Table of Contents
1. Introduction. 4
2. Literature Review.. 7
Airfoil 7
CFD.. 8
Flow
around airfoil 8
Lift
and drag optimization. 10
Lift/Drag. 11
Jet
Aircraft/Propeller Aircraft 11
Slow-speed
flight 11
Maneuvering
Performance. 12
Lateral
stability and control 12
3. Computational Modeling. 13
Methodology. 13
4. Results. 16
5. Discussion. 18
Influence
of Angle of Attack Optimization. 19
Influence
of Camber Optimization. 20
6. Conclusion. 20
7. References. 21
Introduction of Optimization of
thickness of an airfoil by Computational simulation
In a world where we seem to have little to no time, we are always
seeking out opportunities to increase efficiency. A main concern which consumes
a lot of our time is travelling. Flight is the most efficient mode of transport
for covering long distances in a short amount of time. Aeroplanes are the most
common mode of flight transportation. Despite this, the engineering behind the
plane is commonly overlooked, from the aerodynamics of the flight to the effect
of the tail on the direction of the plane. The question is then raised, is
there small changes in these vast engineering marvels that could make our
flight more efficient.
The inspiration behind this report stems from the great works of Abbas
ibn Firnas, a scholar from the Andalusia period. His scientific studies helped
revolutionise the world, from designing a ‘mechanised planetarium’ to a ‘water
clock’. His work on clear glass contributed massively towards the development
of lenses for correcting eyesight. Despite all these accomplishments, what
inspired me most is his work on aviation. Attaching a flying contraption made
from bamboo to himself, he jumped off a cliff and stayed aloft for 10 minutes
before crash landing. Thus, as stated by Lynn Townsend White Jr., Firnas (Wikipdia, 2010), is best known as
being the first to demonstrate flight successfully. Having learnt from his
mistakes, Firnas wrote a book highlighting the significance of having an
appropriate landing mechanism for stability. This inspired many to develop
flight.
This report, will look at how a change of thickness of an aerofoil can
affect the flow around the aerofoil, it will specifically look at how the lift
and drag is affected under incompressible flow. Two 4 digit NACA aerofoils will
be chosen both with the same first 2 digits but different last 2 digits as this
is what determines the thickness of the aerofoil. Using computational fluid
dynamics to run these results, a sound conclusion will be determined.
An
aerofoil is a shape mainly used for wings of an airplane, but can also be used
for their tails or even on formula 1 cars. The aerofoil shape is considered the
optimum shape for aerodynamic travel and its main purpose is to produce lift
and drag. The official definition of an aerofoil according to (Airfoil, 2020) is “a body (such as an airplane
wing or propeller blade) designed to provide a desired reaction force when in
motion relative to the surrounding air”. Figure 1 shows an aerofoil and what
makes an aerofoil.
Aerofoil’s were not always the optimum shape they are now,
earlier aerofoils had a much shorter maximum thickness in when they were first
used for flight, as can be seen in figure 2. From 1919, the upper surface
curved out more, (Boyne, 2000) claims that during
this period of development the greatest height achieved was in the first third
of the chord. As time went on both the lower surface was starting to curve and
then greatest thickness moved more towards the centre of the aerofoil. After
this, the next problem was traveling at supersonic speed, in 1949 “The
Bell X-1 had broken the so-called "sound barrier," and both the Air
Force and the Navy were looking for next generation aircraft that could operate
at supersonic speeds”, (Wallace, 2001), in the 1950’s
Richard Whitcomb came up with the area rule, the purpose of the area rule also
known as the transonic area rule is “a design technique used to reduce an
aircraft’s drag at transonic and supersonic speeds” (Wikipedia, Area
Rule, 2020).In this report, I will be mainly
concerned with the NACA (National Advisory Committee for Aeronautics) airfoils.
These are specific airfoil shapes created for aircraft wings. Each wing is
different, and the shape can be identified by the set of numbers after NACA.
These numbers when inserted into an equation determine the cross section of a
specific wing. There are two main series of digits that follow “NACA”, 4-digit
series and 5-digit series. However, for this report I will be comparing only the
4-digit series airfoils Two 4
digit NACA aerofoils will be chosen both with the same first 2 digits but
different last 2 digits as this is what determines the thickness of the
aerofoil. Using computational fluid dynamics to run these results, a sound conclusion
will be determined.
The 4 digits define the profile by the following:
1st digit – describes max camber as a
percentage of the chord length
2nd digit – position of the maximum camber from the leading
edge as percentage of the chord length divided by 10,
3rd and 4th digit – the
maximum thickness as a percentage.
As an
example, I will use to explain this is NACA 6412:
The 6
tells us that the camber is 6% (0.06) of the chord length.
The 4
tells us that the maximum camber is 40% (0.4) of the chord length.
The 12
tells us that thickness is 12% (0.12) of the chord.
Literature Review of Optimization
of thickness of an airfoil by Computational simulation
Airfoil
According to the
author Sullivan
(2010), the aerodynamics as well as the Airfoils is the unique
characteristics of the Swept Wing aerodynamic; in which airfoil is a cross
section of a body which is placed in the airstream in order to create the
useful aerodynamic force in an efficient manner. Examples of the airfoils are a
Windmill blades, propeller blades as well as cross section of wings,
hydrofoils. The subsonic flow concepts is demonstrated the speed 50 m/s of the
wind tunnel. And the lift along with the drag coefficients for the symmetric
airfoils is attained through an analysis of the measured pressures which
distributes a various pressure taps in the surface of the airfoils (Koziel et al
, 2011).
Then the test of
the wind tunnel is conducted on the NACA 0012, NACA 0018, and airfoils. And the
drag along with the lift forces is acting on the every of the airfoils which is
successfully measured the velocity of the airfoils along with the attacks of
the airfoils.
The comparison of
the optimization of airfoil among the airfoils that are generated along with
the expected range of the drag as well as lift forces. More lift is expected in
the NACA 0012 airfoils where the correct theory is lifted to identify as well
as visually confirmed (Sullivan, 2010).
According to the
author Anitha et al (2018), it is conducted that
by the application of CFD( computational fluid dynamic) at a time, then an
absence which is reliable for the flow solver and that could also accurately predict
the difference viscous effect, turbulence and it often seemed the practicality
and reduced the empirical application for the optimized design of solutions. Thus
the practical application for their solution is also limited through the
unreliability of the CFD tools, and the studies which are reliable for flow
solver also have a big issue in the airfoil designs. By the availability of the
cutting edge design tools in the modern era, there are various errors among the
simulated as well as empirical results which become negligible. Thus the use of
the reliable flow of the slover like the XFOIL fro the single element of
airfoils (Anitha et al , 2018).
According to author Günel et al
(2016), it is conducted that Analysis of CFD for performance of
aerodynamics of airfoil were completed by utilizing ANSY-FLUENT. A FLUENT code
explains the RANS conditions utilizing limited volume discretization.
Consistent state solver, SIMPLE weight based solver as well as Green-Gauss cell
based discretization were utilized in this analysis. Likewise, second system
was utilized for the force and disturbance conditions discretization. While
applying a CFD investigation to airfoil at low Reynolds numbers, it is hard to
measure limit layer components with regular choppiness techniques. Therefore,
more error has been gotten in estimation of drag power. To acquire
progressively right expectation of drag power, change choppiness models are
increasingly appropriate. By SST k-w progress model of turbulence, the outcomes
were obtained. The assembly of the numerical arrangement was constrained by
observing numerical mistake of a arrangement. O-ring type area structure was
picked. An outer area is a circle which has a distance across of 25 m. It was characterized as
a limit state of "Speed Inlet". Airfoil bases as well as top surfaces
were characterized as "Divider" limit conditions. A space which is
characterized as air which has a thickness (ρ) of 1.225 kg/m3 and dynamic
consistency (μ) of 1.7894e-05 Pa s (Günel et al , 2016).
Flow around airfoil of
Optimization of thickness of an airfoil by Computational simulation
The characteristic
of the aerodynamic of the NACA0012 by the wing geometry at a very low Reynolds
number along with the angle of attacks which is also investigated by using the
numerical simulations along with the results that are validated through the
experiments (Sereez et al , 2016). A lift coefficient
is increased by the angle of attack where its units reach the maximum that is
the stall angle. In the angel attack the further increments and the decrement
of the lift coefficients until it reaches the minimum values. The fluid domain
that is generated around the rectangular by the wing geometry with respect to ratio,
as shown in the below figure 1. Whereas in the below figure the C-type grid is
used to generate a mesh around boundaries of the domain, and it is located the
20 chords away from the wing geometry that allows the developments of flow
around a wing (Eftekhari & et al, 2019).
Figure 1: Fluid
domain around the wing
The
characteristics of the lift of the NACA0012 in the subsonic tunnel. Various
velocities for the air which is observed in the different angles of attack by
the two-degree increments. The calculate the lift coefficients which is plotted
with each other along with the angel attacks and then compared the results. In the airplanes the primary features are
Airfoil, and it is also providing the lift. Then the airflow disturbances,
which are caused through the moving objects in the results of fluid and the
shear stress, which is acting on the said objects and the pressure distribution
in this object ( Rubel & et al, 2016).
In the flowing
fluid, the body is immersed for both viscous forces and pressure. The forces
sum which also acts the normal to a free stream in the direction lift as well
as the sum is also acted the free stream in the direction of drag. The dynamic
and geometric characteristic of the airfoil which is shown in the below figure;
Figure: dynamic
and geometric characteristic of the airfoil
Lift and drag optimization of
Optimization of thickness of an airfoil by Computational simulation
According to the author
Ai & et al (2016), it is conducted
that there are different methods to calculate the lift, whereas, in this
research of the lift forces L, the airfoil would be calculated by the
integrations of the measured pressure distribution over an airfoil surface. The
projection of an airfoil and pressure distribution of airfoil is normally shown
in the below figure;
Figure: Pressure
distribution on an airfoil
Lift/Drag of Optimization of
thickness of an airfoil by Computational simulation
Resultant of the
aerodynamics is a sum of the forces which are acting on an airfoil which is
placed in the flow. There are two components and the two forces where the
Resultant of aerodynamics is broken into it is the drag as well as lift.
Lift is
perpendicular to a relative of a wind that opposes the weight of the aircraft.
To a relative wind, Drag is the parallel
that opposes a forward movement of an aircraft.
In the above of
two forces, the action of one of two forces is to modify the aerodynamics
resultant which consequently affects the other forces (Ai & et al, 2016)..
Then the relationship of the drag
and a lift is shown below;
Jet Aircraft/Propeller Aircraft
of Optimization of thickness of an airfoil by Computational simulation
In the Jet
Aircraft, it is the type of aircraft that produced the forward forces on an
account that have high speed and exhaust the gases which are released from the
engine. The Jet aircraft is fixed with the wing aircraft, as well as with the
propelled by the engine. At the lower speed along with the attitudes, the
maximum efficiency of the engine is achieved in the propeller aircraft, whereas
the aircraft engine is automatically achieved the maximum efficiency. Jet aircraft
which is generally the cruise for the faster speed around about it has the 0.8
and the 981km of the altitudes by the aircrafts (Mukesh, 2014)
And in the
Propeller aircraft, it is the oldest type of the aircraft which driven the
piston of the engine along with the Turbo of the engine and has the various
difference of the construction features. The propeller aircraft which is the
aircraft that use the electrohydrodynamics that provides the thrust or the lift
without requiring the moving parts or the combustion of the engine.
Slow-speed flight
In most of the aircraft's, the airplanes maintain their
speed, which does not excess of the 1.3 times of the VSO of the instrument
approach. Aircraft are normally used the slowed which is the landing speed, and
it is the final approach, for the prior landing. As by the information of the
swept wings aerodynamics, the power as well as pitch coordination which is
needed due to the stability of the speed and it the comparatively neutral where
speed tends to remain a new value which is not returning for an original speed.
The precise
airspeed which is control, by the pilot and it’s normally changed the
configuration of the aircraft through the extending of the landing flaps. And
the variation of the configurations which means that the pilot and it must be
alert to unwanted the changes of pitch at the low attitude (Dole, 2016).
Maneuvering
Performance
Relationship and
its effect on aircraft design then the performance of the
Maneuverability/controllability is the aircraft quality which refers the
maneuvers easily as well as withstand the different stresses which is imposed
through the maneuvers. Performance of the Maneuverability/controllability which
is governed through the weight of the aircrafts , along with the size , inertia
as well as the location of the controls of the flights with the strength of the
structural plus the power plant. Performance of the Maneuverability/controllability
is includes in the design characteristics of the aircrafts.
Performance of the
controllability the aircraft capability which is responded to the control of
the pilot, especially by the regard of the flight path as well as the by the
attitude. Quality of the aircraft which is response the performance of the
controllability for the application of the pilot control when the maneuvering
of the aircraft is regardless controls the characteristics of the stability (pilotsofamerica.com, 2018).
Latera l stability and control
of Optimization of thickness of an airfoil by Computational simulation
In a Longitudinal
stability, which is the pitch of the stability, and its tendency of an aircraft
reduces the pitching along with the return for the level of the positions,
where unless it is countered through the elevators.
The roll of the
stability is the Lateral stability, which tendency is the to reduce the
aircraft for the return as well as for the rolling to the upright positions
unless which is continually maintained due to the positions of the ailerons (Lu, 2006).
Computational Modeling
of Optimization of thickness of an airfoil by Computational simulation
Methodology of Optimization of
thickness of an airfoil by Computational simulation
The method which is used in this
research study is the SST-k turbulence model which is the two equation
eddy viscosity model and it became very popular. A shear stress which is also transports
the SST formulation and combines by two worlds. The use of k formulation for the inner parts of the
boundary layer also creates the model directly which is usable for all methods
down and by the viscous sub layer, thus the SST- kmodel could also be
used by the Low-Turbulence model (Cfd-online, 2019).
The kinematics Eddy
viscosity is given below;
The segregated implicit
solver, ANSYS fluent which is used to simulate the problem. An airfoil profile
which is simulated the design modeler as well as boundary condition where the
meshes are created. By the help with a commercial CFD software
ANSYS
fluent, two dimensional airfoil of aerodynamics performances is simulated
numerically.
In this research we
supposed the flow around the fully parameterized NACA airfoil at the various
attack angles 4, 6 and 8 as well as also have the wide thickness of the
0.08 to 0.2 like the percent of chord. The optimization solver evaluates the
optimal geometry which order to maximize the lift to drag ratio (ZHANG et al ,
2016).
The SS-k model is similar;
If airfoil is positioned at a
dramatically increased angle of attack, the separation can occur at a point of
maximum thickness of airfoil as well as tremendous wake will grow behind a
point of separation. Due to this phenomenon a list is significantly reduced and
there can be condition of aerodynamic stall. In this condition, the aircraft
can further lose speed due the very high pressure drag caused the wake. The
wall of the boundary layers is approximately thick, where the test section is
the turbulence, and it is also measured less than the 0.12% over the tunnel on
the operating range. The downstream of a transition in the boundary layer
development as well as Reynolds’s numbers which also capture the local effect
of turbulence intensity (Sreejith & et al, 2018) . The following
governing equations;
Results
|
NACA 0012
|
NACA 0018
|
AOA
|
CL
|
CD
|
CL
|
CD
|
4
|
0.010225797
|
0.43895841
|
0.011555257
|
0.43194301
|
6
|
0.010871912
|
0.64242083
|
0.012891825
|
0.64644119
|
8
|
0.012786779
|
0.84848094
|
0.014747308
|
0.85728051
|
Discussion of Optimization of
thickness of an airfoil by Computational simulation
This study was conducted
by using the ANSYS fluent simulation software for a NACA airfoil. The airfoil
which is used is the asymmetrical structure as well as the airfoil is changing
the thickness along with also operating the Reynolds number. The drag as well
as lift coefficient is determined by using a same methods as well as graphs
which is generated for the drag and lift coefficient , and lift to drag ratio ,
pressure as well as distribution of velocity over the airfoil surface. At the
start the numerical analysis for the initial airfoil NACA 0018, and NACA 0012
is performed plus it also optimized the airfoil which is compared by the original
NACA 0012 (Muftah, 2019). The effect of the roughness
is maximum on lift and drag which is increases by increasing the airfoil
thickness as well as also decrease slightly by increasing the maximum lift. To
separate an effects of airfoil thickness as well as maximum lift coefficient,
two of the airfoils (NACA 0012 and NACA 0018) have a common maximum lift
coefficient and two (NACA 0012 and NACA 0018) have a common airfoil thickness (Somers ,
2005).
In the above
analysis experiment examine the errors in the experimental investigation, and
it is also discussed some basic theory which is necessary for the understanding
of the aerodynamic. Among the Sources of inaccuracy, the care is also taken as
distinguish, which is also emphasized by the physical understanding rather than
the analytical complexity.
By the errors the experimental
measurements which inevitably influenced, practical limitation of the types of
equipment like the minimum scale of the pressure gauge ( Higazy,
2019). The accuracy of the experiment is mostly
right; all the result is according to the theoretical calculation.
The drag equation is used by this where
the lower of the drag coefficient is also presented the object which has the
less aerodynamics and the hydrodynamics drag. Then the drag coefficient is
always connected by the particular surface of area.
Now a drag on the
cylinder is not zero, but it could also estimate for the measured pressure
distribution as in the below; Now suppose the cylinder element of surface of
cylinder where the length is . Now a force per the unit span on a different
element is due to the normal pressure;
Influence of Angle of Attack Optimization
Ratio of drag to lift of NACA was determined. As indicated
by results, Ratio of drag to lift increment with an expanding working Reynolds
number. Lift coefficient addition is relative to the Reynolds number
simultaneously as well as during process of optimization the most angle of
attack is related with low Reynolds number yet it isn't after 10 degree. A
performance gets most extreme at angle of attack is optimized and changing from
4.65 to 5.85 degree by with expanding Reynolds number. It very well may be seen
that all airfoils with various Reynolds number requires a positive approach (Srinath et al , 2010). Be that as it may,
with expanding Reynolds, the expansion in the enhanced lift coefficient and
lift to drag proportion turns out to be moderate when it is contrasted with
starting airfoils, and the drag coefficient increment simultaneously, and the
limit of drag coefficients are expanded in low rate with Re = 103 to 105
Influence of Camber
Optimization
Tool for the optimization of the airfoil likewise, in
contrasted as well as a past case, it should have an option to change a state of
the airfoil, it must have an option to straightforwardly to alter its outside
shape by change greatest thickness of airfoil to acquire an optimum camber as well as its situation along a chord
line. The research objective is to optimization of the airfoil that will be
utilized. Meanwhile a most extreme camber are mutually dependent as well as both have
been improved simultaneously. As the state of the airfoil changes, a stream
around it additionally changes, this prompts a rotated distribution of pressure
which thus alters an optimal design property of a model. Simply, a constrain
circulation are delicate to changes of geometry. As a camber expands an
inclination to upper surface limit layer division become progressively
noteworthy. It very well may be seen likewise as an ideal camber expanded, an
airfoil takes an asymmetry structure as well as is normally used to control its
zero - lift approach. In light of CFD optimization as well as modeling
technique, an airfoil was enhanced legitimately with a greatest lift to drag
proportion as a goal (Bu et al , 2013).
Conclusion of Optimization of
thickness of an airfoil by Computational simulation
Summing up all the
discussion, the report is about the optimization of airfoil of the
Aerodynamics, which have the different unique characteristics. Aerodynamics of optimization
of airfoil introduced the various concepts which are used in the aircraft, as
it mentioned in the above discussion. For a specific aspect ratio, an optimization
of airfoil structural span is lengthened by it which means that it requires a
heavier structure. Aerodynamics of optimization of airfoil specifications is
explained along with their role in the aircraft. The weight of optimization of
airfoil is raised even more for resisting the twist of aerodynamic which is
incurred during the process of bending. Finally, the numerical method is
applied to calculate aerodynamic characteristics of airfoils of different
relative thicknesses, to investigate the effects of relative thickness on
airfoil performance. Increasing the thickness will
increase the lift.
Increasing the area will increase the lift.
References of Optimization of
thickness of an airfoil by Computational simulation
Higazy, M. (2019). Analysis and Accuracy of
Experimental Methods. InternationalJournal of Petrochemistry and Research,
3(1).
Rubel, R. I., & et al. (2016). Numerical and
Experimental Investigation of Aerodynamics Characteristics of NACA 0015 Airfoil.
INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES, 2(4).
Afs.enea.it. (2019). 4.5.2 Shear-Stress Transport
(SST) $k$- $\omega$ Model. Retrieved from
https://www.afs.enea.it/project/neptunius/docs/fluent/html/th/node67.htm
Ai, Q., & et al. (2016). Experimental
investigation of aerodynamic performance of airfoils fitted with morphing
trailing edges. Conference: 54th AIAA Aerospace Sciences Meeting, 2-12.
Airfoil. (2020, May 02). Airfoil. Retrieved
from Merriem-webster: https://www.merriam-webster.com/dictionary/airfoil
Alper, A., McCall, A., Leyne , K., Fulton, N., &
Laird, W. (2012, December 02). Hydrofoil. Retrieved from University of
Strathclyde:
http://www.esru.strath.ac.uk/EandE/Web_sites/11-12/MORE/hydrofoil/introduction.html
Anitha et al , D. (2018). Air foil Shape Optimization
Using Cfd And Parametrization Methods. Materials Today Proceedings, 5(2),
5364–5373.
Boyne, J. E. (2000, January 12). Airplane.
Retrieved from Brittanica:
https://www.britannica.com/technology/airplane#ref64146
Bu et al , Y. (2013). Aerodynamic optimization design
of airfoil based on CST parameterization method. J. Northw. Polytech. Univ,
829–835.
Century of flight. (2005, November 14). Develpment
of aviation technology. Retrieved from Century of flight:
http://www.century-of-flight.freeola.com/Aviation%20history/evolution%20of%20technology/Airfoils.htm
Cfd-online. (2019). SST k-omega model.
Retrieved from https://www.cfd-online.com/Wiki/SST_k-omega_model
DeSena, G. (2012). Pressure Distribution on an
Airfoil. United States Naval Academy.
Devenport, W., & et.al. (2019, janurary 29). Experiment
3 - FLOW PAST A CIRCULAR CYLINDER. Retrieved from
http://www.dept.aoe.vt.edu/~aborgolt/aoe3054/manual/expt3/index.html
Dole, C. (2016). Flight Theory and Aerodynamics: A
Practical Guide for Operational Safety. John Wiley & Sons, .
Eftekhari, S., & et al. (2019). Investigation of
a NACA0012 Finite Wing Aerodynamics at Low Reynold’s Numbers and 0° to 90°
Angle of Attack. 11.
Günel et al , O. (2016). COMPARISON OF CFD AND XFOIL
AIRFOIL ANALYSES FOR LOW REYNOLDS NUMBER. International Journal of Energy
Applications and Technologie, 3(2), 83 – 86.
Guo,, D. (2019). Cross Cylindrical Flow: Measuring
Pressure Distribution and Estimating Drag Coefficients. Retrieved from
https://www.jove.com/science-education/10451/cross-cylindrical-flow-measuring-pressure-distribution-estimating
Koziel et al , S. (2011). Computational
Optimization, Methods and Algorithms. Springer,.
Lu, J. (2006). Patent No. US8712639B2. US.
metu, c., & et al. (n.d.). EXPERIMENT 6
CHARACTERISTICS OF AN AIRFOIL. Retrieved from
http://courses.me.metu.edu.tr/courses/me410/exp6/exp6.pdf
Muftah, A. (2019). CFD Simulation and Optimization of
4-Digit NACA Airfoils. CFD Modeling in Measurement Systems.
Mukesh, R. (2014). Airfoil shape optimization using
non-traditional optimization technique and its validation. Journal of King
Saud University - Engineering Sciences, 191-197.
pilotsofamerica.com. (2018, November 2). Controllability
vs Maneuverability? Retrieved from
https://www.pilotsofamerica.com/community/threads/controllability-vs-maneuverability.114767/
Sereez et al , M. (2016). Computational Simulation of
Airfoils Stall Aerodynamics at Low Reynolds Numbers. Applied Aerodynamics.
Somers , D. (2005). Effects of Airfoil Thickness
and Maximum Lift Coefficient on Roughness Sensitivity. National Renewable
Energy Laboratory.
Sreejith, B., & et al. (2018). Numerical study on
effect of boundary layer trips on aerodynamic performance of E216 airfoil. Engineering
Science and Technology, an International Journal, 21(2), 77-88.
Srinath et al . (2010). Optimal aerodynamic design of
airfoils in unsteady viscous flows. Computer Methods in Applied Mechanics
and Engineering, 1976-1991.
Sullivan, A. (2010, May 6). Aerodynamic forces acting
on an airfoil.
Wallace, L. E. (2001). The Whitcomb Area Rule: NACA
Aerodynamics Research and Innovation. In P. E. Mack, FROM ENGINEERING
SCIENCE TO BIG SCIENCE (p. 396). Washington: John Henry.
Webster, M. (2020, May 02). airfoil. Retrieved
from Merriem-Webster.com: https://www.merriam-webster.com/dictionary/airfoil
Wikipdia. (2010, May 1). Abbas Ibn Firnas.
Retrieved from Enacademic: https://enacademic.com/dic.nsf/enwiki/768576
Wikipedia. (2010, May 21). Abbas Ibn Firnas.
Retrieved from enacademic: https://enacademic.com/dic.nsf/enwiki/768576
Wikipedia. (2020, April 17). Area Rule.
Retrieved from Wikipedia : https://en.wikipedia.org/wiki/Area_rule
ZHANG et al , T. t. (2016). A study of airfoil
parameterization, modeling, and optimization based on the computational fluid
dynamics method. Journal of Zhejiang University-SCIENCE A (Applied Physics
& Engineering), 17(8), 632-645.