MAE 3241 AERODYNAMICS & FLIGHT MECHANICS

Introduction
Yongki Go

Mechanical & Aerospace Engineering

MAE 3241 Overview

Course contents:

Aerodynamics (70%)

Forces and moments Fundamental principles and equations Inviscid incompressible flow Flow over airfoils (2D) Flow over finite wings (3D) Effect of compressibility and viscosity Modeling concept in flight performance analysis Steady flight performance Accelerated flight performance

Flight mechanics (30%)

Textbooks

Primary:
John Anderson, Fundamentals of Aerodynamics, 5th edition, 2011

Other useful books:

John Anderson, Aircraft Performance and Design, 1998 John Bertin, Aerodynamics for Engineers, 4th edition, 2001

Lecture Style

Ppt lecture notes will be posted in ANGEL before the lecture time

Some parts may be delivered by writing on whiteboard

Lecture notes are in summary form and contain parts that you will need to complete during lecture

Not a replacement for textbook It is best to have the relevant lecture notes while attending lecture It is strongly suggested that you add your own notes to enhance your understanding on certain topics Some of the exams may be open notes (open lecture notes and your own notes but not open book)

Aerodynamics Overview

Aerodynamics: study of interaction of air and object due to their relative motion Purpose of learning aerodynamics:

Calculate and predict: lift, drag, moments, heat transfer Understand how these forces and moments are generated Understand how interaction depends on flow conditions

Fluid properties Relative velocities Temperature, pressure, density Body geometry

Knowledge of aerodynamics is very important in aircraft design

Flight Mechanics Overview

Flight Mechanics: the science of predicting and controlling the motion that results from the forces and moments acting on a flying object

Flying object of interest in this course: fixed-wing aircraft Flight performance Flight stability (statics and dynamics) and control Flight simulation Flight control systems

Sub-areas of flight mechanics:

MAE 3241 covers fundamental flight performance of fixedwing aircraft

Flight Performance

Flight Performance concerns about how an aircraft responds to the forces experienced during its motion through the atmosphere

Mainly looks at translational motion Often sufficient to consider aircraft as point mass at its CG with all forces acting through it Four forces of flight
Lift Drag Lift Drag CG Thrust Thrust 2 Weight Weight

Thrust 1

CG

Importance of Flight Performance

Examples of questions of concern in aircraft performance:

How fast, how slow and how high can it fly? How rapidly can it climb? How far and how long can it fly? How maneuverable is it? How long a runway is needed for its takeoff and landing?

Performance is one of the main drivers in aircraft design!

The Four Forces of Flight

Aircraft flight performance estimation/analysis is based on these four forces Aerodynamic and propulsive characteristics of the aircraft depend on airflow conditions

Depend on the atmospheric properties and aircraft motion itself

Earths Atmosphere

Earths atmosphere is a mixture of several gases

78% nitrogen, 21% oxygen, 1% others

Atmospheric properties (pressure, temperature, density) are constantly varying

These variations affect aerodynamics and aircraft performance

Need a standard for aircraft performance comparison and flight testing purposes Standard Atmosphere (SA) is defined

Commonly used:

International Standard Atmosphere (ISA) US Standard Atmosphere

Identical up to 32 km

Standard Atmosphere (SA)

Based on defined average variation of T with altitude

p = RT

From observational data SA consists of isothermal and constant gradient layers

Assumed to behave as perfect gas R = 287 J/(kg.K) p = RT = 1716 ft.lb/(slug.R) Standard sea-level values for pressure, density, and temperature:

Layers in ISA (1976)

Layer Level Name Base Geopotential Height h (in km) 0 11 20 32 47 51 71 84.852 Base Geometric Height z (in km) 0 11.019 20.063 32.162 47.35 51.413 71.802 86 Lapse Rate (in C/km) -6.5 0 1 2.8 0 -2.8 -2 Base Temperature T (in C) Base Atmospheric Pressure p (in Pa) 101,325 22,632 5,474.90 868.02 110.91 66.939 3.9564 0.3734

0 1 2 3 4 5 6 7

Troposphere Tropopause Stratosphere Stratosphere Stratopause Mesosphere Mesosphere Mesopause

15 -56.5 -56.5 -44.5 -2.5 -2.5 -58.5 -86.2

Calculation of SA Properties

In the gradient layer:

T = T1 + a ( h h1 )

p T = p1 T1

g0 aR

T = 1 T1

g 0 +1 aR

a is the lapse rate (-6.5 x 10-3 K/m in the troposphere) g0 = 9.81 m/s2
g 0 ( h h1 ) RT g (h h ) RT =e 1
0 1

In the isothermal layer:

T = constant

p =e p1

Software for SA properties calculation can easily be found in the internet (beware of which SA model is used!) Properties of SA are usually tabulated

Sample of SA Table

Aerodynamics = Fluid Dynamics?

Aerodynamics: subset of fluid dynamics

Fluid dynamics encompass all fluids, aerodynamics focus on air Aerodynamics focus on the forces generated on bodies in air flow (i.e. lift and drag) Aerodynamics typically concern more to external flows (i.e. flows around bodies like aircraft, car, etc.) Aerodynamics provide the necessary parameters for flight mechanics and control studies

Specifically:

Much of the governing concepts between aerodynamics and fluid dynamics are similar

Some Fundamentals Aerodynamic Variables

m: dimension of mass l: dimension of length t: dimension of time

Variable
Pressure Density Temperature Viscosity (dynamic)

Symbol Dimension
p
T

SI Unit
Pa (N/m2) kg/m3 K

English Unit
psf (lb/ft2) lb/ft3
oR

ml-1t-2 ml-3 ml-1t-1

Pas (kg/(sm)) lbs/ft2

Airfoil vs. Wing

Airfoil: cross-section geometry of aerodynamic force generator elements (wings, tails, control surfaces)

In analysis:

Airfoil Wing

2D flow (part of infinitely-long wing) 3D flow

Aspect Ratio

b2 Definition: AR S
S

b: wingspan S: wing area

Tip

Some Important Dimensionless Parameters (1)

Reynolds number: ratio of inertia forces to viscous forces V: flow speed Vl Re = l: reference length

Reynolds number indicates when viscous forces are important and when viscosity may be neglected
High Re: viscosity can be neglected Low Re: viscosity cannot be neglected Outside B.L. flow (high Re)

Within B.L. flow: highly viscous (low Re)

Some Important Dimensionless Parameters (2)

Another important quantity that is usually extracted from the flow property is the speed of sound

Speed of sound depends on temperature only

a = RT

cp cv

For perfect gas: = 1.4

Mach number: ratio of flow velocity to the speed of sound

V M= a
Subsonic
Incom- Compressible pressible

Transonic

Supersonic

Hypersonic

0.3

Mcrit

1.0

2.0 Mach number, M

3.0

4.0

5.0