>> Properties of the Atmosphere
>> Aerofoil Section 2D Geometry
>> Joukowski Flow Mapping and Aerofoils
>> 2D Thin Aerofoil Theory
>> 2D Panel Methods
>> 2D Boundary Layer Modelling
>> 3D Lifting Line Theory
>> 3D Vortex Lattice Method
>> Compressibility Corrections
Aerofoil Section Geometry Definition
Aerofoil
sections come in a variety of shapes and sizes. Some are classified
by their geometric properties while others by their aerodynamic
properties. One of the earliest and simplest naming conventions is
that derived by the National Advisory Committee for Aeronautics
(NACA, now renamed NASA). Early NACA 4 and/or 5 Digit aerofoil
families used simple geometry based definitions to define the shapes.
In this series, the designation numbers determine the mean line and
thickness distribution of the section.
More
modern designation numbers, such as the 6 and 6A series sections
incorporate values related to the aerodynamic behaviour of the
section and are constructed by mapping from the desired aerodynamic
properties to a geometry that will then produce these. All section
designation techniques will have methods for determining the surface
x,y coordinates. The NACA systems below represent a first attempt at
a parametric representation of camber and thickness.
NACA 4 and 5 Digit Aerofoil Sections.
The
NACA 4 and 5 Digit aerofoils represent two families of aerofoil
section that can be generated by the use of a set of simple
polynomial equations. While these sections are slightly out of date
in terms of current aircraft usage, they still represent useful
sections and are easy to create. The aerofoils are created by summing
a thickness distribution with a given mean line equation.
For both families of aerofoil section the thickness distribution is as
follows,
where
x is a position along the chord line, given as a fraction of
chord and t is the value of maximum thickness as given by the last
two digits of the aerofoil designation number. (ie 0012 = symmetric
section with t(max)=0.12c)
For
the 4digit family, the mean line is given as,
Values
p and m are given
from the first two digits of the designation number. m being
the value of maximum camber height (1/100ths chord) and p
being the position of maximum camber height (1/10ths
chord). (ie 2412 = maximum camber height =0.02c located at 0.4c).
For
the 5digit family, the mean line is given as,
Values
p, k_{1} and m are found from the
following table based on the first three digits of the designation
number.
Mean Line No.

p

m

k_{1}

210

0.05

0.0580

361.4

220

0.10

0.1260

51.64

230

0.15

0.2025

15.957

240

0.20

0.2900

6.643

250

0.25

0.3910

3.230

The
value of maximum camber height (m) and its position (p)
will now be determined by the section construction process. (ie 23012
= maximum camber height =0.02c located at 0.15c).
The
construction of the section is then done numerically by identifying
surface points which are the sum of camber and thickness effects.
Points are normally generated using a cosine distribution of chord x
coordinates. For each x coordinate an upper (x_{u},y_{u})
and lower surface (x_{l},y_{l})
data point is created by applying the above equations and
construction method.
here
is the angle of the mean line gradient at the coordinate x
location. A leading edge radius r is applied to smooth the front data
points.
NACA 6 and 6A Series Aerofoil Sections
These
aerofoil sections are designed to produce laminar flow and low drag
over a reasonable range of angles of attack. The thickness
distribution is thus based on a prescribed velocity distribution for
the specific symmetric section required. The camber line is a
polynomial function based on the desired ideal lift coefficient.
For
6 Series Sections the designation numbers represent the aerofoil
aerodynamic properties as shown in the following example,
64(1)215   
 6   6 series designation number. 
 4   location of Cp(min) as 1/10ths chord. 
 (1)   1/2 width of drag bucket in C_{L} counts (0.2) 
 2   Ideal (or Design) C_{L} value. 
 15   Max thickness to chord ratio, 1/100ths chord 
References
"Theory
of Wing Sections" I.H.Abbott & A.E.Von Doenhoff, Dover, NY,
1959.
"Computer
Program to Obtain Ordinates for NACA Aerofoils." Ladson,
Brooks, Hill & Sproles, NACA Langley, NASA TM4741
Software
The
following applications can construct the various families of NACA 4,5
6 and 6A series sections using the techniques described by Ladson,
Brooks, Hill and Sproles.
In
these cases the data file contains 175 coordinate points with compact
spacing closer to the leading edge of
the section.
Links
to Other Aerofoil Section Data
Page
with a large number of aerofoil sections. ( Martin
Selig's pages at UIUC)
