...
This is a report written by Conall Kingshott as a work-term report with the intention of eventually being turned into WARG documentation. I am not sure some of it is fully correct, and would strongly suggest it is taken more as inspiration on where to look to do some analysis instead of being taken as a prescriptive guide to how to do something. I especially would now no longer advocate for symmetric airfoils as I previously did.
Introduction
During the early part of the 20th Century, the National Advisory Committee for Aeronautics (NACA), the
predecessor to NASA, created a series of airfoils to be used on aircraft wings [1]. Earlier in history, airfoils
were experimentally tested, and the creation of their shape relied on the intuition and experience of
engineers and aircraft designers. The improvement that NACA brought on was generating the airfoils
mathematically and measuring their flight characteristics consistently. They also developed a numbering
scheme for the airfoils which allowed a user to derive properties from the airfoil’s numerical designation
[2].
While NACA airfoils have largely fallen out of use in modern high-performance aircraft because of the
advent of computer modeling and simulations, they are still in use in commercial aircrafts, and in hobby
aircrafts, where their excellent documentation and the variety of available online tools makes them
convenient for novice aircraft designers. This report will start with a general overview of aircraft wing
design and characteristics, followed by a summary of NACA airfoils and their characteristics. The report
will then have notes on special considerations for wing design with respect to hobby aircraft.
For the purpose of this report, hobby aircraft are defined as unmanned craft capable of powered flight, with
a wingspan under 5 meters that is designed outside of a professional setting, with no intention of
commercialization, or adhering to professional engineering standards. This is a definition created
specifically by the author of this report to manage the scope of this report and clarify what would otherwise
be a nebulous designation.
Wing Design and Characteristics
The lift required for an aircraft to fly is a product of the mass of the aircraft, and the gravitational
constant, as shown in the equation below.
𝐿 [𝑁] = 𝑚 [𝑘𝑔] ∗ 9.81[𝑚
...
/s^2]
Equation 1
Mass, m has the standard SI unit of Kg, and the gravitational constant at sea level on earth is 9.81 m/s^2.
To determine the lift required to keep an aircraft at a constant height, the mass of the aircraft must simply
be entered into the lift equation. Once the required lift is determined, the designer must specify the wings
accordingly. The lift created by a wing is governed by the equation:
𝐿 = 𝐶𝑙 ∗ (1
...
/2 )∗ 𝜌 ∗ 𝐴 ∗
...
𝑉^2
Where Cl is the coefficient of lift, a property of the airfoil, ρ is the density of air at a given altitude, A is the
2D area of the wing, and V is the velocity of the aircraft. L is the lift created by the wings [3]. Treating lift
as the dependent variable, the coefficient of lift is the important remaining independent variable.
The contributing factors to the coefficient of a lift of an airfoil in a given configuration are the angle of
attack, and the Reynolds number of the environment in which the aircraft will be flying. The angle of attack
is the angle, in degrees, above parallel with the flight of the aircraft that the cord of the wing is [4]. The
Reynolds number for wing in an environment is determined by the following equation.
𝑅𝑒 = (𝜌 ∗ 𝑣 ∗ 𝑙
...
) / μ
Equation 3 [4]
Where ρ is the density of air at a given altitude, v is the anticipated velocity of the aircraft, l is the cord
length of the wing, and μ is the kinematic viscosity of air at a given temperature and air pressure [4].
Once the optimal angle of attack has been determined, the designer can then find the corresponding
coefficient of lift for the airfoil they are using. This gives the designer the appropriate coefficient of lift, a
single dimensionless quantity that allows for simple aircraft design without the user being required to carry
out complex analysis like CFD, and wind tunnel testing.5
NACA airfoils are commonly used in asymmetric configurations, but as will be detailed in the next section,
they do not necessarily need to be asymmetric. Symmetric airfoil shapes have even pitch authority upwards
and downwards, while asymmetric airfoil shapes with more area above the chord can more easily pitch the
aircraft upwards. Because of this, symmetric airfoils, or airfoils with more symmetric profiles are more
commonly used on stunt, or fighter aircraft, where it is important to be able to quickly move the aircraft
upwards, and downwards [5]. Conversely, asymmetric airfoils are more able to pitch the aircraft upwards,
while they struggle to pitch it downwards which is helpful in passenger aircraft, or aircraft designed for
long-haul flight. The major downside of symmetric airfoils is that they increase the drag and mass of wings.
The final wing characteristic that this report will address is wing sweep. The sweep of a wing describes
whether a wing’s chord length decreases towards the edge of the wing. Swept wings have two major
advantages over straight wings. Swept wings decrease turbulent airflow at the wing tip [6]. This is
particularly important on aircraft where the aircraft, or the air passing over the wings is faster than Mach 1
[6]. The second advantage of the swept wing is that it moves the wing’s center of lift closer to the center of
the aircraft along the pitch axis. It does however move the center of lift backwards from the wing-spar along
the roll axis unless the wing is swept specifically to align the center of lift with the center of mass of the
aircraft [6].
...
Special Considerations for Hobby Aircraft
The benefit of using NACA airfoils in hobby aircraft is that their excellent documentation and known
properties allows them to be used with limited research, to create properly specified aircraft [5]. Hobby
aircraft designers often do not have access to computer simulations, and do not have formal education on
aerospace engineering. Because of this, controlling the scope of a hobby aircraft project is extremely
important. When designing wings, if lift is treated as dependent, the only independent variable cannot be
easily determined by a hobby aircraft designer. The density of air at a given elevation can be obtained with
sufficient accuracy with an internet search. The area of the wing used in this equation is a 2D cross-sectional
area [4] which can be measured using a measuring tape or other rudimentary measuring device. It can also
be easily checked in a CAD model. The coefficient of lift being clearly defined for a given airfoil with
consideration for the many factors that contribute to it is one of the main advantages of using NACA airfoils.
The equation for Reynolds number is shown in equation 3. For most model aircraft applications, the
Reynolds number will lie between 500,000 and 1,000,000 [5]. What this means is that the air going over
the wing has very turbulent flow. This is because most model aircraft are flown at low speeds and low
altitudes where air is denser compared to the speeds and altitudes of commercial aircraft which are flown
at much higher speeds and altitudes than model aircraft. The comparative shortness of model aircraft wings
with respect to commercial aircraft is also a factor in their Reynolds numbers being higher. The general
effect of this higher Reynolds number is that model aircraft often need to be configured with wings that
have a lower angle of attack because the more turbulent flow creates more drag, and thus a lower lift/drag
ratio at a given angle of attack.
If the aircraft that is being optimized for has fixed thrust it can generate, the coefficient of lift should be set
so that the lift generated at the desired speed is sufficient to keep the craft airborne. An example of this in
hobby aircraft would be if the pusher motor and propellor are fixed for availability or pricing reasons. If
the thrust of the aircraft is not fixed, a common strategy is to optimize the lift/drag ratio. This should result
in the most efficient wing configuration, and thus, the most efficient aircraft possible using a NACA airfoil.
It is however of note that if the construction of the wings means they contribute significantly to the overall
mass of the aircraft, a thinner, and thus lighter, wing profile can result in a more efficient aircraft overall
[5].
Swept wings are often not used on hobby aircraft for multiple reasons. The first reason is that the decrease
in turbulent airflow above Mach 1 is not relevant to hobby aircraft due to their generally low speeds. The
difficulty in creating swept wings as opposed to straight edge wings is also a consideration. More complex8complex
geometry is difficult to achieve, especially with rudimentary construction methods. In fact, if wings are
swept improperly, they can generate extra drag, or even downforce which is extremely undesirable, and
extremely difficult to deal with on the scale of a hobby aircraft.9
Conclusions
To conclude this report started by summarizing the history of NACA airfoils, their history, and their modern
use. NACA airfoils are still used in some commercial aircraft, and the work that was done to characterize
them properly has made their use common is hobby aircraft. Hobby aircraft were defined for this report as
“unmanned craft capable of powered flight, with a wingspan under 5 meters that is designed outside of a
professional setting, with no intention of commercialization, or adhering to professional engineering
standards”.
This report then detailed an overview of aircraft wings, starting with an explanation of lift equations, both
the equation needed to determine how much lift is needed for the aircraft to fly, and the equation of the lift
generated by wings. Next, an overview of the properties that need to be optimized for when choosing wings
was given, with special focus given to the Reynolds number, and its relationship with the lift coefficient.
The properties and use-cases of symmetric and asymmetric airfoils were then reviewed, as well as the
effects of wing sweep on aircraft flight.
Next, the naming scheme, and how the airfoils are specified for the NACA 4-digit, and 5-digit naming
schemes were outlined. The many components of the airfoil are all specified in relation to the chord length,
with the max thickness, and its distance from the leading-edge common characteristics that were shown in
the 4- and 5-digit codes.
Finally, the limitations that hobby aircraft designers, namely lack of ability to run simulation, and lower
general resources for knowledgeable design, and sophisticated construction were laid out. Other notes on
the Reynolds numbers that should be used for hobby aircraft, and the effect of swept wings on hobby aircraft with the speeds they traditionally fly at.
References
[1] B. Dunbar, "NACA Airfoils," National Aeronautics and Space Administration, 6 August 2017. [Online].
Available: https://www.nasa.gov/image-feature/langley/100/naca-airfoils. [Accessed 21 May 2023].
[2] B. J. Cantwell, "http://Stanford.edu ," 12 May 2013. [Online]. Available:
https://web.stanford.edu/~cantwell/AA200_Course_Material/The NACA airfoil series.pdf.
[Accessed 21 May 2023].
[3] T. Benson, "The Lift Equation," National Aeronautical and Space Administration, 13 May 2021.
[Online]. Available: https://www.grc.nasa.gov/www/k-12/rocket/lifteq.html. [Accessed 21 May
2023].
[4] H. A. Ira and E. V. D. Albert, THEORY OF WING SECTIONS, New York: Dover Publications, 1959.
[5] A. Lennon, R/C MODEL AIRCRAFT DESIGN, Wilton, CT: Air Age Inc., 1996.
[6] A. Wood, "Sweep Angle and Supersonic Flight," Aero Wood, 28 September 2022. [Online]. Available:
https://aerotoolbox.com/intro-sweep-angle/. [Accessed 21 May 2023].
[7] W. contributors, "NACA airfoil," Wikipedia, The Free Encyclopedia, 09 April 2023. [Online]. Available:
https://en.wikipedia.org/w/index.php?title=NACA_airfoil&oldid=1148957775. [Accessed 20 05
2023]