Physics Investigation: The Rotational Speed of a Windmill and Distance

A windmill is a mill that converts the energy of wind into rotational energy by means of vanes called sails or blades, according to Wikipedia. In Physics’ perspective, it converts the wind energy from the air into the kinetic energy on its blades so that they move. When it rotates, it does a centripetal motion. The faster it rotates, the more kinetic energy it has. Windmills have a very long history. Centuries ago, windmills usually were used to mill grain and pump water. Modern windmills are used to produce electricity and pump water for land drainage or to extract groundwater. Therefore, windmills are an important sign which shows that human beings make good use of renewable green energies.

Once I asked myself: “Well, the wind provides energy and forces the windmill to rotate. But in what way can we change how fast it rotates?”

THE RESEARCH QUESTION

Last week, I found a windmill in my old toy box. I tried to blow away the dusts on it. It rotates really fast. But when I was on my bed after I made it standing on my table, it rotates slowly and peacefully when I blowed. I thought of the question that I had wondered for many years since I was a child: how can the distance from the origin of the wind to the windmill affect its rotational speed? I might guess the answer, but I needed to prove that. I needed to design an experiment to examine the specific relationship.

EXPERIMENTAL VARIABLES

Since I only want to how the distance affects the rotation speed, I have to eliminate other factors that may influence the results of the experiment. For example, the original speed of the wind must be constant. The angle made by the direction of the wind and the front of the windmill must be constant too. Other factors such as the air resistance and the external temperature must also be kept unchanged.

In this experiment, the independent variable is the distance from the origin of the wind to the windmill. The dependent variable is the speed of rotation of the windmill. I change the independent variable, the distance, and examine how the dependent variable, the rotational speed, changes in response to the independent variable.

EXPERIMENTAL DESIGN

The purpose of this experiment is to test the relationship between the distance from the origin of the wind to the windmill and the rotational speed of the windmill.

I prepare all the following equipments needed to finish this experiment:

  • To make sure the original speed of the wind is constant, I need a hair drier and always set it to the LOW power output. (Though I do not know the exact speed of wind, it does not matter because it is not the factor involved in this experiment)
  • To measure the specific distance from the hair drier and the windmill, I need a 1-meter-long ruler with clear scales on it.
  • I need a motion sensor to test the rate of rotation of the windmill.
  • Two retort stands are needed to fix the positions of all the equipments.
  • And of course, I have a colorful toy windmill with four blades.

EXPERIMENTAL PROCESS

  • First, I attach the windmill to the first resort stand.
  • Then I setup the sensor on the second resort stand and make sure that the four blades of the windmill can pass through the sensor when they rotate without touching the sensor.
  • After that, I attach the ruler to the first stand in the horizontal direction. The ruler must make a right angle with the stick of the stand.
  • In addition, I need to make sure the front opening of the hair drier (where the wind comes from) perfectly directs at the mid-point of the four blades so that the wind direction does not change.
  • Finally, I power on the hair drier, set it to LOW power to make sure the wind speed is unchanged, and change the distance according to the readings on the ruler by my hand.
  • I choose the distance once every 10 centimeters. The distances I pick are 20 cm, 30 cm, 40 cm, 50 cm, 60 cm and 70 cm.
  • I measure the rotational speed 3 times for the same distance, and then use the average. Repeating experiments makes my data and results more accurate.

DATA COLLECTION

The sensor is connected to the Verner Lab Pro interface and then is connected to the computer. The Logger Pro software automatically senses the motion sensor and displays graphs axes of rotational speed against time.

DATA PROCESSING

Mean rotational speed = (V1 + V2 + V3) ÷ 3

For example, the mean rotational speed of trial 0.20m is (0.756 + 0.760 + 0.765) ÷ 3 = 0.760

Uncertainty = (Vmax – Vmin) ÷ 2

For example, the uncertainty of trial 0.30m is (0.688 – 0.594) ÷ 2 = 0.047

DATA ANALYSIS

The mean rotational speed is graphed against the distance in the following diagram:

And the ln(mean speed of rotation) or lnV is now graphed against the distance in the following diagram:

CONCLUSION

From the first graph plotted, we can deduce that the rotational speed of a windmill has an exponential relationship with the distance from the origin of the wind to the windmill. As the distance from origin of the wind to the windmill increases, the rotational speed of the windmill decreases.

If we graph the ln value of the average rotational speed against distance, we can find that lnV has a linear relationship with the distance. This also proves that the rotational speed of a windmill has an exponential relationship with the distance.

EVALUATION

Though the data does show an exponential relationship, the data is not accurate enough. When we are collecting the data of rotational speed, we find out that for the same distance, the rotational speed fluctuates a lot. Every trial has a large difference from the other ones for the same distance. Because we do not have any equipment to fix the position of the hair drier on the ruler, we have to do that by man power. This means that we are not able to make sure that the front opening of the drier (where the wind comes from) directs precisely at the mid-point of the four blades. In addition, human hands may  shake a lot during the experiment. Therefore, we can not make sure that the direction of the wind is always constant. The rotational speed may change due to the change in wind direction. Further more, I did not take the distance from the wind origin to the opening of the hair into consideration of the whole distance. Instead, I used the distance from the opening to the windmill when calculating. This may have a slight influence on the results of my experiment.

IMPROVEMENTS

I can make some improvements to make the data in the experiment more precise:

  1. I can do the experiment in a perfectly windless indoor room to avoid some fluctuations because of the change in strength of airflow.
  2. I should use an equipment to fix the position of the hair drier during the experiment, so that we can make sure the wind direction does not change during the experiment and the front opening of the drier (where the wind comes from) directs precisely at the mid-point of the four blades.
  3. I should take the distance from the wind origin to the opening of the hair into consideration of the whole distance instead of only using the distance from the opening to the windmill when calculating. Therefore, the real distance should include both the distance from the wind origin to the opening of the hair, and the distance from the opening to the windmill.
  4. I can also do further experiments in the future to find how other factors such as wind direction influences the rotational speed of the windmill.

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