ACTIVITY DESCRIPTION
Kepler's Laws are not always easily understood, especially by younger students or students from professional schools, who tend to see it as a technicism far from their interest. mBot and its flame sensor allow to simulate this motion so it can be easily grasped at once, and the supporting material suggests a way to pose the topic in the larger context of cosmological research, in order to better understand its importance.
The activity uses the flame sensor - when the mbot is closer to fire, it runs faster.
Simulate the motion of a planet around the sun, following an elliptic pathway with speed variable according to Kepler's second law (actually a consequence of the conservation of angular momentum).
"The line joining a planet and the Sun sweeps out equal areas during equal intervals of time"
The flame sensor is exploited to simulate the motion of a planet around the sun. From the sensor output, related to distance, the power of the motor is selected. In the following, we list the simple steps needed to play the activity, discuss the characteristics of the Flame sensor and give reasons for our choice of the algorithm. Finally we comment the code and the variables used therein. Through the text, useful tips leading to better results are mentioned and highlighted in orange color.
- Turn on the candle and position it in a focus of the ellipse. It is better to use an ellipse with relatively large eccentricity to see easily the change in speed. (We used an ellipse with semi-axes of 40 cm and 25 cm).
- Place the mBot on the path, oriented to run clockwise.
- Press the on board button to start the simulation.
- Mbot's speed will change during the experiment accordingly with the distance from the candle.
The experiment works better if you turn off the lights and, most important, avoid sunlight (or it is low at least). Indeed remember that not light but infrared radiation (=heat) is detected.
The Me Flame Sensor is an infrared radiation detector. According to the documentation available [1] it is able to detect radiation with wavelength in the range from 760 nm to 1100 nm, with the highest sensitivity reached near 940 nm. It should be able to detect radiation up to a distance of 1 m and within an angle of 60°. When a flame is detected, its blue indicator will light on.
The flame sensor has both analog and digital outputs. The possible digital values are only Fire and NoFire; Analog reading returns values from 10 to 1023: a smaller number means that the sensor is closer to fire. In a dark room you will get 1023.
An experimental test to detect the sensor output as a function of distance, returns the data plotted in the figure below.
When the "Fire” status will be active the blue led on the sensor board will turn on.
Due to the sensor non-linear response and to its limited accuracy (repeated results give slightly different values) we decide to skip the intermediate calculation for speed and just made a correspondence table (sensor output in a certain range) ---> (select a power) . The power increase when approaching, and decrease when going away from the "sun”. As already stated in the introduction, the accuracy is limited as the flame sensor detects not only to the flame but also to the light in the room, especially sunlight. It is therefore very difficult to calculate the exact speed according to Kepler's Law and the activity results more qualitative than quantitative. Nevertheless in a classroom dark enough you will appreciate the speed change and get a satisfying picture of what's going on during the planetary motion.
We may suggest two possible improvements:
- Use a smaller ellipse, with maximum Sun-Earth distance of 40 cm, in order to be within the linear response region of the sensor. This might allow to use the sensor exact value and evaluate the corresponding speed (distance*speed = costant) without using the correspondence table, which cannot be so accurate. A smaller ellipse, however, may be suitable to show the simulation only to small groups of students.
- Go back to the "speed” experiment and select the engine's power in relation with effective speed (again the relation proved to be not linear). This small correction might be appreciated only in the linear response region of the sensor.
