MAE 278 Introduction to Aerospace Engineering Practice
3 Dec 2015
Question 1:
The pilot of a propeller driven aircraft traveling from Albany, NY to Buffalo, NY is 150 miles
away from Buffalo at an altitude of 5,000 feet when he notices that the aircraft h
Lift, Drag, Pitching Moment Coefficients
Infinite wing (unit span) coefficients
L
WHERE : L WING LIFT PER UNIT SPAN
qS
D
cd
WHERE : L WING DRAG PER UNIT SPAN
qS
M
cm
WHERE : M WING PITCHING MOMENT ABOUT THE AERO
qSc
DYNAMIC CENTER UNIT PER UNIT SPAN
c
Ceilings
(1)
How high can the
airplane climb?
Absolute Ceiling: 0 fpm
Service Ceiling: 100 fpm
Absolute Ceiling
MAE 278
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Ceilings
(2)
The ceiling is the altitude at which R/C has
reached some minimum value
Absolute Ceiling
Is defined as the altitude
Power
(2)
How power required varies with drag
P O W E R R E Q U IR E D , (h o r s e p o w e r )
5000
A IR P L A N E D A T A
W = 1 5 ,0 0 0 lb s
b = 4 0 ft
e = 0 .8 2 7
S ea Level
4000
f = 1 0 .8 s q . ft.
f = 7 .2 s q . ft.
3000
M in im u m P o w e r R e
Total Drag Coefficient
Adding the induced drag to the profile drag gives
total drag
2
CL
C D cd
eAR
This expression gives the total drag coefficient for a
finite (3D) wing at subsonic speeds
The profile drag coefficient (cd) can be obtained from
Appen
Correction for Compressibility
The Prandtl-Glauert Rule
Cp
C p ,0
2
1 M
Substituting cp values into the Prandtl-Glauert correction
equation into the cp definition
1 c C p ,l C p ,u 0
1
1 c
cl
dx
C C p ,u dx
0
0
0 p ,l
2
2 c
c
1 M
1 M
Remember, the s
Force/Moment Coefficients
(1)
Now we define the airfoils section lift coefficient
1
cl
Z
M
2
e
1
Re
c
f
1
2
L V Sc l
2
Or we could have simply defined lift coefficient as
L
cl
qS
Notice that cl is dimensionless
It is represented as a functio
Energy Approximation
dh
dV
and
0
dt
dt
Es AND Ps
*APOLOGIES TO
SCHULTZ
MAE 278
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Performance Models
Point-mass approximations suffice for static
performance problems
Breguet equations provide performance estimates
A combination of graphical and analyti
Elements of Stability And Control
Body-fixed coordinates
The CG location is chosen as the origin of the xyz coordinate
frame
U
It is fixed to the airplane
xz is a plane of symmetry
u, v, w are linear
velocities
p, q, r are angular
velocities
L, m,
Component Buildup
(2)
Wing-body contribution to Mcg
Lwbsin wb
(h - hacwb ) c
Lwb
Lwbcos wb
Dwb
Mac,wb
Wing/body
zero lift line
Dwbsin wb
wb
zc
Dwbcos wb
V
M cg M ac , wb Lwb cos wb h hacwb c Lwb sin wb zc
Dwb sin wb h hacwb c Dwb cos wb zc
MAE 278
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Com
Absolute Angle of Attack
R E L A T IV E W IN D
G
Consider a wing
producing no lift
C
L
a = 0
R E L A T IV E W IN D
C
L
G
a = | L O |+ G
G
a
MAE 278
Now consider the
same wing producing
lift
1
FORCES AND MOMENTS
(1)
Equilibrium = Trim
Wing
Lift
Tail
Lif
Aerodynamic Efficiency
(1)
Lift/Drag ratio is a measure of aerodynamic efficiency
It indicates the ability to produce lift without generating
excessive drag
L /D
MAX L/D
0.3-0.4
12.8
26
(L /D )
VEHICLE
GEMINI
T-38
SAILPLANE
Character of drag
CL
2L
2
V
Rate of Climb
(1)
Now lets analyze a steady climb
Forces include a gravity component now
T D W sin D W sin
L W cos W cos
V
is more
commonly
used for
flight path
angle
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Rate of Climb
(2)
For low climb angles (up to about 20):
We can assume c
Airfoils
(1)
An airfoil is a section of a wing (or a fin, or a
stabilizer, or a propeller, etc.)
Cambered
Symmetrical
Laminar Flow
Reflexed
Supercritical
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Airfoils
(2)
Nomenclature
Chord line
Straight line connecting
the LE and TE
Mean cambe
Pitot-Static Equations
(1)
FLOW WITH
VELOCITY V1
TOTAL
PRESSURE
MEASURED
HERE
STATIC PRESSURE ORIFICE;
p IS MEASURED HERE
DIFFERENTIAL
PRESSURE GAGE
PITOT TUBE
The total pressure is: (Bernoulli)
Total Pressure
Static Pressure
p0 p
1 2
V
2 1
Solving for
B.L. Computations Laminar Flow
(1)
We seek the thickness of a laminar boundary
layer at some point X along the one-dimensional
flow over a flat plate
Reynolds number is defined as:
Experiments have shown that:
Substituting the definition of Re
V x
Re
Viscous Flow
Accounting for viscous friction
Frictionless flow
The streamline right on the surface
slips over the surface
Viscosity
Affects the resultant momentum exchange between
layers of fluid
Shear stress results
The shear stress
Is proportiona
Thermodynamic Processes
So far, we have only considered two thermodynamic
processes:
Constant volume processes
Constant pressure processes
Other important processes defined:
Adiabatic: a process in which no heat is added or taken
away
Reversible: on
Design of Flight Vehicles
Four major disciplines are involved
Aerodynamics
Flight Dynamics
Propulsion
Performance
Stability and Control
Engines
Structures
Stress and strain
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Basic Aerodynamics
MAE 434
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Overview
Aerodynamics defined as:
The dynam
Physical Principles
Conservation of mass
Leads to the continuity equation
Different for compressible or incompressible
Conservation of momentum
Comes from Newtons 2nd Law: F = ma
Leads to Eulers Equation (compressible or
incompressible)
Leads to Be
Atmosphere and Flight
Air-breathing vehicles depend on the atmosphere
Some vehicles do better with no atmosphere
Others are hybrids
MAE 278
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Standard Atmosphere
A standard atmosphere is a mathematical model which,
on average, approximates the real at
Introduction to
Aerospace Engineering
MAE278
Fall2014
MAE 278
1
Course Overview
Objectives
Motivate each of you to enjoy the Aerospace Engineering
profession.
Introduce you to all facets of Aerospace Engineering.
Be available to mentor you.
Pace of course
RANGE AND ENDURANCE
(7)
PROPELLER-DRIVEN AIRPLANE
To maximize range
L W0
R
ln
c D W1
Increase propeller efficiency,
Choose cruise propeller
Use a constant speed propeller
Reduce specific fuel consumption
Use optimum fuel/air ratio (mixture control
Landing Roll
(1)
The landing roll is very similar to the takeoff ground
roll, except:
Thrust = 0 (or near zero)
The sign of the acceleration is negative
dV
D r W L average m
dt
We seek an approximate expression like
STO for landing, again
using an av