NACA Airfoil Series
Please send me information on the NACA 4, 5 and 6 digit airfoils. I
would like to know some general information, their applications, advantages,
disadvantages, and the formulas used to calculate the coordinates.
I'm currently trying
to design a 3D model of the B-58 bomber, but I lack the mathematical
definitions of NACA profiles such as 0003.46-64.069 (root section) and
0004.08-63 (tip section). I've found 4- and 5-digit NACA airfoil generators,
but they don't seem to do the job. Can you provide any help?
As you suggest in your questions, the early NACA airfoil series, the
4-digit, 5-digit, and modified 4-/5-digit, were generated using analytical
equations that describe the camber (curvature) of the mean-line (geometric
centerline) of the airfoil section as well as the section's thickness
distribution along the length of the airfoil. Later families, including the
6-Series, are more complicated shapes derived using theoretical rather than
geometrical methods. Before the National Advisory Committee for Aeronautics
(NACA) developed these series, airfoil design was rather arbitrary with nothing
to guide the designer except past experience with known shapes and
experimentation with modifications to those shapes.
This
methodology began to change in the early 1930s with the publishing of a NACA
report entitled The Characteristics of 78 Related Airfoil Sections from
Tests in the Variable Density Wind Tunnel. In this landmark report, the
authors noted that there were many similarities between the airfoils that were
most successful, and the two primary variables that affect those shapes are the
slope of the airfoil mean camber line and the thickness distribution above and
below this line. They then presented a series of equations incorporating these
two variables that could be used to generate an entire family of related
airfoil shapes. As airfoil design became more sophisticated, this basic
approach was modified to include additional variables, but these two basic
geometrical values remained at the heart of all NACA airfoil series, as
illustrated below.
NACA airfoil geometrical construction
NACA Four-Digit
Series:
The
first family of airfoils designed using this approach became known as the NACA
Four-Digit Series. The first digit specifies the maximum camber (m) in
percentage of the chord (airfoil length), the second indicates the position of
the maximum camber (p) in tenths of chord, and the last two numbers provide the
maximum thickness (t) of the airfoil in percentage of chord. For example, the
NACA 2415 airfoil has a maximum thickness of 15% with a camber of 2% located
40% back from the airfoil leading edge (or 0.4c). Utilizing these m, p, and t
values, we can compute the coordinates for an entire airfoil using the
following relationships:
1.
Pick values of x from 0 to the
maximum chord c.
2.
Compute the mean camber line
coordinates by plugging the values of m and p into the following equations for
each of the x coordinates.
3.
Calculate the thickness
distribution above (+) and below (-) the mean line by plugging the value of t
into the following equation for each of the x coordinates.
4.
Determine the final coordinates
for the airfoil upper surface (xU, yU) and lower surface
(xL, yL) using the following relationships.
NACA Five-Digit Series:
The
NACA Five-Digit Series uses the same thickness forms as the Four-Digit Series
but the mean camber line is defined differently and the naming convention is a
bit more complex. The first digit, when multiplied by 3/2, yields the design
lift coefficient (cl) in tenths. The next two digits, when divided
by 2, give the position of the maximum camber (p) in tenths of chord. The final
two digits again indicate the maximum thickness (t) in percentage of chord. For
example, the NACA 23012 has a maximum thickness of 12%, a design lift
coefficient of 0.3, and a maximum camber located 15% back from the leading
edge. The steps needed to calculate the coordinates of such an airfoil are:
1.
Pick values of x from 0 to the
maximum chord c.
2.
Compute the mean camber line
coordinates for each x location using the following equations, and since we
know p, determine the values of m and k1 using the table shown
below.
3.
Calculate the thickness
distribution using the same equation as the Four-Digit Series.
4.
Determine the final coordinates
using the same equations as the Four-Digit Series.
Modified NACA Four- and Five-Digit Series:
The
airfoil sections you mention for the B-58 bomber are members of the Four-Digit
Series, but the names are slightly different as these shapes have been
modified. Let us consider the root section, the NACA 0003.46-64.069, as an
example. The basic shape is the 0003, a 3% thick airfoil with 0% camber. This
shape is a symmetrical airfoil that is identical above and below the mean
camber line. The first modification we will consider is the 0003-64. The first
digit following the dash refers to the roundedness of the nose. A value of 6
indicates that the nose radius is the same as the original airfoil while a
value of 0 indicates a sharp leading edge. Increasing this value specifies an
increasingly more rounded nose. The second digit determines the location of
maximum thickness in tenths of chord. The default location for all four- and
five-digit airfoils is 30% back from the leading edge. In this example, the
location of maximum thickness has been moved back to 40% chord. Finally, notice
that the 0003.46-64.069 features two sets of digits preceeded by decimals.
These merely indicate slight adjustments to the maximum thickness and location
thereof. Instead of being 3% thick, this airfoil is 3.46% thick. Instead of the
maximum thickness being located at 40% chord, the position on this airfoil is
at 40.69% chord. To compute the coordinates for a modified airfoil shape:
1.
Pick values of x from 0 to the
maximum chord c.
2.
Compute the mean camber line
coordinates using the same equations provided for the Four- or Five-Digit
Series as appropriate.
3.
Calculate the thickness
distribution above (+) and below (-) the mean line using these equations. The
values of the ax and dx coefficients are determined from
the following table (these are derived for a 20% thick airfoil).
4.
Determine the "final"
coordinates using the same equations as the Four-Digit Series.
5.
As noted above, this procedure
yields a 20% thick airfoil. To obtain the desired thickness, simply scale the
airfoil by multiplying the "final" y coordinates by [t / 0.2].
NACA 1-Series or 16-Series:
Unlike
those airfoil families discussed so far, the 1-Series was developed based on
airfoil theory rather than on geometrical relationships. By the time these
airfoils were designed during the late 1930s, many advances had been made in
inverse airfoil design methods. The basic concept behind this design approach
is to specify the desired pressure distribution over the airfoil (this
distribution dictates the lift characteristics of the shape) and then derive
the geometrical shape that produces this pressure distribution. As a result,
these airfoils were not generated using some set of analytical expressions like
the Four- or Five-Digit Series. The 1-Series airfoils are identified by five
digits, as exemplified by the NACA 16-212. The first digit, 1, indicates the
series (this series was designed for airfoils with regions of barely supersonic
flow). The 6 specifies the location of minimum pressure in tenths of chord,
i.e. 60% back from the leading edge in this case. Following a dash, the first
digit indicates the design lift coefficient in tenths (0.2) and the final two
digits specify the maximum thickness in tenths of chord (12%). Since the 16-XXX
airfoils are the only ones that have ever seen much use, this family is often
referred to as the 16-Series rather than as a subset of the 1-Series.
NACA 6-Series:
Although
NACA experimented with approximate theoretical methods that produced the
2-Series through the 5-Series, none of these approaches was found to accurately
produce the desired airfoil behavior. The 6-Series was derived using an
improved theoretical method that, like the 1-Series, relied on specifying the
desired pressure distribution and employed advanced mathematics to derive the
required geometrical shape. The goal of this approach was to design airfoils
that maximized the region over which the airflow remains laminar. In so doing,
the drag over a small range of lift coefficients can be substantially reduced.
The naming convention of the 6-Series is by far the most confusing of any of
the families discussed thus far, especially since many different variations
exist. One of the more common examples is the NACA 641-212, a=0.6.
In
this example, 6 denotes the series and indicates that this family is designed
for greater laminar flow than the Four- or Five-Digit Series. The second digit,
4, is the location of the minimum pressure in tenths of chord (0.4c). The subscript
1 indicates that low drag is maintained at lift coefficients 0.1 above and
below the design lift coefficient (0.2) specified by the first digit after the
dash in tenths. The final two digits specify the thickness in percentage of
chord, 12%. The fraction specified by a=___ indicates the percentage of the
airfoil chord over which the pressure distribution on the airfoil is uniform,
60% chord in this case. If not specified, the quantity is assumed to be 1, or
the distribution is constant over the entire airfoil.
NACA 7-Series:
The
7-Series was a further attempt to maximize the regions of laminar flow over an
airfoil differentiating the locations of the minimum pressure on the upper and
lower surfaces. An example is the NACA 747A315. The 7 denotes the series, the 4
provides the location of the minimum pressure on the upper surface in tenths of
chord (40%), and the 7 provides the location of the minimum pressure on the
lower surface in tenths of chord (70%). The fourth character, a letter,
indicates the thickness distribution and mean line forms used. A series of
standaradized forms derived from earlier families are designated by different
letters. Again, the fifth digit incidates the design lift coefficient in tenths
(0.3) and the final two integers are the airfoil thickness in perecentage of
chord (15%).
NACA 8-Series:
A
final variation on the 6- and 7-Series methodology was the NACA 8-Series
designed for flight at supercritical speeds. Like the earlier airfoils, the
goal was to maximize the extent of laminar flow on the upper and lower surfaces
independently. The naming convention is very similar to the 7-Series, an
example being the NACA 835A216. The 8 designates the series, 3 is the location
of minimum pressure on the upper surface in tenths of chord (0.3c), 5 is the
location of minimum pressure on the lower surface in tenths of chord (50%), the
letter A distinguishes airfoils having different camber or thickness forms, 2
denotes the design lift coefficient in tenths (0.2), and 16 provides the airfoil
thickness in percentage of chord (16%).
Further Sources:
This
is probably the most theoretical and mathematically-intense answer we have yet
given on this site, but let me point out that coordinates for many of these
airfoils already exist in print or on the web. In addition, many programs and
web sites now exist that can automatically compute the coordinates once the
user enters the desired airfoil name or characteristics. Some excellent tools
include:
- NACA 4-Digit Series Airfoil Generator
- NACA 5-Digit Series Airfoil Generator
- SNACK -- download this program that includes NACA airfoil coordinate generators for all of the families we have discussed
- XFOIL -- download this airfoil analysis code that includes a 4-Digit and 5-Digit airfoil generation tool, but this program is difficult for a novice to use (program is 100% free)
- UIUC Airfoil Coordinates Database -- vast library of coordinates for many airfoils, including those of the NACA families discussed above
- The Incomplete Guide to Airfoil Usage -- check out the airfoils used on a huge assortment of aircraft
Summary:
Though
we have introduced the primary airfoil families developed in the United States
before the advent of supersonic flight, we haven't said anything about their
uses. So let's briefly explore the advantages, disadvantages, and applications
of each of these families.
Family
|
Advantages
|
Disadvantages
|
Applications
|
4-Digit
|
1. Good stall
characteristics
2. Small center of pressure movement across large
speed range
3. Roughness has little effect
|
1. Low maximum lift
coefficient
2. Relatively high drag
3. High pitching moment
|
1. General aviation
2. Horizontal tails
Symmetrical:
3. Supersonic jets
4. Helicopter blades 5. Shrouds 6. Missile/rocket fins |
5-Digit
|
1. Higher maximum lift
coefficient
2. Low pitching moment
3. Roughness has little effect
|
1. Poor stall behavior
2. Relatively high drag
|
1. General aviation
2. Piston-powered bombers, transports 3. Commuters 4. Business jets |
16-Series
|
1. Avoids low pressure
peaks
2. Low drag at high speed
|
1. Relatively low lift
|
1. Aircraft propellers
2. Ship propellers |
6-Series
|
1. High maximum lift
coefficient
2. Very low drag over a small range of operating
conditions
3. Optimized for high speed
|
1. High drag outside of
the optimum range of operating conditions
2. High pitching moment
3. Poor stall behavior
4. Very susceptible to roughness
|
1. Piston-powered fighters
2. Business jets 3. Jet trainers 4. Supersonic jets |
7-Series
|
1. Very low drag over a
small range of operating conditions
2. Low pitching moment
|
1. Reduced maximum lift
coefficient
2. High drag outside of the optimum range of
operating conditions
3. Poor stall behavior
4. Very susceptible to roughness
|
Seldom used
|
8-Series
|
Unknown
|
Unknown
|
Very seldom used
|
Today,
airfoil design has in many ways returned to an earlier time before the NACA
families were created. The computational resources available now allow the
designer to quickly design and optimize an airfoil specifically tailored to a
particular application rather than making a selection from an existing family.
To learn about some more recent developments, check out other questions on
supercritical airfoils and airfoil design.
Tidak ada komentar:
Posting Komentar