Water Rocket Design - Research Paper Example

? Water Rocket Design number Introduction Water rockets act according to Newton’s third law of motion. The working fluid in the case of a water rocket is compressed air. The compressed air transfers its energy to an underlying water mass that propels itself out of the rocket body. The typical construction of a water rocket consists of household materials such as discarded plastic bottles, water, duct tape etc. Typical water rockets are constructed out of plastic bottles. The plastic bottles may be used individually or in combination after cutting out their bases and joining them together. Water is filled inside the plastic bottle rocket body but some space is left empty. The plastic bottle filled with water and partially empty is then turned upside down and sealed. This aids preserving the water inside. Compressed air or other gas injected into the water filled plastic bottle pressurizes the water inside. Typical sources of compressed air include bicycle pumps or portable air compressors. Similarly, other gases such as carbon dioxide or nitrogen may be used using compressed gas cylinders. However, using nitrogen may be dangerous given the high compression ratios used to store nitrogen. The compressed gas tends to provide the means to store potential energy inside the rocket body. The stored potential energy is releasable from the rocket when desired. The mass fraction of the water rocket increases with the use of water. This allows the provision of greater impulse when compressed air and water escape from the water rocket body. In addition to water, other additives are also used to increase the mass fraction of water rockets. Adding other substances allows the modification of water’s properties in order to change the thrust characteristics. Once the compressed air or gas begins to escape, the rocket lifts itself from the ground. When the compressed gas and water combination is exhausted the rocket returns to the ground in the form of a projectile. Hobbyist water rockets employ landing mechanisms such as parachutes but these add to the complication of construction. Water rockets present a simplified method of delivering physics and mathematics to students. However, water rockets also present a number of dangers during their construction, use and their return to the ground. This paper will look into the construction of water rockets to teach students mathematical principles while looking into learning styles, safety and other pedagogical considerations. Water Rocket Design Principles Water rockets are a direct application of Newton’s third law of motion describing action and reaction. The release of compressed gas and water allows the rocket to lift itself skywards for considerable distances. The exact physics behind water rockets depends in large part on the stored energy inside the rocket and the air drag encountered by the moving rocket. However, a lack of standardized construction techniques means that a number of different physics models are used to delineate how water rockets operate. The final outputs from a water rocket include the total height achieved as well as the total duration of flight. These outputs depend on a number of different inputs including the pressure of compressed gas, the volume of water used, the nozzle configuration and the weight of the water rocket body. The relationship between these inputs and outputs are expressible in a variety of different ways. Various models are available to delineate the relationship between these inputs and outputs. However, none of the available models guarantees a high degree of accuracy so these models can be best used as approximations. Mathematical Relationships In order to simplify the relationship between the inputs and outputs for a water rocket, students were presented with a simple water rocket mathematical model. The physics behind water rockets requires exploration of advanced concepts such as (Gommes, 2010): incompressibility of water; compressibility of the compressed gas and its dependence on temperature and transient effects; flow patterns through the discharge nozzle; the effects of viscous drag inside the water mass; the effects of viscous drag in the flow from the discharge nozzle; decreases in the pressure of the compressed gas and decreases in the exit velocity from the discharge nozzle. It is assumed that for the purpose of this paper and for the purpose of the project that these concepts do not affect water rocket operation. In addition to these concepts, the presence and effect of aerodynamic drag on the water rocket operation was neglected to simplify calculations. Aerodynamic drag can be expressed mathematically as: However, the presence of aerodynamic drag can be neglected largely given that plastic bottles based water rockets do not approach very high velocities. Moreover, estimating the area of the plastic bottle is a challenge in itself given the irregular shapes in use. To simplify this entire procedure, the presence of aerodynamic drag was neglected to provide acceptable approximations through a fitting mathematical model. The mathematical model used to predict the output height of the water rocket is based on the work of Kagan and Buchholtz (1995) that focused on the simplified physics behind water rockets. The output height from a simple water rocket can be expressed as (Kagan & Buchholtz, 1995): Where:  is the maximum altitude the water rocket achieves  is the mass of water used in the water rocket  is the mass of the water rocket body when it is totally empty  is the pressure of the compressed gas inside the water rocket  is the density of air  is the acceleration due to gravity For the purpose of this project, the pressure of the compressed air inside the water rocket was taken as the gauge pressure on the portable air compression device. The density of air was taken to be constant at 1.2 kg/m3 while acceleration due to gravity was taken to be constant at 9.8 m/s2. Construction of Water Rocket The water rocket was constructed using a typical soft drink plastic bottle with a volume of 2 liters. Hobbyist water rockets are often constructed using these plastic bottles since they are easy to procure and handle. Moreover, operating on these plastic bottles is relatively simple using native instruments such as scissors and duct tape. The total volume of these plastic bottles presents enough water and compressed air to create a sustained water rocket flight without providing enough compressed air volumes to be dangerous. Students were guided to procuring soft drink plastic bottles of around 2 liters volume. The plastic bottle was used as is without any need for cutting or other operations. The capped end of the plastic bottle was fitted onto a launch tube that would allow better launching characteristics and simplified handling. The use of launch tubes precludes the use of valves or other such mechanisms for release control of compressed air and water. The launch tube is any piece of tube (metal or plastic) which fits the diameter of the water rocket exit nozzle. The compression device used was a bicycle pump that can produce pressures of up to 75 psi. The outlet of the bicycle pump was connected to the launch tube that was positioned at a slightly inclined angle away from the participants. A participant held the water rocket in place over the launch tube. Another participant pressurized the contents of the water rocket using the bicycle pump. The water rocket was released when required by the participant holding the plastic bottle. The water rocket was released away from the direction that participants were standing in to ensure safety. A cord attached to the base of the rocket provided measurements for the total height achieved. As the water rocket moved skywards, the total length of the cord attached to the base provided the total height achieved. Student Specifics This lesson plan covers students of the seventh grade who are capable of understanding basic instructions in the English language. Caucasian students dominate the overall composition of the class followed by African Americans, Hispanics and a few Asian children. All children understand English that serves as the primary medium of instruction. Lesson Plan The lesson plan serves to accommodate learning styles according to Fleming’s VAK model (Leite, Svinicki, & Shi, 2009). The VAK model tends to accommodate the learning styles of visual learners, auditory learners and tactile learners at the same time. Most students in class respond to any one of the learning styles listed above (Jackson, 2005) so using this model provides adequate learning coverage. Students will be introduced to the concept of water rockets including how they operate and how they are constructed. After water rockets are introduced to the students, they will be asked to speculate how a person could estimate how high his water rocket would fly. This would ensure that the students are all involved due to the interactive nature of the lecture. Once the ideas from students are written down on the blackboard, students will be introduced to the idea that height could be estimated using mathematical formulas. Students already possess the concepts of fractions and equations so it is expected that students can perform height estimation using fractions and equations. Students would then be asked to relate inputs and outputs related to a water rocket design. These inputs and outputs would be jotted onto the blackboard. Once the interactive session is over, the teacher will classify which inputs and outputs matter and which do not. Once this segregation is complete, the mathematical formula relating height as an output to the inputs will be shared with the students using the blackboard. These methods would provide active learning coverage for visual learners and auditory learners but would provide little coverage for tactile learners. A water rocket will be made in class to enhance the learning of tactile learners. Since making a water rocket is relatively simple and straightforward so it can be carried out in class in less than ten minutes. Volunteers will be asked for in the class to make a water rocket. The required materials are a plastic bottle, a launch tube and a bicycle pump. These materials will be assembled together in class in front of the students but the plastic bottle will not be filled with water. These materials will be used to explain the various quantities that are involved in the equation such as air pressure, mass of plastic bottle and mass fraction. Water will be filled in the plastic bottle to delineate the concept of mass fraction. Once the plastic bottle is filled with water, students will be asked to scribble the quantities in their own notebooks. Students will then be taken outdoors and a demonstration will be carried out. The mass fraction will be varied along with the air pressure as students take these new values and inject them into the equation to find out how high the water rocket flies. Students will be taken indoors once ten or so entries are available for the equation quantities and the total height achieved. Students will then be asked to tabulate the equation’s results against the total height achieved and to relate the sources of error as homework. Summary Students will be exposed to the mathematical relationship between the height achieved by a water rocket and the inputs. Learning coverage will be provided to visual, auditory and tactile learners using different learning techniques in class. Demonstration of water rocket launches will be carried out outdoors to allow students to connect the mathematical relationship to the actual height achieved. Self Evaluation The lesson plan provides adequate learning coverage to all kinds of learners. The implementation of the water rocket allows the students to experience such phenomenon first hand. This allows the development of independent thinking skills such as improvements in water rocket design or changes to the mathematical equation in use. The homework supplied with in class activities will trigger students to compare the efficacy of mathematics in their everyday lives. References Gommes, C. (2010). A more thorough analysis of water rockets: Moist adiabats, transient flows, and inertial forces in a soda bottle. American Journal of Physics 78(3) , 236-243. Jackson, C. J. (2005). An applied neuropsychological model of functional and dysfunctional learning: Applications for business, education, training and clinical psychology. Melbourne: Cymeon. Kagan, L. D., & Buchholtz, L. K. (1995). Soda-bottle water rockets. The Physics Teacher 33 , 150-157. Leite, W. L., Svinicki, M., & Shi, Y. (2009). Attempted Validation of the Scores of the VARK: Learning Styles Inventory With Multitrait–Multimethod Confirmatory Factor Analysis Models. New York: SAGE Publications. Read More