Aerodynamics 1 Flashcards
(87 cards)
1
Q
What’s φ?
A
Wing Sweep angle
2
Q
What’s Λ?
A
Aspect Ratio = b 2 / S
3
Q
What’s λ?
A
Taper Ratio = la(tip chord) / l i(root chord)
4
Q
What is U∞?
A
Free stream velocity
5
Q
What is β?
A
Sideslip Angle
6
Q
What is α?
A
Angle of Attack
7
Q
What is p*?
A
Roll angular Velocity
8
Q
What is q*?
A
Pitch angular velocity
9
Q
What is r*?
A
Yaw angular velocity
10
Q
what is lμ?
A
Mean aerodynamic chord
11
Q
What is q∞?
A
Dynamic Pressure = (ρ/2) x V∞2
12
Q
What is Cl?
A
Rolling Moment
13
Q
What is Cm?
A
Pitching moment
14
Q
What is Cn?
A
Yawing Moment
15
Q
How to calculate CL?
A
CL=L/q∞S
16
Q
What is s?
A
=b/2 (half wingspan)
17
Q
How to calculate CD?
A
CD=D/q∞S
18
Q
What is p∞?
A
Static Pressure
19
Q
What is Γ?
A
Circulation
20
Q
What is the relation between CL and CLα?
A
CL=(α-α0)(CLα)
21
Q
How to calculate Zero Angle of Attack?
A
α0=-CL0/CLα
22
Q
What is the relation between CD and CL?
A
CD =CD0 + k(CL2)
23
Q
What is Zero Drag?
A
Drag that does not depend on lift, mostly friction and pressure drag.
24
Q
What is ε?
A
Glide Angle. Angle in steady gliding flight in relation to the horizontal plane. = CD / CL = ∆h (loss of altitude) /∆s (covered distance
25
What is the center of Pressure?
The intersection point of the line of action of the resulting aerodynamic force R (composed of Lift and Drag) with the airfoil chord.
26
What is xD? and Formula
The Center of Pressure.
xD=-Cm0/CL - dCm/dCL
27
What is the Neutral Point?
Intersection point of the line of action of the additional forced based on Δα with the airfoil chord.
Point at which the overall pitching moments of the aircraft does not change with Δα, this point does not change with a change in CL
28
What is xN? And Formula
Neutral Point.
xN = -dCm/dCL
29
How to calculate Mach Number?
M∞ = V∞/c∞
30
How to calculate Reynolds Number?
Re = (ρ)(V∞)(l)/v∞
where v∞ is the Kinematic Viscosity
31
What are the steady level flight conditions?
L=W, and D=T
32
What is γ?
Path angle
33
What are the steady gliding flight conditions?
ε = -γ
-L sin(ε) + D cos(ε) = 0
L cos(ε) + D sin(ε) - W = 0
34
What is B? What units?
Specific Fuel Consumption
[kg/s * 1/N]
35
How is Range Calculated (Breguet Range Equation?
R = (CL/CD) (V∞/B*g) ln (mFA/ (mFA-mK))
36
What is ηH?
Horizontal tail deflection.
Positive deflection means, control surface pointing down, aircraft nose Down Moment.
Negative deflection means control surface pointing up, aircraft nose Up Moment.
37
Conditions for Stable Flight regarding moments?
CL = n * CW
Cm0 > 0
dCm/dCL < 0
38
How can the efficiency or Range of the aircraft be improved?
By Breguet equation we can tell that if we can improve the Specific Fuel Consumption (B), Weight (W) or the Lift to Drag Ratio CL/CD
39
What is the symbol ∇?
Nabla Operator (vector).
|∂/∂x|
|∂/∂y|
|∂/∂z|
40
What are some assumptions for incompressible flow?
c tends to infinity, Ma tends to 0 (generally lower than 0.3), and density is constant through a streamline (∂ρ/∂t = 0 ).
41
What are the 2 conservation equations used in incompressible flow?
Continuity equation, and the Momentum Equation.
Energy doesn´t matter because of the density being constant.
42
By what is the surface pressure distribution for attached flow given? (Prandtl Hypothesis)
Approximately by the pressure distribution present at the outer border of the boundary layer set by the irrotational outer flow.
43
What is Φ?
It is the Velocity Potential. Represents the Irrotational Flow
44
What is the Velocity Potential Equation?
∇2Φ = 0
45
What is rN in Airfoil Theory?
Leading-edge radius
46
How is the pressure coefficient calculated for the Thickness Problem? (linearized)
cp = 2 (p - p∞)/ (ρ∞ U∞) = -2u/U∞
47
What is q(x)?
Source strength, q(x) = U∞ dD/dx
48
What is the Kutta condition? (In airfoil theory)
The requirement that the flow at the trailing edge of an airfoil must be tangent to the surface. The flow has to leave the trailing edge smoothly (No vortexes), no pressure difference at the Trailing Edge.
Normally this is done by creating a small angle of attack at the trailing edge.
"Root Singularity"
@ x=0 (@Root): γ and ΔCp -> ∞
"Kutta Condition (KAB)"
@ x=1 (@Trailing Edge) , γ = 0 and ΔC = 0
49
What is γ in airfoil Theory?
Circulation Distribution.
50
For incompressible flow or a symmetrical airfoil, what are the values for CLα and CL? and What about the Lift (L)?
CLα = 2π
CL = 2πα
L = ρ U∞2 π α l
51
For a symmetrical airfoil, what is the value of Cmα and the value for the Circulation (Γ)?
Cmα = -(π/2)
Γ = π α l U∞
52
For a symmetric airfoil, where is the Neutral Point (Aerodynamic Center) and Center of Pressure?
xN = xD = l/4
A quarter of the chord.
53
What is the condition for a symmetrical airfoil?
No camber. dS/dx = 0
54
For a non symmetrical airfoil (with camber), what is the value for CL? What do its components mean?
CL = π(2A0 + A1)
A0 represents the value of the circulation around the airfoil at the trailing edge.
A1 is a complex constant obtained from the Boundary conditions at the the trailing edge.
55
How do Trailing-edge and Leading-edge devices (Flaps/slats/etc.) affect the lift coefficient?
Leading edge devices Provide a higher CL,max along with higher Angle of attack, without moving the CL,0. Essentially extending the curve at the CL α graph for a higher CL,max.
Trailing edge devices move the CL,0. Essentially only moving the CL α curve up or down.
56
What are the 3 main types of wind tunnels?
Free jet type, Eiffel Type, Göttingen Type
57
What are some characteristics of he Göttingen Type Wind Tunnel?
Most used wind tunnel design type
Return passage
Closed or open test section
Fan induced disturbances on the test section are low due to the distance between the fan and the test section.
58
How is the Reynolds number adjusted in wind tunnel testing?
By adjusting the density, velocity, and dynamic viscosity of the fluid used in testing (air). But also the size of the test model can be adjusted to scale the Reynolds number, as this value is directly proportional to the characteristic length of the model.
59
What is the Helmholtz vortex theorem and how is it related to aerodynamics?
This theorem states that the circulation around a closed path in an inviscid, incompressible fluid is constant as long as the fluid is not subjected to external forces.
This theorem helps define how induced Drag can be calculated, as well as the Lift. More specifically how the trailing vortexes generated at the wing tips of an aircraft behaves and how they affect the aircraft.
60
What are some assumptions and conditions used for Prandtl's Lifting Line Theory?
Small CL, therefore small |Γ|.
Induced downwash is small.
High Aspect Ratio, AR>5,
The roll-up effects of the trailing vortex are neglected downstream of the trailing edge.
61
Where is the Lifting Line position on the wing?
At the 1/4 line
62
How is the induced angle of attack calculated using Lifting Line Theory?
Using the "downwash integral"
ai(y) = wi(y)/U∞
= 1/(4 π U∞) * ∫-b/2b/2 (dΓ/dy') dy'/(y-y')
63
How is the contribution to the lift coefficient calculated using Lifting Line Theory? What are the different angles of attack?
CL = (dCL∞/dα)(α-αi-α0)
αi is the induced angle of attack, calculated using de downwash integral.
α0 is the angle of attack produced simply by the camber and twist of the wing
α is the general angle of attack
64
How is the effective angle of attack calculated?
αeff = α-αi
65
How can the Circulation Distribution relate to the CL calculation?
Γ(y) = (1/2)(dCL∞/dα) U∞ (α-αi(y) - α0 (y)) l(y)
66
How is Lift calculated using the Lifting Line Theory
L = π/4 b ρ U∞ Γ1
67
How is induced Drag calculated using Lifting Line Theory?
Di = π/8 ρ ∑n nΓn2
68
How is the minimum induced Drag calculated? What conditions must be fulfilled?
Di, min = π/8 ρ Γ12
A circulation type 1 must be fulfilled, which is an elliptical circulation distribution.
69
For elliptical circulation distribution what are the equations needed to calculate CDi and αi?
CDi = CL2/ (πΛ)
αi = CL / (πΛ)
70
For non elliptical circulation distribution how is the CDi calculated?
CDi = CL2 / (eπΛ)
Where e is the Oswald efficiency factor
However an elliptical circulation distribution can be assumed for a first approximation
71
What is Prandtl's Lifting Line Theory?
It is a technique used to calculate a lot a lot of aerodynamic properties for a finite wing. It consists of using an infinite amount of trailing horseshoe vortices that create a Lift distribution over the finite wing. These vortices have a bound vortice at the 1/4 chord of the wing or the "Lifting Line"
72
When can Prandtl's Lifting Line Theory be used?
It can be used only for moderate to high aspect ratio wings. For small Aspect ratios, the vortex lattice method can be used.
73
What is the Vortex Lattice Method?
An extended more complex Lifting Line Theory, in which, instead of only 1 Lifting Line, the calculation goes for an infinite amount of Lifting Lines over the whole Wing.
74
What are the 2 methods of Airfoil Design?
Direct and Inverse Design
75
How to "Directly" Design an Airfoil?
-The geometry of the airfoil is given
-Pressure Distribution and Aerodynamics Coefficients are to be calculated
-The geometry is modified in order for improvement in performance.
76
What are the geometric aspects that most affect airfoil aerodynamics?
Airfoil Thickness Distribution and Camber line
77
How to "Inversely" Design an Airfoil?
-The pressure distribution is given
-A geometry is designed using numerical approximations
-Constraints are taken into account to optimize the airfoil
-The airfoil is designed
78
What are some Design objectives and constraints that must be taken into account when designing an airfoil?
-Flow separation must be prevented
-High Lift coefficients require high negative pressures on the upper side of the airfoil
-Optimal Airfoils are achieved if attached flow is maintained.
-Laminar flow achievable through smooth surface and a negative pressure over a wide range of the airfoil. (Other methods: Suction of BL, Active Flow Control)
-Problems at small Reynolds numbers
-Pressure minimum cannot be shifted too far downstream (NP must be behind CG)
-Resistance to Separation (eg. with respect of a changing angle of attack)
79
What is the difference between the aerodynamics Frame and the Body Fixed Frame?
[x,y,z]aero = [-x,y,-z] body
Aerodynamic Forces positive in aerodynamic frame
Aerodynamic Moments positive in Body fixed Frame
80
What is the Linearized Kinematic Boundary Condition?
It states that the fluid velocity must be tangent to the body as a superposition of linearized potential flow solutions.
81
What are the main aircraft components used for stability and high lift?
Ailerons, Elevator, Rudder, Leading Edge Slats, Trailing Edge flaps
82
What does the Prandtl Hypothesis say? Include Sketch
The fluid flow around an airfoil can be divided into two regions, the Boundary Layer (Viscous flow) and the far-field region (Inviscid flow)
83
What are 4 flow characteristics of the Kutta condition? Include Sketch
1.- Smooth flow detachment from the trailing edge of the airfoil
2.- Smooth transition of the flow from the airfoil surface to the wake, no abrupt changes in velocity or pressure
3.- Absence of any vortices shed from the trailing edge, circulation is finite.
4.- Sharp, Well- defined wake is formed behind the airfoil
84
3 Assumptions made for flows described by velocity potential function? characteristic Function?
1.- Flow is Inviscid
2.- Flow is Incompressible
3.- Flow is irrotational
∇^2 * Φ = 0
85
What are the 2 modelling approaches for airfoil theory?
Symmetric (Thickness Problem) and Antimetric (Lift Problem)
86
What are the elementary solutions for sources/sinks and vortices?
For sources ϕ = Q ln r
For Vortices ϕ = Γθ
87
What is the Pistolesi Point of a Wing? What
Point at which the downwash velocities of both the vortex sheet modelling and the horshoe modelling are the same. located at 3/4 l
