My prediction for the speed of the helicopter is that as the wingspan decreases the vertical speed of the paper helicopter increases, which I believe is as a result of the rotation of the wings going through a different cylinder of air each occasion, which suggests the fact that a wing span of 8cm would have a cylinder volume of air of πr2. Therefore, as the wingspan decreases, the amount of air molecules contained inside the cylinder of air would be decreased proportionally to the wingspan. Furthermore, this would conclude in less air resistance against the force of gravity that forces the paper helicopter to fall because of the reduction of the wingspan, less air resistance would be needed to restrain the overall vertical acceleration. Although, as the helicopter gradually gains speed, the air resistances would increase likewise, until it becomes so great that it pushes against forces of Gravity, which ultimately forces the helicopter to vertically accelerate downwards. Nevertheless, eventually the resistance force will become equal to the opposing force, which in this case is Gravity, thus resulting the helicopter in not accelerating anymore since the forces are balanced. Therefore, it has met its Terminal Velocity (maximum speed).
In relation to other theories, the three laws of Motion by Sir Isaac Newton begin to investigate Gravitational attraction and discovered that there’s a gravitational attraction between all masses, giving everything a weight. This suggests that everything without air must have the same acceleration, which is ten m/s. This would mean that without gravity applying forces to push the helicopter downwards, it would still eventually land, because of its mass and because of this I would be made to believe that this may another reason for the acceleration of my helicopter. He also discovered that in most changes of Velocity, more than one force is acting on the accelerated object, such concurrent forces produce a signal net force. If the force pushing down on the helicopter is greater than the upwards draft, there will be a net force in the downward direction, therefore the helicopter will accelerate in that direction. This further proves my prediction since the gravitational forces applied on the helicopter are far greater then the air resistance when the wings are longer.
Diagram to describe forces acting upon Helicopter
Apparatus
- Printer Paper
- Scissors
- Paperclip (0.25g)
- Stopwatch
- 2x Metre Ruler
Diagram
Method
Assembly of Helicopter
Initially I would have to explore what materials were needed for my investigation and set them up and use them accordingly if I want to achieve precise results. Now I will explain how to conduct my experiment:
- Create template for paper helicopter, which then must be folded and cut accordingly to instructions.
- Attach 0.25g paperclip to the bottom of the helicopter near the cut line.
- Use the metre stick to measure out two metres exactly from the floor.
- Find work surface, and measure twp metres from the floor.
- Place helicopter wings flat against metre stick and release from the two-metre mark from the floor.
- Drop the helicopter three times, get helper to start the stopwatch when the helicopter is released and stop once it has reached the floor
- Record time to 2 decimal places e.g. 2.78
- Cut of 1 cm and repeat 3 more times, add the cut pieces to the paper clip.
Stopwatch
Note: To reset the time, the start must be pressed followed by stop time. In order to make sure results were as accurate as possible, a second person was needed to operate the stopwatch whilst the first person dropped the helicopter. Two stopwatches were needed if at any time the first one was faulty.
In order to keep my experiment flawless, I will have to ensure that my control (mass) stays the same, I will do this by attaching the cut off wing spans to the paper clip as specified above, which will overall allow me to be assured that the helicopter has lost no mass and has only lost its wing span as the changed variable. The results will be recording into a table in a notebook to start with; the table devised will have all the labels and scientific units, so that the results are as precise as possible. My reasoning behind doing the test 3 different times is that, my philosophy is that the most times the experiment has been completed, the higher the accuracy is because some anomalous results may be an outcome of not using stopwatch properly or plainly just the awareness or co-ordination or the person using the stopwatch. This also allows me to identify any anomalous results in my conclusion and logically explain why those took place.
Preliminary Work
I was lead to believe that prior investigations were needed to be conducted, which would allow me to get an insight into what possible errors may occur in the investigation and also help me in devising a prediction and ultimately understand the type of results I would be achieving. Firstly, I began to observe and practice with different methods of constructing helicopters such as a variety of templates and also the best size for the helicopter in general. After the helicopter was successfully constructed, I changed the variables of the helicopter such as changes in the mass of the helicopter (adding more paper clips) and also changing the wingspan (shortening the wings), I realized that the greater the mass, the harder it was to record the data since in some occasions when the mass was too heavy it became too quick to calculate the data and also harder to use the stopwatch. Therefore I decided to choose to do wingspan, and I have a much larger scientific knowledge and reasoning of why the speed would increase due to a smaller wingspan.
Results
Attempts
From my results, I can gather that the fastest wingspans were indeed the shorter ones ranging from 7cm downwards to 4cm, in comparison to the 10cm to 7cm range there was a considerable amount of differences in the time taken. The reason for this may be due to the helicopter reaching its maximum speed but since the air resistance taking longer to build up because of the speed being slower than the upper wingspans. The gradual increase in the resistance force will amplify until it becomes equal to the accelerating force, until the helicopter cannot accelerate anymore. Using the terminal velocity theory, I can conclude that it would take longer for a 4cm wing spanned helicopter to fall 1 metre than for it to fall 2 metres.
Risk Assessment
Before commencing with my experiment I will have to take several precautions to ensure that there will not be any risks that can cause accidents for either myself or others working nearby.
Foremost, the risk of falling of the work surfaces will have to be analysed since the experiment involves me dropping a helicopter from three metres, I have to ensure I will not be going down along with it. In order to do this, I will have to ensure the work surface is completely tidy by removing all excess books, paper, or any other materials not needed for the investigation away and the things which are required must be placed on another table. Another dangerous factor would be making sure that I am not near the edge of the work surface because that could lead to the most dangerous fall, which can result into very harmful pain and in some circumstances, fatal injury. One of the minor precautions would be to ensure I use the scissors properly so I don’t cut myself with the scissors will removing the helicopter from the template but more importantly I should be aware to safely restore the scissors into a much safer spot such as a teachers cabinet so others cannot get injured by them.
Results
In order to be able to observe my results to trace patterns and correlations through the data, I have created a table, which shows the length of the helicopters wingspan, and also the results for each wingspan, which was taken individually three times. These results are yet again to 2 decimal places to achieve a more precise range of results, and an average is used to calculate the average of all the three attempts.
My results show major anomalous result through Test 1 & 2, however throughout the averages this becomes very minor and proves that overall it could have been a mistake with the stopwatch or the person conducting it.
Conclusion
To conclude my data from my investigation, I can interpret that my prediction was overall correct. This was as a result of my results showing a distinct pattern, where a constant speed is shown, due to the length of the wingspan decreasing in proportion. The graphs illustrated display a steady increase in speeds between the upper wingspans (9cm to 6cm), then wing span 5cm shows a steeper gradient, which means there has been an increase in speed, but may seem misleading as it looks like there has been a quick deceleration in my graph, yet the time differences are the sack of a few milliseconds in comparison to the earlier results where there is about 25 milliseconds different in increased speed. My suggestions is that the increase in speed is due to the lower wingspans ranging from 4 cm to 2cm having a much higher terminal velocity, which is a result of the paper helicopter that is smaller being much more compact and a more denser object then the helicopter with a longer wingspan this causes it to have a higher maximum speed.
By using the Speed formula, I can conclude that a helicopter with a wingspan of 9cm has a speed of 1.26 by using the formula Speed= distance/ time (2.98/2.28), this compares to the smallest wingspan, which was 2cm having a speed of 3,63(2.98/0.82) that ends up being 2 mph faster! I believe this is a result of the decrease in wingspan size my helicopter has more than doubled the speed from the starting length of 9cm. To substantiate this point furthermore, the graph shows that each different wingspan lands quicker than the one before it, there is a positive correlation that as the wing span decreases the speed increases, which overall aids my prediction even further. Since I predicted my helicopter’s wingspan decreases less air resistance will be needed to push against the gravitational force, which is forcing my helicopter to gradually fall. Therefore, the accelerating force, the gravity would be greater then the drag force, otherwise known as air resistance, and because the forces are unbalanced there would be greater acceleration, also bearing in mind that Newton calculated that everything has a mass of 10 m/s. So because of the unbalanced forces and the added mass of 10 m/s the helicopter with fewer wingspans should and has shown from my results to land much quicker. The main reason for this is that the gravitational force is greater than the resistance force.
Evaluation
Overall, my investigation was successful because the results, which were gathered very precise, the method in which I would obtain results was also very accurate since it was a very easy guide to follow and the results gained helped to further prove my prediction correct and supplementary giving me a firm and transparent knowledge of forces in motion.
The overall accuracy of my results was good since it allowed me to illustrate a very clear graph with a relatively easy line of best fit since the results followed a positive correlation making the outcome reliable, their were not many anomalous results but some did occur throughout the first two tests, which were very considerably out of line. I believe these results were overall human error since they ended up following the average correlation in the end. For next time, I would have considered taking more trials such as five instead of three to ensure that an even higher reliability in results would be gathered. Nevertheless, my final three results from wingspan 4cm to 2cm were anomalous at the time, not because they weren’t increasing in speed, but because they seemed grouped together, which I came to a reasoning for, which was that they had met there overall terminal velocity.
To improve upon my investigation, I would perhaps begin to introduce different variables such as different sized helicopters in general to see if they would have made an overall difference in the results or would have tried differing the size of the paper clips or the width of the wings, or even make different cuts into the wings as wind breakers, which would allow me to discover new logic behind the aerodynamics of a helicopter and how shape affects the speed. The other variable in my prior investigation, mass of the helicopter might have been a more reasonable choice since it was much less predictable and overall the outcome of this investigation was inevitable. To carry out this investigation, I would consider attaching extra mass by adding a new paper clip each time, as a I know paper clips weigh 0.25g, If I was to do the experiment ten times I would have added a total mass of 2.5g, which I think would make a considerable effect in the rate at which my helicopter would descend, but to drop this from the ceiling would not be significant enough and a much higher height would have to be used. It wouldn’t be very sensible to stand on a roof and drop this since it would be affected by other variables outside, and instead using the stairs would be a much greater idea.
To develop my current experiment for next time, I would consider dropping it from the ceiling therefore I wouldn’t have to hold the metre stick each time and it would have ended up being a much fairer trial since the height of the ceiling would never change and the metre stick might have gradually differed each time. Nevertheless, the differences would not have been drastic and would not have caused even milliseconds of difference.
In the end, I believe my investigation was very successful in what I was intending to do.