Introduction
This chapter discusses glider-related aerodynamics. A pilot who understands how forces affect a glider can operate safely
while maximizing performance. To obtain a more detailed description of general aerodynamics, see the Pilot's Handbook
of Aeronautical Knowledge (FAA-H-8083-25).
A glider maneuvers around three axes of rotation: vertical, lateral, and longitudinal. Each axis is perpendicular to the other
two, and all three axes intersect at one central point called the center of gravity (CG), which varies with the loading of
the glider. Any object on the ground will balance in any orientation if supported from the CG or a point directly above or
below the CG.
Yaw describes movement around the vertical axis, represented by an imaginary straight line drawn through the CG.
[Figure 3-1] In flight, moving the rudder left or right causes the glider to yaw. The lateral axis runs parallel to a line from
wingtip to wingtip. Pulling the stick back or pushing it forward changes the pitch of the glider and controls its movement
around the lateral axis. Roll describes movement around the longitudinal axis caused by displacing the ailerons in opposite
directions. This axis runs parallel to a line drawn from the nose to the tail.
Vertical axis
Longitudinal axis
Lateral axis
YAW
PITCH
ROLL
CG
Figure 3-1. Three axes of rotation with each perpendicular to the other two and all intersecting at the CG.
Forces of Flight
Three forces act on an unpowered glider while in flight—lift, drag, and weight. Thrust is another force of flight that enables
self-launching gliders to launch on their own and stay aloft when soaring conditions subside.
Chapter 3: Aerodynamics of Flight
Flight Path
Lift
Drag
Weight
Flight Path
Weight
Thrust Drag
Lift
Figure 3-2. Vector components of lift, thrust, drag, and weight (gravity).
Lift
Newton’s laws and Bernoulli’s principle explain lift from different perspectives. Newton’s third law describes the overall
interaction between atmosphere and wing, while Bernoulli’s principle looks at the effect of air changing speed as it moves
past the wing. Together, these models provide a valid explanation of lift.
Newton’s Third Law
According to Newton’s Third Law of Motion, for every action there is an equal and opposite reaction. As air deflects
downward because of interaction with the wing, the wing experiences an upward (lifting) reaction.
Bernoulli’s Principle
Bernoulli’s Principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid
decreases. This principle explains what happens when air moves faster to pass over the top of a wing positioned at an angle
to the relative wind, i.e., the wind resulting from the forward motion of the glider. The increase in speed of the air as it
travels over the top of the wing produces a drop in pressure against the wing, and the higher air pressure below the wing
results in a net lifting force.
Lift Formula
A mathematical relationship exists between lift, the coefficient of lift, airspeed, air density, and the size of the wing.
Figure 3-3 shows the relationship.
L = Lift
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, below
the stall, it is proportional to angle of attack.)
V = Velocity (feet per second)
ρ = Air density (slugs per cubic foot)
S = Wing surface area (square feet)
L = CL V2 2 S
ρ
Figure 3-3. Lift Equation.
The lift equation shows that total lift changes as the factors on the right side of the equation change. For example, lift varies
directly with the coefficient of lift. A pilot should understand the concept of angle of attack (AOA) to understand how the
coefficient of lift varies. The angle of attack is the acute angle between the chord line of the wing and the relative wind
developed by the motion of the glider through the air. [Figure 3-4] The coefficient of lift increases linearly until reaching
a critical angle, at which point lift decreases even though the angle of attack increases. Once reaching the critical angle,
any further increase in the angle of attack disturbs the smooth airflow over the top of the wing and causes a decrease in lift
or a stall. Lift also varies with the square of velocity or airspeed. Doubling airspeed quadruples the amount of lift. As air
density decreases with increasing altitude or rising temperature, lift decreases.
Flight path
Relative wind
Flight path
Relative wind
Flight path
Relative wind
3° Angle of Attack 6° Angle of Attack 12° Angle of Attack
Figure 3-4. Angle of attack.
When describing lift as a vector, the total lift acts through a point known as the center of lift (CL). This point occurs aft of
the center of gravity. Therefore, lift creates a pitching moment on the glider, which the tail must counteract. The total lift
vector acts perpendicular to the flightpath through the CL and perpendicular to the lateral axis.
Drag
The force that resists the movement of the glider consists of parasite and induced drag, which combine to form total drag.
Parasite Drag
Parasite drag includes the resistance of the air to any object moving through it created by skin friction, the shape of the
object, and interference patterns within the airflow around the object. While glider wing designs generate minimal induced
and parasite drag, other parts of the glider may create significant parasite drag. Parasite drag increases with the square of
speed. Simply put, if the speed of the glider doubles, parasite drag increases four times. [Figure 3-5]
Drag
Speed
Parasite drag
Figure 3-5. Parasite drag versus speed.
Induced Drag
As the angle of attack increases, more air flows around the wingtip from the lower to the upper surface, which creates
larger wingtip vortices. [ Figure 3-6]. Panel 4 of Figure 3-6, depicts the wing moving horizontally in level flight. The
vertical lift vector develops perpendicular to the flight path and oncoming relative wind. Since wingtip vortices cause
a downward divergence of the average relative wind from the flightpath, the total lift vector, which is perpendicular to
the average relative wind, tilts back. This backward tilt of the total lift vector creates induced drag as a byproduct of lift.
Factors that increase the angle between the total lift and vertical lift vectors, such as low airspeed and high angle of attack,
increase induced drag.
Induced Drag
Flight Path Relative Wind
Vertical liftTotal lift
Average relative wind
2 Wingtip vortices develop.
4 The average relative wind is inclined downward
and rearward, and lift is inclined aft. The rearward
component of lift is induced drag.
3 The downwash increases behind the wing.
1 High pressure air joins low pressure air at the
trailing edge of the wing and wingtips.
Low
pressure Low
pressure
High pressure High pressure
Atmospheric pressure
Atmospheric pressure
Figure 3-6. Induced drag from the production of lift.
As a glider flies faster, the wings can generate the same amount of lift with a reduced angle of attack. Increased speed with
a smaller angle of attack reduces the backward slant of the total lift vector and reduces induced drag.
Total Drag
The total drag curve represents the combination of parasite and induced drag and varies with airspeed. [Figure 3-7]
Drag
Speed
Induced drag
Parasite dragTotal drag
Stall Speed
(L/DMAX
)
Minimum
Drag
Figure 3-7. Parasite drag, induced drag, and total drag versus airspeed.
Ground Effect
Operating within one wingspan above the ground modifies the three-dimensional airflow pattern around the glider. This
ground effect decreases downwash, reduces the size and effect of wingtip vortices, reduces induced drag, and results in
more efficient flight. This effect allows the glider to fly at a lower airspeed during takeoff and reduces the sink rate of a
glider on landing.
Weight
Weight results from the force of gravity acting on the mass of the glider. The vertical components of both lift and drag act
in opposition to the weight vector, which acts vertically downward through the center of gravity.
Thrust
Unpowered gliders use an outside source, such as a tow plane, winch, or vehicle, to launch. Once released, these gliders
maintain forward motion from conversion of potential energy to kinetic energy. A glider descends through the surrounding
air to make this conversion. Powered gliders have engines, which can provide thrust for launch or to sustain flight.
Unpowered Glide Vector Analysis
What propels an unpowered glider in a continuous descent in the surrounding airmass? A vector diagram with the flight
path as one axis and a second axis perpendicular to the flight path depicts how the forces of weight, lift, and drag balance
each other during an unpowered straight-line descent. [Figure 3-8] Weight (W) always points to the ground (center of the
Earth). Lift (L) develops perpendicular to the flight path. Drag always acts backward along the flight path. While weight
does not align with either axis on the diagram, the weight vector can resolve into two perpendicular components, one
forward along the flight path opposing drag (Wf) and the other perpendicular to the flight path opposing lift (Wp). As
shown in the figure, Wp balances lift, while Wf balances drag during an unaccelerated descent. Thus, gravity is the external
engine that pulls the glider forward by acting on Wf.
Horizontal
Flight Path
Chordline
Wf
Wp
γ α
γ
L = Lift
D = Drag
W = Weight
Wp = perpendicular component of weight
Wf = forward component of weight
γ = flight path angle (or angle of descent)
α = angle of attack
Balance of forces acting perpendicular to the flight path:
L - Wp = 0 or L = Wp
Where Wp = W cos γ
Balance of forces acting along the flight path:
Wf - D = 0 or Wf = D
Where Wf = W sin γ
Figure 3-8. The forces along an unpowered glider’ s flight path and its perpendicular.
An unpowered descent converts the glider’s potential energy of height above the ground into kinetic energy of motion on
a continuous basis. The flight path angle or angle of descent (ɣ) is the same as the angle between Wp and W. Wf, Wp, and
W could form three sides of a right triangle. Trigonometry gives the Wf and Wp components of weight using the formulas
shown within the balance of forces boxes in Figure 3-8. A steeper flight path angle (ɣ) increases the forward component of
weight (Wf) and decreases the perpendicular component of weight (Wp).
Glide Ratio & Wing Design
One specific point appears in Figure 3-7 above. The point displayed, (L/DMAX), corresponds to a speed where the total lift
capacity of the glider, when compared to the total drag reaches a maximum value. In calm air, this speed yields maximum
glide distance and the published glide ratio for a glider. The glide ratio gives the distance the glider can travel during a
given descent in altitude. For example, a glide ratio of 50:1 means a glider could travel 50 feet forward while losing one
foot of altitude.
Wing Planform
The shape (planform) of the wings affects the amount of lift and drag produced. The four most common wing planforms
used on gliders are elliptical, rectangular, tapered, and swept forward. [Figure 3-9]
Elliptical Wing
Tapered Wing
Swept-Forward Wing
Rectangular Wing
Figure 3-9. Planforms of glider wings
Aspect Ratio
Dividing the wingspan (from wingtip to wingtip) by the average wing chord determines the aspect ratio for a glider. Glider
wings have a high aspect ratio, as shown in Figure 3-10, which generates significant lift at low angles of attack with
minimal induced drag.
51' wing span
Wing area = 219 ft 2 Maximum gross weight = 1,040 lb
Aspect ratio = 11.85:1
Glide ratio = 22:1
Wing area = 193 ft 2 Maximum gross weight = 1,808 lb
Aspect ratio = 39:1
Glide ratio = 60:1
86.9 ' wing span
Chord lines 4.3 feetChord lines 4.3 feet
Chord lines 2.22 feet Chord lines 2.22 feet
Aspect ratio is determined by dividing the wingspan (from wingtip to wingtip), by the average chord.
Figure 3-10. Aspect ratio
Winglets
Wingtip devices, or winglets, also improve efficiency of the glider by altering the airflow near the wingtips and reducing
induced drag.
Washout
The wing root refers to the portion of the wing nearest the fuselage. Washout refers to a slight wing twist between the
wing root and wingtip, which causes the wing root to have a greater angle of attack (AOA) than the wing tip. If the AOA
becomes excessive, airflow will separate at the wing root before separation occurs at the wing tip. This wing design
provides warning of any impending stall or overall separation of air from the wing and allows for continued aileron control
at the onset of a stall.
Stability
Vertical gusts, a sudden shift in CG, or deflection of the controls by the pilot can displace the glider from its orientation
in flight. Static and dynamic stability define how the glider reacts after a displacement. Static stability describes the initial
direction of the response. A glider with positive static stability initially moves back toward its original orientation after
a change. A glider with negative static stability would increase displacement after a change. A glider with neutral static
stability tends to hold any new orientation. The level of stability about each axis of a glider results from its design and
loading.
A glider with positive static stability will swing past its original pitch attitude and undergo a series of oscillations. If that
glider has positive dynamic stability, the size of any oscillations will dampen out over time. The same glider with negative
dynamic stability would experience oscillations that increase in amplitude over time. That glider with neutral dynamic
stability would experience a series of constant oscillations over time. [Figure 3-11]
Neutral dynamic stability
Positive dynamic stability
Negative dynamic stability
Figure 3-11. Three types of dynamic stability.
Gliders have a CG in front of the center of lift—the single point through which the sum of all lift acts. This design requires
an opposing tail-down force to maintain control and to create positive static stability for pitch. [Figure 3- 12] For example,
if a pilot displaces a glider’s nose upward and releases the controls, the glider will lose airspeed. The resulting reduction
in down force provided by the tail causes the glider’s nose to drop back toward its original position. This design results in
positive initial longitudinal stability (stability around the lateral axis). When a positive dynamically stable glider oscillates
in pitch, the amplitude of the oscillations diminishes through each cycle and eventually stops at the speed where downward
force on the tail offsets the tendency to nose down.
Center of gravity
Center of lift
Negative AOA
(Exaggerated in
this illustration)
Figure 3-12. The horizontal stabilizer offsets the natural tendency of a glider to pitch down.
The glider POH lists an acceptable range for the CG, and the pilot normally computes the CG location before flight to
verify the glider will fly as designed. A glider with an aft CG requires less tail-down force, which makes pitch oscillations