Name: Trinh Ngoc Thanh
Student ID: 2052709
Week 1 - Chapter 1
Exercise
1.
 The relationship between pressure, temperature, density of the atmosphere
relative to altitude can be expressed via following equations.
Temperature:
θ=
T
B
=1−h
T
T
In which:
T: ambient temperature (K)
T : sea - level temperature (K)
h: altitude (m)
B: Earth’s lapse rate (B = 0.0065 K/m)
Pressure:
δ=
P
=θ
P
In which:
P: ambient pressure (Pa)
P : atmospheric pressure at sea - level (Pa)
g: gravitational acceleration (g = 9.806 𝑚⁄𝑠 )
B: Earth’s lapse rate (B = 0.0065 K/m)
R: gas constant of air (R = 287 𝐽⁄𝑘𝑔 ∙ 𝐾 )
Density:
σ=
ρ
=θ
ρ
In which:
ρ: ambient air density (kg/𝑚 )
ρ : air density at sea - level (kg/𝑚 )
g: gravitational acceleration (g = 9.806 𝑚 ⁄𝑠 )
B: Earth’s lapse rate (B = 0.0065 K/m)
R: gas constant of air (R = 287 𝐽⁄𝑘𝑔 ∙ 𝐾)
Speed of sound:
a=
γRT
In which:
γ: specific heat of air (γ = 1.4 for air)
R: gas constant of air (R = 287 𝐽⁄𝑘𝑔 ∙ 𝐾)
T: ambient temperature (K)
 At sea - level, we have several numbers to memorize:
T = 288.15 K
P = 101325 Pa
ρ = 1.225 kg/𝑚
B = 0.0065 K/m
R = 287 𝐽⁄𝑘𝑔 ∙ 𝐾
a = 340.2626 m/s
 Airliners typically operate at 10000 m (in cruising conditions), under which:
T = 223.3 K
P = 26200 Pa
ρ = 0.4136 kg/𝑚
a = 299.8 m/s
 Airliners cruise at that altitude for a number of reasons:
─ Low air density and high engine performance and efficiency: The higher
it is, the lower the density of air at that altitude. This means less drag
and the plane can operate much more efficient here. This allows the
plane to be much more fuel efficient. This means a lot for an airline in
optimizing cash flow and maximizing profit.
─ Avoidance of hazardous weather conditions: Flying at this altitude
means that the plane can ignore negative weather conditions, in
example: Storm.
─ Vertical clearance: This cruising altitude also allow more vertical space
for air traffic control personals to operate and direct a large number of
planes in the air. Moreover, in case of emergencies, higher cruising
altitude means much higher energy for the plane to glide to safety,
which also means more time for the pilots to consult checklists and
support from ATC or any actions to save the aircraft.
 Examples of operating characteristic of Airbus A340 - 600 and Boeing
B777 - 300:
Airbus A340 - 600:
Boeing B777 - 300:
2.
Using this image as a reference:
Lets analyse each picture.
In the first one, we are looking directly at the front view of this aircraft. If we
look at the wing, it is quite noticeable that the wing is not built perfectly
horizontal but it point up a little at a certain angle. This angle is called dihedral
angle, or góc nghiêng in Vietnamese.
The second picture presents the top view of this aircraft. There are a lot of
things to discuss about in this picture. Looking at the wings of this aircraft, the
first thing we notice is that the wing is swept back a certain angle, this angle is
called wing sweep (Λ) or góc quét in Vietnamese. Looking at the wing from
North to South, the first boundary (line) we encounter is called the leading
edge (cạnh trước) in contrast to the trailing edge (cạnh sau), the last boundary
(line) we encounter. The leading edge of the wing is the first part of the wing
that encounter fluid flow and the trailing edge is where the flow exits the wing
surface. The distance from the leading edge to the trailing edge is called the
chord line (c) (dây cung cánh) while the distance from one wing tip to the other
is called wing span (b) (sải cánh). The wing area is denoted as A. The ratio of
wing span over chord line is called the aspect ratio (AR). We express this
relationship as AR = 𝑏 𝑐 . In case the aircraft has a rectangular wing, this
expression can be rewritten as AR = 𝑏 𝑐 = 𝑏 × 𝑏 𝑐 × 𝑏 = 𝑏 𝐴. If we consider
the ratio of the chord line at the wing tip over the chord line at the wing root,
we call this ratio as taper ratio. These terms is illustrated in the picture shown
below, which will also be used to describe the third picture above (the
wingspan in the illustration below is denoted as s instead of b like i described
above):
Considering the third picture, which is the side view of the wing, we can notice
several characteristics. First, the wing of an airplane is not flat, but rather it has
significant thickness and a weird shape to it.The bend of the wing, or rather the
significance of the bend - the maximum distance between the upper bend of the
wing and the chord line - is called the camber, and the changes in camber at
each coordinate respectively to the chord line is called the mean camber line.
For a clearer look at the side view, this picture might show exactly that. The
overall shape of the side view of the wing is called the airfoil.
The meanings behind the 4 - digit and the 5 - digit NACA wing family:
NACA 4 - digit series:
 First digit describing maximum camber as percentage of the chord.
 Second digit describing the distance of maximum camber from the airfoil
leading edge in tenths of the chord.
 Last two digits describing maximum thickness of the airfoil as percent of
the chord.
For example: NACA 2412
Number ‘2’ means: Max camber is 2% of the chord or 0.02 x c.
Number ‘4’ means: The location of of max chamber on the chord line, 4
signifies 40% so it actually is 0.4 x c.
Number ‘12’ means: Thickness according to the chord line, 12% of c.
NACA 5-digit series:
 The NACA five-digit series describes more complex airfoil shapes. Its
format is L - P - S - T - T, where:
 L: a single digit representing the theoretical optimal lift coefficient at ideal
angle of attack 𝐶 = 0.15 x L.
 P: a single digit for the x coordinate of the point of maximum camber (max.
camber at x = 0.05 P).
 S: a single digit indicating whether the camber is simple (S = 0) or reflex (S
= 1).
 TT: the maximum thickness in percent of chord, as in a four - digit NACA
airfoil code.
For example: NACA 36015
Number ‘3’ is L so 𝐶 = 3 x 0.15 = 0.45.
Number ‘6’ is x = 0.05 x 6 = 0.3 , so maximum camber is at 0.3 x c.
Number ‘0’ means camber is simple.
Number ‘15’ is the maximum thickness as percentage, here it means 15%
of the chord line.