Chapter 1 - Terminology in Aerodynamics.pdf

CHAPTER 1:Terminology in aerodynamics
Compiled by: Ahmad Hussein Abdul Hamid 1

Pressure and Velocity

What is Aerodynamics?
“A branch of dynamics that deals with the
motion of air and other gaseous fluids, and
with the forces acting on bodies in motion
relative to such fluids” – Webster’s
Dictionary
https://www.grc.nasa.gov/www/k-12/airplane/foil3.html

Energy
• Definition: Energy is the ability to do work.
• Energy cannot be created or destroyed. We can
only change its form.
• A fluid in motion has (mainly) two forms of energy:
• kinetic energy (velocity),
• potential energy (pressure).
• PRESSURE:
total, stagnation, static, dynamic, atmospheric,
gage, absolute

Pressure
𝑃absolute = 𝑃gauge + 𝑃𝑎𝑡𝑚
Gauge pressure is positive for pressures above
atmospheric pressure, and negative for
pressures below it

The Venturi Tube and Bernoulli’s Principle
Bernoulli's equation
𝑃total =
1
2
𝜌𝑉2 + 𝑃 + 𝜌𝑔𝑧 = constant
dynamic pressure
static pressure
hydrostatic pressure
𝑃stagnation =
1
2
𝜌𝑉2 + 𝑃
(a) Applies to inviscid, incompressible flows
only.
(b) Holds along a streamline for a rotational
flow.
(c) Holds at every point throughout an
irrotational flow (outside boundary
layer).

The Venturi Tube and Bernoulli’s Principle
By the continuity equation the
speed at station 2 V2 is greater
than that at station 1 V1 - the
speed at the throat also is the
highest speed achieved in the
venturi tube.
By Bernoulli's equation the total
pressure Pt is constant everywhere
in the flow (assuming irrotational
flow).

Pitot Tube and Velocity Measurement

Forces and Moments of an Airfoil

Surface Pressure and Shear Stress
• At first glance, the generation of the aerodynamic
force on a giant Boeing 747 may seem complex,
especially in light of the complicated three-
dimensional flow field over the wings, fuselage,
engine nacelles, tail, etc.
• However, no matter how complex the body shape
may be, the aerodynamic forces and moments on
the body are due to the only two basic sources:
1. Pressure distribution over the body surface
2. Shear stress distribution over the body surface
p acts normal to the surface, and
τ acts tangential to the surface.

Resultant Aerodynamic Forces
The net effect of the p and τ distributions integrated
over the complete body surface is a resultant
aerodynamic force R and moment M on the body.

Components of Aerodynamic Forces
In turn, the resultant R can be split into components, either normal and axial forces,
or lift and drag.

Sign Convention for Aerodynamic Forces and Moments
Front view
Top view
Side view

Moments Reference Points
The aerodynamic moment exerted on the body depends on the point about which
moments are taken.
• Leading edge: the foremost edge of an airfoil section.

moments are taken.
• Quarter chord point: a point one-fourth of the chord length from the leading
edge.
c
0.25c

moments are taken.
• Center of pressure: a point on the body about which the aerodynamic
moment is zero.
• Aerodynamic center: a point on an airfoil where aerodynamic moments are
independent of angle of attack
• Center of gravity : a point on an airfoil about which the moment due to gravity
forces is zero.

Aerodynamic Moments
The center of pressure is
a point on the body
about which the
aerodynamic moment is
zero.

Center of Pressure for Symmetric Airfoil
• The center of pressure is at the quarter-chord point for a symmetric
airfoil.
• The moment about the quarter chord of a symmetric airfoil is zero for all
values of α. Hence, for a symmetric airfoil, we have the theoretical (thin
airfoil theory – will be covered in Chapter 3) result that the quarter-chord
point is both the center of pressure and the aerodynamic center.
Quarter-chord point ≡ Center of pressure ≡ Aerodynamic center

Center of Pressure for Asymmetric Airfoil
The Centre of Pressure keeps moving forward when the
angle of attack increases due to the increased lift at the
upper surface of the forward part of airfoil.
When the stall occurs, the lift
force at the upper surface of
the forward part of airfoil is
now “lower”, the center of
pressure moves backward.

Aerodynamic Center
• As discussed in the previous slide, the location of the
center of pressure moves significantly with a change in
angle of attack and is thus impractical for aerodynamic
analysis.
• Instead the aerodynamic center is used and as a result
the incremental lift and drag due to change in angle of
attack acting at this point is sufficient to describe the
aerodynamic forces acting on the given body (since
moment is independent of AoA).
• NACA has chosen the systems of reporting lift, drag,
and moments about either the quarter-chord point or
the aerodynamic center due to the above-mentioned
reason.

Aerodynamic Center
• Aerodynamic center does not vary with angle of attack.
• For subsonic airfoils, xac ≈ c/4
• For supersonic airfoils, xac ≈ c/2
where c is chord.

Dimensionless Force and Moment Coefficients
S = planform area
l = mean chord length
For a circular cylinder:
where

Dimensionless Force and Moment Coefficients
For a two-dimensional body, the forces and
moments are per unit span. For these two-
dimensional bodies, it is conventional to
denote the aerodynamic coefficients by
lowercase letters, i.e.
where S = c(1) = c. The primes on L, D and
M denote force per unit span.
Two additional dimensionless quantities
of immediate use are
where p∞ is the freestream pressure.

Drag

What is Drag?
❑Aerodynamic force that opposes an aircraft’s motion
through the air, caused by interaction and contact of a solid
body with a fluid
❑Aerodynamic friction
❑Aerodynamic resistance to motion
❑Depends on wing shape, angle of attack, effects of air
viscosity and compressibility

How Bad is Drag?
According to The New York Times, American and Southwest
Airlines have taken to scrubbing a few jet engines every night to
eliminate the drag caused by dirt and debris. The process has
saved Southwest $1.6 million in fuel costs since April. American
predicts the practice will shave $330.7 million (3.5%) from its
$9.26 billion fuel bill this year (2008).
https://www.nytimes.com/2008/06/11/business/11air.html

Drag
Total Drag
Induced Drag
Parasite
Drag
Profile Drag
Skin Friction Drag Form/Pressure Drag
Interference
Drag
Wave Drag
Total drag = Induced drag + Skin friction drag + Form drag + Interference drag + Wave drag
Can exists even in an
idealized, inviscid fluid
Due to viscous effect

Profile Drag
The skin friction drag Df and the pressure drag Dp (due to flow
separation) are due to viscous effects.
The sum of these two viscous-dominated drag contributions is
called profile drag.
At moderate angle of attack, the profile drag coefficient for a
finite wing is essentially the same as for its airfoil sections.

Skin Friction Drag
Skin friction is the force between the free stream air and any
object passing through it. An example of this is the boundary
layer of an airfoil. The magnitude of skin friction depends upon:
1) The surface area of the aircraft
2) The nature of the boundary layer –i.e. laminar or turbulent
flow
3) The nature of the surface – i.e. smooth or rough
4) Airspeed (Reynolds number)
As the surface roughness increases, the point of first occurrence
of turbulent flow will move upstream along the airfoil. The
Reynolds number and surface roughness are dependent of each
other and both contribute to the determination of the laminar
to turbulent transition. A very low Reynolds number flow will be
laminar even on a rough surface and a very high Reynolds
number flow will be turbulent even though the surface of a body
is highly polished.

Form/Pressure Drag
❑ Form drag is caused by the shape of the airfoil created
when the airflow is separated from the airfoil. This can
be thought of as the turbulent wake vortices that are
created after the air has separated from an airfoil.
❑ The magnitude of form drag is measured by the pressure
differential from in front and behind a moving object.
❑ If a flat plate is placed perpendicular to the airflow in a
wind tunnel: The air must flow around the plate creating
a disturbance. Once the air has passed the plate, the air
separates and form drag is produced

Streamlining to Form Drag
❑ The best way to reduce form drag is by streamlining
shapes on an aircraft.
❑ By streamlining shapes is prevents large changes in
the shape of the object and therefore reducing the
vortices.
❑ A reduction in vortices = a reduction in form drag. This
can be measured by the fineness ratio of an airfoil.
❑ For the best results, the ratio should be about 4:1.
This depends on the intended speed range of use.

Skin Friction vs Form Drag: Shape effect

Skin Friction vs Form Drag: Re effect
❑ At a very high Reynolds number (applications such
as cars and airplanes – see next slide) , the
boundary layer becomes turbulent and therefore
delays separation.
❑ The separation point moves further downstream
of the body and the size of the wake reduces.
Consequently there is a sudden drop in form drag.
❑ On the contrary, skin friction drag will increase
due to increased wetted surface and turbulent BL
(see next two slides).
❑ However, at this high Reynolds number, form drag
plays more significant role than skin friction drag.
❑ Therefore the priority is to reduce form drag.
Constant drag coefficient due to fixed
separation point

Typical Reynolds number

Skin Friction Drag vs Local Re

Flight of a Golf Ball

Interference Drag
❑ It is noted that the drag for a wing-body combination
is usually higher than the sum of the separate drag
forces on the wing and the body, giving rise to an
extra drag component called interference drag.
❑ Interference drag is caused by the interference of
airflow between parts of an airplane (wings and
fuselage or fuselage and empennage).
❑ Interference drag can comprise contributions from
induced drag, shock drag, and viscous drag.

Induced Drag
❑ Induced drag is associated with the difference in
pressure that exists above and below a wing and
occurs even in inviscid flow. As airspeed decreases,
an airfoil must produce an increased low pressure
above the wing, and an increased high pressure
below the wing.
❑ These pressures meet at the wingtip and form a
vortex. The greater the pressure differential, the
greater the vortices are at each wingtip, and the
greater the drag will be.

Minimizing Induced Drag
❑ Induced drag is inversely proportional to aspect ratio.
❑ To reduce the induced drag, we want a finite wing with
the highest possible aspect ratio.
❑ Unfortunately, the design of very high aspect ratio wings
with sufficient structural strength is difficult.
❑ Therefore, the aspect ratio of a conventional aircraft is a
compromise between conflicting aerodynamic and
structural requirements.

Induced vs Parasite Drag
Induced drag is about 25 percent of the total drag at
cruise, but can be 60 percent or more of the total drag
at takeoff (where the airplane is flying at high CL ).

Wave Drag
Wave drag is produced by the presence of shock waves at
transonic and supersonic speeds. It is the result of both
direct shock losses and the influence of shock waves on the
boundary layer.

Drag Breakdown
• The figure on the right shows the drag
breakdown of transport aircraft in
cruise.
• It clearly shows that both lift induced
drag and viscous drag contributed most
to the total drag.

Drag Breakdown
• The figure on the right shows typical drag breakdowns
for five different airplanes.
• It is seen that the wing and fuselage constitute the
largest drag contributions in these airplanes.
• This is to a significant extent due to the large amount of
wetted area of these components.
Learjet M25 Citation 550 Cessna 340
Piper Arrow Cessna 150

Lift

Lift
NASA software you will use in your
homework assignment
https://www.grc.nasa.gov/www/k-12/airplane/foil3.html

Lift Generation
Lift can be generated through:
1. Buoyancy and Archimedes principle
(Balloons)
2. Flapping and Newton’s third law (Birds)
3. Airfoils and Bernoulli + Newton’s third
law (Airplanes)

Lift Generation of an Airfoil
Lift, unlike drag, would exist in a frictionless world. This is due to the fact that lift is created by the surface
pressure distribution; i.e. an inviscid phenomenon. Generally, the generation of lift can be explained by
i. momentum theorem and
ii. Bernoulli theorem
i. Momentum Theorem
The momentum theorem explains lift as the consequence of a wing moving through a mass of air and giving it
a downward motion (see figure below). Since the mass of air is initially at rest, the downward motion means
the vertical speed of the air changes from zero to some finite value in a given amount of time. This, in turn,
means that a force will be generated in the opposite direction in accordance with Newton’s third law of
motion. The downward motion of the air is called downwash, and it represents the vertical speed of air behind
the wing.

Lift Generation of an Airfoil
The magnitude of this force can be estimated using Newton’s second law of motion. The second law of
motion states it is the rate of change of momentum of the mass of air that generates the force. The third
law states an equal force that acts in the opposite direction of the motion of the mass is also generated. It is
this force that we call lift.
ii. Bernoulli Theorem
The Bernoulli theorem postulates that lift is the consequence of the difference in pressure between the
upper and lower surfaces of an airfoil. Named after the Swiss mathematician Daniel Bernoulli (1700-1782),
the theorem stipulates there is a relationship between the pressure and speed of the fluid at a point and
along a streamline that goes through that point.
𝑃total =
1
2
𝜌𝑉2 + 𝑃 + 𝜌𝑔𝑧 = constant

Maximum Thickness and Thickness Distribution
Airfoil section Cl,max
NACA 2408 1.5
NACA 2410 1.65
NACA 2412 1.7
NACA 2415 1.63
NACA 2418 1.48
NACA 2424 1.3
• The maximum thickness and the thickness distribution strongly
influence the aerodynamic characteristics of the airfoil section as well.
• The data show that a low-speed airfoil has an optimum thickness for
maximizing the lift of the airfoil. In the case of the data shown on the
right, the optimum thickness to maximize Clmax is approximately 12%.
• For a very thin airfoil section, boundary layer separation occurs early.
As a result, the maximum section lift coefficient for a very thin airfoil
section is relatively small.
• The maximum section lift coefficient increases as the thickness ratio
increases from 8% of the chord to 12% of the chord.

Maximum Thickness and Thickness Distribution
Airfoil section Cl,max
NACA 2408 1.5
NACA 2410 1.65
NACA 2412 1.7
NACA 2415 1.63
NACA 2418 1.48
NACA 2424 1.3
• As the thickness ratio increases beyond 12% of the chord, the minimum
local pressure value becomes smaller (i.e. the maximum local velocity
to which a fluid particle accelerates increases as the maximum
thickness increases).
• As a result, the adverse pressure gradient associated with the
deceleration of the flow from the location of this pressure minimum to
the trailing edge is greater for thicker airfoil.
• As the adverse pressure gradient becomes larger, the boundary layer
becomes thicker (and is more likely to separate producing relatively
large values for the form drag).
• The separation phenomenon causes the maximum section-lift
coefficients for the relatively thick airfoil sections to decrease.

Vortex Lift
• Recent finding regarding vortex lift:
https://www.nature.com/articles/d41586-020-00418-5
• Votex lift definition:
https://en.wikipedia.org/wiki/Vortex_lift
• Good reference on vortex lift:
https://aviation.stackexchange.com/questions/21069/what-
is-vortex-lift

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