This slide shows the balance of forces on a descending
Wright 1902
glider.
The flight path of the glider is along the thin black line, which
falls to the left. The flight path intersects the horizontal, thin, red ground line at an
angle "a" called
the glide angle.
There are
three forces
acting on the glider; lift, weight, and drag.
The weight of the glider is given by
the symbol "W" and is directed vertical, toward the center of
the earth. The weight is then perpendicular to the horizontal red
line drawn parallel to the ground and through the
center of gravity.
The drag
of the glider is designated by "D" and acts along the flight
path opposing the motion. Lift, designated
"L," acts perpendicular to the flight path. Using some
geometry theorems on angles, perpendicular lines, and parallel lines,
we see the glide angle "a" also defines the angle between the
lift and the vertical, and between the drag and the horizontal.
Assuming that the forces are
balanced
(no acceleration of
the glider), we can write two vector component equations
for the forces. In the vertical direction, the weight (W) is equal to
the lift (L) times the
cosine (cos)
of the glide angle (a) plus
the drag (D) times the
sine (sin)
of the glide angle.
L * cos(a) + D * sin(a) = W
In the
horizontal direction, the lift (L) times the sine (sin) of the glide
angle (a) equals the drag (D) times the cosine (cos) of the glide angle.
L * sin(a) = D * cos(a)
If we use algebra to re-arrange the horizontal force equation we find that
the drag divided by the lift is equal to the
sine of the glide angle divided by the cosine of the glide angle.
This ratio of trigonometric functions is equal to the
tangent
of the angle.
D / L = sin(a) / cos(a) = tan(a)
We can use the
drag equation
and the
lift equation
to relate the glide angle to the drag coefficient (cd)
and lift coefficient (cl) that the Wrights
measured in their
wind tunnel tests.
D / L = cd / cl = tan(a)
During the operation of the
drag balance
the brothers made measurements of the effects of wing
design on glide angle through the drag to lift ratio.
The inverse of the drag to lift ratio is the
L/D ratio
which is an efficiency factor for aircraft design.
The higher the L/D, the lower the glide angle, and the greater the distance that
a glider can travel across the ground for a given change in height.
Navigation..
- Re-Living the Wright Way
- Beginner's Guide to Aeronautics
- NASA Home Page
- http://www.nasa.gov
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