The effect of increasing the weight on the terminal velocity of an auto-gyro

The aim of this investigation is to find out what effect of increasing the weight of an auto-gyro has on the terminal velocity of an auto-gyro, which is made to my specification.

Input variables

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In this experiment the input variables that I have are:

* The weight of the auto-gyro by adding more paper clips

* The length of the wing of the auto-gyro

* The width of the wing of the auto-gyro

The variable that I will change is the weight of the auto-gyro by adding more paper clips.

Preliminary experiment

We did a preliminary experiment to ensure that the experiment will work efficiently with the variables chosen and that the experiment would give us a suitable range of results.

After doing this experiment I found out that the auto-gyro does reach terminal velocity after about half a metre of drop.

Prediction

I predict that as more paper clips are added to the auto-gyro, the terminal velocity will increase.

Explanation

I believe the terminal velocity will be higher as the size of terminal velocity depends on the weight of the auto-gyro. This is because terminal velocity is reached when air resistance equals the weight of the object.

If the auto-gyro is heavier then its velocity will be higher than if the auto-gyro is lighter. So the object will follow the drag equation:

D = Cd*p*A*V�

Where: Cd is the drag coefficient

p is the density of air

A is the surface of the auto-gyro

V is the velocity

So I think that the auto-gyro will be effected by drag, therefore, the heavier the auto-gyro the higher the terminal velocity.

Fair Test

To make this experiment a fair test I will ensure I will keep the following factors the same:

* Height that the auto-gyro is dropped from – 3m

* Length of the wing – 10cm

* Width of the wing – 1cm

* Height that the terminal velocity is measured from – 1m

* Same apparatus

The variable that I will change is:

* The weight of the auto-gyro

Safety

To ensure that this experiment is safe I will take the following procedures:

* Don’t fall of the stool

Apparatus

In this experiment I will have the following apparatus:

* 3x 1metre rulers

* Stop watch

* Stool or chair

* Paper clips

* Auto-gyro – made to my specification

Diagram

The apparatus listed above, will be set up as follows:

Procedure

To do this experiment I will change the weight of the auto-gyro. First I will design and make my auto-gyro to the specification:

* Length of wing – 10cm

* Width of wing – 1cm

Once I have done that I will hold the auto-gyro 3m above the ground (using a stool to reach this height) and drop the auto-gyro from this height, first with no paper clips attached then each time adding one paper clip up until 5 paper clips have been added.

I will then use a metre ruler placed against the wall from the ground and use a stopwatch to time how long it takes for the auto-gyro to travel this distance.

When doing this experiment I will have to make sure I drop the auto-gyro from a suitable height so that I can make sure that terminal velocity is reached and it can be seen clearly.

I will repeat this experiment several times to ensure my results are accurate and reliable enough so that I can hopefully notice a trend and prove my prediction.

Once I have obtained these results I will plot them on a graph.

Measurements

In this experiment I will take the following measurements:

* Number of paper clips – 1, 2, 3, 4 and 5

* Time the auto-gyro falling at 1metre at terminal velocity

* Length and width of wing

* Repeat experiment several times to get consistent results

Results

From the experiment these are the results I have obtained:

Time (secs)

Number of paper clips

1st

results

2nd results

3rd

results

4th results

5th

results

Average

0

0.97

0.93

0.93

1.05

0.99

0.97

1

0.81

0.93

0.86

0.91

0.83

0.87

2

0.70

0.72

0.73

0.78

0.78

0.74

3

0.53

0.57

0.57

0.52

0.59

0.56

4

0.47

0.52

0.47

0.49

0.49

0.49

5

0.40

0.37

0.34

0.39

0.32

0.36

To plot these results on a graph I will find the terminal velocity, by using the formula:

Speed = Distance

Time

Number of paper clips

Speed (m/s)

0

1/0.97 = 1.03

1

1/0.87 = 1.15

2

1/0.74 = 1.35

3

1/0.56 = 1.74

4

1/0.49 = 2.04

5

1/0.36 = 2.78

Using the graph I found that the speed is effected by weight, when the weight of the auto-gyro increases so does the speed.

This is because when an object is dropped from a certain height it speeds up this is due to two factors; air resistance (drag) and weight. If there is more weight in an object, then the terminal velocity will be higher (when the object has reached its maximum speed) therefore the air resistance force and the weight force are equal.

Conclusion

The graph shows that the speed of terminal velocity is effected by the weight, as shown by a smooth curve. The curve on the graph proves that the terminal velocity is NOT directly proportional to the weight.

The graph also shows that the weight effects the terminal velocity at a greater force, so it can be said that the velocity is directly proportional to the weight squared:

Terminal velocity w�

To see if this is correct I will plot a suitable graph of weight squared against terminal velocity.

Number of paper clips

Speed (m/s)

1

1.15

4

1.35

9

1.74

16

2.04

25

2.78

After drawing the graph you can see clearly with a straight line with only a little scatter that the speed is proportional to the weight squared, therefore it generally shows that my prediction is accurate.

This showed that the speed is directly proportional to the weight squared and the drag equation: D = Cd*p*A*V [NM1]� applies.

Evaluation

Fair Test

I think that my experiment was a fair test as all the factors that I said I would keep the same I did.

I made sure I used the auto-gyro with the same width and length of wing by having the same auto-gyro throughout the whole experiment. I also ensured that I dropped the auto-gyro from the same height and timed the terminal velocity from exactly one metre above the ground for each of my results.

Accuracy of measurements

I think that the measurements that I took were quite accurate as I used a stopwatch, which was accurate to 0.01 of a second, so my timing was very accurate.

Also my measurements were accurate as I made sure the amount of weight is increased by always the same amount (1 paper clip).

Anomalous (odd) results

For this experiment the odd result that I obtained was with 3 paper clips as the speed was quite fast.

I think I obtained this anomalous result due to the fact that the paper clip might not have been fastened on properly (not in the middle) therefore one side may have been heavier so the weight of the auto-gyro would become unbalanced.

Suitability of procedure

I think that my plan was good and the experiment worked very well, as I managed to obtain a suitable range of results and the results did what I expected them to (see prediction).

In this experiment I had to be careful when measuring the time of the terminal velocity reached.

Improvements to plan

I think that my procedure was quite good and it gave me suitable results as I predicted. The improvements that I could have made to the plan is that at the heaviest weights the auto-gyro took slightly longer to reach terminal velocity and in the metre that I was timing the terminal velocity the auto-gyro was still speeding up so it was not completely accurate.

To improve this I would drop the auto-gyro from a higher height such as 4 metres.

Reliability of results

I ensured that the results were reliable by repeating the experiment five times and there was very little variation between them, which showed that the results were good and gave a good average and showed a good trend/pattern on the graph.

Strength of results

I think that my results are quite good and reliable as it showed good trends. The results proved that my prediction was correct.

Conclusion

From this experiment I have come to the conclusion that the terminal velocity of the auto-gyro is effected by the weight of the auto-gyro, the greater the weight the faster the terminal velocity.

My conclusion also proves that the velocity is proportional to the velocity squared and that the drag equation applies, which demonstrates that my conclusion and prediction are correct.

Further work

To do further work I would investigate the length of the wing and see what the effect of the wing length is on the terminal velocity.

To do this I would do the same experiment as this one but instead of adding more paper clips I will just have one and I will decrease the length by 1cm each time.

For this experiment I think that as I decrease the length the time of terminal velocity will also decrease. When the length is shorter the faster the terminal velocity, this is due to air resistance.