Parachute Problem, Figuring out largest load it can hold

In summary, the conversation involved calculating the largest load that can be accommodated by a circular parachute with a diameter of 100 feet, given that it can withstand an impact speed of 20 mph. The equation for terminal velocity was used, with constants such as the gravitational constant and drag coefficient. The final answer was calculated to be approximately 845 pounds, assuming the given drag factor of 0.1. However, a more realistic drag factor of 1 would result in a larger load capacity of around 8450 pounds.
  • #1
mathguy2
16
0

Homework Statement



A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations



Vt = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]

The Attempt at a Solution



First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, Vt
Then I calculated the area of the circular chute. Since r = 50 and using piR2... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.
 
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  • #2
mathguy2 said:

Homework Statement



A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations



Vt = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]


The Attempt at a Solution



First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, Vt
Then I calculated the area of the circular chute. Since r = 50 and using piR2... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.
mathguy2 said:

Homework Statement



A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations



Vt = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]


The Attempt at a Solution



First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, Vt
Then I calculated the area of the circular chute. Since r = 50 and using piR2... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.
I don't know where your numbers are coming from. Firstly, if you want to calculate the largest load in pounds (weight), don't multiply W by g, W is already in force units. And then, please show how you arrived at the drag factor and that 0.0805 value, and write out the equation you are using for terminal velocity using letter symbols.
 
  • #3
PhanthomJay said:
if you want to calculate the largest load in pounds (weight), don't multiply W by g
Yes, the answer, as a mass, has effectively been computed in slugs.
mathguy2 said:
I got 848.24 pounds for the mass
I got 845 slugs.
 
  • #4
W
haruspex said:
Yes, the answer, as a mass, has effectively been computed in slugs.

I got 845 slugs.
with a drag coef of 0.1 for a parachute? Where does that come from , seems off by an order of magnitude
 
  • #5
PhanthomJay said:
W

with a drag coef of 0.1 for a parachute? Where does that come from , seems off by an order of magnitude
I should have clarified that I was trusting the given numbers.
 
  • #6
I
haruspex said:
I should have clarified that I was trusting the given numbers.
Using a drag factor of 0.1 , I get around 845 pounds for the weight. Using a more realistic drag factor of around 1, it's more like 8450 pounds
 

1. What is the purpose of the Parachute Problem?

The Parachute Problem is a commonly used problem in physics to determine the maximum load that a parachute can hold. This information is important for designing and testing parachutes for various applications, such as skydiving or aerospace engineering.

2. How is the largest load that a parachute can hold determined?

The largest load that a parachute can hold is determined by analyzing various factors such as the size and shape of the parachute, the material it is made of, the air resistance, and the weight of the load. These factors are used to calculate the maximum force that the parachute can withstand without failing.

3. What are the key components of a parachute that affect its load capacity?

The key components of a parachute that affect its load capacity include its canopy size and shape, the number and type of suspension lines, and the material used for the canopy and suspension lines. Additionally, the air density and wind speed also play a role in determining the load capacity of a parachute.

4. Can the largest load a parachute can hold be increased?

Yes, the largest load that a parachute can hold can be increased by making changes to its design and materials. For example, a larger parachute with a more aerodynamic shape and stronger materials can hold a larger load compared to a smaller parachute with a less efficient design.

5. Are there any safety considerations when determining the largest load a parachute can hold?

Yes, safety considerations are an important factor in determining the largest load a parachute can hold. It is crucial to ensure that the parachute can withstand the calculated load without failure, as failure can result in serious injury or even death. Proper testing and quality control measures must be in place to ensure the safety of those using the parachute.

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