Challenge: To design a battery-powered or capacitor-powered, propeller-driven flying device that can orbit with a desired period.
Parameters: Your flyer can be powered by up to four 1.2 V rechargeable cells or up to three 2.5 V 10 F super-capacitors provided by Mr. Jamieson. You may use Mr. J’s propellers and motors, or found ones. Your flyer must be supported from the ceiling (but cannot damage it in any way) or electrical drop-down above your desk, and cannot extend to the table height. (Moving tables is not allowed). You will be asked to make your flyer orbit with two different periods in the range of 1.10 seconds to 2.20 seconds.
Scoring: Mr. J will give your group the desired period, and you will have up to one minute to set up your flyer and get it going. At your instruction, Mr. J will time 20 revolutions (10 for the longer period trial), and find your result. Your score will be based on how close you get to the desired period. You will only have to do one, and Mr. J will move to another group until everyone has done one before asking you to do the second one.
Score = | % difference short period | + | % difference long period |
Rank will be based on score, with lowest score earning highest rank.
Physics: The description of the dynamics of centripetal acceleration is necessary for the complete model of your orbital flyer, and for understanding how you can adjust it to obtain a desired period of revolution. You can adjust thrust and drag, length of string, or anything about your flyer. Note that the propeller thrust matches drag at steady speed, and that drag is proportional to the square of speed. A powerful propeller will result in a faster speed of orbit. Also note that the propeller must push the flyer and should be located well behind the centre of mass of the flyer.
Extensions: The mathematical relationship between any variable and the period of revolution can be calculated as long as the other variables are known and held constant. The thrust and drag would be difficult to measure, but can be assumed to be balanced if the flyer is moving at a constant speed. Please include the circuit diagram for your flyer, with current and voltage measurements and resistance and power calculations. For an extra challenge, try to figure out why the propeller cannot be in front, pulling the flyer.
Help/Hints: It would be unwise to have more than one adjustment (eg. Length of string and thrust), unless you have a low range and a high range system. For example, you might have two strings that are both calibrated, but the shorter one is used for shorter periods and the longer one is used for longer periods. Calibration of your device is essential so you can reliably make adjustments during the competition. Graph your calibration data and experimental results and draw a line of best fit. Use the equation of the fit line to find make your adjustment once you are given the target period. Put in a switch so you can avoid wasting the energy of the batteries. The output voltage of a worn-out battery will drop, and therefore decrease the thrust. That may impact your calibrations!
Quiz Topics: Circular Motion
Newton’s Laws
Universal Law of Gravitation
Online Text: chapter 6