Aero

Doublet

effectively a source and sink at the same point

Stream Function

Velocity Potential

What is circulation in fluid dynamics?

Measure of how fluid tends to go around a closed loop

What does circulation also represent in a closed loop?

Total vorticity (local spinning) enclosed by a loop

When is high/low circulation/what does it mean?

High: fluid is moving strongly along a loop

Low/Zero: fluid motion cancels out, no net rotational movement around the chosen loop

Desrcibe why lift is generated with increased circulation.

Kutta-Joukowski Theorem says that lift is proportional to the amount of circulation around a wing.

If the wing profile is the closed loop of a circulation calculation the top and bottom will contribution opposite to each other. With faster flow on the bottom, the circulation on the bottom is more which means lift is generated

If the wing profile is the closed loop of a circulation calculation the top and bottom will contribution opposite to each other. With faster flow on the bottom, the circulation on the bottom is more which means lift is generated

What else is pressure drag called?

Form Drag

What types of drag is profile drag made up of

Pressure (form) and skin-friction

Interference drag

Flow over indvidual components != flow assembled plane

• Additional drag from assembly airflow

Parasite drag

Includes Profile Drag and Interference drag

Skin friction drag

Caused by shear stress from fluid pulling on the object due to viscous effects

Pressure drag

Caused by flow separation (occurs when the boundary layer seperates from the object leading to recirculation of the flow)

• Recirculation causes more pressure on the flow

Boundary layer separation

As pressure increases along streamline, velocity decreases (Bernoulli), eventually leads to flow reversal on the surface and the boundary layer seperates from the object

Prandtl's Lifting Line Theory

Chord Line

Straight line spanning from leading edge to trailing, no bends/always straight, can pass outside of the wing

Chord Length

Length from leading edge to trailing edge

Mean Camber Line

Line defining the half thickness throughout the wing, middle of the wing profile moving from front to back

Kutta-Joukowski Lifting Theorem

Lifting flow over an object is a function of flow density, velocity, and circulation.

Applies to shapes of any smooth cross section

Airfoil

2D closed shape cross section that is used for wing, prop, turbine applications.

Shape is designed to have a favorable lift/drag (L/D) ratio

Quarter Chord Resultant Force Location

1/4 of chord length from leading edge, used as an approximation of where resultant force acts; includes a moment to account for not being center of pressure; for a symmetric airfoil, quarter chord is the true location of the resultant force (center of pressure)

Leading Edge Resultant Force Location

Using the leading edge as a guess for where the center of the pressure acts on a wing profile (characterized through Lift, Drag, and a Moment). The moment accounts for the fact that the center of pressure is elsewhere along the wing profile in such a way that it will create moment about the leading edge

Largest distinguishers of airfoil performance

Thickness and camber

NACA WXYZ

NACA methodology for classification of wing profiles based on camber and thickness. All characteristics are normalized by a profile's respective chord length

W - max camber (diff. btwn mean camber line and chord line

X - location of maximum camber

YZ - maximum thickness

NACA 1234

1,2: How asymmetircal airfoil is

34: How thick airfoil is

Angle of Attack

Angle between the incoming flow and the chord line

Effect of angle of attack

Significant effect on lift and drag generation on a wing. Changing the angle of attack creates a curve of characteristic cofficient of lifts

When less than stall angle: ncreasing AofA creates a different flow pattern that has more circulation and thus pressure differences that generate more lift which translates to a higher CL

Zero Lift Angle of Attack

The angle at which a wing profile generates no lift

Zero Lift Angle of Attack for a Symmetric Wing

Angle of attack at which wing produces no lift is zero degrees (chord line is in line with flow)

Zero Lift Angle of Attack for a Cambered Wing

Angle of attack where lift is zero for a cambered (cambered upwards like plane) wing is negative. This means that the wing must be pitched down in order to have no lifting force

Stall

The state at which a wing is generating so much drag that it can no longer move forward despite the lift generation; because the drag is so great, the velocity of the flow around the wing decreases and so does the lift (Lift is a function of velocity)

Ailerons

Outer edge of wings, can angle up or down, control roll

Rudder

Back of the vertical tail, controls yaw

Elevators

Bottom of tail, can move up or down, controls pitch

Slats

Front of the wings, increase lift

Flaps

Inner edge of wings, increases lift

Spoilers

Top of wings, increases drag, used for landing

Thin Airfoil Theory

Zooming out far enough from a wing profile that it can be treated as a vortex sheet along the camber line

Thin Airfoil Theory Advantages

• Accurately predicts coefficient of life, CL = 2xPIxAlpha, Zero lift angle of attack

• Center of pressure is located at quarter chord

Thin Airfoil Theory Disadvantages

• Inviscid flow representation, meaning does not account for drag

• Not accurate at large angles of attack

-

span efficiency factor

e

induced drag factor

tabulated, lowercase delta

Wave Drag

An additional form of pressure drag (usually formed by recirculation from boundary layer separation) that only happens at supersonic speeds

Shock wave generation on the surface of a wing generates wave drag, often at an angle meaning generation of pressure distributions that translates into || and L forces on the wing mean both lift and drag

Zero Lift Drag

The drag amount when a wing profile is pitched in a way that it generates net zero lift

Indicated Air Speed

Pitot-based velocity value based on sea-level air density,

Not the true velocity value, usually slower than actual velocity as the density of air decreases moving up in the atmosphere

Knot

• Convetional unit of airspeed

• Nautical mile: distance covered by 1/60˙ of earth's radius

• Nautical mile: 1825 m = 1.15 mi

• 1 knot = 0.514 m/s = 1.15 mph

• Common crusing speed: 520 kt = 600 mph

Straight and Level Assumptions

• Velocity is constant

• Altitude is constant

• No acceleration --> Forces on body ∑ = 0

Velocity in Straight and Level Flight

Thrust in Straight and Level Flight

Stall Speed for Straight and Level Flight

Same as S&L velocity with the maximum CL

Straight and Level Drag Force

• Uses the S&L assumption in plugging CL of a function of body weight (L = W in S&L flight)

Flight Envelope

Range of conditions between avaibale and required thrust —> physically possible thrust and velocity combinations

Thrust Available

Max amount of thrust an engine can produce

Thrust Required

Amount of thrust required based on drag

Ceiling

The maximum altitude that an engine can operate while still generating enough thrust to overcome the minimum drag

• Higher altitude —> less thrust available —> min drag (convex point) > Tav —> plane can no longer move forward

Drag Polar

Combination of Parasite (Profile and Skin-friction), Wave, and Induced drag coefficients

• Parasite: Split into zero lift and lift-dependent terms

• Wave: Split into zero lift and lift-dependent terms

• Induced: Prandtl’s Lifting Theory term

Designing with Drag in Mind

• Drag is the sum of all of the air molecules resisting an object in motion

• Cut down on the amount of drag so it takes less energy to move forward

Coanda Effect

Airflow will follow the shape of whatever it encounters

- Tendency of a fluid to remain attached to a curved surface

• Representative of Newton’s Third Law — Equal and Opposite reactions

Airflow at trailing edge of the wing is shoved downwards, the downwards shove creates an equal and opposite upwards shove (lifting force on the wing)

Paper Airplane Design

• Trade height for speed?

• More forward center of gravity —> plane points more nosedown —> can gain speed that is lost from drag —> plane can gain enough speed to deflect off ‘winglet’ on back of plane pushing the tail of the plane down/lift nose —> create a balanced glide

• Keep wide wingspan for effieicny to go farther

• Sturdy/Structurally sound to handle the thrust

• Winglets make wingtip vortices shed more cleanly, controls L/R roll — more stable in flight

• Give front wing slightly higher angle of incidence —> front wing will stall first —> drops the nose of the plane —> main wing keeps flying

Wing Loading

• Weight of whole plane divided by the lifting surface

High wing loading: plane must move much faster to lift the weight

Low wing loading: plane can move slower to lift the weight

• For a constant weight, wing area is the factor changing the wing loading

Big wings slow, small wings fast

Glide ratio

L/D ratio

Stall

Caused by:

• Too slow of airspeed

• Too high angle of incidence (angle of attack)

Available Power in Flight

Thrust x velocity (TV)

• Amount of power that can be provided to the aircraft

Required Power

Drag x velocity

• Amount of power required in order to move forward as determined by the amount of drag at a given velocity

Excess Power

Available Power - Required Power

Specific Excess Power

Excess Power normalized by the weight of the aircraft

Excess Power during Climb and its uses

Can be used for:

• Climbing faster

• Change Speed

• Do both of the above!

Altitude Change with Energy Conservation

Moving from some state 1 to state 2 in flight, based on energy conservation:

• A relative decrease in state 2 velocity leads to a greater change in altitude

• This means slowing down can allow (causality?) for an aircraft to climb

Glide Angle

dependent on the L/D ratio

Glide Range

• How far aircraft can travel with no thrust

• Is a function of altitude and L/D ratio

Quasi-Level

Essentially the small angle approximation: angle from horizontal is <= 5˙

• cos a ~= 1

• For perp to flow: L - Wcos(a) = 0

  • —> L ~= W for Quasi-Level Flight

Planiform Surface Area

Outline of aircrafts wings as seen from above or below

• Defines the leading edge, trailing, and chord lengths of the wing

Kolmogorov Time and Length Scales

Used to characterize the smallest eddies within a flow

• Defined by: kinematic viscosity and energy dissipation rate

Scales correspond to the point at which intertial forces and viscous forces of the flow are in equilibrium —> any smaller and the viscosity will overwhelm the eddy motion and it will dissipate entirely