Chapters 2 and 3 of the Pilot’ s Handbook of Aeronau-
tical Knowledge (FAA-H-8083-25) apply to powered
parachutes and are a prerequisite to reading this book.
This chapter will focus on the aerodynamic fundamen-
tals unique to powered parachute (PPC) operations.
Aerodynamic Terms
Airfoil is the term used for surfaces on a powered
parachute that produce lift, typically the wing itself.
Although many different airfoil designs exist, all air-
foils produce lift in a similar manner.
Camber refers to the curvature of a wing when look-
ing at a cross section. A wing possesses upper cam-
ber on its top surface and lower camber on its bottom
surface. Leading edge describes the forward edge of
the airfoil. The rear edge of the airfoil is called the
trailing edge. The chord line is an imaginary straight
line drawn from the leading edge to the trailing edge.
[Figure 2-1]
Longitudinal axis is an imaginary line about which
the aircraft rolls; it is also called the roll axis. The
longitudinal axis is not a fixed line through the cart
because the angle of incidence changes in turbulence
and with loading changes.
Angle of incidence is the angle formed by the chord
line of the wing and the longitudinal axis of the PPC
cart. The cart longitudinal axis is not the same as the
aerodynamic longitudinal axis defined in the previous
paragraph. [Figure 2-2] Unlike an airplane, the angle
of incidence can change in flight because of the flex-
ible line attachment between the wing and the cart.
Angle of incidence can change for different types of
flight configurations and PPC designs; this is covered
in detail in the “Moments” section.
Trim angle is the angle between the chord line of the
wing and the horizontal plane when the PPC is in non-
powered gliding flight. [Figure 2-3] The PPC wing is
designed at a slight angle, with the chord line inclined
downward to the horizontal plane to maintain the
manufacturer-designed angle of attack during gliding,
level and climbing flight. This “trim angle” is built
into the powered parachute by the manufacturer and
cannot be adjusted by the pilot moving the controls.
Pitch angle is the angle the PPC wing chord makes
with the horizontal plane. Pitch angle is what you can
see. Many pilots confuse the pitch angle, which you
can easily see and feel, with the angle of attack which
may not be as perceptible. [Figure 2-4] For example,
the pitch angle in an engine-out glide could be minus
8 degrees, in level flight 10 degrees above the hori -
zon, and in a climb it could be 28 degrees above the
horizon. These are significantly different angles you
easily see. Pitch angles are covered in greater detail
in Chapter 6.
Deck angle is the angle of the cart’s lower frame
(from the front wheel to the rear wheels), to the land-
ing surface. The deck on the lower part of the conven-
tional cart frame can be used to visualize deck angle.
An imaginary line between the front and back wheel
axles can also be used on unconventional carts.
Figure 2-1. Aerodynamic terms of an airfoil.
Leading edge
Chord line
Lower camber
Upper camber
Trailing edge
Relative wind
Flight path
Relative wind is the direction of the airflow with re -
spect to the wing; it is usually parallel to and opposite
the PPC flight path. Relative wind may be affected
by movement of the PPC through the air, as well as by
all forms of unstable, disturbed air such as wind shear,
thermals, turbulence, and mountain rotors. When a
PPC is flying through undisturbed air, the relative
wind is parallel to and opposite the flight path.
Angle of attack is the angle between the relative wind
and the wing chord line. [Figure 2-2]
Planform is the shape or form of a wing as viewed
from above. The PPC wing comes in two wing plan -
forms: rectangular, and elliptical. [Figure 2-5] The el-
liptical planform leading and trailing edges are curved
to form an elliptical shape when viewed from the top
or bottom. These two shapes have unique flying char-
acteristics. Rectangular wings typically produce more
drag, are lower-performance, and do not move fore
and aft, relative to the cart, as quickly as elliptical
wings. These characteristics are more obvious when
the wing is inflating, during pitch changes, and when
flying in turbulence. Rectangular wings are therefore
more stable and require less effort to fly. Elliptical
wings are higher-performance and more efficient due
to less drag. Elliptical wings react more quickly with
changing conditions and require greater pilot experi-
ence and skill during inflation, in turbulent air, and
with abrupt throttle changes.
Aspect ratio is the wingspan divided by the average
chord line. A PPC with a common 500-square foot
rectangular wing (about a 38-foot wingspan) and with
a typical mean chord line of 13 feet, would have an
average aspect ratio of about 3. This relatively low
aspect ratio is less efficient at producing lift. An ellip-
tical wing with the same 500 square feet and a 45-foot
wing span and an 11-foot average chord would have
an aspect ratio of about 4. The PPC wing is similar to
airplane wings in that the aspect ratio will differ with
the specific design mission for the aircraft. Generally,
Figure 2-2. Angle of incidence.
Figure 2-3. Angle of trim and center of pressure in gliding
flight.
rectangular wings have lower aspect ratios and lower
efficiency than the higher aspect ratio and higher effi-
ciency elliptical wings. Generally, a high aspect ratio
wing, compared to a low aspect ratio wing, produces
higher lift at lower angles of attack with less induced
drag. [Figure 2-6].
Wing loading is a term associated with the total
weight the ram-air wing must support. Wing loading
is found by dividing the total weight of the aircraft, in
pounds, by the total area of the wing, in square feet.
Wing loading is found by dividing the weight of the
aircraft, in pounds, by the total area of the wing, in
square feet. For example, the wing loading would be
2.0 pounds per square foot when 1,000 pounds—a
common weight for a two-seat PPC with two people
— is under a 500-square foot wing. If flying with one
person the aircraft weight might be 700 pounds and
the wing loading would decrease to 1.4 pounds per
square foot.
Gliding flight is flying in a descent with the engine at
idle or shut off.
Powered Parachute Wing
Pressurization and Flexibility
The powered parachute has two distinctive modes: (1)
inflated, it is a ram-air wing with a curved arc—a rec-
ognizable airfoil shape; and (2) deflated, it is a canopy
that is either lying flat on the ground or packed into
a bag.
Figure 2-4. Gliding and climbing pitch angles.
Figure 2-5. Planform view of a PPC inflated wing:
rectangular and elliptical.
Note: Chapter 7, Takeoffs and Departure Climbs, will
detail the methods of getting the uninflated canopy
laying on the ground turned into a flying wing. Since
the aerodynamics of the PPC do not start until the
wing is completely inflated, this chapter will assume
each reference to the PPC wing is to an inflated ram-
air wing already in the shape of an airfoil.
The powered parachute ram-air wing retains its air -
foil shape due to the air pressurizing the inside cells
via the relative wind airflow being rammed into the
front openings of the canopy —thus the term “ram-air
wing.” The pressure inside the wing is much higher
than the outside top and bottom because the dynamic
pressure from the relative wind is converted to static
pressure to pressurize the wing. The greater the speed,
the greater the pressure inside the wing and the more
rigid the wing. The cell openings are designed to be
perpendicular to the relative wind to achieve maxi -
mum pressure from the relative wind. This static in -
ternal pressure harnessed from the relative wind is
called dynamic pressure (q), and is determined by the
velocity squared times the air density factor. [Figure
2-7] Note the dynamic air pressure converted to static
pressure at point A is constant throughout the wing
points B and C. This static pressure is always greater
than the pressure outside the wing at points X and Z.
Cross-port openings are placed in the ribs of each cell,
connecting the adjoining cells. These cross-ports are
dispersed throughout the wing (with exception to the
outboard side of the end cells) to maintain positive
pressure throughout. The pressure is constant inside
the wing because the dynamic pressure hitting the
opening is the same for each cell and the speed is
the same. The cross-ports aid the complete wing in
becoming pressurized during inflation and maintain -
ing the pressure throughout the wing in turbulence.
[Figure 2-8]
The inflatable wing airfoil generally remains a consis-
tent shape as designed by the manufacturer. However,
pilot control of the wing to make a turn significantly
changes the relative aerodynamic qualities of the PPC
wing by pulling down the trailing edge similar to a
flap on an airplane. [Figure 2-9]
Figure 2-7. Dynamic pressure.
Figure 2-8. Cell openings and cross-port view.
Figure 2-6. Aspect ratio comparisons for wings with similar areas.
Faster speeds from smaller wings or more weight cre-
ate a higher pressure in the wing resulting in higher
control forces because of the higher internal pressure.
Forces in Flight
Like all aircraft, the four forces that affect PPC flight
are thrust, drag, lift, and weight. [Figure 2-10] In
steady PPC flight:
1. The sum of all upward forces equals the sum of
all downward forces.
2. The sum of all forward forces equals the sum of
all backward forces.
Figure 2-9. PPC wing flexibility in flight.
Figure 2-11. The lift equation.
Figure 2-10. Level flight forces.
3. The sum of all moments equals zero.
THRUST – the forward force produced by a power -
plant/propeller as it forces a mass of air to the rear (usu-
ally said to act parallel to the longitudinal axis).
vs.
DRAG – the aerodynamic force acting on the airfoil
lines and cart in the same plane and in the same direc-
tion as the relative wind.
LIFT – the aerodynamic force caused by air flowing
over the wing that is perpendicular to the relative
wind.
vs.
WEIGHT – the force of gravity acting upon a body.
Lift
Lift opposes the downward force of weight and is pro-
duced by the dynamic effects of the surrounding air -
stream acting on the wing. Lift acts perpendicular to
the flight path through the wing’s center of lift. There
is a mathematical relationship between lift, angle of
attack, airspeed, altitude, and the size of the wing. In
the lift equation, these factors correspond to the terms
coefficient of lift, velocity, air density, and wing sur -
face area. The relationship is expressed in Figure 2-11.
This shows that for lift to increase, one or more of the
factors on the other side of the equation must increase.
Lift is proportional to the square of the velocity, or
airspeed, therefore, doubling airspeed quadruples the
amount of lift if everything else remains the same.
Small changes in airspeed create larger changes in
lift. Likewise, if other factors remain the same while
the coefficient of lift increases, lift also will increase.
The coefficient of lift goes up as the angle of attack
is increased. As air density increases, lift increases.
However, you will usually be more concerned with
how lift is diminished by reductions in air density on
a hot day, or if you are operating at higher altitudes.
All wings produce lift in two ways:
1. Airfoil shape creating a higher velocity over
the top of the wing and a lower velocity over
the bottom of the wing with Bernoulli’s venturi
effect.
2. Downward deflection of airflow because of
the curvature of the wing with the principle of
Newton’s Third Law of Motion: For every action,
there is an equal and opposite reaction.
Both principles determine the lifting force. Review
Chapter 2 in the Pilot’ s Handbook of Aeronautical
Knowledge to understand Newton’s laws of motion
and force and Bernoulli’s principle of pressure.
Drag
Drag is the resistance to forward motion through the
air. Drag opposes thrust. Aerodynamic drag comes in
two forms:
1. Induced drag: a result of the wing producing lift;
2. Parasite drag: resistance to the airflow from
the cart, its occupants, suspension lines from
the wing, interference drag from objects in the
airstream, and skin friction drag of the wing.
Induced drag is the result of lift, and its amount var -
ies as discussed above for lift. Induced drag creates
organized circular vortices off the wing tips that gener-
ally track down and out from each wingtip. [Figure 2-
12] This is true for all aircraft that use wings including
PPC, weight-shift control and fixed wing aircraft. The
bigger and heavier the aircraft, the greater and more
powerful the wingtip vortices will be. This organized
swirling turbulence is an important factor to understand
for flight safety. Refer to Section 7-3 of the Aeronau-
tical Information Manual (AIM) or Chapter 12 of the
Pilot’ s Handbook of Aeronautical Knowledge (FAA-H-
8083-25) for additional discussion.
Parasite drag is caused by the friction of air moving
over the structure. Just as with lift, parasite drag in -
creases as the surface area of the aircraft increases
and dramatically increases as airspeed increases,
at the square of the velocity. Therefore, doubling
the airspeed will quadruple your parasite drag.
[Figure 2-13]
The PPC has relatively slow speeds, but plenty of
items (area) for the wind to strike including wing,
lines, pilot, cart, engine, wheels, and tubes. Parasitic
drag can be reduced by streamlining the items but
since the PPC flies at relatively slow airspeeds, the
extra weight, cost, and complexity of streamlining the
PPC is generally not incorporated into the design.
Total Drag is the combination of parasite and induced
drag. Total Drag = Parasitic Drag + Induced Drag
To help explain the force of drag, the mathematical
equation D = Cd · q · S is used. In this equation drag
(D) is the product of drag coefficient (Cd), dynamic
pressure (q) determined by the velocity squared times
the air density factor, and surface area (S) of the cart
and the ram-air wing (S). The drag coefficient is the
ratio of drag pressure to dynamic pressure.
Figure 2-12. Turbulence — induced drag wingtip vortices
— created by lift of the ram-air wing.
Figure 2-13. Frontal areas of the cart, wing, and occupants
are the source of parasitic drag.
Induced and parasitic drag have opposite effects as
angle of attack decreases and speed increases. Note
the total drag. It is high at the slowest air speeds at
high angles of attack near the stall, decreases to the
lowest at the most efficient airspeed, and then pro -
gressively increases as the speed increases. The PPC
wing is typically designed to fly at a speed generally
above lowest overall total drag. Too slow, and the
wing would be near its critical angle of attack. Too
fast, and the power to maintain level flight or climb
would be excessive. The manufacturer determines the
speed range of the wing based on the weight range,
and the resultant location on the total drag diagram.
[Figure 2-14]
Figure 2-14. Relationship between drag and speed.
are very similar to those for an airplane or gliding
sailplane. [Figure 2-15] Specific numbers presented
in this chapter are examples to serve as a basis to
understand the concepts. Each PPC has unique fly -
ing characteristics and these numbers will be differ -
ent, but can be compared to your PPC to provide a
greater understanding of your unique performance.
Note the component of weight acting along the flight
path. This component of weight is called thrust by
some but is more accurately the weight component
providing the forward force.
Figure 2-15. Typical forces in gliding flight, with no engine
thrust.
Weight
Weight is a measure of the force of gravity acting upon
the mass of the PPC. It is the force that opposes lift,
and acts vertically downward through the aircraft’s
center of gravity. Weight consists of everything di -
rectly associated with the powered parachute in flight:
the combined load of the total PPC (wing, risers, en -
gine, cart, fuel, oil, etc.), people (clothing, helmets,
etc.), and baggage (charts, books, checklists, pencils,
handheld GPS, spare clothes, suitcase, etc.). In stabi-
lized level flight, when the vertical component of lift
is equal to the weight force, the PPC is in a state of
equilibrium and neither gains nor loses altitude.
Because the trim angle is set at the factory, the PPC
airspeed is predetermined, before takeoff, by the
weight of the aircraft and the wing design. The more
weight, the more forward airspeed is generated.
Therefore, gravity is the primary force for creating
forward speed — pulling the wing through the rela -
tive wind while airborne. The forces in gliding flight
Thrust
Compared to an airplane, as discussed in Chapter 3
of the Pilot’ s Handbook of Aeronautical Knowledge,
thrust serves different purposes in the PPC: (1) it is
used to accelerate the PPC to flying speed while in -
flating the wing (2) it is used to climb when at high
thrust, cruise level at medium thrust, and descend at
lower thrust. Variations in thrust have negligible effect
on PPC airspeed which remains relatively constant
whether climbing, descending, or in level flight.
When enough thrust is added to produce level flight,
the relative wind stream becomes horizontal with
the earth; the angle of attack and speed remain about
the same. Just as described in the Pilot’ s Handbook
of Aeronautical Knowledge for the airplane, thrust
equals total drag for level flight. [Figure 2-16]
When in straight-and-level unaccelerated flight:
LIFT (L) = WEIGHT (W)
and
THRUST = TOTAL DRAG (DT)
Figure 2-17. Powered parachute in climbing flight.
Figure 2-16. Powered parachute in level flight.
Center of Gravity
The center of gravity ( CG) is the theoretical point
of concentrated weight of the aircraft. It is the point
within the PPC about which all the moments trying to
rotate it are balanced. The most obvious difference in
the center of gravity for a PPC is the vertical position
compared to an airplane, as it is much lower than the
wing. The Pilot’ s Handbook of Aeronautical Knowl-
edge accurately states the center of gravity is gener -
ally in the vertical center of the fuselage. The same
is true for the PPC. However, the PPC wing is high
above the fuselage (cart) creating the unique pendu -
lum effect flying characteristics of the PPC (which
will be covered in detail later).
In a two-seat PPC, the second seat is typically behind
the pilot’s seat, and the center of gravity is usually
located directly over the rear passenger seat. There -
fore, the center of gravity location does not change
significantly with or without a passenger. Fuel tanks
are typically located near the center of gravity so
any differences in fuel quantity will not significantly
change the center of gravity fore and aft with different
fuel quantities.
When excess thrust is added to produce climbing
flight, the relative air stream becomes an inclined
plane leading upward, while angle of attack and speed
remain about the same. Just as described in the Pilot’ s
Handbook of Aeronautical Knowledge for the air -
plane, the excess thrust determines the climb rate and
climb angle of the flight path. [Figure 2-17]