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Cálculo de Aeronaves © Sergio Esteban Roncero, [email protected] 1
Tema 14.2Sergio Esteban Roncero
Departamento de Ingeniería AeroespacialY Mecánica de Fluidos
Estabilidad y Control DetalladoDerivadas Estabilidad Longitudinal
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Derivadas
Angle of Attack Derivatives
,
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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 contrarioSi las derivadas no están en 1/rad hay que convertirlas
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CD
Estimación
Coeficiente de Oswald(dept. aerodinámica)
Coeficiente de resistencia inducida
Asumiendo modelo polar no compensada
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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 sustentaciónEn 2ª hipótesis se puede estimar la contribución del fuselaje - Mediante métodos experimentales : análisis software XFLR5- Mediante métodos empíricos: ecuaciones analíticas función de geometría
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CL,w , CL,t and CL,c
Fig A1
Fig A2
Fig A3
Cálculo de para cualquier superficie aerodinámicaSe emplean los métodos ya descritos en Aerodinámica- Métodos experimentales (XFLR5)- Métodos analíticos
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Fig A5
Fig A6
2 /
– 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 tox first reaches its lowest value can be estimated from a sketch of the body.)
= body cross sectional area at any body station= body length.
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Fig A6
Body station where flow becomes viscous
= body station where flow ceases to be potential, = the body station where the parameter / first reaches its minimum value.
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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
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Wing-Fuselage Contribution
Estimation of lift-curve slope. The lift-curve slope of the combined wingbody is given by
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Wing-Fuselage Contribution
Fig A4
→ maximum width of the fuselage→ wing span.
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of the entire Airplane
Momento cabeceo planta propulsoraAsumir inicialmente =0
→ representa la pendiente de sustentación del conjunto ala-fuselaje
En 1ª hipótesis sólo las superficies aerodinámicas generan sustentaciónEn 2ª hipótesis se puede estimar la contribución del fuselaje - Mediante métodos experimentales : análisis software XFLR5- Mediante métodos empíricos: ecuaciones analíticas función de geometría
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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 A6 y A7Fig A5
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Método 1
Estimación para fuselajes o nacelles
= empirical factor Fig A8= maximum width of the fuselage or nacelle
= length of fuselage or nacelle
Fig A8
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Fig A8
= empirical factor for fuselage or nacelle contribution to ,
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Method 2: Multhopp modified Munk’s theory
→ local width/diameter, → fuselage length,→ reference (wing) area→ lreference length (wing mean aerodynamic chord).
Se analiza la contribución del fuselaje en 3 zonas1. 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)
Método más complejo
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1. Zona alejada de la influencia up-wash (segmentos 1-5 ejemplo)
2. Zona bajo influencia up-wash (segmento 6 ejemplo)
La distancia se mide desde el borde de ataque Al punto medio de cada sección
Fig A10
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3 - Zona bajo influencia down-wash (segmentos 7-14 ejemplo)
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
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of the Airplane
, /
/
= empirical factor Fig A8= maximum width of the fuselage or nacelle
= length of fuselage or nacelle
1
1
1
290 2 3, , width of the fuselage at the wing
leading esge, mid chord, and trailing edge
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Estimación Derivadas Contribución
Contribución
Contribución
Derivadas en 1/rad si no se indica lo contrarioSi las derivadas no están en 1/rad hay que convertirlas
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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 coefficientstarts risingIt 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
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For CL of the form
then
Estimación
0
At low subsonic speeds (M <0.5), the lift curve slope is practically constant
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Or equivalenty
with
therefore
Estimación
At low subsonic speeds (M <0.5), the drag coefficient is practically constant
→variación del centro aerodinámico con cambio de Mach
0 para 0.5, hay que tenerla en cuenta para 0.5
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Derivadas
Pitch Rate Derivatives
,
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Estimación Derivadas Contribución
Contribución Wing Horizontal/V-tail/canard
Contribución Wing Horizontal/V-tail/canard
Derivadas en 1/rad si no se indica lo contrarioSi las derivadas no están en 1/rad hay que convertirlas
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Pitch Rate Derivatives
The airplane drag-coefficient-due-to-pitch-rate derivative is negligible
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Pitch Rate Derivatives
The airplane lift-coefficient-due-to-pitch-rate derivative is
wing
horizontal
V-tail
canard
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Contribución Ala
Wing contribution→ wing aspect ratio
→compressibility sweep correction factorΛ / →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
Método 1
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Contribución Ala
Método 2The contribution of the wing-body combination
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
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Wing-Fuselage Contribution
Fig A4
→ maximum width of the fuselage→ wing span.
Método 2
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Contribución Ala
Método 2The contribution of the wing-body combination
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
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Contribución Ala
Método 2The body contribution
4 1
– is the apparent mass constant, is the maximum cross-sectional area of the fuselage,total length of the fuselagevolume of the fuselage.
Fig A5
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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.
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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.
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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.
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Pitch Moment Derivatives
The airplane pitching-moment-coefficient-due-to-pitch-rate derivative is
wing
horizontal
V-tail
canard
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Contribución Ala
Wing contribution
→wing contribution to airplane pitch-moment- coefficient-due-to-pitch-rate derivative at Mach=0o
Método 1
→ wing aspect ratio→compressibility sweep correction factor
Λ / →is the wing quarter chord angle.
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Contribución Ala
Wing contribution Método 1
1ª Aproximación → Δ 0
Aproximación 1For surfaces with small gap effects 1.00For surfaces with large gap effects 0.85
@ → @2
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Contribución Ala
The intermediate calculation parameter, , is given by Método 1
The correction constant for the wing contribution to pitch damping is obtained fromFigure 10.40 in Airplane Design Part VI and is a function of the wing aspect ratio:
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Contribución Ala
Método 2The contribution of the wing-body combination
mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wingfuselage 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
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Contribución Ala
Método 2The contribution of the wing-body combination
the aspect ratio of the exposed wing and is the sectional or two-dimensional lift-curve slope of the wing
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Wing-Fuselage Contribution
Fig A4
→ maximum width of the fuselage→ wing span.
Método 2
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Contribución AlaMétodo 2
The body contribution
Fig A5
→ 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 fuselagevolume of the fuselage.
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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.
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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.
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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.
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Derivadas
Angle of Attack Rate Derivatives
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Estimación Derivadas Contribución
Contribución
Contribución
Derivadas en 1/rad si no se indica lo contrarioSi las derivadas no están en 1/rad hay que convertirlas
Angle of Attack Rate Derivatives se suelen despreciar en 1ª aproximación
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Angle of Attack Rate Derivatives
The airplane drag-coefficient-due-to-angle-of-attack-rate derivative is normally neglected:
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Angle of Attack Rate Derivatives
The airplane lift-coefficient-due-angle-of-attack-rate derivative is determined from
Método 1
. . . .
horizontal
V-tail
canard
horizontal
canard
V-tail
2.
2.
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
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Angle of Attack Rate Derivatives
→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.
Método 1
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Angle of Attack Rate Derivatives Método 2The contribution of the wing-body combination
mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wingfuselage length and → contributions of the exposed wing and isolated body
Velocidades subsónicas
.
.
...
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Angle of Attack Rate Derivatives Método 2The body contribution
4,
– is the apparent mass constant, is the maximum cross-sectional area of the fuselage,total length of the fuselagevolume of the fuselage.
Fig A5
...
.
.
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Angle of Attack Rate Derivatives
The airplane pitching-moment-coefficient-due-angle-of-attack-rate derivative is determined from
Método 1
. . . .
horizontal
V-tail
canard
2
2
2
horizontal
canard
V-tail
.
.
. .
.
.
.
.
.
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
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Angle of Attack Rate Derivatives
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.
Método 1
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Angle of Attack Rate Derivatives Método 2The contribution of the wing-body combination
mean aerodynamic chords of the exposed wing mean aerodynamic chords of the total (theoretical) wingfuselage length and → contributions of the exposed wing and isolated body
Velocidades subsónicas
. .. .
. .
.
.
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Angle of Attack Rate Derivatives Método 2The contribution of the wing-body combination
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 fuselagevolume of the fuselage.
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Derivadas
Propulsive Derivatives
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Propulsive Derivatives
The airplane steady state thrust coefficient is defined as:
Steady State Flight
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Propulsive DerivativesAirplanes with pure jets
Airplanes with variable pitch propeller driven engines
Airplanes with fixed pitch propeller driven engines
→ 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.
→ 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.
Modelo propulsivo - RFP
Modelo propulsivo - RFP
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Propulsive Derivatives
Fig A16
The airplane steady state thrust pitching moment coefficient for a jet airplane is given by:
Trim condiitions
Σ 0
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Propulsive Derivatives
The airplane steady state thrust pitching moment coefficient for a propeller airplane is given by:
Aproximación → Δ 0
wing mean geometric chord
The perpendicular distance from the thrust line to the airplane center of gravity is found from
Aproximación → 0
Trim condiitions
For propeller
Σ 0
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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
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Propulsive Derivatives
0
The airplane steady state thrust coefficient is defined as:
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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
Aproximación 0Para aviones jet
Aproximación 0Para aviones con hélice Muy compleja estimación
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Propulsive Derivatives
For propeller driven airplanes:
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Propulsive Derivatives
The perpendicular distance from the thrust line to the airplane center of gravity is found from
For propeller driven airplanes:
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Propulsive Derivatives
The effect of propeller or inlet normal force on longitudinal stability is given by:
For propeller driven airplanes:
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Propulsive Derivatives
For propeller driven airplanes:
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Propulsive Derivatives
Aproximación → 1
The moment arm of the propeller normal force to the airplane center of gravity is given by:
For propeller driven airplanes:
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Propulsive Derivatives
The first intermediate calculation parameter is given by
diameter of prop
The propeller blade radius
Geometría de la hélice
For propeller driven airplanes:
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Propulsive Derivatives
Fig A17
For propeller driven airplanes:
The second intermediate calculation parameter is obtained from Figure 8.130 in Airplane Design Part VI and is a function of the number of propeller blades and the nominal propeller blade angle at 75% radius.
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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
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Propulsive Derivatives
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
For propeller driven airplanes:
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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 1972.
Airplane Aerodynamics and Performance, Dr. Jan Roskam and Dr. Chuan-Tau Edward Lan, DARcorporation, 1997.
Flight Vehicle Performance and Aerodynamic Control, Frederick O. Smetana, AIAA Educaction Series, 2001.
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