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1 College of Engineering Department of Mechanical and Aerospace Engineering MAE-250, Section 001 Introduction to Aerospace Engineering Final Project Bottle Rocket Written By: Jesse Hansen Connor Petersen Jeffrey Balog Date Report Submitted: 12/01/2016

2 Idea Development: Initial Ideas to Final Concept Through online research and course materials, several bottle rocket designs were proposed, analyzed, and discussed within our group. Our primary concern was obtaining stable flight by ensuring the center of pressure stayed below the center of mass (to prevent the rocket from spinning out of control) and through adding fins to the base of the rocket. We selected a basic 2 liter pop bottle as the pressure chamber and removed the label to reduce drag. A non-contoured bottle was used as it provided a flat surface to attach fins to and with the aid of a nose cone, could be very aerodynamic. To maximize the launch height we used a piece of packaging tape to wrap a compression dressing around the pop bottle s label area on the pressure vessel as this would help keep the bottle s walls from expanding as the air was pumped into it. We then grappled with how to maximize our hang time while delivering our payload (an egg) safely to the ground. Initially we tried to attach a small container containing the egg and built from a second two liter bottle directly to the top of the pressure chamber using tape. This method eliminated the possibility of using a parachute to lengthen the rocket s hang time and also removed any chance of receiving points for the complete detachment of the payload. We then looked for ways to include a parachute, primarily a sleeve attached to the top of the pressure vessel, that could contain the parachute with the egg capsule resting on top. This method relies on the weight of the egg to dislodge the payload container from the sleeve and deploy the parachute at the rocket s peak altitude. Figure 1 loosely demonstrates this concept:

3 Figure 1: Initial Rocket Design After construction of this rocket, it was discovered that the egg capsule routinely got jammed in the sleeve containing the parachute, preventing the separation of the payload and deployment of the parachute. To counteract this issue we decided to create the sleeve from a contoured 2 liter pop bottle. The contoured shape would allow the egg capsule to rest in the sleeve without becoming jammed further (see figure 2). Figure 2: Initial Rocket Design with Contoured Sleeve The contoured sleeve design reduced the number of instances of the egg capsule becoming stuck in the sleeve and helps ensure complete separation of the egg capsule and subsequent deployment of the parachute. Our next concern was with the egg capsule itself and designing a system that would allow the egg to remain intact throughout the entire launch, flight, and impact. Our initial instinct was to pad the inside of the capsule with bubble wrap, but the materials list did not include bubble wrap or anything similar. We then set out with a piece of posterboard (or cardboard) and created a cardboard tube (similar to the inner cardboard tube on paper towels or toilet paper) with a diameter that would allow an egg to pass through the tube. This tube kept the egg from sliding horizontally but not vertically (if the tube were positioned vertically - as seen in figure 3). To ensure the egg remained stationary vertically and horizontally, four holes were created on the side of the tube and rubber bands passed through the tube. The egg was then placed in the tube, resting on the rubber bands, and the process repeated a second time to secure the egg from

4 above. The tube was then cut to a height that would sit securely in the egg capsule. Figure 3 shows the egg capsule: Figure 3: Breakdown of Egg Capsule With an egg capsule in mind, we began looking into parachute design. To maximize our hang time and slow the descent of the egg capsule as much as possible we wanted a parachute with the largest surface area possible. We tested two parachute shapes and decided to use a circular shaped parachute attached using braided nylon cord. Each point where the string attached to the parachute was reinforced with tape to avoid tearing through the parachute during deployment. Figure 4: Parachute Design Lastly, we required some method for stabilizing the rocket during launch. We briefly considered attaching a small, hollow, cardboard cylinder to the side of the rocket, through which a metal rod could be passed through and secured into the ground. This

5 would provide a guide for the rocket to launch straight upwards. However, we instead opted to use fins as they re more reliable and do not require a metal rod (metal was forbidden in the project statement). Research was required to determine the best shape and placement for fins on a rocket and it was discovered that the best placement for the fins is as far back on the bottle rocket as possible. We placed the fins approximately 9 cm from the base and used three fins (instead of four) as three provides a lot of stabilization while minimizing the drag. In addition, we wanted to avoid adding any unnecessary weight to the rocket and especially to the bottom of the rocket as it is imperative the center of mass of the rocket be above the center of pressure. The fins were chosen to be small relative to the bottle rocket size, so there would be a decrease in drag and an increase in performance. Cardboard was chosen as the material for the fins because of its low weight and high sturdiness. Finally to finish off the design of our fins, we chose to tape the front and sides of all three fins. This will create a more streamlined airfoil body for our fins similar to the airfoil shape for a realistic rocket s fin. The streamlined body for a fin s airfoil allows the rocket to experience less drag as it tries to escape from Earth s atmosphere while providing some protection from potential poor weather. We then moved on from the designing portion of the fins to the attachment phase. All three fins were separated 120 o from each other and directed in a swept back position. They were then attached to the body of the bottle rocket by splitting the ends along the right side on the cardboard crafted fin. The split ends allowed there to be more surface area for the fin to be attached to the bottle rocket. Initially we attached the fins with super glue but later realized that during the pressurizing phase of pre-launch, the expanding walls of the pressure vessel posed the possibility of popping the glue seal and causing the wings to be ripped off during ascension. We then decided to use tape to attach the rocket s fins. Figure 5 shows an outline of the rocket with fins attached.

6 Figure 5: Rocket Set Up with Fins Experimental Procedure to Tune Concept: In order to tune our initial ideas into the final concept for the bottle rocket design, we had to test multiple designs for both the parachute and containment center for the egg in the capsule. We tested two parachute shapes: rectangle and a circle, by tossing the parachute and capsule off the third floor balcony inside Engineering Building 3. When we tested the rectangular parachute, the egg had a fast descent and wobbled vigorously back and forth, exhibiting a very unstable descent that could result in a damaged egg. We discovered that a circular parachute worked best for safely delivering the capsule to the ground as it had a steadier flight path and a longer hang time in the air. Once we figured out the best shape for the parachute, we also had to test the best method on the containment center for the egg. We tested the several different capsules with the egg inside by dropping the egg capsule and parachute off the third floor balcony inside Engineering Building 3. We experimentally determined the best egg capsule to be one that used a paper towel roll and rubber bands cut to secure the egg. Unfortunately we did not have a means for testing the rocket as a whole prior to the actual launch. To compensate we mathematically determined a few key things as shown below.

7 Mathematical Performance Estimates Bottle Rocket Performance Estimates To optimize our rocket s performance we performed a mathematical analysis of the system to determine several characteristics of our rocket s flight path and flight time. The constants used in these calculations can be found in Table 1. Table 1: Powered Ascent Constants Used in Calculations Variable Metric Units Relevant English Units Gage Pressure at Launch Time, P 0 Water Density, ρ Initial Air Volume in Pop Bottle, V 0 Atmospheric Pressure, P atm Diameter of Pop Bottle Hole, D h Diameter of the Pressure Cylinder, D r Mass of the Rocket, M r V r dv dm 4.137e5 Pa 1000 kg/m^3 1.13e-3 m^ e5 Pa 2.2 e-2 m.1088 m 1 kg 2 e-3 m^3 3e-5m^3 3e-2 kg 60psi

8 To start off, the velocity of the water leaving the bottle rocket, u, was calculated using Equation 1. The initial air volume in the pressure cylinder was 1.13e-3 m 3, which is 65% of the 2 Liter bottle (45% filled with water). A change in volume of.03 Liters (3e-5 m 3 ) was selected and the value V for each iteration was found by adding the change in air volume to the previous air volume. Equation 1 models this relationship where all variables can be found in Table 1. Equation 1 The total change in volume of the air in the pressure cylinder was then calculated using the values obtained from Equation 1 plugged into Equation 2. ΔV 1 2 ΔT = 4 υπdr ΔV ΔT = 1 uπd 2 4 h Equation 2 The change in velocity for each iteration was then calculated using Equation 3 where a C D value of 0.3 was used and the area of the pressure chamber found using the known diameter and height of the bottle. The change in mass was determined by multiplying the density of water by the consistent change in volume. was replaced with the particular iteration s value of u calculated in the first step and M is the mass of the rocket. The calculated change in velocity was added to the last iteration of velocity to update the velocity of the bottle rocket. V f ( mg C AρV )Δt + Δm(V +V ) 2 d Δ V = M 1 2 f Equation 3 Finally, the total time taken for the powered ascent was calculated by adding the change in time to the previous time iteration and the total time for this stage was calculated to be seconds.

The additional height gained after the powered ascent stage can then be calculated using the following equation: V 2 f = V 2 i + 2 * a * Δ y Equation 4 Where V f is the final velocity of the coasting

9 The additional height gained after the powered ascent stage can then be calculated using the following equation: V 2 f = V 2 i + 2 * a * Δ y Equation 4 Where V f is the final velocity of the coasting stage (zero) and V i is the initial velocity of the coasting stage (also the final velocity of the powered stage which was calculated to be m/s). The additional vertical distance travelled after the powered ascent is then calculated to be 5.26 meters and the total time of this period calculated using the following equation: V f = V i + a * t Equation 5 The time for this period was calculated to be 1.03 seconds. These calculations were carried out in an excel spreadsheet which is shown below in Figure 6. All the units are SI units. Figure 6: Figure depicting excel spreadsheet used to carry out the iterative calculations. SI Units.

10 Discussion of Estimates Right after the bottle rocket launches, the velocity of the water coming out of the bottle is highest and decreases as time goes on and less water is left in the bottle. For this reason, the change in volume over the change in time decreases as time goes on. Effectively, the flow rate of the water out of the bottle decreases as time passes. The change in velocity just as the rocket launches is largest, and therefore the acceleration is greatest just when the rocket launches and decreases as time goes on and as the rocket runs out of fuel. The maximum velocity that the rocket is projected to achieve is about 10.3 m/s. After the powered ascent stage, there is a period where the bottle will continue to gain height in the coasting ascent stage. It was calculated that the rocket will travel an additional 5.26 meters in this stage, for a calculated 1.03 seconds. Dimensioned Drawings:

11 Figure 7: Final, dimensioned drawing of bottle rocket showing breakdown of each part from an exterior view.

12 Figure 8: Dimensioned Drawing of Parachute and Egg Capsule Interior Sources:

Objective: To launch a soda bottle rocket, achieve maximum time of flight, and safely land a payload (tennis ball).

Bottle Rocket Project 2016-17 Objective: To launch a soda bottle rocket, achieve maximum time of flight, and safely land a payload (tennis ball). Materials: 2 liter plastic soda bottle (carbonated beverage