5.11 WAVE DRAG (AT SUPERSONIC SPEEDS)
When M is supersonic, shock waves begin to form.
Wave drag is created by supersonic flow.
o Due inherently to the pressure increase across a shock wave.
o To minimize the strength of the shockwave, all supers
Chapter 8 Space Flight (Astronautics)
8.3 LANGRANGES EQUATION
d B B
dt q1 q1
d B B
dt q2 q2
d B B
dt q3 q3
8.4 ORBIT EQUATION
, with G 6.67 1011 m3 kg s
7.12 CONCEPT OF STATIC LONGITUDINAL CONTROL
In order for an airplane to change its velocity and still remain balanced, the only way for
this to be accomplished is to effectively change the moment coefficient curve for the
Effect of elev
7.7 CONTRIBUTION OF THE TAIL TO Mcg
Two interference effects influence the tail aerodynamics:
o The airflow at the tail is deflected downward by the downwash due to the finite
wing; that is, relative wind seen by the tail is not in the same direc
7.4 ABSOLUTE ANGLE OF ATTACK
Absolute Angle of Attack: a
o When the absolute angle of attack is not, then the lift is not, no matter what the
camber of the airfoil.
7.5 CRITERIA FOR LONGITUDINAL STATIC STABILITY
CHAPTER 7 Principles of Stability and Control
While airplane performance is governed by forces along and perpendicular to the flight
path, airplane stability and control is governed by moments about the center of gravity,
o Dynamic Deals with the time history of the vehicles motion after it initially
responds to its static stability.
When an airplane is flying at an angle of attack such that its moments
about the center of gravity are zero, the airplane is therefore in eq
FOR A PULL-UP MANEUVER
g n 1
g n 1
FOR A PULL-DOWN MANEUVER
g n 1
g n 1
Airplanes with lower wing-loadings will have smaller turn radii and larger turn rates.
Minimum Turn Radius:
2 1 CL1 2
W01 2 W11 2
S ct CD
Maximum range for a jet airplane occurs when:
o Minimum thrust-specific fuel consumption ct .
o Maximum fuel weight W f
o Flight at maximum CL CD
o Flight at high altitudes so that is low.
6.14 RELATIONS BETWEE
6.12.3 Breguet Formulas (Propeller-Driven Airplane)
Breguet Range Formula:
o Provides a quick, practical estimate for range that is generally accurate by 10-20%.
To maximize the range for a reciprocating engine, propeller-driven airpla
8.6 KEPLERS LAWS
Keplers First Law: A satellite describes an elliptical path around its center of attraction.
Keplers Second Law: In equal times, the areas swept out by the radius vector of a satellite
are the same.
Keplers Third Law: The periods of any t
8.8 SOME ORBITAL MANEUVERS
The orbit or trajectory of a spacecraft is uniquely determined by the conditions at burnout
of the rocket booster. The motion of a spacecraft after burnout is at the mercy of
gravitational force, and its flight path bec
CHAPTER 9 - Propulsion
The net thrust of a propeller engine is defined as T L cos Dsin where .
P , where P is the shaft brake power, and PA is the
power available from the propeller.
o 1 always be
5.16 SWEPT WINGS
When the wings of subsonic aircraft are swept, we delay drag divergence to higher
M for airfoil
M cr for airfoil < Actual M cr for swept wing < cr
, where is the degree of sweep.
This is caused by the fact th
5.14 CALCULATION OF INDUCED DRAG
Induced Drag The difference in the actual drag and the imaginary drag component
resulting from the force directly perpendicular to the free-stream velocity.
Di L sin i Li because the values of i are generally smal
5.9 CRITICAL MACH NUMBER AND CRITICAL PRESSURE COEFFICIENT
Critical Mach Number The free-stream Mach number at which sonic flow is first
obtained somewhere on the airfoil surface.
o Important because at some Mach number greater than the critical
CHAPTER 6 Elements of Airplane Performance
6.1 INTRODUCTION: THE DRAG POLAR
The airplane is considered a rigid body on which four natural forces are exerted: lift, drag,
propulsive thrust, and weight.
6.2 EQUATIONS OF MOTION
Disadvantages of solid propellants compared to liquid propellants:
o The specific impulse of solid propellants is considerably less than that of liquid
propellants. Generally the specific impulse of solid rockets ranges from 200 to 300 s.
o Once a solid r
CHAPTER 5 Airfoils, Wings, and Other Aerodynamic Shapes
5.2 AIRFOIL NOMENCLATURE
Airfoil The cross-sectional shape obtained by the intersection of the wing with a
Mean Camber Line The locus of the points halfway between the u
9.8 ROCKET ENGINE
Rocket engines are different than other engines because they carry both the fuel and the
oxidizer, and so it is completely independent of the atmosphere for combustion, which
means it can operate in the vacuum of space.
T m fuel
9.6 TURBOFAN ENGINE
A turbofan is a turbojet engine that has a large ducted fan mounted on the shaft ahead of
the compressor. The turbine drives both the fan and the compressor.
o The ducted fan accelerates a large mass of air that flows between
, where b is the bore (girth) size and s is the shaft (length) size.
o Girth is more important than length.
mech rpm dpe
A supercharger compresses the incoming air before it reaches the intake manifold,
Rate of Climb:
R C V sin
TV DV excess power
o Excess Power: A R
6.9 GLIDING FLIGHT
When gliding, the plane has no thrust.
D W sin , L W cos
and the equilibrium flight angle is tan
6.10 ABSOLUTE AND SER
5.3 LIFT, DRAG, AND MOMENT COEFFICIENTS
Variations of L, D, and M depend on a variety of factors
o Free stream velocity V
Free stream density
Size of the aerodynamic surface S
Angle of attack
Shape of the airfoil
o Viscosity coefficient
6.5 POWER REQUIRED FOR LEVEL, UNACCELERATED FLIGHT
Power is the energy per unit time.
Work is the force multiplied by the distance through which the force moves.
SCL CL CD
CD ,0 13 CD,i
6.6 POWER AVAILABLE AND M
Homework 1. Introduction to Flights.
Problem 2.1. Introduction to Flights, by Anderson
Note: Temperature is in Kelvin. If the temperature was given in Celsius, you had to convert it to Kelvin.
Temperature in Celsius = Temperature in Kelvin + 273.15
Homework 2. Introduction to Flights.
An F-15 supersonic fighter is in a rapid climb, passing through a standard altitude of 8 km, with
a rate of climb of 150 m/s (the rate of change of altitude).
(a) Calculate the ambient pressure and temperature