Sergio Esteban Roncero, 47 Contribución V-Tail V-Tail contribution V-tail lift curve slope. V-tail dynamic pressure ratio. V-tail volume coefficient. X-location of V-tail aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. V-tail tail area. wing area.

48 Cálculo de Aeronaves Sergio Esteban Roncero, 48 Contribución Canard Canard contribution canard lift curve slope canard dynamic pressure ratio. canard volume coefficient. X-location of canard aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. canard area. wing area.

49 Cálculo de Aeronaves Sergio Esteban Roncero, 49 Pitch Moment Derivatives The airplane pitching-moment-coefficient-due-to-pitch-rate derivative is wing V-tail horizontal canard

50 Cálculo de Aeronaves Sergio Esteban Roncero, 50 Contribución Ala Wing contribution Método 1 wing aspect ratio compressibility sweep correction factor Λ / is the wing quarter chord angle. wing contribution to airplane pitch-moment- coefficient-due-to-pitch-rate derivative at Mach=0o

51 Cálculo de Aeronaves Sergio Esteban Roncero, 51 Contribución Ala Wing contribution 2 Aproximación 1 For surfaces with small gap effects 1.00 For surfaces with large gap effects ª Aproximación Δ 0

52 Cálculo de Aeronaves Sergio Esteban Roncero, 52 Contribución Ala The intermediate calculation parameter,, is given by Método 1 The correction constant for the wing contribution to pitch damping is obtained from Figure in Airplane Design Part VI and is a function of the wing aspect ratio:

53 Cálculo de Aeronaves Sergio Esteban Roncero, 53 Contribución Ala

54 Cálculo de Aeronaves Sergio Esteban Roncero, 54 Contribución Ala The contribution of the wing-body combination Método 2 mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wing fuselage length and contributions of the exposed wing and isolated body Velocidades subsónicas distance of exposed wing aerodynamic center from the leading edge of the root chord distance of the center of gravity from the leading edge of the exposed wing root chord. and are measured parallel to the exposed wing root chord. The parameter will be positive if the aerodynamic center of the exposed wing is aft of the center of gravity

55 Cálculo de Aeronaves Sergio Esteban Roncero, 55 Contribución Ala The contribution of the wing-body combination Método 2 the aspect ratio of the exposed wing and is the sectional or two-dimensional lift-curve slope of the wing

56 Cálculo de Aeronaves Sergio Esteban Roncero, 56 Wing-Fuselage Contribution Método 2 maximum width of the fuselage wing span. Fig A4

57 Cálculo de Aeronaves Sergio Esteban Roncero, 57 Fig A4 Método 2

58 Cálculo de Aeronaves Sergio Esteban Roncero, 58 Contribución Ala Método 2 The body contribution the distance of the moment reference point from the leading edge of the fuselage, is the axial location where the fluid flow over the fuselage ceases to be potential. is the apparent mass constant, is the maximum cross-sectional area of the fuselage, total length of the fuselage volume of the fuselage. Fig A5

59 Cálculo de Aeronaves Sergio Esteban Roncero, 59 Contribución Horizontal Tail contribution horizontal tail lift curve slope. horizontal tail dynamic pressure ratio. horizontal tail volume coefficient X-location of horizontal tail aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. horizontal tail area. wing area.

60 Cálculo de Aeronaves Sergio Esteban Roncero, 60 Contribución V-Tail V-Tail contribution V-tail lift curve slope. V-tail dynamic pressure ratio. V-tail volume coefficient. X-location of V-tail aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. V-tail tail area. wing area.

61 Cálculo de Aeronaves Sergio Esteban Roncero, 61 Contribución Canard Canard contribution canard lift curve slope canard dynamic pressure ratio. canard volume coefficient. X-location of canard aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. canard area. wing area.

62 Cálculo de Aeronaves Sergio Esteban Roncero, 62 Derivadas Angle of Attack Rate Derivatives

63 Cálculo de Aeronaves Sergio Esteban Roncero, 63 Estimación Derivadas Contribución Contribución Contribución Derivadas en 1/rad si no se indica lo contrario Si las derivadas no están en 1/rad hay que convertirlas Angle of Attack Rate Derivatives se suelen despreciar en 1ª aproximación

64 Cálculo de Aeronaves Sergio Esteban Roncero, 64 Angle of Attack Rate Derivatives The airplane drag-coefficient-due-to-angle-of-attack-rate derivative is normally neglected:

65 Angle of Attack Rate Derivatives The airplane lift-coefficient-due-angle-of-attack-rate derivative is determined from V-tail Método horizontal canard horizontal V-tail canard 2. The equation above is based on the assumption that the contribution of the horizontal tail, V-Tail, and canard are the only important contributions to this derivative Cálculo de Aeronaves Sergio Esteban Roncero, 65

66 Cálculo de Aeronaves Sergio Esteban Roncero, 66 Angle of Attack Rate Derivatives Método 1 canard volume coefficient canard volume coefficient canard volume coefficient X-location of horizontal tail aerodynamic center in terms of wing mean geometric chord X-location of V-tail aerodynamic center in terms of wing mean geometric chord X location of canard aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. canard area. V tail area. canard area. wing area.

67 Cálculo de Aeronaves Sergio Esteban Roncero, 67 Angle of Attack Rate Derivatives The contribution of the wing-body combination Método 2... mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wing fuselage length and contributions of the exposed wing and isolated body Velocidades subsónicas.

68 Cálculo de Aeronaves Sergio Esteban Roncero, 68 Angle of Attack Rate Derivatives The body contribution... Método 2. is the apparent mass constant, is the maximum cross-sectional area of the fuselage, total length of the fuselage volume of the fuselage. 4., Fig A5

69 Cálculo de Aeronaves Sergio Esteban Roncero, 69 Angle of Attack Rate Derivatives Método 1 The airplane pitching-moment-coefficient-due-angle-of-attack-rate derivative is determined from V-tail.... horizontal canard The equation above is based on the assumption that the contribution of the horizontal tail, V-Tail, and canard are the only important contributions to this derivative horizontal.. 2. V-tail.. 2. canard.. 2.

70 Cálculo de Aeronaves Sergio Esteban Roncero, 70 Angle of Attack Rate Derivatives Método 1 The equation above is based on the assumption that the contribution of the horizontal tail, V-Tail, and canard are the only important contributions to this derivative canard volume coefficient canard volume coefficient canard volume coefficient X-location of horizontal tail aerodynamic center in terms of wing mean geometric chord X-location of V-tail aerodynamic center in terms of wing mean geometric chord X location of canard aerodynamic center in terms of wing mean geometric chord X-location of the airplane center of gravity in terms of the wing mean geometric chord. canard area. V tail area. canard area. wing area.

71 Cálculo de Aeronaves Sergio Esteban Roncero, 71 Angle of Attack Rate Derivatives The contribution of the wing-body combination Método 2... mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wing fuselage length and contributions of the exposed wing and isolated body Velocidades subsónicas....

72 Cálculo de Aeronaves Sergio Esteban Roncero, 72 Angle of Attack Rate Derivatives The contribution of the wing-body combination Método 2 Velocidades subsónicas..... the distance of the moment reference point from the leading edge of the fuselage, is the axial location where the fluid flow over the fuselage ceases to be potential. is the apparent mass constant, is the maximum cross-sectional area of the fuselage, total length of the fuselage volume of the fuselage.

73 Cálculo de Aeronaves Sergio Esteban Roncero, 73 Derivadas Propulsive Derivatives

74 Cálculo de Aeronaves Sergio Esteban Roncero, 74 Propulsive Derivatives The airplane steady state thrust coefficient is defined as: Steady State Flight

75 Cálculo de Aeronaves Sergio Esteban Roncero, 75 Propulsive Derivatives Airplanes with pure jets Modelo propulsivo - RFP airplane steady state flight speed. A coefficient in thrust vs. speed quadratic equation. B coefficient in thrust vs. speed quadratic equation. C coefficient in thrust vs. speed quadratic equation. Airplanes with variable pitch propeller driven engines Airplanes with fixed pitch propeller driven engines Modelo propulsivo - RFP airplane steady state flight speed. A coefficient in power versus speed quadratic equation. B coefficient in power versus speed quadratic equation. C coefficient in power versus speed quadratic equation.

76 Cálculo de Aeronaves Sergio Esteban Roncero, 76 Propulsive Derivatives The airplane steady state thrust pitching moment coefficient for a jet airplane is given by: Trim condiitions Σ 0 Fig A16

77 Fig A16 Cálculo de Aeronaves Sergio Esteban Roncero, 77

78 Cálculo de Aeronaves Sergio Esteban Roncero, 78 Propulsive Derivatives The airplane steady state thrust pitching moment coefficient for a propeller airplane is given by: Aproximación Δ 0 For propeller wing mean geometric chord The perpendicular distance from the thrust line to the airplane center of gravity is found from Aproximación 0 Trim condiitions Σ 0

79 Cálculo de Aeronaves Sergio Esteban Roncero, 79 Propulsive Derivatives The airplane thrust-pitching-moment-coefficient-due-to-speed derivative is defined as the variation of airplane pitching moment coefficient due to thrust with dimensionless speed: Fig A16

80 Cálculo de Aeronaves Sergio Esteban Roncero, 80 Propulsive Derivatives The airplane steady state thrust coefficient is defined as: 0

81 Cálculo de Aeronaves Sergio Esteban Roncero, 81 Propulsive Derivatives The airplane thrust-pitching-moment-coefficient-due-to-angle-of-attack derivative is defined as The airplane thust-pitching-moment-coefficient-due-to-angle-of-attack derivative is defined as The airplane thust-pitching-moment-coefficient-due-to-angle-of-attack derivative is defined as Para aviones jet Para aviones con hélice Aproximación 0 Muy compleja estimación Aproximación 0

82 Cálculo de Aeronaves Sergio Esteban Roncero, 82 Propulsive Derivatives For propeller driven airplanes:

83 Cálculo de Aeronaves Sergio Esteban Roncero, 83 Propulsive Derivatives For propeller driven airplanes: The perpendicular distance from the thrust line to the airplane center of gravity is found from

84 Cálculo de Aeronaves Sergio Esteban Roncero, 84 Propulsive Derivatives For propeller driven airplanes: The effect of propeller or inlet normal force on longitudinal stability is given by:

85 Cálculo de Aeronaves Sergio Esteban Roncero, 85 Propulsive Derivatives For propeller driven airplanes:

86 Cálculo de Aeronaves Sergio Esteban Roncero, 86 Propulsive Derivatives For propeller driven airplanes: Aproximación 1 The moment arm of the propeller normal force to the airplane center of gravity is given by:

87 Cálculo de Aeronaves Sergio Esteban Roncero, 87 Propulsive Derivatives For propeller driven airplanes: The first intermediate calculation parameter is given by Geometría de la hélice The propeller blade radius diameter of prop

88 Cálculo de Aeronaves Sergio Esteban Roncero, 88 Propulsive Derivatives For propeller driven airplanes: The second intermediate calculation parameter is obtained from Figure in Airplane Design Part VI and is a function of the number of propeller blades and the nominal propeller blade angle at 75% radius. Fig A17

89 Cálculo de Aeronaves Sergio Esteban Roncero, 89

90 Cálculo de Aeronaves Sergio Esteban Roncero, 90 Propulsive Derivatives For propeller in front of the wing, the propeller upwash gradient is obtained from Figure 8.67 in Airplane Design Part VI. It is a function of the X-location of the propeller relative to the wing root quarter chord point and the wing aspect ratio Fig A18

91 Fig A18 Cálculo de Aeronaves Sergio Esteban Roncero, 91

92 Cálculo de Aeronaves Sergio Esteban Roncero, 92 Propulsive Derivatives For propeller driven airplanes: For propeller behind the wing, the propeller downwash gradient is computed with the same method used to calculate horizontal tail downwash gradient with appropriate substitution

93 Bibliografia Performance, Stability, Dynamics, and Control of Airplanes, Bandu N. Pamadi, AIAA Education Series. Riding and Handling Qualities of Light Aircraft A Review and Analysis, Frederick O. Smetana, Delbert C. Summey, and W. Donnald Johnson, Report No. NASA CR-1975, March Airplane Aerodynamics and Performance, Dr. Jan Roskam and Dr. Chuan-Tau Edward Lan, DARcorporation, Flight Vehicle Performance and Aerodynamic Control, Frederick O. Smetana, AIAA Educaction Series, Dynamics of Flight: Stability and Control, Bernard Etkin and LloyidDuff Reid, John Wiley and Sons, Inc Cálculo de Aeronaves Sergio Esteban Roncero, sesteban@us.es 93