Readings 1-5 – Results for calculated wind speed The anemometer will be able to measure to a degree of accuracy of two decimal places, giving it a resolution of 0. 01ms-1. This is because the least certain measurement of distance, the diameter of the anemometer was measured to two decimal places. This therefore restricts the accuracy of the anemometer to two decimal places when calculating wind speed. A calibration curve for potential difference against speed is now possible: When taking my results, I may find that I encounter wind speeds of over 2.
51ms-1. I predict that as the potential difference in mV increases, so will the rpm in a directly proportional manner, above 160 rpm. 80mv means an rpm of around 155 and a wind speed of 2. 51ms-1. The value for the rpm is the calculated mean from the 5 results taken. I can assume that for the amount of voltage involved in this practical, the relationship between rpm and speed will remain linear. Therefore, I am going to extrapolate the calibration curve, to give me values for wind speed that relate to higher potential differences being obtained.
There will be a point where the relationship between the p. d and rpm will become non-linear. But I do not think that with the wind speeds I will encounter, this limit will be reached. An example of the kinds of rpm involved when the relationship between voltage and rpm may not be linear is when a similar type of motor is used in a motorised milk whisk, or model train. Both these motors are powered by 3v dc. This is a potential difference 75 times greater than produced by the motor turning at an average of 73 rpm.
A wind speed 75 times greater than the wind speed for an average of 73 rpm is 89ms-1; this is around 200mph. This is very unrealistic, and the anemometer would not survive in such conditions. Therefore, I estimate that I will only encounter wind speeds at most, up to 18ms-1 (40mph). Up to this point I would suggest that the relationship between the potential difference and rpm would remain linear enabling me to calculate wind speed for potential differences of over 80mV. Results The table above shows the results obtained measuring the wind speed.
I encountered several problems during the taking of the results. To obtain different potential differences, I needed to obtain different wind speeds. To do this I went to the sea front, and found different points along the sea front where the wind was blowing at different speeds. It was very difficult to accurately obtain a potential difference exactly equal to those recorded for long enough to read off the value for the datum at the same time. The wind source during the calibration was constant, and therefore fluctuations in the potential difference were minimised.
As wind is not at all constant the task of recording the results was made harder. To record the results necessary to determine the accuracy of the anemometer, I found different wind speeds along the sea front and as accurately as possible gained a potential difference as close to those stated in the table. At the same time I measured the wind speed that created this potential difference using the datum. The results are not consistent with the findings from my calibration. Therefore I am able to analyse these results and the factors which contributed to the inaccuracy of the anemometer that I devised.
As I predicted I encountered wind speeds fast enough to produce a potential difference greater than 80 mV. Using calculated data, I would have predicted that the corresponding wind speed was 2. 84ms-1, using values from Appendix 1. In fact using the datum I recorded a wind speed of 8. 20ms-1. The graph shows that the expected values for wind speed, produced from the calibration are all inaccurate. This obviously relies upon the assumption that the datum is accurate, which I can do. The results show that as the potential difference created by my anemometer increases, the inaccuracy increases.
Both sets of results are linear showing that the calibration was successful to a certain degree, but now using this data I can analyse and explain why the results I achieved were inaccurate. Although they are inaccurate, they are not anomalous as they follow the predicted pattern. Analysis There were several factors during the calibration that could have led to these inaccurate results. Firstly, when the anemometer was placed in a very narrow wind stream, the returning cups did not have to pass through the same wind which was turning the cups.
This means there would have been less air resistance during the calibration than when recording results. Contextually, this means that a potential difference of 50 mV created during the taking of results may correspond to a potential difference of 60 or 70 mV created during the calibration. This agrees with the results recorded, although the degree of inaccuracy is greater than this suggested difference. In actual fact using values from Appendix 1, the potential difference required to produce a wind speed equivalent to that recorded for 50 mV using the datum (4. 72 ms-1) is between 140 and 150mV.
Another factor to suggest that the absence of air resistance during the calibration had an effect can also be seen on the graph. The inaccuracy of the results increases as the potential difference increases. This can also be explained using the same idea. During the calibration, a potential difference of 50 mV was calculated to correspond to a wind speed of 1. 51 ms-1; this means the returning cups were not encountering the resistance created by this corresponding wind speed. This can be compared to a potential difference of 80 mV where a corresponding value of 2. 51 ms-1 was calculated.
The returning cups would therefore not be encountering a greater air resistance (because of the faster wind speed), increasing the inaccuracy of the results. The main factor that contributed towards the inaccuracy of the results, which encompasses the previous explanation is the inefficiency of the anemometer. As the wind’s energy was transferred from linear kinetic energy, to rotary kinetic energy (through the centre axle) into electrical energy (through the motor utilising the generator effect). At each stage energy will be lost, therefore making the values obtained for each rpm inaccurate.
The inefficient transfer of energy was caused by several factors; these were friction in the motor, sound created by the turning of the cups, and mainly air resistance. The error seen in the results is a systematic error as all the results were similarly inaccurate; the speed of the cups that was calculated during calibration was slower than the actual wind speed. Obviously the size of error is greater than desirable when making a sensor, but now with this knowledge the results from the calibration could be altered to encompass this systematic error.
Another factor that affected the accuracy of the results from the calibration was the inclusion of user error when measuring the time period for x number of flashes. For example, if I measured 40 flashes in 5. 50 seconds, but due to slow reactions or an error the time it took for 40 flashes to be produced was only 5. 30 seconds the difference in the calculated speeds of the cups would be 0. 11 ms-1. Although this is not a lot, it would still have been influential. The success of the anemometer can be measured by analysing its effectivness in meeting the qualities desirable for a good sensor.
These include a good resolution, fast response time, low systematic drift or error, appropriate sensitivity and low random variation. The sensor had a relatively fast response time; the potential difference displayed on the multimeter was updated very quickly when a change of wind speed occurred. This made the data collection very different as the value kept fluctuating, although it showed a fast response time in respect of changing wind speed. I was able to reduce the effect that unsystematic random error had upon the results from the calibration by taking the average of the five sets of results.
Small unsystematic variations were present in all the readings that I took, but as what I was measuring (thousands of a volt) is a small quantity these small variations had a relatively large affect (this being the sensor’s sensitivity). The sensitivity of a measuring system is the ratio of change of output to change of input; this is where the sensor became inaccurate as the multimeter did not have a sufficient resolution to create a sensitive enough sensor. The sensitivity was limited, as a very small input was inaccurately converted into a large output.
This is why the results were so inaccurate, as the calculations converted very small differences of potential difference containing error (systematic and random) into relatively large values for wind speed therefore amplifying any error that was present in the results. For this same reason, the sensor’s resolution was limited. In conjunction with a high level of random variation caused by the multimeter’s insensitivity in measuring such a small amount of potential difference, the smallest degree of potential difference that I could accurately measure was 10 mV; this is ten, one thousandths of one volt.
Therefore the resolution of the sensor is around 0. 15 ms-1; this is roughly the wind speed calculated from the calibration results for 10mV. This is irrelevant because of the fact that results can be calculated to 2 decimal places, as I can only be sure of results to the nearest 0. 15 ms-1 due to the sensor’s relatively large resolution. In comparison, the datum can accurately measure to 2 decimal places, e. g. 2. 42 ms-1. I was able to detect and explain the systematic error due to the fact that my sensor was relatively inaccurate and I had access to a much more accurate sensor designed to measure the same thing.
The use of a datum enabled me to effectively analyse my results. Overall to create a more successful sensor, I would need to review the complexity of this sensor and devise a method that reduces the margin for error as the current design encompasses too many opportunities for the results to be affected.
Bibliography www. uq. edu. au – Picture of Reed switch Advancing Physics AS – Institute of Physics Lonsdale Science Revision guide – The essentials of OCR science double award. Instrumentation coursework. doc Toby Parnell.