ASEN 2502 Exam 1

What are the four fundamental point properties of a flow field?

1. Temperature

2. Pressure

3. Density

4. Velocity

At what velocities can we assume incompressible flow?

When in subsonic incompressible flow which occurs at M < 0.3

At what Mach numbers do each of the following flow regimes exist?

1. Subsonic incompressible flow

2. Subsonic compressible flow

3. Transonic flow

4. Supersonic flow

5. Hypersonic flow

1. M < 0.3

2. 0.3 < M < 0.75

3. 0.75 < M < 1.2

4. 1.2 < M < 5

5. M > 5

What is the critical Reynold’s number of a flat plate?

Re = 500,000

What is the critical Reynold’s number used for?

To determine whether the flow is turbulent or laminar. It can also be used to calculate what percent of a flow is turbulent.

Define the primary characteristics of subsonic compressible and incompressible flow.

Subsonic incompressible flow has small enough changes in density that the flow can be assumed to be incompressible. In subsonic compressible flow, there is enough change in density between points that you cannot make the same assumption.

What is continuity and what do you have to assume to use it?

ρ₁A₁V₁ = ρ₂A₂V₂

You must assume a steady, 1D flow

What is the continuity equation based on?

Conservation of mass

What assumptions must you make to use Bernoulli’s equation?

• Steady, 1D flow

• Incompressible flow

• Inviscid flow

What is transonic flow and why do people avoid flying in it?

It’s a flow where there are pockets of subsonic and supersonic flow. It’s bad because there’s a high rise in drag and unfavorable shock interactions with the aircraft (shock waves).

At what flow regime does heating and ionization become an issue?

Hypersonic flow

What is Bernoulli’s equation based off?

Conservation of momentum

When can inviscid flow be assumed?

• Away from solid walls

• When there’s no flow separation

• Airfoils at low angles of attack

What is static pressure?

P₀ → pressure from disorganized movement of air

What is dynamic pressure?

q → pressure caused by bulk, organized movement of air

What is total pressure?

The pressure experienced as flow velocity goes to zero

What are the four primary aeronautic forces?

1. Lift

2. Drag

3. Thrust

4. Weight

What are the normal and axial forces?

Resultant force components. The normal force is normal to the airfoil chord. The axial force is parallel to the airfoil chord.

What is the aerodynamic center? Approximately where is it in subsonic and supersonic flows?

It’s the point where the moment doesn’t change while the angle of attack does.

Subsonic flow: ~c/4

Supersonic flow: ~c/2

When do two aircraft have similar dynamic flow properties?

When they have the same Reynold’s and Mach numbers.

What properties of the flow field and aircraft affect lift?

• Velocity → higher velocity = more lift

• Density → thicker air (higher density) = more lift

• Wing area → bigger wing (higher area) = more lift

• How hard the shape is working to create lift (a)

When two flows are dynamically similar, what flow properties do they share?

Same type of…

• Boundary layer

• Profile

• Transition

• Separation

Characteristics

What are the differences between the two kinds of boundary layers?

Laminar boundary layer

• Smooth flow

• Parallel streamlines

• Parabolic shape

Turbulent boundary layers

• Eddies and vortices that whirl

• Momentum transfer from high speed flow changes

When does flow separation occur?

When the flow at the surface of the airfoil isn’t following surface contour

What is the impact of flow separation on lift and drag?

Net decrease in lift. Net increase in drag.

What does the aircraft drag polar depend on?

• Mach number

• Reynold’s number

• Shape/configuration of aircraft

• Orientation of aircraft to flow (expressed by Cᶫ)

How is the body axis system orientated on an aircraft?

+x axis out of the nose of the plane

+y axis out of the right wing

+z axis goes below the plane

What is roll?

Motion about the x-axis

• Lateral axis

• Positive moment is right wing down

• Control surface → aileron

What is pitch?

Motion about the y-axis

• Longitudinal axis

• Positive moment is pitch up (nose up)

• Control surface → rudder

What is yaw?

Motion about the z-axis

• Directional axis

• Positive moment is nose right

• Control surface → rudder

What are the primary and secondary control surfaces?

Primary: Ailerons, rudder, elevator

Secondary: flaps → controls wing camber

What are the definitions of equilibrium, stability, and control?

Equilibrium → a body at rest or in uniform motion

Stability → a body’s response to a disturbance from equilibrium

Control → deflections in control surfaces to make an aircraft move correctly.

What is static stability?

A body’s initial response

• Stable (+) → initial tendency to return to equilibrium

• Neutral → initial tendency to establish a new equilibrium

• Unstable (-) → initial tendency to move away from equilibrium

What is dynamic stability?

A body’s long term response

• Stable (+) → overtime, it converges to the original equilibrium state and remains there

• Neutral → overtime, it doesn’t converge to or diverge from its original equilibrium state

• Unstable (-) → overtime, it diverges from the original equilibrium state

What is downwash?

Downward deflection of air on the tail caused by other components of the aircraft.

What value of ∂C_M / ∂α is desired for stability?

A negative value

How do surfaces in front of/aft of the center of gravity affect stability?

Horizontal surfaces…

Forward of cg → destabilizing

Aft of cg → stabilizing

What is the neutral point of an aircraft?

The point where the pitching moment doesn’t change as the angle of attack changes.

What is the static margin (SM)?

The normalized distance (% chord) between your aircraft neutral point and center of gravity

What is directional static stability?

• Stability in rotations about the z-axis

• Mostly affected by vertical stabilizer

What are the design considerations for directional static stability?

Main design factor → Vᵥ, the vertical tail volume coefficient

The wing and body are directionally destabilizing

The vertical tail aft of the cg is stabilizing

What is lateral static stability?

Stability about the x-axis

What is a dihedral

The angle a wing makes with the horizontal plane.

(+) angle is stabilizing

(-) angle, anhedral, is destabilizing

How does wing placement affect lateral stability?

• High wing → stabilizing

• Mid wing → neutral

• Low wing → destabilizing

How does wing sweep affect directional and lateral stability?

Aft sweep → stabilizing

Forward sweep → destabilizing

What are the five dynamic stability modes?

1. Phugoid mode

2. Short period mode

3. Roll mode

4. Spiral mode

5. Dutch Roll mode

What are the characteristics of phugoid mode?

• Longitudinal mode

• 2nd order → oscillatory

• Trade off in KE and PE

• Aircraft experiences low frequency oscillations

• Easily correctable by the pilot because of long oscillatory period

• Most piloted aircraft are lightly damped or unstable in phugoid

What are the characteristics of short period mode?

• Longitudinal

• 2nd order → oscillatory

• Aircraft experiences high frequency pitch oscillations

• Pilots can’t correct it because of the short oscillatory period

What are the characteristics of roll mode?

• AKA “roll subsidence mode”

• Lateral/Directional

• 1st order → non oscillatory

What are the characteristics of spiral mode?

• Lateral/Directional

• 1st order → non oscillatory

• Constant winding up of roll angle

• Occurs with too much directional stability compared to roll stability

What are the characteristics of Dutch Roll mode

• Lateral/Directional

• 2nd order → oscillatory

• Occurs with too much roll stability compared to directional stability

What does S represent?

Wing planform area

What does b represent?

Wingspan

What does cᵣ represent?

Root chord length

What does λ represent?

Wing taper ratio

What does c̄ represent?

mean aerodynamic chord

What do x̄ₘₐ꜀ and ȳₘₐ꜀ represent?

The x and y locations of the mean aerodynamic chord

What does cₜ represent?

The tip chord length

What does AR represent?

The aspect ratio

What do P and P₀ represent?

Pressure and static pressure

What does ρ represent?

Density

What does R represent?

molar gas constant

What does T represent?

temperature

What does ṁ represent?

mass flow rate

What does A represent?

Area or the axial force

What does N represent?

The normal force

What does v represent?

velocity

What does q represent?

dynamic pressure

What does M represent?

Mach number

What do a and a₀ represent?

slope of the 3D lift curve and the 2D/airfoil lift curve

What does Re represent?

Reynold’s number

What does μ represent?

viscosity

What do c_d, c_l, and cₘ represent?

The drag, lift, and pitching moment coefficients of a 2D airfoil

What do L and D represent?

Lift and drag

What do C_L and C_D represent?

The coefficients of lift and drag for a 3D wing

What does W represent?

Weight

What do α, αₗ₌₀, and αₑբբ represent?

angle of attack, angle of attack when lift is zero, and effective angle of attack

What do e and e₀ represent?

The efficiency factor and the Oswald Efficiency Factor

What does CDᵢ represent?

The coefficient of induced drag

What does CD₀ represent?

Coefficient of parasitic drag

What does k represent?

the lift-dependent drag factor

What does M_cg_wb represent?

The pitching moment about the center of gravity induced by the wing body.

What do V_H and V_V represent?

Horizontal and vertical tail volume coefficients

What does SM represent?

the static margin

In the following chart, identify the type of drag associated with each colored region

Green - induced drag

Blue - pressure drag

Red - skin friction drag

How does skin friction, boundary layer thickness, and likelihood of flow separation change in turbulent boundary layers vs. laminar boundary layers?

Turbulent boundary layers have:

• Higher skin friction due to a higher velocity gradient at the surface

• Larger boundary layer thickness

• Less susceptible to flow separation

How does the ‘Induced Drag’ of a finite wing physically originate?

From the downward deflection of air (downwash) caused by tip vortices, which tilts the local lift vector backward

A symmetric airfoil used on a vertical stabilizer ensures that at zero side slip

The yawing moment N is zero.

How does downwash created by finite wing tip vortices affect the effective angle of attack?

The effective angle of attack is reduced in comparison to the geometric angle of attack

What is the primary conceptual difference between the ‘Span Efficiency Factor’ and the ‘Oswald Efficiency Factor’?

e accounts for only the wing while e₀ accounts for the entire aircraft

What physical phenomenon occurs at the ‘separation point’ on an airfoil?

The velocity gradient at the wall becomes negative, resulting in flow reversal and a recirculation bubble

Why is a neutrally stable or unstable Spiral mode often considered acceptable in aircraft design?

The time constant is very long, making it easy for a pilot to correct.

Why is the characteristic length (L) in the Reynolds number formula typically taken as the ‘mean chord’ for a wing rather than the total wing span?

Because the viscous effects like the boundary layer develop along the direction of the flow (chord-wise)

Why do some high-wing, swept-wing military transport aircraft use anhedral wings?

An aircraft with high, aft-swept wings create excessive roll stability which can make it difficult to turn. Anhedral wings counteract this.

For an aircraft to be longitudinally statically stable, where must the center of gravity be located relative to the neutral point?

The cg must be forward of the NP

What are the stability derivatives for each type of stability and what do we want their values to be in for an aircraft to be stable?

Directional → CN_beta > 0

Longitudinal → CM_alpha < 0

Lateral → CL_beta < 0

What effect does increasing the AR have on longitudinal static stability, assuming the cg is forward of the AC?

It increases stability by increasing wing lift curve slope a

How does ‘Interference Drag’ contribute to the Whole Aircraft Drag Polar?

It arises from the mixing boundary layers where different components meet, increasing total drag.

What could change about the vertical tail size, wing sweep, and wing dihedral of an aircraft to decrease the likelihood of an unstable dutch roll mode?

• Increase vertical tail size

• Decrease wing sweep

• Decrease wing dihedral