The Area of a Parachute Compared To Its Rate of Descent

This experiment is designed to measure the time that it takes in order for different sized parachutes to fall a certain distance. This is done in a specific way that makes this very fair and accurate.

My prediction is that, the larger the area of the parachute, the lower the rate of descent, this is because if the parachute is larger, it will trap more air underneath it, and will take longer to fall. The smaller the parachute, the less air it will trap underneath it, and it will take less time to fall.

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Background Information

Parachutes fall according to their air resistance, this can be calculated by their area, such as an average human body falls at 9.81 m/s, a parachute can have this calculated, which is one of the purposes of this experiment. The area can be calculated by A=?r�, where A is the area, ? is pi and r is the radius. The speed can then be calculated by the time it took to fall to the distance calculated, Distance (m) = Speed (m/s) � Time (s), rearranged to get:

Speed = Distance � Time. The speed that is calculated is the rate of descent.

Parachutes fall by trapping air underneath them and increasing the air resistance. This makes the air resistance larger or equal to gravity so that the parachute now falls at a slow rate. The slow rate of descent is slow enough to stop objects that are very aerodynamic, as long as the object is not too heavy for the size of parachute, such as weights or human bodies.

The structure of a parachute means that it has to displace air in order to float, otherwise, the edges would flap around and there would be little reduction in air resistance. This is achieved by making a small hole in the centre of the parachute, which lets the air escape.

Apparatus

Apparatus

Quantity

Thin Plastic

3m�

String

12.6m

Weight

10g

Scissors

1

Metre Stick

1

Timer

1

Black Marker

1

Safety

Safety Issue

How to Prevent Issue

What to do if the problem occurs

Dropping weights on

Hold all weights firmly and place

Rub any bruises. Cuts should be

feet

them on surfaces when possible

washed and teacher informed

Tripping over on

Refrain from placing equipment

Take equipment off the floor cuts

equipment

on the floor

and bruises dealt with as above

Sheets of plastic over

Keep plastic away from face at

Promptly remove plastic, inform

face prevent breathing

all times

teacher

String choking or not

When tying knots in string, keep

Untie any restricting knots and

allowing blood flow

away from neck

inform teacher

Key Factors

There are many variables in this experiment. The two main types of variable are controlled and manipulated. The manipulated variable is the only varying variable in the experiment. This is used to measure what happens when a something is altered in an experiment. The manipulated variable in this experiment is the area of the parachute and the length of the strings that is being used. This factor is controlled so that it rises at a constant rate, and it keeps the experiment fair.

There are also controlled variables. These variables are ones which do not want to be changed, in order to keep the experiment fair. The variables have to be controlled so that they do not make this an unfair test, hence the name controlled variables. These variables are such things as the height from which the parachutes are dropped, the weight attached to the parachute and the type of plastic used to make the parachute. These can be controlled by keeping them the same for every experiment, but variables such as the hole in the top of the parachute have to be proportional to the area of the parachute itself.

Procedure

This experiment can be conducted very safely and efficiently using the procedure suggested, and it is the procedure I would recommend. First of all, the metre ruler should be used to measure the height of the room being used. The room should be at least 2.86m high, which is the height from which the parachutes were dropped in this experiment. The height should be marked, and this will be the height from which the parachutes will be dropped. The first parachute can now be made. A circle of plastic should be cut with a diameter measured to exactly 10cm. This can be done by using a compass or a piece of spare string tied to a pen, 10 from the nib of the pen to the point where it should be held to the plastic. The plastic can then be marked on to with a near perfect circle, and then cut out with scissors. Six small holes should then be cut into the parachute. The holes should be the diameter of the string being used.

The holes should also be 0.5cm in from the edge of the parachute and equally spaced 60� around the parachute. The string can then be tied around the holes and the edge of the parachute. The string should be tied so that it leaves 3mm of string after the knot has been tied. The weight can then be tied on to the strings that are attached to the parachute. The parachute can now be taken to the 2.86m height and dropped. The parachute should be timed as it falls, and the horizontal distance from the point it was dropped should also be measured. Following the first experiment, the second parachute can be made to similar proportions, but bigger. The sizes are shown below on the following table:

Diameter of

Distance of

Length of

Diameter of

holes in top of

string holes

Length of

string left after

parachute (m)

parachute (mm)

from edge (mm)

strings (m)

knots (mm)

0.1

3.3

5

0.1

3

0.2

6.6

10

0.2

6

0.3

1

15

0.3

9

0.4

1.3

20

0.4

12

0.5

1.6

25

0.5

15

0.6

2

30

0.6

18

Results

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.1

0.33

2.86

0.3

2.88

0.57

5.05

0.1

0.33

2.86

0.37

2.88

0.79

3.64

0.1

0.33

2.86

0.34

2.88

0.71

4.06

Mean speed

4.25

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.2

0.66

2.86

0.33

2.88

1.09

2.64

0.2

0.66

2.86

0.27

2.87

0.98

2.93

0.2

0.66

2.86

0.37

2.88

1.07

2.69

Mean speed

2.75

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.3

1

2.86

1.1

3.06

1.22

2.51

0.3

1

2.86

0.79

2.97

1.23

2.41

0.3

1

2.86

1.69

3.32

1.29

2.57

Mean speed

2.5

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.4

1.33

2.86

0.07

2.86

1.5

1.91

0.4

1.33

2.86

0.12

2.86

1.6

1.79

0.4

1.33

2.86

1.02

3.04

1.97

1.54

Mean speed

1.75

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.5

1.66

2.86

1.52

3.24

2.29

1.41

0.5

1.66

2.86

0.8

2.97

2.03

1.46

0.5

1.66

2.86

0.64

2.93

2.01

1.46

Mean speed

1.44

Diameter of

Central hole

Distance fallen

Distance fallen

Total distance

Time (s)

Speed

parachute (m)

size (cm)

vertically (m)

horizontally (m)

fallen (m)

(m/s/s)

0.6

2

2.86

1.6

3.28

2.37

1.38

0.6

2

2.86

1.18

3.09

2.3

1.34

0.6

2

2.86

1.09

3.06

2.29

1.37

Mean speed

1.36

Proportional Results

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.1

2.86

2.88

0.57

5.05

5.09

0.1

2.86

2.88

0.79

3.64

3.67

0.1

2.86

2.88

0.71

4.06

4.09

Mean speed

4.25

4.28

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.2

2.86

2.88

1.09

2.64

2.66

0.2

2.86

2.87

0.98

2.93

2.94

0.2

2.86

2.88

1.07

2.69

2.71

Mean speed

2.75

2.77

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.3

2.86

3.06

1.22

2.51

2.69

0.3

2.86

2.97

1.23

2.41

2.50

0.3

2.86

3.32

1.29

2.57

2.98

Mean speed

2.5

2.72

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.4

2.86

2.86

1.5

1.91

1.91

0.4

2.86

2.86

1.6

1.79

1.79

0.4

2.86

3.04

1.97

1.54

1.64

Mean speed

1.75

1.78

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.5

2.86

3.24

2.29

1.41

1.60

0.5

2.86

2.97

2.03

1.46

1.52

0.5

2.86

2.93

2.01

1.46

1.50

Mean speed

1.44

1.54

Diameter of

Distance fallen

Total distance

Time (s)

Speed

Proportional

parachute (m)

vertically (m)

fallen (m)

(m/s/s)

Speed (m/s�)

0.6

2.86

3.28

2.37

1.38

1.58

0.6

2.86

3.09

2.3

1.34

1.45

0.6

2.86

3.06

2.29

1.37

1.47

Mean speed

1.36

1.50

Graph

Average

Diameter of

Proportional

parachute (m)

Speed (m/s�)

0.1

4.38

0.2

2.77

0.3

2.72

0.4

1.78

0.5

1.54

0.6

1.50

Standard Deviation of Results

Total

Difference

Distance

Mean

Difference

Squared

Fallen (m)

(2 dp)

(2 dp)

(3 sig. figs)

2.88

2.99

-0.11

0.0121

2.88

2.99

-0.11

0.0121

2.88

2.99

-0.11

0.0121

2.88

2.99

-0.11

0.0121

2.87

2.99

-0.12

0.0144

2.88

2.99

-0.11

0.0121

3.06

2.99

0.07

0.0049

2.97

2.99

-0.02

0.0004

3.32

2.99

0.33

0.109

2.86

2.99

-0.13

0.0169

2.86

2.99

-0.13

0.0169

3.04

2.99

0.05

0.0025

3.24

2.99

0.25

0.0625

2.97

2.99

-0.02

0.0004

2.93

2.99

-0.06

0.0036

3.28

2.99

0.29

0.0841

3.09

2.99

0.10

0.01

3.06

2.99

0.07

0.0049

53.95

Total

0.391

Variance

0.022

Standard

0.148

Deviation

Histogram of Results

Total

Distance

Fallen (m)

Frequency

Width

Height

2.86

2

2

1.43

2.87

1

1

2.87

2.88

5

5

0.58

2.93

1

1

2.93

2.97

2

2

1.48

3.04

1

1

3.04

3.06

2

2

1.53

3.09

1

1

3.09

3.24

1

1

3.24

3.28

1

1

3.28

3.32

1

1

3.32

Anomalous Results

In this experiment, I have found 1 set of anomalous results. These anomalous results could be put down to a number of factors including:

* Parachute made wrong size

* Hole on centre of parachute too small or too large

* Strings wrong length

* Timing on descent inaccurate

* Wind affected parachute on descent

* Holes made in wrong place

Trends

The trends of the results included the fact that the speed increased at an exponential rate, as shown on the graph. The total distance fallen averaged 2.99, but the standard deviation of those results was 0.148, which is comparatively close. The histogram shows that this a direct proportion in the histogram.

Evaluation – Accuracy and Reliability

The accuracy of my results was fairly good from my opinion. There was one anomalous result in the graph. The graph actually showed a positive result in that it was a particular shape, exponential. The results were fairly accurate, there may have been one or two anomalous results within the group that was misplaced. The reasons for this are stated in the anomalous results section. The measurement of the data was also fairly accurate according to the trends in the graph. The precise accuracy will be shown below.

Percentage Error Calculation

The best way to calculate the accuracy of one’s results is to do a calculation based on them. This is shown in steps below.

1. Collect results

2. Calculate the mean (average) of one set of results.

3. Find the range by subtracting the largest number from the smallest number for each group of results

4. Divide range by 2

5. Divide the product of step 4 by the mean

6. Multiply by 100

The number that is left is a percentage error. From this, how accurate the results are can be calculated

1% – The data is very accurate

5% – The data is reasonably accurate

10% – Middling error value

25% – Error value is too high, unreliable results. Retest is needed

Diameter of

Proportional

Percentage

parachute (m)

Speed (m/s�)

Range

Mean

Error

0.1

5.09

1.42

4.28

16.61%

0.1

3.67

0.1

4.09

0.2

2.66

0.28

2.77

5.09%

0.2

2.94

0.2

2.71

0.3

2.69

0.48

2.72

8.82%

0.3

2.50

0.3

2.98

0.4

1.91

0.27

1.78

7.67%

0.4

1.79

0.4

1.64

0.5

1.60

0.10

1.54

3.31%

0.5

1.52

0.5

1.50

0.6

1.58

0.13

1.50

4.49%

0.6

1.45

0.6

1.47

Evaluation – Procedure

There were some fundamental problems with the fairness if the experiment, some of them I was able to overcome, some of them mattered so minutely that they did not need controlling, or I was not able to control them. I closed the windows and made as little movement as possible while conducting the experiment in order to prevent the wind from blowing the parachute. This was quite effective, as the wind could have easily blown the parachute off course or blown it up or down. I also used the same weight each time, in case the other weights were different weights, either by manufacturing fault or by usage of the weights, getting chips out of them or being otherwise damaged. This was useful because it made the test fairer, because lighter weights would make the parachute fall slower than normal, and bigger weights would make the parachute fall faster than normal.

There was the problem of not have very accurate measuring instruments, that could measure to the nearest millimetre accurately. This could not easily be solved, so we had to use the only available instruments. The parachutes were made exactly circular, using a piece of string and a pen. This proved useful, as we could be sure that the parachutes were exactly circular. The plastic that was available, was not the best of materials to make parachutes from. This is for a number of reasons, the plastic was prone to being stretched and misshaped quite easily, distorting the shape of the parachute and making it descend at a different rate. The plastic was also very easy to fold and crumple, so it was not always flat, which could have changed the rate of descent again.

Evaluation

The overall experiment was fairly precise and accurate as far as I can see. The problems encountered were minor, and there was only one anomalous result. If I had more time, I would have re-done the experiment at least 10 times in order to get an accurate result from that particular parachute area. This experiment could also be expanded into more areas than just parachutes, there are also many types of parachute, such as the parafoil, where it is designed to travel both forwards and down, very efficiently. This could be compared to the results of the original parachutes or even another further type of parachute. The parachutes could also be extended, so that they were much larger or much smaller in area than the sizes used in the above experiment. There are also other areas of study with the same parachutes, so instead of changing the area of the parachute, change the weights on the bottom to 20g or 5g for example.