Effect of Surface Area on the Drag Coefficient of a Parachute

[pasta-lord]

Summary:: Does the surface area of a parachute affect its drag coefficient? If so, how?

I have been trying to figure out the effect of surface area on the drag coefficient of a parachute. I have designed a lab in which parachutes of different surface areas are dropped and the terminal velocity is recorded which is then used to calculate the drag coefficient using the formula

. By doing the experiment this way, I have gotten the result that Cd is inversely proportional to the surface area. However, by theory, shouldn't it be a positive relationship between surface area and drag coefficient since a larger surface area means the object will have more difficulty traversing through fluids which represents a larger drag coefficient? I am not sure if this lab is designed incorrectly or if I did something wrong.

 

[berkeman]

[Thread moved to the Schoolwork forums]

Welcome to PF.

Can you provide more information about your test setup? Also, can you upload PDF copies of your data? That would help a lot for us. Also, the equation you posted does not seem to take into account the fact that the velocity decreases for larger Cd values, does it? I guess we'll have to see your setup and calculations to figure that out...

 

[pasta-lord]

[Thread moved to the Schoolwork forums]

Welcome to PF.

Can you provide more information about your test setup? Also, can you upload PDF copies of your data? That would help a lot for us. Also, the equation you posted does not seem to take into account the fact that the velocity decreases for larger Cd values, does it? I guess we'll have to see your setup and calculations to figure that out...

Hello,

Thanks for replying, I have attached what I have written for the lab so far to this message.
This is probably a really poorly designed lab and there are a lot of errors that could have happened.

Here is my procedure:

1. Cut circles of radius 0.05 m, 0.1 m, 0.15 m, 0.2 m and 0.25 m using a compass and a knife from a garbage bag.
2. Put a dime in the middle of each cutout circle and connect them using string and tape.
3. Measure the mass of each parachute using a scale.
4. Tape a meter stick perpendicular to the ground.
5. Record the experiment with a recording device (phone).
6. Drop the parachute from 1 m above the ground.
7. Using the video recorded, use a video analysis program (Logger Pro) to find the terminal velocity.
8. Do steps 4-6 five times for each surface area.

Thanks again.

 

[berkeman]

Nice report. I only skimmed it so far, but have a few questions:

** How did you try to inflate the parachutes before dropping them? It seems like it might be best to add some light supporting members inside the parachutes to hold them in their expanded shape for the drop (to reach terminal velocity sooner).

** You cut the parachutes from flat garbage bag material, but you'd like to have them be more spherical in shape instead of 2-D disks, no?

** A 1-meter drop height seems kind of short to me. You mention that the video logger data was looking for when the parachutes seemed to have reached the same velocity in several frames -- did they always max out before hitting the ground?

Have you found any similar studies online about parachute size and Cd? The NASA paper you cite at the end of your report seems to be about airplanes...

 

[pasta-lord]

I did not try to inflate the parachutes, I just used my hands to try and get them to be as dome like as possible before dropping.

I do not have any other materials which I can used to make the parachutes so I just stuck with the garbage bags. would that affect the overall experiment that much though? All of my parachutes are made of the same material. I am not too sure about this part.

As for the drop height, I am pretty sure the parachutes all reached terminal velocity at the end since the mass I attached is relatively small.

As for the studies, I could not really find any that relates the surface area of a parachute to its drag coefficient. However, I did use the formula on this website for my lab.
https://www.grc.nasa.gov/www/k-12/V... coefficient,produces a low terminal velocity.

Thanks for all the help.

 

[berkeman]

Hmm. I think you'd get better results if you added some ribs and maybe some folding/taping to the parachute to get it into more of a spherical shape and added more weight to the payload (and increased the drop height, obviously). But that's easy for me to say and not so easy for you to do (a whole repeat of the experiment).

BTW, I used a Google search on how is parachute size determined and got some good hits. This page here:

https://www.google.com/search?q=how...termined&ie=utf-8&oe=utf-8&client=firefox-b-1

mentions that the "size/diameter" of the parachute that should be used in the Cd calculation is the inflated diameter while in descent, not the diameter of the material that you used to cut it out:

Values for a parachute are 0.8 < Cd < 1.2. Note that Cd is unitless.

The term Ap is the projected area of the object. Imagine shining a light directly on an object. The surface area of the shadow equals projected area. Thus, for a hemisphere, the projected area equals the area of circle of radius r.

It looks like your Cd values fall outside of the expected range -- I wonder if this radius correction can help.

Here is the full hit list from my Google search, in case it helps:

https://www.google.com/search?q=how...termined&ie=utf-8&oe=utf-8&client=firefox-b-1

 

[pasta-lord]

Thanks for the help! I will check it out and see if it improves my results!