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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 13-1/2 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 13-1/2 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 "off-road" 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 

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:

Don't forget to calculate the air density at the altitude you expect this parachute to open at!

2. Determining Impact Forces

Once you have calculated how much drag the parachute imposes on an object the next step is to determine how much damage an object (payload) can sustain at the descent speed indicated.

Find the descent speed of your object under parachute in the column marked "Velocity in Feet per Second"  and read the column to the right indicating "Distance in Inches".  This table shows the speed at which a relatively dense object like a can of soda or a golf ball will fall.  A light object with a large surface area (a feather) will fall slower than a heavy object with a small or streamlined surface (like a bullet).

Velocity in 
Feet per Second
in Inches
Velocity in 
Feet per Second
in Inches

Let's say you have a carton of eggs tethered to a parachute and you know your parachute will give you a descent speed of 18 feet per second. From how high will it appear to the eggs that you are dropping them from? Look up 18 in the feet per second column and you'll see that indicates a drop height of 61 inches.  Now test that on your carton of eggs.  Go out to the refrigerator (which is about 63 inches tall), open the door, remove a carton of eggs, and drop it from the top of the refrigerator. 

Did the eggs survive? 

At what distance could you drop that carton so all the eggs remained unbroken? 

Looking at the table, that distance would give you the minimum descent speed your eggs could tolerate, simply size the parachute accordingly.  If you could sustain half the eggs being broken then a higher descent rate would be acceptable.

3.  What happens if the rocket doesn't separate into multiple components and returns to earth ballistically?

Some rockets are launched and never intended to recover.  Other times a separation event does not occur and the rocket returns in a streamline fashion always with a sudden stop at the end of the flight.  How do you determine at what velocity the rocket is impacting the ground?

The question is what will the terminal velocity, Vt, of my rocket be?

Vt = sqrt( 2W/(Cd * p * A))

Vt = terminal velocity in feet/second
W = weight in pounds
Cd = drag coefficient, assume 0.55
p = atmospheric density (about 0.0024 at sea level) = rho
A = surface area in square feet

Vt = sqrt( (2*30)/(0.55 * 0.0024 * 0.196)) = 481 ft/sec = approx. 327 mph

Another case might be the rocket that separates into two tethered components.  This can vary widely due to different drag characteristics of the components but a rule of thumb from empirical analysis indicates somewhere between 40 and 80 feet per second.

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Make your choices and take personal responsibility for the outcome of your experiment!
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