This slide shows the balance of forces on a descending
There are three
acting on the glider; weight,
having both a magnitude and a direction.
The magnitude of the weight is given by the
and depends on the mass of the aircraft and its payload.
The direction of the weight is always towards the center
of the earth. On the figure, the direction is along the vertical
axis, pointed towards the bottom of the figure.
The magnitude of the lift
is given by the
and depends on several
The lift is directed perpendicular to the flight path which is
shown as a thin red line which fall to the left on the figure.
The magnitude of the drag
is given by the
and depends on
factors associated with the design.
The drag is directed along the flight path opposed to the motion.
A horizontal, thin red line has been drawn parallel to the ground
and through the
center of gravity of the glider.
The flight path of the glider
crosses the horizontal at an angle a called
the glide angle.
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
(no acceleration of
the glider), we can write the two
vector component equations
for the forces. In the vertical direction,
the lift L times the
cos of the glide angle a plus
the drag D times the
sin of the glide angle
minus the weight W equals zero:
Vertical: L * cos(a) + D * sin(a) - W = 0
horizontal direction, the lift times the sine of the glide
angle minus the drag times the cosine of the glide angle equals zero:
Horizontal: L * sin(a) - D * cos(a) = 0
Rearranging the horizontal component equation:
L * sin(a) = D * cos(a)
L / D = cos(a) / sin(a) = 1 / tan(a)
gives the relation that the lift divided by the drag is equal to the
cosine of the glide angle divided by the sine of the glide angle.
This ratio of trigonometric functions is equal to the cotangent of
the angle, or the inverse of the
of the glide angle. For
small angles, the tangent of the angle is almost the value of the
angle in radians. This gives us the following relationship:
L / D = 1 / a
the lift divided by the drag is equal to the inverse of
the glide angle for small angles.
What good is all this for aircraft design? The lift divided by
drag is called the L/D ratio and is an
efficiency factor for aircraft. From the last equation we see that
the higher the L/D, the lower the glide angle.
The glide angle
determines how far a glider will fly horizontally for each
vertical foot (or meter) that it falls. The lower the glide angle,
the farther the glider can fly. Therefore, designers of long distance
gliders want a high L/D. We can also use measurements of the glide angle
and weight of the glider to determine the L/D ratio as shown on
- Beginner's Guide Home Page