naca 2412 airfoil experimental data

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Appendix A: Airfoil Data

In Chapter 3 of this text we discussed many of the aspects of airfoil design as well as the NACA designations for several series of airfoils. Lift, drag, and pitching moment data for hundreds of such airfoil shapes was determined in wind tunnel tests by the National Advisory Committee for Aeronautics (NACA) and later by NASA, the National Aeronautics and Space Administration. This data is most conveniently presented in plots of lift coefficient versus angle of attack, pitching moment coefficient versus angle of attack, drag coefficient versus lift coefficient, and pitching moment coefficient versus lift coefficient and is found in literally hundreds of NACA and NASA Reports, Notes, and Memoranda published since the 1920s.

Many of the more important airfoil shapes have their test results summarized in the Theory of Wing Sections , a Dover paperback publication authored by Ira Abbott and Albert Von Doenhoff and first published in 1949. While the date of original publication might lead one to think this material must be out of date, that is simply not true and the Theory of Wing Sections is one of the most valuable references in any aerospace engineer’s personal library.

In the following appendix material a selection of airfoil graphical data is presented which can be found in the Theory of Wing Sections and in the non-copyrighted NACA publications which are the source of the Dover publication’s data. The airfoils presented represent a cross section of airfoil shapes selected to illustrate why one would select one airfoil over another for any given aircraft design or performance requirement.

Figure A-1 shows data for the NACA 0012 airfoil, a classic symmetrical shape that is used for everything from airplane stabilizers and canards to helicopter rotors to submarine “sails”. Note that for the symmetrical shape the lift coefficient is zero at zero angle of attack. These graphs show test results for several different Reynolds numbers and for “standard roughness” on the surface. They also show what happens when a 20% chord flap is deflected 40 degrees. Note that the flap deflection shifts the lift curve far to the left giving a zero lift angle of attack of roughly minus 12 degrees while it increases the maximum lift coefficient (Re= 6 x 106) from just under 1.6 to 2.4, a huge increase in lifting capability that can contribute to large decreases in takeoff and landing distances. Also note that the pitching moment coefficient at c/4 (in the left hand graph) is essentially zero from -12 degrees to+ 14 degrees angle of attack and then goes negative in stall at positive angle of attack. In the right hand graph the moment curve shown is for the moment at the “aerodynamic center” rather than the quarter chord but since it is also zero in this plot it confirms the theoretical prediction that for a symmetrical airfoil the center of pressure (where the moment is zero) coincides with the aerodynamic center.

Figure A-2 gives similar data for the NACA 2412 airfoil, another 12% thick shape but one with camber. Note that the lift coefficient at zero angle of attack is no longer zero but is approximately 0.25 and the zero lift angle of attack is now minus two degrees, showing the effects of adding 2% camber to a 12% thick airfoil. Also note that the moment coefficient at the quarter chord is no longer zero but is still relatively constant between the onset of positive and negative stall. The moment coefficient is negative over most of the range of angle of attack indicating a nose down pitching moment and positive stability. Adding 2% camber has also resulted in a slight increase in CLmax from about 1.6 to 1.7 when compared to the 0012 airfoil.

When Figure A-3 is compared with A-I and A-2 one can see the effect of added thickness as the percent thickness increases from 12 to 15 percent. This shows up primarily as a slight increase in drag coefficient and a slight reduction in CLmax compared to the 12% thick equally cambered airfoil in A-2.

Figure A-4 returns to a 12% thick airfoil but one with 4% camber and a comparison with the previous figures will show how the increase in camber increases the lift at zero angle of attack, takes the zero lift angle of attack down to minus four degrees and increases the nose down pitching moment which is still constant between stall angles when measured at the quarter chord (aerodynamic center).

Figures A-5 and A-6 are for “6-series” airfoils, the so-called “laminar flow” airfoil series developed in the 1930s and used extensively in wing designs well into the late 1900s. Both figures show 12% thick airfoils. The distinguishing features of these graphs are the pronounced “drag buckets” in the right hand plots. Note that the first number to the right of the hyphen in the airfoil designation tells the location of the center of the drag bucket; i.e., the center of the bucket is at a CL of 0.1 for the 641-112 and at 0.4 for the 641-412. In this manner the airfoil designation in the “6-series” is a handy tool for the designer, allowing easy selection of an airfoil that has its “drag bucket” centered at perhaps the cruise lift coefficient for a transport aircraft or at the lift coefficient which is best for climb or maneuver in a fighter. Also note that the difference in camber produces the same kind of shifts in the lift curve as noted in the 4 digit series airfoils in the earlier plots.

These 6 plots are just the tip of the iceberg when exploring the many airfoil shapes which have been investigated by the NACA, NASA, and others over the years but the general features noted above will hold true for almost any variations in airfoil shape.

The airfoil is shown to have a linear section lift coefficient, c sub l, between section angle of attacks, alpha knot, between negative 16 and 16 degrees for Reynolds numbers of 9, 6, and 3 times 10 to the 6, with hooks on each end fo the linear portion as stall sets in. For a standard roughness at a Reynolds number of 6 times 10 to the 6, the linear portion is between negative 16 and positive 8 degrees before shifting down slightly and turning at 12 degrees. Two additional curves are shown when a 0.2 times c simulated split flap is added with a deflection fo 60 degrees, which shifts this final curve upward by 1.4 c sub l. The moment coefficient for each aforementioned line is shown to be roughly 0 in the linear portions, only deviating as stall sets in. The moment coefficients for the airfoil with flap defection follow the same shape, but are centered on negative 0.24, rather than 0. B) Section drag coefficient, c sub d, is shown as a function of section lift coefficient, c sub l. For Reynolds Numbers of 9, 6, and 3 times 10 to the 6, c sub d follows a parabolic shape, growing from a y-intercept of roughly 0.006 as c sub l moves away from 0. The same parabolic shape is present for the standard roughness line, but with the parabolic shape much steeper, and now centered off of a c sub d value of 0.010. The moment coefficient, c sub m a c, is 0 for all values shown. The aerodynamic center is at x over c of 0.25 and y over c of 0 for all cases.

Figure A1.1: Kindred Grey (2021). “NACA 0012 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/0012_20210805

Figure A1.2: Kindred Grey (2021). “NACA 2412 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/2412_20210805

Figure A1.3: Kindred Grey (2021). “NACA 2415 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/2415_20210805

Figure A1.4: Kindred Grey (2021). “NACA 4412 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/4412_20210805

Figure A1.5: Kindred Grey (2021). “NACA 64_1-112 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/64-112

Figure A1.6: Kindred Grey (2021). “NACA 64_1-412 Airfoil Data.” CC BY 4.0 . Adapted from NACA. Public domain. Available from https://archive.org/details/64-412

Aerodynamics and Aircraft Performance, 3rd edition Copyright © 2004, 2021 by James F. Marchman III is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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(naca2412-il) NACA 2412 NACA 2412 airfoil Max thickness 12% at 30% chord. Max camber 2% at 40% chord Source The dat file is in Selig format		No parser warnings

E207 (12.04%)
E220 (11.48%)
S8055 (12%)
NACA CYH
RAF 38 AIRFOIL
LDS-2 AIRFOIL
MH 120 11.57%
GOE 704 AIRFOIL
ONERA OA212 AIRFOIL
NACA 1412

Polars for NACA 2412 (naca2412-il)

Airfoil	Reynolds #	Ncrit	Max Cl/Cd	Description
naca2412-il	50,000	9	32.5 at α=7.25°	Mach=0 Ncrit=9
naca2412-il	50,000	5	34.6 at α=6.5°	Mach=0 Ncrit=5
naca2412-il	100,000	9	50 at α=6.75°	Mach=0 Ncrit=9
naca2412-il	100,000	5	49.4 at α=6°	Mach=0 Ncrit=5
naca2412-il	200,000	9	66.6 at α=6°	Mach=0 Ncrit=9
naca2412-il	200,000	5	62.6 at α=5.25°	Mach=0 Ncrit=5
naca2412-il	500,000	9	87.3 at α=5°	Mach=0 Ncrit=9
naca2412-il	500,000	5	78.3 at α=4°	Mach=0 Ncrit=5
naca2412-il	1,000,000	9	101.4 at α=4.5°	Mach=0 Ncrit=9
naca2412-il	1,000,000	5	87 at α=4.5°	Mach=0 Ncrit=5

Set Reynolds number and Ncrit range		Low	High
	Reynolds Number
	NCrit

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NACA 2412 Airfoil Data

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Uploaded by Kindred Grey on August 5, 2021

Design of NACA 2412 and its Analysis at Different Angle of Attacks, Reynolds Numbers, and a wind tunnel test

Related Papers

Aakash Srivastava

This project simulates NACA2415 airfoil on ANSYS Workbench and ANSYS FLUENT at low Reynolds numbers at different angles of attack. This is a 2-D simulation andSpalart-Allmaras is the preferred turbulentmodel solver for this process, it yielded more results closer to experimental results when compared against K-epsilon and other turbulent models.Contours of Pressure and Velocity are presented in this paper with their inferences discussed while Plots of Coefficient of Pressure (CP) about the chord lengths along the airfoil and Coefficient of Lift (CL) are plotted to compare the CFD and the experimental results. Effect of Reynolds number and Angle of Attack is thus studied and investigated.

Prabowo Galih Mahanendra

Analyze the behavior of the turbulent airfoil flow of the lift coefficient and drag coefficient values, velocity magnitude, static pressure, and turbulent viscosity on the surface of the airfoil with respect to the angle of attack, free stream velocity, and altitude is the scope of this study. Lift and drag coefficient values will be calculated for 1.4 × 10 6 Reynolds number. The airfoil that is selected it is NACA-2406 and will be analyzed with ANSYS. The geometry of the airfoil is created by using JAVAFOIL or can be find out in the website http://airfoiltools.com/ .This geometry will be imported into SOLIDWORKS and then CFD analysis is carried out using FLUENT at angle of attack 6 degrees. The results of ANSYS analysis will be compared with XFOIL's results.

International Journal for Research in Applied Science and Engineering Technology

Mahima Haque

A comparison between NACA 0012 and NACA 2412 has been made by comparing the lift co- efficient, drag co-efficient, pressure contour and velocity contour at various angles of attack. The process has been done taking steady state flow around NACA-0012 and NACA-2412 airfoil using 1m chord length and a velocity of 88.65m/s. The main aim is to understand the aerodynamic characteristics of both the airfoils at different angles of attack and draw a conclusion on which performs better under the same conditions. Modelling and numerical analysis has been carried out by using commercially available CFD software, which is a convenient method of analysis since computational methods are more preferred to experimental methods due to low expenses involved. The numerical results demonstrated are compatible with those of the theory. This confirms the validity of using Computational Fluid Dynamics (CFD) as a reliable alternative to experimental procedures.

IJRAME Publications

IJRAME Journal

Two dimensional models for the airfoils were created, drawn and meshed in ANSYS Mechanical using geometry data gathered by the National Advisory Committee for Aeronautics. ANSYS FLUENT is used for computing flow over the two dimensional NACA 2415 and 23012 airfoil at an angle of attack of 4°. The computations are carried out at high Reynolds number at standard roughness conditions. One of the popular meshes for simulating an airfoil in a stream is a C-Mesh, and that is what we will be using. At the inlet of the system, we will define the velocity as entering at a 4° angle of attack, and at a total magnitude of 1. We will also define the gauge pressure at the inlet to be 0. As for the outlet, the only thing we can assume is that the gauge pressure is 0. As for the airfoil itself, we will treat it like a wall. From the analysis, C P (Coefficient of Pressure) distribution, C L (Coefficient of Lift) and C D (Coefficient of Drag) is estimated and compared with the experimental results.

G.M Hasan Shahariar

The numerical analysis of the two dimensional subsonic flow over a NACA 0012 & NACA 4412 airfoil at various angles of attack which is operating at a Reynolds number of 3×10 6 is presented. A commercial computational fluid dynamic (CFD) code ANSYS FLUENT based on finite volume technique is used for the calculation of aerodynamics performance. The two dimensional model of the airfoil and the mesh is created through ANSYS Meshing which is run in Fluent for numerical iterate solution. The steady-state governing equations of Reynolds averaged Navier -Stokes is calculated for analyzing the characteristics of two-dimensional airfoils and the realizable k-epsilon model with Enhanced wall treatment is adopted for the turbulence closure. The aim of the work is to show the behavior of the airfoil at these conditions and to compare the aerodynamics characteristics between NACA 0012 & NACA 4412 such as lift co-efficient, drag co-efficient and surface pressure distribution over the airfoil surface for a specific angle of attack. Calculations were done for constant air velocity altering only the angle of attack for every airfoil model tested. This analysis can be used for the wing design and other aerodynamic modeling correspon ds to these airfoil.

5th International Conference on Engineering, Research, Innovation and Education (ICERIE)

Study of a two-dimensional CFD analysis is done to investigate the effects of angle of attack and Mach number on the aerodynamic characteristics of NACA (National Advisory Committee for Aeronautics) 0012 airfoil considering turbulent flow around it. Different parameters used, and its effects, in analysis like domain shape, grid cells, number of nodes in meshing, various boundary conditions are surveyed. Change in Reynolds number of fluid results in different output, hence the variation of lift & drag coefficient with the change in Reynolds number is analyzed. To show the behavior of the airfoil at these conditions is the main objective of this paper. The simulation is done in ANSYS Fluent and both the k-omega and k-epsilon turbulence modeling method was used to compare the results. From the CL (life Coefficient)/ CD (Drag Coefficient) ratio, it shows that when the Mach number (M) increases, CL increases but CD remains constant at different operating conditions. Moreover, it is observed that the CL/CD ratio decreases because of a rapid downward for the CL and an abrupt upward for the CD with velocity approaching the sonic velocity. Computational results are validated with the results of NASA Langley Research Center validation cases.

2016 ASEE Annual Conference & Exposition Proceedings

John Matsson

Chiemezuo Emmanuel Umeaka, Ing., M.Ing

The main aim of this project is to write a plug and play dynamic MATLB code that would generate airfoil coordinates from any given NACA 4 digits airfoil nomenclature (regardless of type but tested with NACA 2411). Also, using source panel method and the generated coordinates, source strengths needed to define the airfoil, coefficient of pressures, coefficient of pressure plot of given airfoil with sample lift coefficient(𝐶𝐿), drag coefficient(𝐶𝐷), moment coefficient (𝐶𝑚), (to show the limitations of the source panel method) are calculated. Finally, thin airfoil theory is used together with the airfoil shape and chamber coordinates to properly generate plots of lift coefficient(𝐶𝐿), moment coefficient (𝐶𝑚), location of centre of pressure (𝑋𝑐𝑝) with respect to a wide range angle of attacks.

Journal of Mechatronics and Automation

Ali Kamranpey

Aircraft post-flight reduction is one of the most important research topics, since postreduction is effective in all parameters of bird performance, such as maximum speed, fast acceleration, shortening the runway required, high maneuverability, and reduced fuel consumption. Therefore, it is important to examine how the force applied to the airfoil changes in different streams from an industrial point of view. In this study, NACA(National Advisory Committee for Aeronautics) Airfoil 0012 has been studied. Numerical solution is used for the study. In the simulations, the air fluid and Mach number 0.5 are considered and the lift, drag and pressure coefficients at different attack angles are investigated. The results show that this airfoil has a lift factor of 0 due to its symmetric geometry at angle of attack 0 but its drag coefficient is about 0.01384 and its pressure coefficient is about-0.483. By varying the angle of attack from-12 to +12, it was observed that for the positive attack angle the lift coefficient increases and for the negative attack angle increases the lift coefficient decreases. Also with increasing angle of attack the drag coefficient always increases and the coefficient of pressure coefficient decreases.

ibrahim gov

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Airfoil experimental database

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This app queries an aerodynamic database of NACA 4 digits, 5 digits, 6 series, and NASA supercritical airfoils. Data for the NACA sections has been derived from the book Theory of Wing Sections, by Abbott and Von Doenhoff. Data for NASA supercritical (cambered) airfoil is extracted from NASA TM 81912. The app reports airfoil characteristics, lift curve and drag polar with a few inputs. The user has only to select airfoil family and assign relative thickness and Reynolds number. The characteristics of the curves are reported in a table, which can be exported on a spreadsheet file. All data are at low Mach number, incompressible flow regime. Very useful in preliminary aircraft design, when the user needs a reliable source of data but has only few global parameters to play with.

Check the website for binaries: MATLAB app and Windows standalone executable.

The code should work with earlier versions of MATLAB, although I did not check it.

engdancili (2024). Airfoil experimental database (https://github.com/dciliberti/experimentalAirfoilDatabase), GitHub. Retrieved September 8, 2024 .

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IMAGES

NACA 2412 with 4 Degree Flap Deflection. The NACA 2412 airfoil with a
Solved Define The experimental data for the NACA 2412
VAS1715 lift and moment curves compared to NACA 2412 experimental data
Contour of the NACA 2412 airfoil with and without trailing edge flap
NACA 2412 aerofoil based on 14 control points.
Solved 3. A NACA 2412 airfoil is at an angle of attack of

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CFD- Wingtip Vortices off a NACA 2412 Airfoil
Airfoil NACA 0012 O-type Meshing in Gambit

COMMENTS

Experimental Studies of Flow Separation of the NACA 2412 Airfoil at Low
Wind tunnel tests have been conducted on an NACA 2412 airfoil section at Reynolds number of 2.2 x 10(exp 6) and Mach number of 0.13. Detailed measurements of flow fields associated with turbulent boundary layers have been obtained at angles of attack of 12.4 degrees, 14.4 degrees, and 16.4 degrees. Pre- and post-separated velocity and pressure survey results over the airfoil and in the ...
PDF Aerodynamic Performance of the NACA 2412 Airfoil at Low Reynolds Number
Airfoil at Low Reynolds Number. Abstract. This paper shows a project by three honors students in an undergraduate engineering program. Students used a 3D printer to fabricate a wing section of the NACA 2412 airfoil. The section has. a chord length of 230 mm and a total assembled width of 305 mm.
Experimental Investigation of Lift forNACA 2412 Airfoil without
At high Reynolds number, XFOIL results were not found to be accurate for full-scale flow. Havaldar et al. [21] concluded that the lift coefficient for NACA 2412 airfoil with internal passage was ...
CFD Validation of NACA 2412 Airfoil
The NACA 2412 cambered airfoil experimental model of has been analyzed and validated to determine the impact of aerodynamic performance at lower Reynolds number and constant velocity. Validation ...
PDF Improvement of Aerodynamic Performance of NACA 2412 Airfoil using
with experimental data. Simulations conducted were closely aligned with experimental data [1], as shown in Figure 2. Results illustrate the accuracy of the computational approach in capturing aerodynamic characteristics. This sets the benchmark for the simulation of various modified NACA 2412 airfoil configurations.
PDF AR77-3 Aeronautical Report 77-3
to broaden the base of experimental data it was considered important to obtain additional experimental data for an older NACA airfoil section, one having a different thickness and camber distributions than the GA(W)-l. With this objec tive in mind a NACA 2412 airfoil model was selected for the separated flow research of this report.
Aerodynamic Performance of the NACA 2412 Airfoil at Low ...
The conceptual model of baseline NACA 2412 airfoil has been compared to the experimental wind tunnel results carried out by Matsson, Voth et al. (2016) for validation purposes. The validation ...
PDF -- Experimental Studies o ow Separation of Three foils at Low eeds
Mod, NACA 2412 and NASA GA(W)-2 airfoil sections at a Reynolds number of 2.2 x 106 and a Mach number of 0.13. Detailed measure- ... In order to broaden the base of experimental data it was considered important to obtain additional experimental data for an older NACA airfoil section and two newer NASA sections,
PDF Design Methodology for Aerodynamically Scaling of a General Aviation
The wing airfoil of the full-scale Cessna 182 is the NACA 2412 airfoil and is shown in Fig. 1(a).10 The NACA 2412 airfoil performance taken using XFOIL (N crit = 9) at Reynolds numbers of 2,700,000 and 230,000 are coplotted in Figs. 1(b-d). In addition, wind tunnel data for the NACA 2412 airfoil taken from Ref. 11 at a Reynolds number of of (a)
PDF Investigation of Aerodynamic Efficiency on NACA 2412 Airfoil
An experimental investigation on the effect of surface roughness on a NACA 2412 airfoils is performed. The experiments include measurements for the pressure distribution, drag co-efficient and lift co-efficient. Two different rough surfaces are analyzed and their data are compared to those over a smooth surface.
Appendix A: Airfoil Data
Figure A-2 gives similar data for the NACA 2412 airfoil, another 12% thick shape but one with camber. Note that the lift coefficient at zero angle of attack is no longer zero but is approximately 0.25 and the zero lift angle of attack is now minus two degrees, showing the effects of adding 2% camber to a 12% thick airfoil.
NACA 2412 (naca2412-il)
NACA 2412 (naca2412-il)
NACA 2412 Airfoil Data : Kindred Grey : Free Download, Borrow, and
Kindred Grey (2021). "NACA 2412 Airfoil Data." CC BY 4.0. Adapted from NACA. Public domain. Alternative text: (a) Lift curve slopes are shown for Reynolds numbers of 3.1, 5.7, and 8.9 times 10 to the 6. The curves are linear between angles of attack, alpha knot, of negative 14 and 14 degrees, with stall resulting in curves back towards 0 past ...
(PDF) Design of NACA 2412 and its Analysis at Different Angle of
A comparison between NACA 0012 and NACA 2412 has been made by comparing the lift co- efficient, drag co-efficient, pressure contour and velocity contour at various angles of attack. The process has been done taking steady state flow around NACA-0012 and NACA-2412 airfoil using 1m chord length and a velocity of 88.65m/s.
CFD Simulation of NACA 2412 airfoil with new cavity shapes
The conceptual model of baseline NACA 2412 airfoil has been compared to the experimental wind tunnel results carried out by Matsson, V oth et al. (2016) for validati on purposes. The validation
PDF Cfd Analysis of Effect of Flow Over Naca 2412 Airfoil Through the Shear
regimes. When an airfoil or any wing moves through air, the flow of air splits up and passes above and below the airfoil. Figure1: Nomenclature of Airfoil Airfoil design is a major facet of aerodynamics. Airfoil's upper surface is designed in such a way that the air rushing over the top of the airfoil, speeds up and stretches out.
PDF APPENDIX D Airfoil Data -.3 2.0 -12 —1.6 -16 NACA 2412 Wing Section
APPENDIX D Airfoil Data -.3 2.0 -12 —1.6 -16 NACA 2412 Wing Section . APPENDIX D Airfoil Data o 209 57 240 0 89 247 57 N ACA 2412 Wing Section . Title: John Anderson - Introduction to Flight (2011, McGraw-Hill Education).pdf Author: lucaraki Created Date:
Airfoil experimental database
Airfoil experimental database. Get airfoil characteristics from an experimental database. This app queries an aerodynamic database of NACA 4 digits, 5 digits, 6 series, and NASA supercritical airfoils. Data for the NACA sections has been derived from the book Theory of Wing Sections, by Abbott and Von Doenhoff.
(PDF) Design of NACA 2412 and its Analysis at Different Angle of
The lift to drag coefficient ratio of NACA 2412 airfoil is also higher than that of the NACA 0012 airfoil indicating NACA 2412 airfoil to be more fuel economic. View Show abstract
Theoretical and Experimental Data for a Number of NACA 6A-Series
The NACA 6A-series airfoil sections were designed to eliminate the trailing-edge cusp which is characteristic of the NACA 6-series sections. Theoretical data are presented for NACA 6A-series basic thickness forms having the position of minimum pressure at 30-, 40-, and 50-percent chord and with thickness ratios varying from 6 percent to 15 percent.
(PDF) Analysis of NACA 2412 Airfoil
In this project, we selected a NACA 2412 slow-speed Airfoil with maximum thickness 12% (at 30% chord line) from the leading edge, and maximum camber 2% at 40% chord line. This airfoil is used in ...
Coefficient of Lift and Drag of NACA 2412, NACA 2414 and NACA 2415
The newly developed modified blended airfoil had a top surface made of S809 (bottom NACA 2412), while the second had a bottom surface built of NACA 2412 (top S829). Together, S829 and NACA 2412 ...
Summary of Airfoil Data
The historical development of NACA airfoils is briefly reviewed. New data are presented that permit the rapid calculation of the approximate pressure distributions for the older NACA four-digit and five-digit airfoils by the same methods used for the NACA 6-series airfoils. The general methods used to derive the basic thickness forms for NACA 6 and 7-series airfoils together with their ...