Developing Ordinary Differential Equations to Describe the Motion of a Paper Helicopter

Since George Box's article was published in 1991, paper helicopters have been used to teach students experimental design [2]. It is simple and inexpensive to produce and can easily provide physically measurable data for use in experiments. This paper attempts to create a model that describes the motion of a paper helicopter using engineering, physical and statistical knowledge. A search for the optimum/maximum flight time of a helicopter was conducted in order to provide a design allowing for the largest amount of data collection possible. This data collected was then used to build and test a model that can be described by two separate equations: one describing the helicopter's linear velocity and the other describing its angular velocity. These equations may be able to be solved exactly, but the path that was chosen to best fit our time constraint was to use a numerical analysis approach to create these estimations of the equations. It is important to keep in mind that although Box's paper is often quoted it still remains true: "All models are wrong, however some are useful [2]." Future work on this approach to the problem may contain exact solutions to our equations, but the model designed for use here is sufficient enough for one to accurately predict the flight velocities within small discrepancies compared to the physically collected data. This article is available in The Review: A Journal of Undergraduate Student Research: http://fisherpub.sjfc.edu/ur/vol8/iss1/8 Developing Ordinary Differential Equations to Describe the Motion of a Paper Helicopter Matthew B. Mac Williams December 12, 2005 Abstract: Since George Box's article was published in 1991, paper helicopters have been used to teach students experimental design [2]. It is simple and inexpensive to produce and can easily provide physically measurable data for use in experiments. This paper attempts to create a model that describes the motion of a paper helicopter using engineering, physical and statistical knowledge. A search for the optimum/maximum flight time of a helicopter was conducted in order to provide a design allowing for the largest amount of data collection possible. This data collected was then used to build and test a model that can be described by two separate equations: one describing the helicopter's linear velocity and the other describing its angular velocity. These equations may be able to be solved exactly, but the path that was chosen to best fit our time constraint was to use a numerical analysis approach to create these estimations of the equations. It is important to keep in mind that although Box's paper is often quoted it still remains true: "All models are wrong, however some are useful [2]." Future work on this approach to the problem may contain exact solutions to our equations, but the model designed for use here is sufficient enough for one to accurately predict the flight velocities within small discrepancies compared to the physically collected data. Since George Box's article was published in 1991, paper helicopters have been used to teach students experimental design [2]. It is simple and inexpensive to produce and can easily provide physically measurable data for use in experiments. This paper attempts to create a model that describes the motion of a paper helicopter using engineering, physical and statistical knowledge. A search for the optimum/maximum flight time of a helicopter was conducted in order to provide a design allowing for the largest amount of data collection possible. This data collected was then used to build and test a model that can be described by two separate equations: one describing the helicopter's linear velocity and the other describing its angular velocity. These equations may be able to be solved exactly, but the path that was chosen to best fit our time constraint was to use a numerical analysis approach to create these estimations of the equations. It is important to keep in mind that although Box's paper is often quoted it still remains true: "All models are wrong, however some are useful [2]." Future work on this approach to the problem may contain exact solutions to our equations, but the model designed for use here is sufficient enough for one to accurately predict the flight velocities within small discrepancies compared to the physically collected data.