# Terminal Velocity in a Parachute

The aim of this experiment was to see how several factors like the length of the string, mass of the object hung to the parachute and height of drop affect the terminal velocity in a parachute. When we would throw the parachute from a certain height it will accelerate and will continue to increase until a drag force acts on it causing the acceleration to decrease. There will be a point of time when the parachute accelerates at a constant speed (drag force equal to weight of the object). So in order to find this constant acceleration the research was divided into three different experiments. The three factors I was investigating were the mass, length and height of drop of the parachute where in each experiment one variable was being changed.

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I hypothesized in the first experiment that a heavy object will be more prone to reaching terminal velocity because it will travel faster and achieve a greater speed and this hypothesis was correct. With the second experiment when the length of the string was changed I had bit of problems because it was hard to get the object hung to the parachute when the length was small as it constantly got loosened. In the third and final experiment I predicted that a smaller height will have a greater speed because of which it will experience a greater force and hence terminal velocity will be reached and this assumption was correct. The measured heights though were not very accurate because I dropped the parachute in an open area under various different heights.

Wind played a huge role in affecting some of the trials and I had to perform the experiment many times in order for the air resistance force be equal to the gravitational force.

CONTENTS

COVER PAGE

1

ABSTRACT

2

ACKNOWLEDGEMENTS AND CONTENTS PAGE

3

BACKGROUND KNOWLEDGE

4

HYPOTHESIS

5

EXPEIRMENTAL DESIGN

6

EXPERIMENT PROCEDURE

7

VARIABLES

8

DATA COLLECTION – EXPERIMENT 1

9

EXPERIMENT 2

10 & 11

EXPERIMENT

12 & 13

FURTHER EVALUATION

14

ERRORS

15

IMPROVEMENTS AND CONCLUSION

16

BIBLIOGRAPHY

17

INTRODUCTION

Background Knowledge

I always have wondered how the military men used skydiving to intrude behind enemy lines and conduct various missions. After doing a bit of research I found out that Military skydivers are deployed from a large aircraft or at times from a helicopter in order to do their respective jobs which are mostly in the form of missions. They carry more gear then the normal skydivers, aside from the parachute they carry additional equipment’s like oxygen tank, weapons and other equipment’s which are needed for their missions so this becomes more challenging for these daredevils. So factors like mass of the skydiver, equipment they carry and the surface area [1] or height by which they fall from will affect the speed at which the travel. It would be hence interesting to design an experiment to see how these factors affect the terminal velocity of a parachute.

Terminal Velocity occurs during free fall [2] when a falling body experiences zero acceleration that is when there is no acceleration in the parachute. It varies directly with the ratio of drag to weight. Terminal velocity reaches when the force of gravity [3] acting on the object is equal to the air resistance or viscous force of air on the body. Air resistance [4] is a major factor contributing in a falling object to reach terminal velocity as it can easily contribute to the speed at which the body falls.

HYPOTHESIS

A formula was derived by Sir Isaac Newton for one of the force considered in our experiment, air resistance:

Fg =

{Where, Fg = Force in Newton’s

G = 6.67 A- 10 -11

M1 = Mass 1 in Kilograms

M2 = Mass 2 in kilograms

r = Distance between m1 and m2 }

When the parachute will be falling down there will be an acceleration of 9.8 ms-2 independent of the factors in the parachute. Terminal velocity won’t always be the same; it will be different for different variables.

My hypothesis is that a heavier object will have a greater terminal velocity than a light one. For an object to experience terminal velocity, air resistance must balance weight. When the force of gravity is equal to the air resistance the object will travel at a constant velocity (newton’s first law) so in the case of a heavy object the force of air resistance in the atmosphere will cause the body to decelerate [5] . A light object won’t be able to equal resistance the way a heavy object will

Like the weight, surface area also has a great effect on a parachute reaching zero acceleration. The surface area is the height at which the parachute is falling down. If the object falls from a smaller height the time for it to touch the ground will be less and henceforth a greater terminal velocity is likely to be seen

The third factor which I am taking in to consideration is the length of the string of the parachute. According to me the best string length will be the longest length since it allows the parachute to be more stable. As the parachute will be more stable the velocity will increase and hence there will be less time taken for the parachute to reach terminal velocity.

EXPERIMENTAL DESIGN

The main aim of the essay is to see how various factors affect the terminal velocity of a parachute. In general there are many factors affecting the terminal velocity of a parachute like the air pressure [6] , drop time, canopy area, size of the apex vent, number of length of strings and canopy shape. But according to me the most important factors that play a vital role in the speed at which the parachute descents [7] are the mass of the object in the parachute, surface area (Height of drop) and the length of the string. As discussed above these factors are the main ones when a parachute descents, be it a small object, military men or a parachutist. One factor may be prone to reach zero acceleration at a faster rate than the other so in my experiment I will be seeing how these factors affect the parachute reaching a terminal velocity.

To see how various factors affect the parachute in reaching zero acceleration three different experiments will be performed. The amount of time taken for each of the parachute to hit the ground will be calculated and one variable in each of the experiment will be changed. The parachute will be made out of a garbage bag of 60 by 84 inch size. Then a big circle will be cut out of the bag of which four holes will be made and then the string will pass through each of the holes and will be stuck by glue. All the four strings will be made into one by attaching a small ribbon onto it and the length of each the strings will be about 80 cm. After the parachute is the three experiments will be performed and after it we will be able to determine when the parachute will travel at a constant speed in order to reach terminal velocity. In each of the experiments there will be two controlled and one independent variable and will see how these variables affect the others.

EXPERIMENTAL PROCEDURE

For the first experiment the height from which the parachute is being dropped will be kept constant and the length of the string in the parachute will remain the same. The factor that is being changed here is the weight of the object. Two different masses one of 50 and the other of 100 grams will be used and they will be hanged to the parachute one after the other in order to see which one is more prone to reach constant acceleration and they will be dropped many a times till I achieve accurate results. Time will be calculated here to see the speed at which the parachute reaches the ground when the mass is 50 and 100 grams. The weights will be measured by putting each of the masses on to a balance on by one.

In the second experiment the length of the string will be kept as constant but the other factor that is kept constant here is the mass of the object. The mass of the object will be a constant 50 grams and using this amount of weight will make it easier for the parachute to reach zero acceleration. The height at which the parachute is being dropped will be changed in this experiment. I will start from a height of say 280 cm and will go up to 350 and see the time at which the parachute hits the ground in each of the case.

In the third and final experiment the height of drop will remain the same (540cm) and again the weight of the object will be kept constant, the mass will be 50g. With the same parachute with the constant variables mentioned in these experiment strings of different length 80cm, 70cm, 60cm, 50cm, 40cm and 30cm will be attached. The parachute will be then dropped by 540cm in all the cases so that the parachute reaches terminal velocity. By this the variations in time will be known and hence we will be able to come to a conclusion. We will have to try our level best to avoid external force like wind to affect the experiment.

VARIABLES

Experiment

Number

Independent Variable

Dependent Variable

Controlled Variable

1

Mass of the object

Terminal Velocity and the time elapsed until terminal velocity is reached.

Surface area and the length of the string. They are the other two factors taken into consideration for the object reaching terminal velocity.

2

Height of drop of the parachute

Terminal Velocity and the time elapsed until terminal velocity is reached

Mass and the length of the string in the parachute will be the same in this experiment and they are the two factors taken into consideration.

3

Length of the string

Terminal Velocity and the time elapsed until terminal velocity is reached.

Mass and Surface area are kept constant in experience three. This time the Mass and Surface area won’t be altered.

DATA COLLECTION

Experiment 1

In the first experiment the independent variable is the mass of the object hung to the parachute. The controlled variables are the height of drop and length of the string

Height of drop of the parachute = 540 cm

Length of the string is 80cm

Object 1 (50g)

Trials

Time(±0.1s)

1

6.52

2

7.46

3

6.38

4

8.36

5

7.94

6

7.81

7

6.63

8

7.32

Object 2 (100g)

Trials

Time(±0.1s)

1

4.32

2

3.21

3

3.97

4

3.73

5

4.18

6

4.35

7

3.36

8

4.57

Experiment 2

In the second experiment the independent variable is the height of drop, it is being changed and the factor that is kept constant is the length of the string and the mass of the object used.

Length of the string – 80cm

Mass of the object – 50g

Height of Drop (±0.05cm)

Time(±0.1s)

Average

Trial 1

Trial 2

Time(±0.1s)

280

0.89

0.74

0.82

290

0.98

1.17

1.01

300

1.39

1.27

1.33

310

1.34

1.56

1.45

320

1.71

1.82

1.77

330

2.03

2.11

2.07

340

2.34

2.49

2.42

350

2.72

2.77

2.75

After plotting the datas with appropriate error bars and the line of best fit I found out that as the height of drop increases the time for the parachute to fall down increases. When you drop the parachute from a height of above 325 m then the parachute will be more prone to reach terminal velocity. When the parachute was falling down the drag force increased with increase in terminal velocity. It reaches a maximum velocity when the drag force equals the driving force. From a height of 280 to 310 m the parachute fell at a very fast rate (0.5 – 1.0 s) because of which constant velocity wasn’t reached. Also noticed in this graph was that there is constant acceleration at a height od 330 cm which shows us that terminal velocity has been reached.

Experiment 3

For the third and final experiment the factor that is being changed is the length of the string. This time the mass of the object and height of drop is kept as the controlled variables.

Mass of the object – 50g

Height of drop – 540cm

Trials

Length of the string (±0.05cm)

Time (±0.1s)

1

80

7.21

2

70

6.39

3

60

5.85

4

50

5.77

5

40

4.32

6

30

3.97

After plotting the graph for the third experiment where the length of string in the parachute was changed I found out that when there was a decrease in the length of the string then the time for the parachute to fall down also decreased. This means that a longer string will be more prone to terminal velocity. When the length of the string decreased then the air resistance increased due to the increase in length which resulted in the parachute to fall down at a constant velocity. For a string of length of more than 50 cm terminal velocity will be reached at a faster rate. In this experiment also constant acceleration is seen at higher lengths of around 65 to 80cm

FURTHER EVALUATION

In each of the experiments we can now successfully say that terminal velocity was there at some point or the other. The question posed how factors like the surface area, mass of the object and length of the string affects the parachute in reaching a terminal velocity and we can say that all of these factors have an effect in reaching zero acceleration. When the length of the string was greater than terminal velocity was seen very quick and when you would increase the height of drop of the parachute also terminal velocity will be successfully reached. The air resistance depends on the height of drop and the speed at which the parachute travels. But as the height of drop, length of the string and mass of the object was not big with greater values there was a lower terminal velocity seen.

In the first experiment we noticed that speed changes as we change the mass of the object. So we can say that terminal velocity is affected when we change the weight. According to Newton’s Second law, the force of gravity is proportional to mass under free fall.

So, F = mg where g is the acceleration due to gravity directed downwards

When terminal velocity is reached mg = drag force of the object

If we assume this drag force to be the same, when the mass of the object increases then terminal velocity also increases to correspond to the increase in force. In the experiment when the mass of the object hanged to the parachute was more the terminal velocity was reached at a faster rate than object with a lighter mass because in this case the drag force of the object equaled mg more quickly. But one thing noticed in this experiment was that the parachute traveled at a faster rate not only because of the weight but also due to the surface area. The object with mass 50 grams had a greater surface area due to which the terminal velocity resulted to be low. When the weight of 100g was measured the surface area was comparatively low due to which the terminal velocity was higher. The greater weight increases the terminal velocity by acting as an extra force against gravity and air resistance.

In the case of different heights we noticed that when we increase the height of drop then naturally the speed would increase and hence terminal velocity would be reached. For the experiment I performed, the last trial when the parachute was dropped at a height of 350 m the recorded time was 2.75 seconds. At a time of approx. 1.80 seconds terminal velocity was reached because as mentioned above this was the time when the drag force was equal to mg. However as the height gets lower the terminal velocity would decrease. Under gravity an object falls at a rate of 9.8 m/s2 which tells us that per second that the parachute falls its velocity increases by 9.8 m/s2. When the parachute is falling form a higher distance(350m) it will have more time to speed up which will result in a higher terminal velocity.

It was clear that when the best length string was that of 80cm. The larger the size of the length of the string was the greater was drag force and hence faster it equaled the other forces. When the string had a greater length the parachute was more spread out. The open parachute lets the air resistance to increase. If the length of the strings are short then less air will enter the parachute which would lower the parachutes drag force or resistance

ERRORS

In each of the experiments there were difficulties faced and one of the main ones was the force of wind. For some of the readings taken the wind speed increased so much that it changed the direction of the parachute. Even though direction does not have any effect on a parachute reaching terminal velocity most of the times but at some cases this change of direction can increase or decrease the speed of the parachute. In one of the readings taken for the change in the length of the string the parachute at the beginning travelled at a decent treat but all of a sudden it changed directions and was falling down vertically. This case happened when the length of the string was short (30cm) also in one of the readings taken for the same experiment of length 40cm the parachute collapsed in no time. Another difficulty that was encountered in all of the experiments was that the region of drop of the parachutes (540cm) there was a lot of wind because of which the parachutes would get blown away at times resulting a significant error in some of the readings taken.

There were a few human errors in the experiment for example the height of drop was not constant for the experiments. For each of the readings we took a rough value after first measuring what 540cm was. This could result in the time going a few seconds up or down. These changes dint allows the calculations to be accurate for the average velocity.

Another error I encountered was the mass of the object hung to the parachute. I assumed the mass of 100 grams to be a good one for this experiment but instead it increases the acceleration of the parachute which dint allow the parachute to open well so to create and upward force and hence reach terminal velocity.

When the parachutes length was 30 and 40 cm terminal velocity was not reached because the parachute reached the ground before so the air resistance was not there.

IMPROVEMENTS

We could improve on the results by performing the experiment when there was very less wind as that would not then affect the height of drop (540cm). Another thing we could do is that of adding nets to the parachute in order to see how much of air is blocked in the material which affects the velocity at which the parachute travels. This results in the experiment to be more precise as only the part when the parachute reaches terminal velocity will be measured. I could perform the experiment at various high lengths which would result in more readings where terminal velocity will be reached because when the length of the string was 30 and 40cm there was no constant acceleration sees as the parachute hit the ground as a fast rate.

CONCLUSION

The aim of the experiment was to see how various factors affect the terminal velocity of a parachute and my results were such that the heavier mass, larger length and greater height were more prone to reach terminal velocity. The graph had constant acceleration toward the higher region which proved our hypothesis. In each of the experiments when drag force equaled mg at a faster rate, there was constant acceleration seen quickly.

But we should know that in reality terminal velocity is not very well defined because external factors such as air density, constant gravity and wind keep changing with time and will have an effect on the experiments we perform. For example in the experiment where the height of drop was changed the factors mentioned above will change with height due to which the terminal velocity also changes.

More or less the results obtained were quite accurate and has a good scope for others to keep researching on this topic