IT’S A DRAG
Drag is a force that opposes the
motion of an object. If it’s stationary, then
the force of drag equals zero, and the
faster it moves, the greater the force of
drag. In the case of a falling object, the
force of gravity governs the speed at
which it falls until it reaches a terminal
velocity balanced by drag. The two forces
— gravity pulling down and drag pulling
up — equal each other at terminal velocity.
The force of drag acting on a body
moving through a medium can be
described with this formula:
Fd = ½ ρv2CdA
where
• ρ is the density of the medium the body
is moving through
• v is the velocity (speed) of the body
• Cd is the body’s coefficient of drag
• A is the frontal area of the body
These factors are easy to understand
except for one: Cd. The coefficient of
drag is a dimensionless constant. Being
dimensionless means it has no units like
meters, seconds, or grams. The Cd for
a flat plate is around 1, while more
streamline bodies have a Cd less than 1.0.
The weight of a parachute and its
payload doesn’t change in any real way
for a descent from near space. Since the
drag force (Fd) must equal the parachute
and payload weight, as the air density
(ρ) increases, the velocity squared must
decrease in proportion (assuming Cd and A
for the parachute don’t change appreciably
during the descent). This indicates the square
root of the parachute’s descent speed is
inversely proportional to the air density.
Source: http://en.wikipedia.org/wiki/
Drag_coefficient
the tapes wrap around the end of
the canopy and into the inside of
the parachute. Now you can sew the
seams between gores and their
reinforcing tapes together. There
should be a small loop at the bottom
of the parachute where the twill tape
was wrapped around.
Now sew the twill tape onto the
canopy. As it’s sewn, the sewing
machine is also sewing the gores
together. The ends of the twill tapes
must be sewn extra strong. Wrap the
end of the twill tape around the
underside of the
canopy and run
extra stitches
through it and the canopy as
illustrated in Figure 13. That’s it
for making a parachute canopy.
The next column will discuss the
shroud lines and the parachutes
spreader ring. There will also be
a recovery aid to attach to the
parachute.
A PARACHUTE
DESCENT FROM
NEAR SPACE
■ FIGURE 13.
The light gray
bars represent
closely spaced
stitches that
reinforce the
twill’s attachment
to the parachute
canopy.
■ FIGURE 12. Images
— recorded every
1/3rd of a second —
showing the opening
of a deployed
parachute. The fully
deployed parachute
appears at the top of
the frame and looks
like a semicircle with
a zig-zag edge.
Let’s look at two aspects of
parachute performance in the near
space environment. First, a parachute
returning from near space
experiences an extreme change in
air density and pressure. A parachute
deployment at 100,000 feet takes
place at an atmospheric pressure of
10 mb, or 1% of the average air pressure at sea level (1,013 mb). As the
parachute descends, the air density
becomes greater and the parachute
becomes more effective at slowing
the payload down. The parachute’s
drag — and therefore its ability to
slow a payload down — depends on
the air’s density. So, let’s compare a
parachute’s descent speed as a function of atmospheric pressure to see if
it agrees with the equation for drag.
A parachute descends at a speed
where the drag it creates is equal to
the weight of the parachute and its
payload. When the two oppositely
directed forces are equal, there is no
net force acting on the parachute
and therefore, it experiences no
acceleration. A constant velocity
is the result of no acceleration.
Now according to the equation
for drag, the force a parachute
experiences is proportional to its
speed and to the square root of
the air density. Using data from
a previous near space mission,
I created a chart comparing the
square root of the air pressure
(a good surrogate for air density)
and the near spacecraft’s descent
speed as a function of altitude.
■ FIGURE 14. Not a bad match.
The descent speed of a parachute
does vary proportionally to changes
in air pressure (and density).
86
September 2008