Introduction
This chapter focuses on the aerodynamic fundamentals unique
to weight-shift control (WSC) operations. The portions of the
Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-
25) on principles of fl ight and aerodynamics apply to WSC
and are a prerequisite to reading this chapter.
Aerodynamic Terms
Airfoil is the term used for a surface on an aircraft that
produces lift, typically the wing itself. Although many
different airfoil designs exist, all airfoils produce lift in a
similar manner. Camber refers to the curvature of a wing
Aerodynamics
Chapter 2
Chord Line Upper Camber
Lower Camber
Chord Line Upper CamberLower Camber
Relative Wind
Flightpath
Single Surface Wing
Double Surface Wing
Trailing Edge
Leading Edge
Figure 2-1. WSC airfoil terms showing a single surface and a
double surface wing.
CG
Top View
Leading Edge Trailing Edge
Sweep Angle
Flightpath
Wing TipWing Root Chord
Tip Chord
Nose Angle
Wing Chords
Quarter Chord
Figure 2-3. Top view of a WSC wing and aerodynamic terms.
Chord Line
Typical Airplane Airfoil
Airplane Airfoil
WSC Airfoil
Airfoil Shape of WSC Compared to Airplane
WSC High Point
Farther forward
for stable airfoil
Airplane High Point
WSC Airfoil
Figure 2-2. Airplane airfoil compared to WSC airfoil.
when looking at a cross-section. A wing possesses upper
camber on its top surface and lower camber on its bottom
surface. WSC airfoils can be single surface, with one piece of
fabric for most of the airfoil, for slower wings. Faster airfoils
have two surfaces and are called double surface wings, which
are more like an airplane wing. [Figure 2-1] This double
surface allows the wing structure to be enclosed inside the
wing, similar to an airplane wing, reducing drag and allowing
for faster speeds for the same thrust. The leading edge is the
forward edge of the airfoil, and 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.
The WSC airfoil typically uses a different camber with the
airfoil high point farther forward than the airplane airfoil,
creating a more stable airfoil. [Figure 2-2]
The WSC wing is a unique design of airfoils that differ
throughout the wing span. Looking at a top view of the wing,
in the center is the wing root and on each end is the wingtip.
Wing chord is any section of the wing parallel to the wing
root. [Figures 2-3 and 2-4] The wingtip chord is the chord
where the trailing edge is furthest to the rear of the wing. This
can be inboard of the tip (as shown) and can vary depending
on the specifi c wing design. The nose angle is the angle made
by the leading edges, typically ranging from 120° to 130°.
Sweep is the angle measured between the quarter chord line
(line of 25 percent chords) and a line perpendicular to the
root chord. [Figure 2-3]
Rear View
Leading Edge
Wing Span
Wing Tip
Wing Root Tip Chord
Anhedral Angle
(Dihedral would be the
wing angled up)
Trailing Edge
Figure 2-5. Rear view of a WSC wing and aerodynamic terms.
CG
CG
Side View
Flightpath
Wing Root
Tip Chord
Wing Root
Figure 2-4. Side view of a WSC wing and aerodynamic terms.
Looking at the rear view of the wing, anhedral is the angle
the wings make angling down and dihedral is the angle the
wings make angling up. [Figure 2-5] Dihedral is the positive
angle formed between the lateral axis of an airplane and a line
which passes through the center of the wing. Anhedral is the
similar negative angle. Wings with sweep have an “effective
dihedral” characteristic that counteracts the physical anhedral
to develop the required roll stability for the particular make/
model design objective. This is explained in the Pilot’s
Handbook of Aeronautical Knowledge in much greater detail
for further reference. Unlike airplanes which typically have
signifi cant dihedral as viewed from the front or back for
roll stability, WSC wings typically have a slight amount of
anhedral as shown in Figure 2-5 and effective dihedral which
is a characteristic of the swept wing design.
Wing twist is the decrease in chord angle from the root
to the tip chord, common to all WSC wings and ranging
from 5° to 15°. This wing twist is also called washout as
the wing decreases its angle of attack from root to tip. The
term billow was originally used for the early Rogallo wings
as the additional material in degrees that was added to the
airframe to create the airfoil. It is still used today to defi ne the
amount of twist or washout in the wing. The WSC may not
have twist/washout when sitting on the ground, and must be
fl ying and developing lift to display the proper aerodynamic
twist characteristic of WSC wings. [Figure 2-6]
The longitudinal axis is an imaginary line about which the
aircraft rolls around its center of gravity (CG); it is also
called the roll axis. The longitudinal axis is not necessarily a
fi xed line through the carriage because the roll axis changes
for different fl ight confi gurations, but can be approximated
by the middle of the propeller shaft for a properly designed
WSC aircraft and is typically parallel with the fl ightpath of
the aircraft as shown in Figure 2-7. Angle of incidence is
the angle formed by the root chord line of the wing and the
longitudinal axis of the WSC aircraft.
Wing twists from root to tips
Relative
Wind
Relative
Wind Relative
Wind
AOA high at Root AOA lower at m
idpo
int
AOA low at tip
Chord Line
Cho
rd Line
Chord Line
Figure 2-6. Wing twist shown for a WSC wing in flight.
Relative Wind
Flightpath
Relative Wind
Flightpath
Longitudinal Axis
Longitudinal Axis
CG
CG
Low Angle of Incidence
High Angle of Incidence
Control Bar Out—Slow Flight
Control Bar In—Fast Flight
Root Chord of Wing
Control Bar
Control Bar
Root Chord of Wing
Carriage Hang Point
Carriage Hang Point
Figure 2-7. Angle of incidence.
Unlike that of an airplane, the WSC angle of incidence has a
signifi cant change in fl ight because the carriage is attached to
the wing, which allows the wing to rotate around the carriage
hang point on the wing and is controlled by the pilot as shown
in Figure 2-7.
Pitch angle is the angle the WSC wing root chord (center
of wing) makes with the Earth’s horizontal plane. Many
pilots confuse the pitch angle, which is easily seen and felt,
with the angle of attack (AOA) which is not as perceptible.
For example, if fl ying in a glide with the engine idle and
the nose lowered, the pitch angle can be below the horizon.
Another example would be fl ying at full power climb with
the nose raised, resulting in the pitch angle being well above
the horizon. [Figure 2-8] Pitch angles are covered in greater
detail in chapter 6.
Deck angle is the angle of the cart’s wheel axles to the landing
surfaces, as in the powered parachute (PPC) deck angle.
Relative wind is the direction of the airfl ow with respect to
the wing; it is parallel to and opposite the WSC fl ightpath.
Relative wind may be affected by movement of the WSC
through the air, as well as by all forms of unstable, disturbed
air such as wind shear, thermals, and turbulence. When a
Figure 2-8. Pitch angle examples of nose high (top) and nose low
(bottom).
Low Speed (near stall)Cruise Speed (trim)High Speed
Control bar pulled in No control bar pressure Control bar pushed out
18°
Angle of Attack
10°
Angle of Attack
3°
Angle of Attack
Relative Wind
Flightpath
Relative Wind
Flightpath
Relative Wind
Flightpath
Figure 2-9. Angle of attack effect on speeds, relative wind, and flightpath for level flight.
WSC is fl ying through undisturbed air, the relative wind is
parallel to and opposite the fl ightpath. [Figure 2-7]
AOA is the angle between the relative wind and the wing
chord line. Because of the wing twist, the AOA is greatest
at the wing root and decreases along the wing span to the
tips. This is an important concept covered in the stability
section of this chapter. For changing speeds during gliding,
level fl ight, and climbs, AOA is the primary control for speed
changes. Lower angles of attack produce higher speeds, and
higher angles of attack result in slower speeds.
The pilot changes the AOA by moving the control
bar forward for high angles of attack and slow speeds
as shown in Figure 2-7 (top) for high angle of incidence and
Figure 2-8 (top) for high pitch angle. Low angles of attack for
fast speeds are shown in Figure 2-7 (bottom) for low angle of
incidence and Figure 2-8 (bottom) for low pitch angle.
Most of the time, the pilot is fl ying at the cruise AOA,
which is the trim position of the control bar, and the pilot is
neither pushing out nor pulling in on the control bar. This
trim position is the AOA and speed the aircraft fl ies if the
pilot is fl ying straight and releases the control bar in calm
air. [Figure 2-9, middle]
Planform is the shape or form of a wing as viewed from
above. The WSC wing comes in a number of planforms
ranging from the larger and slower wings to the smaller and
faster wings.
Aspect ratio is the wingspan divided by the average chord
line. A WSC aircraft with a common 200 square foot training
wing (about a 35 foot wingspan), and with a typical mean
chord line of 7 feet, would have an average aspect ratio of 5.
This relatively low aspect ratio is less effi cient at producing
lift. A higher performance wing with 140 square feet, a 35
foot wing span, and an average 5 foot average chord would
have an aspect ratio of 7. The WSC wing is similar to airplane
wings in that the aspect ratio differs with the specifi c design
Slow Trainer—Low Aspect Ratio
Fast Cross-Country—High Aspect Ratio
Figure 2-10. Wing planforms showing the slow trainer with a low
aspect ratio and the fast cross-country with a high aspect ratio.
Foam or mylar maintains the airfoil
shape up to the high point.
Rigid ribs called battens
maintain the airfoil shape.
Figure 2-11. Rigid airfoil preformed ribs called battens and leading
edge stiffener maintain the rigid airfoil shape.
mission for the aircraft. For the same wing area and similar
design, the lower aspect ratio wings produce less lift and
more drag; higher aspect ratio wings produce more lift, less
drag, and may require more pilot effort to fl y, depending on
the design. [Figure 2-10]
Wing loading is a term associated with total weight being
carried by the wing in relation to the size of the wing. It is the
amount of load each square foot of the 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. For example, the wing loading would be 5.0 pounds per
square foot when 1,000 pounds total weight for a two-seat
WSC aircraft with two people is supported by a 200 square
foot wing. If fl ying the same wing with one person and a
lighter total weight of 500 pounds, the wing loading would
be 2.5 pounds per square foot. In the small, high performance
wing of 140 square feet loaded at 1,000 pounds, wing loading
would be 7.1 pounds per square foot.
Gliding fl ight is fl ying in a descent with the engine at idle
or shut off. For example, use a glide ratio of 5, which is fi ve
feet traveled horizontally for every foot descended vertically.
Glide ratios vary signifi cantly between models.
WSC Wing Flexibility
The WSC wing retains its rigid airfoil shape due to rigid
preformed ribs called battens, which are inserted from the
root to the tip along the span of the wing (similar to ribs
for an airplane wing) and a piece of foam or mylar running
along the top side of the leading edge to the high point, which
maintains its front part of the airfoil shape in between the
battens. [Figure 2-11]
Some WSC double surface wing designs use a rib similar
to a PPC wing that attaches to the lower surface and the
upper surface to maintain the wing camber in addition to
the battens.
Even though the airfoil sections are rigid, the WSC aircraft is
called a “ fl ex wing” for two reasons. First, it is designed so
the outboard leading edges fl ex up and back when loaded. The
fl exing of the outboard section of the wing also allows load
relief because the tips increase twist and decrease AOA—the
greater the weight, the greater the fl ex and wing twist. This
fl exing allows the WSC aircraft to automatically reduce loads
in unstable air, providing a smoother ride than a rigid wing.
Since the wing fl exes and reduces the load for a given angle
of attack at the root chord, WSC aircraft cannot obtain loads
as high as those obtained by a rigid wing. This fl exing of the
outboard leading edges also assists in initiating a turn.
Second, the wing is designed to fl ex as it changes twist from
side to side for turning, historically known as wing warping.
WSC wing warping is similar to what the Wright Brothers
did on their early aircraft, but they did it with wires warping
the wing. The WSC aircraft uses no wires and warps the
wing by shifting the weight, which is covered in Chapter 3,
Components and Systems.
This fl exibility is designed into the wing primarily for turning
the aircraft without any movable control surfaces like the
ailerons and rudder on an airplane.
L = CLV
L = Lift (pounds)
CL = Coefficient of lift
(This dimensionless number is the ratio of lift
pressure to dynamic pressure and area. It is
specific to a particular airfoil shape and, above
the stall, it is proportional to angle of attack.)
V = Velocity (feet per second)
= Air density (slugs per cubic foot)
S = Wing surface area (square feet)
Figure 2-13. The lift equation.
Weight
Lift
CG
Thrust Drag
Relative Wind
Flightpath
Figure 2-12. The four basic forces in level fl ight.
Forces in Flight
The four forces that affect WSC fl ight are thrust, drag, lift,
and weight. [Figure 2-12] In level, steady WSC fl ight:
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.
3. The sum of all moments equals zero.
Note that the lift and weight forces are much greater than
the thrust and drag forces. A typical example for many
WSC aircraft is that the lift/weight forces are fi ve times the
thrust/drag forces.
Thrust—the forward force produced by a powerplant/propeller
as it forces a mass of air to the rear (usually acts parallel to
the longitudinal axis, relative wind, and fl ightpath).
Drag—the aerodynamic force acting on the wing and carriage
in the same plane and in the same direction as the relative
wind.
Lift—the aerodynamic force caused by air fl owing over the
wing that is perpendicular to the relative wind.
Weight—the force of gravity acting upon a body straight
down and perpendicular to the Earth.
During level fl ight, these forces are all horizontal and vertical.
During descents or climbing, these forces must be broken
down into components for analysis.
Dynamic Pressure (q)
Both lift and drag are a direct result of the dynamic pressure
of the air. Dynamic pressure (q) is created from the velocity
of the air and the air density. An increase in velocity has a
dramatic effect on dynamic pressure (q) because it increases
with the square of the velocity. Doubling the velocity means
“q” increases by four times. Increasing the velocity by a
factor of three means that the dynamic pressure (q) increases
by a factor of nine. This is a very important concept in
understanding the aerodynamics of WSC.
Formula for dynamic pressure: q = V2 x ρ/2
V = velocity
ρ = density factor
Lift
Lift opposes the downward force of weight and is produced
by the dynamic effects of the surrounding airstream acting
on the wing. Lift acts perpendicular to the fl ightpath through
the wing’s center of lift. There is a mathematical relationship
for lift which varies with dynamic pressure (q), AOA, and the
size of the wing. In the lift equation, these factors correspond
to the terms q, coeffi cient of lift (CL), and wing surface area.
The relationship is expressed in Figure 2-13.
Figure 2-13 shows that for lift to increase, one or more of
the factors on the other side of the equation must increase.
Generally, the lift needed is about the same for most fl ight
situations. A slower speed requires a higher AOA to produce
the same amount of lift. A faster speed requires a lower AOA
to produce the same amount of lift.