Table Of Content081 PRINCIPLES OF FLIGHT
© G LONGHURST 1999 All Rights Reserved Worldwide
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EDITION 2.00.00 2001
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EDITION 2.00.00 © 1999,2000,2001 G LONGHURST
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TABLE OF CONTENTS
© G LONGHURST 1999 All Rights Reserved Worldwide
Aerodynamic Principles
Lift
Drag
Stalling
Lift Augmentation
Control
Forces in Flight
Stability
High Speed Flight
Limitations
TABLE OF CONTENTS
© G LONGHURST 1999 All Rights Reserved Worldwide
Special Circumstances
Propellers
081 Principles of Flight
© G LONGHURST 1999 All Rights Reserved Worldwide
Aerodynamic Principles
Units
Systems of Units
Newton's Laws of Motion
The Equation of Impulse
Basic Gas Laws
Airspeed Measurement
Shape of an Aerofoil
The Equation of Continuity
Bernoulli’s Theorem
Aerodynamic Principles
Chapter 1 Page 1 © G LONGHURST 1999 All Rights Reserved Worldwide
1Aerodynamic Principles
Units
1.
In order to define the magnitude of a particular body in terms of mass, length, time,
acceleration etc., it is necessary to measure it against a system of arbitrary units. For example, one
pound (lb) is a unit of mass, so the mass of a particular body may be described as being a multiple
(say 10 lb), or sub-multiple (say ½ lb) of this unit. Alternatively the mass of the body could have
been measured in kilograms, since the kilogram (kg) is another arbitrary unit of mass.
Systems of Units
2.
There are a number of systems of units in existence and it is essential when making
calculations to maintain consistency by using only one system. Three well-known consistent systems
of units are the British, the c.g.s. and the S.I. (Systeme Internationale). These are illustrated in
Figure 1-1 below:
Aerodynamic Principles
Chapter 1 Page 2 © G LONGHURST 1999 All Rights Reserved Worldwide
FIGURE 1-1
Units of
Measurement
3.
The S.I. system of units is the one most commonly used. In this system, one Newton is the
force that produces an acceleration of 1 M/s² when acting upon a mass of 1 kg.
Newton's Laws of Motion
4.
The motion of bodies is usually quite complicated, involving several forces acting at the same
time as well as inertia and momentum. Before considering the Laws of Motion, as described by Sir
Isaac Newton, it is necessary to define force, inertia and momentum.
BRITISH
C.G.S.
S. I.
SYSTEM
LENGTH
Foot
Centimetre
Metre (m)
TIME
Second
Second
Second (s)
ACCELERATION
Ft/s²
C/s²
M/s²
MASS
Pound
Gram
Kilogram (kg)
FORCE
Poundal
Dyne
Newton (N)
Aerodynamic Principles
Chapter 1 Page 3 © G LONGHURST 1999 All Rights Reserved Worldwide
5.
Force is that which changes a body's state of rest or of uniform motion in a straight line. The
most familiar forces are those which push or pull. These may or may not produce a change of
motion, depending upon what other forces are present. Pressure acting upon the surface area of a
piston exerts a force that causes the piston to move along its cylinder. If we push against the wall of
a building a force is exerted but the wall does not move, this is because an equal and opposite force is
exerted by the wall. Similarly, if a weight of 1 kilogram is resting upon a table there is a force
(gravitational pull) acting upon the weight but, because an equal and opposite force is exerted by the
table, there is no resultant motion.
Force Can Be Quantified
6.
Where motion results from an applied force, the force exerted is the product of mass and
acceleration, or:
F= ma
Where: F = Force m = mass and a = acceleration
7.
Inertia is the tendency of a body to remain at rest or, if moving, to continue its motion in a
straight line. Newton's first law of motion, often referred to as the law of inertia, states that every
body remains in a state of rest or uniform motion in a straight line unless it is compelled to change
that state by an applied force.
Aerodynamic Principles
Chapter 1 Page 4 © G LONGHURST 1999 All Rights Reserved Worldwide
Momentum
8.
The product of mass and velocity is called momentum. Momentum is a vector quantity, in
other words it involves motion, with direction being that of the velocity. The unit of momentum has
no name, it is given in kilogram metres per second (kg m/s). Newton's second law of motion states
that the rate of change of momentum of a body is proportional to the applied force and takes place in
the direction in which the force acts.
9.
Newton's third law of motion states that to every action there is an equal and opposite
reaction. This describes the situation when a weight is resting upon a table. For a freely falling body
the force of gravity (gravitational pull), measured in Newtons , acting upon it is governed by:
F = mg
where g is acceleration due to gravity 9.81M/s², and m is the
mass of the body in kilograms.
10.
If the same body is at rest upon a table it follows that, since there is no motion, there must be
an equal and opposite force exerted by the table.
Motion with Constant Acceleration
11.
When acceleration is uniform, that is to say velocity is increasing at a constant rate, the
relationship between acceleration and velocity can be expressed by simple formulae known as the
equations of motion with constant acceleration. Under these circumstances velocity increases by the
same number of units each second, so the increase of velocity is the product of acceleration (a) and
time (t). If the velocity at the beginning of the time interval, (the initial velocity), is given the symbol
(u) and the velocity at the end of the time interval, (the final velocity), is given the symbol (v) then the
velocity increase for a given period of time can be expressed by the equation:
Aerodynamic Principles
Chapter 1 Page 5 © G LONGHURST 1999 All Rights Reserved Worldwide
v = u + a.t
12.
If it is required to calculate the distance travelled (s) during a period of motion with constant
acceleration, this can be done using the equation:
13.
By substitution, using the above two equations, it is possible to develop two more equations:
And:
These are the equations of motion with constant acceleration.
The Equation of Impulse
14.
Given that the momentum of a body is the product of its mass and its velocity it follows that,
providing mass and velocity remain constant, momentum will remain constant. A change of velocity
will occur if a force acts upon the body because:
s
1
2-- u
v
+
(
)t
=
s
ut
1
2--at2
+
=
v2
u2
2as
+
=
F
ma
=
Aerodynamic Principles
Chapter 1 Page 6 © G LONGHURST 1999 All Rights Reserved Worldwide
And therefore
15.
If the force acts in the direction of motion of the body for a period of time (t), the resultant
acceleration will cause a velocity increase from (u) to (v). This must also cause an increase in
momentum from (mu) to (mv). Combining the equations F = ma and v = u+at gives:
Which transposes to:
16.
The change in momentum (final momentum minus initial momentum) due to a force acting
on a body is the product of that force and the time for which it acts. This change in momentum
called the impulse of the force and is usually identified by the symbol J. Hence:
Or:
a
F
m----
=
v
u
t F
m----
�
�
�
+
=
Ft
mv
mu
–
=
J
Ft
=
J
mv
mu
–
=
Aerodynamic Principles
Chapter 1 Page 7 © G LONGHURST 1999 All Rights Reserved Worldwide
17.
This is the equation of impulse. The S.I. unit of impulse, being the product of force and time,
is the Newton second (Ns). NOT, it should be noted, Newton per second (N/s).
Basic Gas Laws
18.
The Gas Laws deal with the relationships between pressure, volume and temperature of a gas.
They are based upon three separate experiments carried out at widely differing times in history.
These experiments investigated:
(a)
The relation between volume (V) and pressure (P) at constant temperature (Boyle's
Law).
(b)
The relation between volume (V) and temperature (T) at constant pressure (Charles'
Law).
(c)
The relation between pressure (P) and temperature (T) at constant volume (Pressure
Law)
Boyle's Law
19.
Boyle's Law states that the volume of a fixed mass of gas is inversely proportional to the
pressure, provided that the temperature remains constant. In other words, if the volume of a given
mass of gas is halved its pressure will be doubled or, if its pressure is halved its volume will be
doubled, providing its temperature does not change.
20.
This may be expressed mathematically as:
P1V1
P2V2 or PV
cons
t
tan
=
=
Aerodynamic Principles
Chapter 1 Page 8 © G LONGHURST 1999 All Rights Reserved Worldwide
Charles' Law
21.
Charles Law states that the volume of a fixed mass of gas at constant pressure expands by 1/
273 of its volume at 0°C for every 1°C rise in temperature. In other words, the volume of a given
mass of gas is directly proportional to its (absolute) temperature, providing its pressure does not
change.
22.
This may be expressed mathematically as:
Pressure Law
23.
The pressure law is the result of experimentation during the nineteenth century by a professor
called Jolly and states that the pressure of a fixed mass of gas at constant volume increases by 1/273
of its pressure at 0°C for every 1°C rise in temperature. In other words, the pressure of a given mass
of gas is directly proportional to its temperature, providing its volume does not change.
24.
This may be expressed mathematically as:
V1
T1
------
V2
T2
------ or V
T----
cons
t
tan
=
�
�
�
=
P1
T1
------
P2
T2
------ or P
T---
cons
t
tan
=
�
�
�
=
