PARAGLIDER DESIGN HANDBOOK

CHAPTER 2. AEROFOILS

2.2 Cylinder in an airflow

2.3 Joukowsky transformation

2.4 Airfoil geometry and parameters

2.5 Aerodynamic forces

2.6 NACA profiles

2.7 Paraglider airfoils

2.8 XFOIL program

2.9 XFLR5 program

2.10 AIrfoil fitting

2.1 Introduction

It is a fact of common experience
that a body in motion throught a fluid experiences a resultant force.
In most cases, is mainly a resistence to the motion. In the case of an
aerofoil the resultant force normal to the direction of motion is many
times grater than the component resisting the motion. The possibility
of the flight of the paraglider depends on the use of an aerofoil for
the wing structure.

2.2. Cylinder in an airflow

(...)

2.3. Joukowsky transformation

The Joukowsky transformation converts a circle in an airfoil section. Explained here.

2.4 Airfoil geometry and parameters

Airfoil geometry can be characterized by the coordinates (x,y) of the upper and lower surface, and the following:

- Leading edge

- Trailing edge

- Extrados

- Intrados

- Chord: line joining the centres of curvature of the leading anf trailing edges.

- Mean or camber line

- Trailing edge

- Extrados

- Intrados

- Chord: line joining the centres of curvature of the leading anf trailing edges.

- Mean or camber line

Geometric parameters that summarize the airfoil:

- maximum
thickness (% of chord)

- position of max thickness (% of chord)

- maximum camber (% of chord)

- position of max camber (% of chord)

- nose radius

- trailing edge angle

- position of max thickness (% of chord)

- maximum camber (% of chord)

- position of max camber (% of chord)

- nose radius

- trailing edge angle

Fig. 2.1. Airfoil geometry

2.5 Aerodynamic forces

Angle of incidence: alpha defined as the angle between the chord and the direction of motion relative to the fluid

Resultant aerodynamic force: resultant of the pressure distribution

The line of action of the resultant
aerodynamic force intersects the chord in a point CP center
of pressure

The resultant force is resolved into
two components:

The Lift
L at right angle to the direction of motion

The Drag D parallel to direction of motion but opposing

The Drag D parallel to direction of motion but opposing

Resultant moment

Its value depends of the reference point for moments. The sense is such that a positive moment tends to increase the angle of incidence. Using the leading edge A as a point of reference for moments the magnitude is:

M(A) = -CP · (L cos (alpha) + D sin (alpha))

where CP is the distance of the centre of pressure behind the leading edge of the chord

It can be shown that there is a point on the chord, for which the aerodynamic moment does not vary with the angle of incidence. dM/dalpha=0 This point is called the aerodynamic center AC and has been found experimentally and theoretically that is within a quarter of the chord from the edge.

Then assuming CP=AC+(CP-AC) = AC + e ( e = distance between the aerodynamic center and center of pressure )

For small alpha values and assuming L>> D can be simplified as follows:

M(A) = -CP · L or

M(A) = -(AC + e) · L = -AC · L - e · L

By unitary chord AC=1/4 then

M(A) = - e · L - L/4

M(A) = M(AC) - L/4

M(AC) = moment about the aerodynamic center (does not vary with the angle of incidence)

For L = 0 , M(A)=M(AC)=M(0) (M(AC) = constant with alpha)

Then

M(A) = M(0) - L/4

The forces and moments can also be expressed by their respective lift, drag, and moment coefficients:

L = Cl · (1/2) · rho · V^2 · S (rho air density, V= air speed, S = wing projected area)

D = Cd · (1/2) · rho · V^2 · S

Cma = -CP · (Cl cos (alpha) + Cd sin (alpha))

Cma = Cm0 - Cl/4 (Cmo = Cm at zero lift)

The value and sign of Cm0 has an important role in the behavior and stability of the wing:

If Cmo<0 Cma will be more negative when alpha (Cl) increases, and CP moves backward

If Cmo>0 Cma will be positive for small alpha and CP moves forward

If Cm0=0 Cma follows Cl, and CP does not move located at a quarter of the chord from the leading edge

Cmo < 0 aerofoils will be called "unstable"

Cmo > 0 aerofoils will be called "stable"

Cmo < 0 aerofoils will be called "indiferent"

You
may use the three
types
of
Cm0 aerofoils in
paragliding. In
general, the
gliders
with
Cm0
<0 behave
in a more lively
and the easy
to
turn.
While whith
Cm> 0
we
have a more
stable wing, but
difficult
to
turn
(reflex airfoils). Depending
on
the use of
the
wing and its
performances
can
be used either
type. The
trend
is
to
use
profiles
Cm0
zero
or
slightly positive
on
the wings of
competition
to
temper
his
natural aggressive behavior. But
there is no fixed
rule on this issue.

The overall stability of the wing is controlled by the position of center of gravity. Should be discussed in another section.

The overall stability of the wing is controlled by the position of center of gravity. Should be discussed in another section.

Fig 2.2. Airfoil resultant

2.6 NACA profiles

The NACA aerofoils can be generated by the use of a set of simple polynomial equations.

(...)

2.7 Paraglider aerofoils

The paraglider airfoils, despite being pressurized fabric, behave like the rest of the gliders.

But besides the geometric and aerodynamic parameters described above, the following are also interesting:

- Position of air
inlets

- Position of anchors

- Internal rib holes

- Position of anchors

- Internal rib holes

Position
of air inlets: Must
ensure
the
air
entry
inside
the wing to
keep the pressure
inside
slightly
higher
than outside pressure. Can
be located by
theoretical
approaches, or
even
more frequent, by past
experiences. Air
intakes: 1% to 6% . Values in % of chord.

Position of anchors: It has to do with the transmission of loads to the inflated structure. Usual place from 5 to 2 anchorage points along the chord. As normal in many years has been to use 4 anchors "A", "B", "C", "D". In more hight AR competition wings, may be used only 2 locations on the chord, in order to reduce drag. The position of these anchors must be determined experimentally and from previous experiences. The reduction of anchors may require the use of internal reinforcements to secure the transmission of loads over a wide area.

Position of anchors: It has to do with the transmission of loads to the inflated structure. Usual place from 5 to 2 anchorage points along the chord. As normal in many years has been to use 4 anchors "A", "B", "C", "D". In more hight AR competition wings, may be used only 2 locations on the chord, in order to reduce drag. The position of these anchors must be determined experimentally and from previous experiences. The reduction of anchors may require the use of internal reinforcements to secure the transmission of loads over a wide area.

Internal holes: The general rule is, to distribute the holes to allow free air circulation between cells, and at the same time maintaining structural strength of the rib.

Example | Max thickness | Thickness location |
Max camber | Camber location |
Inlet begin | Inlet end | Lo A | Loc B | Loc C | Loc D |

1992 Comp |
17.09 |
23.3 |
3.09 |
29.8 |
2.16 |
6.6 |
9.6 |
30 |
51.1 |
72.4-85.3 |

1995 Bi |
19.19 |
24.3 |
2.06 |
21.9 |
1.38 |
5.83 |
9.4 |
32.02 |
55.9 |
79.9 |

gnuEASY |
15.52 | 24.2 | 4.8 | 31.6 | 0.25 | 6 | 7.8 | 33.3 | 57.7 | 79.4 |

gnuLAB1 | 14 | 21.4 | 1.83 | 39.6 | 0.12 | 3 | 8.5 | 31 | 53.5 | 75.8 |

Ascender | 18 | 21.9 | 2.03 | 15.7 | 1.2 | 5 | 8.5 | 27.5 | 53 | 78.5 |

gnuLAB2 |
18 | 21.9 | 2.03 | 15.7 | 1.2 | 5.5 | 8.5 | 27.5 | 53 | 78.5 |

gnuLAB3 |
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gnuA |
20 |
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gnuLAB4 |
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gnuLAB5 |

Fig 2.3 Paragliders airfoils

Fig 2.4: 1992 DHV-3 competition airfoil

Fig 2.5: 1995 Bi DHV-2 paraglider

Single skin airfoils

2.8 XFOIL program

XFOIL is an interactive program for the design and analysis of subsonic isolated airfoils. It consists of a collection of menu driven rutines which perform various useful functions such as:

- Analysis of an existing airfoil

- Airfoil design and redesign by interactive modification of surface speed distributions

- Airfoil redesign by interactive modification of geometric parameters

- Plotting of geometry, pressure distributions, and multiple polars

XFOIL is released under GNU General Public License. The detailed
manual and the program can be obtained from the website: http://web.mit.edu/drela/Public/web/xfoil/- Airfoil design and redesign by interactive modification of surface speed distributions

- Airfoil redesign by interactive modification of geometric parameters

- Plotting of geometry, pressure distributions, and multiple polars

2.9 XFLR5 program

2.10 AIrfoil fitting

LE procedure to obtain the paraglider aerofoil of any wing. Method based on the grid ripstop fabric.

Aerofoil fitting

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