Aerodynamics –IBasics

UNIT-3

Forces and Moments

AIRFOILS VERSUS WINGS

Forces on airplane atlevel speed and constantheight and speed.

Lift force is the component of R that is perpendicular tofree stream velocity, and drag is the component of R parallel to the free stream velocity. If planes height is not changing then: Lift = Weight

Ap and c are independent of

CL =L/(1/2 V

2Ap)

CD =D/(1/2 V

2A)

Ap = planform areamax. proj. of wing

A

As angle of attack increasesstagnation point moves downstream along bottom surface, causing an unfavorable pressure gradient at the nose*.

*

*

The tendency for flow to leak around the wing tipsgenerally cause streamlines over the top surface ofthe wing to veer to the wing root and streamlinesover the bottom surface veer to the wing tips.

Endplates (winglets) at end of wing reduces tip vortex

Airfoil Nomenclature

Reynolds No, Boundary Layer Transition and surface roughness

NACA Conventional Airfoils

An airfoil designed for minimum drag and uninterrupted flow of the boundary layer is called a laminar airfoil.

Laminar Flow Airfoils

Whitchomb supercritical airfoils

Many theories have been developed on how a wing generates lift. The most common one is the “Longer Path Theory”.

This theory describes how the shape of the aerofoil produces a pressure difference which generates lift. As the aerofoil is designed in such a way that its upper surface is longer than the bottom, and because the molecules that hit the leading edge must meet again at the trailing edge, the ones that travel on the upper surface do so with greater velocity than the lower

Drag Reduction And lift Augmentation Methods

Flap system Leading edge devices Multi element airfoils Circulation control Laminar flow control winglets

Flap is an element attached to the aileron of the wing section

It is always possible to reduce stall speed by increasing wing area

Flap systems

Different types of flap system

Flaps change the airfoil pressure distribution, increasing the camber of the airfoil and allowing more of the lift to be carried over the rear portion of the section

Leading Edge Devices

Leading Edge Devices Leading edge devices such as nose flaps,

Kruger flaps, and slats reduce the pressure peak near the nose by changing the nose camber. Slots and slats permit a new boundary layer to start on the main wing portion, eliminating the detrimental effect of the initial adverse gradient.

A Wing with slats and Flaps

Multi Element Airfoils

Winglets

Winglets

NACA FOUR-DIGIT SERIES

First set of airfoils designed using this approach was NACA Four-Digit Series

First digit specifies maximum camber in percentage of chord Second digit indicates position of maximum camber in

tenths of chord Last two digits provide maximum thickness of airfoil in

percentage of chord

Example: NACA 2415 Airfoil has maximum thickness of 15%

of chord (0.15c) Camber of 2% (0.02c) located 40%

back from airfoil leading edge (0.4c)

NACA 2415

INFINITE VERSUS FINITE WINGS

SbAR2

Aspect Ratiob: wingspanS: wing area

High AR

Low AR

First airplane designed for sustained flight at Mach 2 Very sharp leading edge on wings (razor sharp leading edges, thickness

3.4 %) Designed to minimize wave drag at supersonic speeds Very poor low-speed aerodynamic performance Such wings tend to stall at low angles of attack, CLmax is only about 1.15 Vstall (full of fuel) ~ 198 MPH Vstall (fuel empty) ~ 152 MPH Vstall proportional to W1/2

EXAMPLE: F-104 LOCKHEED STARFIGHTER

AIRFOILS VERSUS FINITE WINGSHigh AR

Low ARSbAR2

Aspect Ratio

Mean Chamber Line: Set of points halfway between upper and lower surfaces◦ Measured perpendicular to mean chamber line itself

Leading Edge: Most forward point of mean chamber line Trailing Edge: Most reward point of mean chamber line Chord Line: Straight line connecting the leading and trailing edges Chord, c: Distance along the chord line from leading to trailing edge Camber: Maximum distance between mean chamber line and chord line

◦ Measured perpendicular to chord line

AIRFOIL NOMENCLATURE

STREAMLINES OVER AN AIRFOIL

Aerodynamic forces exerted by airflow comes from only two sources Pressure, p, distribution on surface

◦ Acts normal to surface

Shear stress, tw, (friction) on surface◦ Acts tangentially to surface

Pressure and shear are in units of force per unit area (N/m2) Net unbalance creates an aerodynamic force

“No matter how complex the flow field, and no matter how complex the shape of the body, the only way nature has of communicating an aerodynamic force to a solid object or surface is through the pressure and shear stress distributions that exist on the surface.”

“The pressure and shear stress distributions are the two hands of nature that reach out and grab the body, exerting a force on the body – the aerodynamic force”

WHAT CREATES AERODYNAMIC FORCES?

Relative Wind: Direction of V∞◦ We used subscript ∞ to indicate far upstream conditions

Angle of Attack, : Angle between relative wind (V∞) and chord line

Total aerodynamic force, R, can be resolved into two force components Lift, L: Component of aerodynamic force perpendicular to relative wind Drag, D: Component of aerodynamic force parallel to relative wind

RESOLVING THE AERODYNAMIC FORCE

RESOLVING THE AERODYNAMIC FORCE Aerodynamic force, R, may also be resolved into

components perpendicular and parallel to chord line◦ Normal Force, N: Perpendicular to chord line◦ Axial Force, A: Parallel to chord line

L and D are easily related to N and A

For airfoils and wings, L and D most common For rockets, missiles, bullets, etc. N and A more

useful

cossinsincosANDANL

Total aerodynamic force on airfoil is summation of F1 and F2 Lift is obtained when F2 > F1 Misalignment of F1 and F2 creates Moments, M, which tend to rotate

airfoil/wing Value of induced moment depends on point about which moments are taken

◦ Moments about leading edge, MLE or quarter-chord point, c/4, Mc/4

◦ In general MLE ≠ Mc/4 F1

F2

Lift, Drag and M on a airfoil or wing will change as changes

Variations of these quantities are some of most important information that an airplane designer needs to know

Aerodynamic Center◦ Point about which moments essentially do not vary with ◦ Mac=constant (independent of )◦ For low speed airfoils aerodynamic center is near quarter-

chord point

VARIATION OF L, D, AND M WITH

Lift due to imbalance of pressure distribution over top and bottom surfaces of airfoil (or wing)◦ If pressure on top is lower than pressure on bottom surface, lift is

generated◦ Why is pressure lower on top surface?

We can understand answer from basic physics:◦ Continuity (Mass Conservation)◦ Newton’s 2nd law (Euler or Bernoulli Equation)

Lift = PA

1. Flow velocity over top of airfoil is faster than over bottom surface◦ Streamtube A senses upper portion of airfoil as an obstruction◦ Streamtube A is squashed to smaller cross-sectional area◦ Mass continuity AV=constant: IF A↓ THEN V↑

HOW DOES AN AIRFOIL GENERATE LIFT?

Streamtube A is squashedmost in nose region(ahead of maximum thickness)

AB

HOW DOES AN AIRFOIL GENERATE LIFT?2. As V ↑ p↓

◦ Incompressible: Bernoulli’s Equation◦ Compressible: Euler’s Equation◦ Called Bernoulli Effect

3. With lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction → Lift

VdVdp

Vp

constant21 2

Most of lift is producedin first 20-30% of wing(just downstream of leading edge)

Can you express these ideas in your own words?

Curved surface of an airfoil is not necessary to produce lift even a flat plate can generate lift

A

B

Behavior of L, D, and M depend on , but also on velocity and altitude◦ V∞, ∞, Wing Area (S), Wing Shape, m ∞, compressibility

Characterize behavior of L, D, M with coefficients (cl, cd, cm)

Re,,21

21

2

2

Mfc

SqL

SV

Lc

ScVL

l

l

l

Matching Mach and Reynolds(called similarity parameters)

M∞, Re

M∞, Re

cl, cd, cm identical

LIFT, DRAG, AND MOMENT COEFFICIENTS Behavior of L, D, and M depend on , but also on velocity and

altitude◦ V∞, ∞, Wing Area (S), Wing Shape, m ∞, compressibility

Characterize behavior of L, D, M with coefficients (cl, cd, cm)

Re,,21

21

3

2

2

Mfc

ScqL

ScV

Mc

SccVM

m

m

m

Re,,21

21

2

2

2

Mfc

SqD

SV

Dc

ScVD

d

d

d

Re,,21

21

1

2

2

Mfc

SqL

SV

Lc

ScVL

l

l

l

Note on Notation:We use lower case, cl, cd, and cm for infinite wings (airfoils)We use upper case, CL, CD, and CM for finite wings

SAMPLE DATA TRENDS Lift coefficient (or

lift) linear variation with angle of attack, a◦ Cambered airfoils

have positive lift when =0

◦ Symmetric airfoils have zero lift when =0

At high enough angle of attack, the performance of the airfoil rapidly degrades → stall

Lift (

for n

ow)

Cambered airfoil haslift at =0At negative airfoilwill have zero lift

To understand drag and actual airfoil/wing behavior we need an understanding of viscous flows (all real flows have friction)

Inviscid (frictionless) flow around a body will result in zero drag!◦ Called d’Alembert’s paradox (Must include friction in theory)

THE REYNOLDS NUMBER One of most important dimensionless numbers in fluid mechanics/

aerodynamics Reynolds number is ratio of two forces

◦ Inertial Forces◦ Viscous Forces◦ c is length scale (chord)

Reynolds number tells you when viscous forces are important and when viscosity can be neglected

m cVRe

Within B.L. flowhighly viscous(low Re)

Outside B.L. flowInviscid (high Re)

Reynolds number also tells you about two types of viscous flows◦ Laminar: streamlines are smooth and regular and a fluid element moves

smoothly along a streamline◦ Turbulent: streamlines break up and fluid elements move in a random,

irregular, and chaotic fashion

LAMINAR VERSUS TURBULENT FLOW

Stability & Control

yaw

roll

pitch The 3 axes of motion:

roll, pitch, yaw

CENTER OF PRESSURE AND AERODYNAMIC CENTER Center of Pressure: Point on an airfoil (or

body) about which aerodynamic moment is zero◦ Thin Airfoil Theory: Symmetric Airfoil:

4cxcp

Aerodynamic Center: Point on an airfoil (or body) about which aerodynamic moment is independent of angle of attack

Thin Airfoil Theory:Symmetric Airfoil:

4..cx CA

DragThe resistance to an object’s passage through the air

Types of DragInduced

Profile

Parasite

Induced Drag•Drag that is incurred as a result of the production of lift•Parallel to and in the same direction as relative wind•Increases with increased angle of attack•Decreases with increased airspeed

Each blade passes through the previous blade’s disturbedair this condition is most pronounced at high power settings and no or low forward airspeeds.

Profile Drag

•Parasitic drag of the rotor system•At a constant RPM, profile drag is relatively constant but does increase slightly with airspeed. •Increases rapidly with very high airspeeds due to onset of blade stall or compressibility•Profile drag is greater on 3, 4, 6, etc. bladed systems

Parasitic DragThe resistance offered by the fuselage and other nonliftingsurfaces to the flow of air

Causes

•Form or shape of the helicopter, the more streamlined the helicopter, the less parasitic drag•Skin friction, the smoother the skin of the fuselage, the less parasitic drag

Increases rapidly with airspeed

Total Drag CurveThe summation of all drag forces acting on the helicopter

Total drag is high at a hover, decreases to a minimum value at a particular airspeed, then starts increasing with airspeed

Minimum rate of descent for autorotationMaximum endurance airspeedMaximum rate of climb airspeedBest maneuvering airspeed

The above are airspeeds that fall within the lowest drag area of the total drag curve. Theses speeds typically range from 60 to 80 kts

Drag Forces

Dra

g

Forward Speed

Torque Available

Induced Drag

ProfileDrag

ParasiteDragTotal Drag