Flight Testing / Modeling

	Aim To compare the flight of the water rockets and ballista bolts used in the second impact comparison test.
	Method The water rockets and ballista bolts used in the second impact comparison test were fired from the cannon and ballista shown below at a number of different angles. The angle, time of flight and range for each shot were recorded.
	Ballista Cannon
	Results
	The results of the flight testing for the water rockets and ballista bolts are show below.
	Water Rocket 46 Degrees 30 Degrees 15 Degrees Range Time Range Time Range Time 71 4.22 65 2.87 54 1.89 80 4.77 67 3.31 49 2.07 71 4.63 80 3.89 61 2.38 66 4.55 80 4.03 50 2.06 60 3.17 70 3.98 52 2.08 Average 69.6 4.28 72.4 3.6 53.2 2.01 Ballista 17 Degrees 27.5 Degrees 35 Degrees Range Time Range Time Range Time 40 1.7 57 2.65 55 3.02 42 1.75 56 2.84 52 2.64 54 2.67 Average 41 1.72 54.75 2.7 55 3.02

Discussion To help compare the flight characteristics of the water rockets and ballista bolts a mathematical model was used. The model calculates the trajectory of a missile based on the following variables: Mass Angle of Elevation Time of flight Range Initial velocity Coefficient of friction The first four variables can be fairly simply measured. The last two variables can be inferred by choosing values for them that cause the flight path generated by the model to most closely match an actual flights measured range and duration. A genetic algorithm was used to select the values for initial velocity and coefficient of friction that most matched the flight of each type of missile. The results of the modeling are compared, in the table below, with the average measured values for each elevation used. Also shown are values of initial velocity and coefficient of friction used by the model along with the simulated energy and momentum of each missile once it had traveled a distance of 5 m. Water Rocket - Modeled vs. Measured Values Average 69.6 4.28 72.4 3.6 53.2 2.01 Modeled 68.8 4.64 72.4 3.4 54.0 1.88 Modeled Initial Velocity 38.3 m / s Kinetic Energy @ 5 meters 97 Joules Modeled Friction Coefficient 0.04069 Momentum @ 5 meters 5.3 kg m / s Ballista - Modeled vs. Measured Values Average 41 1.72 54.75 2.7 55 3.02 Modeled 40.1 1.72 52.25 2.6 55.2 3.17 Modeled Initial Velocity 30.5 m / s Kinetic Energy @ 5 meters 156 Joules Modeled Friction Coefficient 0.08992 Momentum @ 5 meters 10.7 kg m / s This Section is Incomplete, Sorry This Section is Incomplete, Sorry

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