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Wind resistance and terminal velocity


A typical trace is shown below:

PC oscilloscope trace obtained when measuring wind resistance

Answers to questions

For trace WIND1

Q1. Why does the output from the generator increase with time in each trace? Which law of electromagnetism applies?
A1. The falling weight starts from rest and accelerates vertically downwards due to gravity. As the speed increases the rate of rotation increases and the generated emf from the generator increases. This is Faraday’s Law.

Q2. Does the AC period on the trace remain constant or change with time? Explain your observation.
A2. The traces all show that the period (time between peaks) starts off long and gradually decreases. The AC component is caused by the basic nature of the coil commutator which results in approximately three peaks per revolution of the generator shaft. As the shaft rotates more quickly the period will decrease.

Q3. Does the average output from the generator (the DC component) increase linearly with time? (i.e. can you draw a straight line with a ruler through the trace?) What does this tell you about the speed of the falling weight?
A3. The output increases linearly for the first 0.1 s or so but a straight line cannot be drawn through the whole trace. This shows that the acceleration is not constant and the rate of speed increase gets less as time goes on. The effect can be explained by considering the resultant forces on the load. We have gravity pulling downwards and resistive forces due to friction in the bearings and generator, air resistance on the weight and electromagnetic forces in the generator armature (Lenz’s Law) all acting upwards. The gravitational force downwards remains constant but all the upward forces increase as the speed increases. The resultant downward force gets less as the speed increases and hence the acceleration gets less.

For traces WIND2, 3 and 4

Q1. How does the maximum output value reached compare in each of the traces as more vanes are fitted? What does this tell you about the maximum speed reached by the falling weight? 
A1. The maximum output reached gets less as more vanes are fitted. This shows that the maximum velocity attained gets less as well.

Q2. In the traces with vanes fitted the output increases and then maintains a steady value. Describe the motion of the falling weight during the time of descent. 
A2. During the first part of the descent the speed of the weight is increasing but the acceleration is not constant. The speed eventually reaches a steady value (the horizontal part of the trace), the acceleration is then zero.

Q3. What is the name given to this final motion?
A3. Terminal Velocity

Q4. The traces enable you to deduce how long it takes to attain a constant output value. How does this time vary with number of vanes?
A4. As the vanes are increased in number the time taken to reach terminal velocity falls.

Teachers' notes

If several sets of windmill apparatus are available but there are only one or two PC oscilloscopes, the students can be given the further study topics to investigate by simply monitoring the time of descent rather than the electrical output. Each group can take its turn at the oscilloscope to do the main study. There are many other variables which can be introduced such as whether vane area, length or width has the most effect. It is not expected that the effect of adding vanes bears a simple proportional relationship to time of descent. There is a shielding effect which means that the three additional vanes from 9 to 12 will have less effect than from 3 to 6.

Credits, comments and further info

This experiment was written by the design team at Lascells Ltd.


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