1. Calculating Drag
Parachutes are used to slow objects down as they fall through an atmosphere.
They increase the area resisting the flow of air and so offer higher "drag".
For instance, a human may fall at 120 miles per hour without a parachute.
This is pretty fast and would be splatsville when s/he hit. With a parachute
a person may descend at 15 miles per hour or even slower.
If you are looking for descent rate only, go
here
How much "drag" does a parachute have? You would like to know
this since that tells you how much weight you can put on a parachute for
any descent speed. If you got in a car as a passenger and you had a fish
scale attached to a small parachute (a big one would take you right out
of the car!), as the driver was holding at a certain speed, you could extend
the scale out the window, the parachute would open and the fish scale would
read a certain value. A 131/2 inch diameter parachute would read 1 pound
at 30 feet per second (20 miles per hour). That means that if you put a
1 pound object on a 131/2 inch diameter parachute, it would fall with
a descent rate of 30 feet per second. Incidentally, if you try this it
will have to be on private property and "offroad" since the Highway Patrol
probably would not be fond of your doing this. Also, under no circumstances
would you drive the car and try to do this at the same time! Another way
you can test a parachute is by dropping it from a high place and timing
its descent. Again, be careful from where you drop it and make sure no
spectators are below!
Yet another way to test a parachute (small ones) is with a blower
or fan. You could make a science fair project out of this idea.
Here is the equation for calculating the drag of a parachute:
D = Cd *.5* p* V^2
Where:
D=Drag (which will be expressed in pounds force or lbf)
.5 = constant
Cd = Coefficient of Drag, a value from .8 to 1.0, but possibly higher
if there is a cross breeze giving the parachute lift
p = Air Density in slugs/cubic foot (roughly .0024 at sea level) =
rho
V = Air Velocity in feet per second squared
We know from tests that the 13.5 inch parachute exerts 1 pound of force
on the fish scale so if we plug those numbers into the drag equation we
get:
D=.9 (average of .8 and 1.0)*.5*.0024*(30*30)
D = .45*2.16 (simplifying a bit)
D=.972 lbf or roughly One Pounds Force
Important Notes:
It's very easy to generate extreme shock loads during the deployment
of a parachute into an airstream!
If the parachute is modeled as a constant CdA, the drag force is proportional
to the square of the airspeed.
If the parachute is sized to recover a 33 pound object at a descent
rate of 16 fps, for example, then we know that if the parachute opens at
an airspeed of 164 fps, it will initially develop a drag force of 3300
lbf.
Design load factors of 50 to 100 times the static recovered weight are
not unreasonable for such systems.
You might think about a reefing system for your parachute, a sliding
ring on the suspension lines that slides down the lines as the parachute
opens works nicely if tested properly. Some square parachutes use
a sliding "diaper" to achieve this effect and slow the opening of the canopy
so it doesn't snap open. A reefing line is also an option, this is
a line that goes from the apex of the parachute to the riser, the place
all the suspension lines collect, which is cut or burned when the parachute
and payload is descending at an appropriate speed or at a desired
altitude. There are several other methods.
Having trouble determining the air density in your locale? Go
here for a wonderful explanation:
USA Today "Understanding
Air Density"
You might also need to know what the barometric pressure in your area
is, go here and click on your state on the map:
http://www.anythingweather.com/
Don't forget to calculate the air density at the altitude you expect
this parachute to open at!
