Engineering Fundamentals Project #3 - Model Rockets

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Abstract Our third and final project, the rocket project, focused on the application of mathematical sciences in order to correctly build, fire, and measure the effects of numerous negative factors that attempted to detriment the rocket’s performance. Essentially, we constructed the rocket, fired it, obtained results such as time, and underwent the necessary calculations in order to understand the overall performance the rocket and its engine can put out. 1.0 Introduction The third and final project our section underwent involved the constructing of model rockets and its various components, such as, the engine, tail fins, and parachute, in order to correctly launch and land the rocket. Mathematical sciences played an integral role in determining theoretical calculations, such as, thrust and impulse. We utilized four important methods of determining the total possible reachable elevation. Firstly, we used Method 1, which is the “Analytical solution using Newton’s Second Law,” which in a sense, allows us to utilize the basic formula, (F) = (m)*(a) to determine the total impulse. [1] Additionally, we used Method 4, the use of simulation by an executable program called “Rocksim” to simulate the flight of multiple rocket models and engines to see their performances and results for method 4. [1] Essentially, by using these simple methods we were able to correctly estimate the theoretical elevation the rocket would reach. The components that were utilized in this physical rocket simulation include devices like an engine mount, ejection charge, nose cone, and parachute. [2] When we went to go and launch the device we were met with miserably cold conditions that actually caused us to skip over the important business of measuring the angle of the rockets for Method 3, Trigonometry. [1] Consequently, some of our calculations were put off and we were not able to fully experience the entire project, however, the rocket launches went on without a hitch nonetheless. Our rocket, number 13, launched after a slight issue with the way the cords from the control panel were setup, but we were able to reach high up in the air with the parachute successfully ejecting. For the most part, the rocket landed safely inside on of Old Dominion University’s tennis courts with the only damage being one of the slightly misplaced wings coming off. We had to take necessary measures of jumping over the fence in order to retrieve the device but we were proud to see the device work to its full potential. Our group hypothesized that the reason the device took a large deviation toward a faraway area was because of the malignant tail fin. The tail fin was to provide the stability needed in order for the rocket to work properly but, as always, nothing is perfect. [2] During the next lab, we used our measurements to calculate all of the necessary components of determining rocket simulation flight and how many forces, such as, thrust duration, gravitational force, and the overall quality of the rocket build effected the overall rocket launch. [1] Conclusively, the mathematics that were utilized in this project and the overall physical experience of launching a model rocket only to see that the rocket worked very well lead us to believe that our group of engineers has a bright future ahead of them and that we will be able to overcome an necessary challenge the industry will throw at us.

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Shown below are pictures from the model rocket project. The basics of rocket construction and makeup is shown in Figure 1.

Figure 1. Construction of the model rocket. [2] Construction of the rocket using various components is shown in Figure 2.

Figure 2. Group construction of the model rocket. The completed model rocket, before painting and decals, being weighed.

Figure 3. A completed model rocket being weighed.

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The application of decals to the model rocket can be seen in Figure 4.

Figure 4. Decals being applied to a model rocket. The finished product constructed, painted, and decaled can be seen in Figure 5.

Figure 5. Finished model rocket constructed, painted, and decaled. The insertion of the engine, followed by preliminary duct tape, can be seen in Figure 6.

Figure 6. Inserted engine, along with the duct tape.

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The finished rocket about to be launched, alongside the teammates, can be shown in Figure 7.

Figure 7. Teammates about to launch the rocket. The rocket close to being launched connected to the control panel can be show in Figure 8.

Figure 8. The rocket a moment away from being launched.

Now we are going to look into some variables on how model rockets operate!

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2.0 Discussion Definition of Variables a is Acceleration d is a constant (0.5  0.8) F is Thrust (N or lbs) (f) & (mΔv (N-Sec or lb-Sec)) is Impulse g is Gravitational Acceleration (ft/sec2) m is Force [1] m is Mass [2] S is actual altitude Sb is Ascend Distance Sc is the Ascend Distance while Coasting St is the Sum of the Ascend Distance and Coasting Distance T is Time (Δt) & (t) is Burn Time v is Velocity v1 is vmax V0 is Initial Velocity Vav is Average Velocity Vmax is Maximum Velocity W is Weight Newton’s Second Law F = (m)*(a) [1] Impulse Calculation (m*Δv) = (F)*(Δt) [2] Thrust Calculation (F) = (Total Impulse (mΔv))/(Δt) [3] Net Force on the Model (T-W) = ((W/g)*(v1/t)) [4]

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Maximum Velocity Calculation V1 = ((T/W)-1)(g*t) [5] Average Velocity Vav = ((V0+Vmax)/2) [6] Ascend Distance during Thrusting Sb = (v)*(t) = (vav)*(t) [7] Ascend Distance during Coasting Sc = ((Vmax)2/(2g)) [8] Sum of Ascend Distances St = (Sb)+(Sc) [9] Actual Altitude S = (St)*(d) [10]

Now let us take a look at how we implement these formulas in some manual calculations!

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Manual Calculations

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3.0 Programming Results Project 003 – A8-3 Engine Analysis Table 1. Model Rocket Analysis: A-Engine Table. Project 003 - Model Rocket Analysis Project ENGN110 - MON 2:00 PM 4/6/2015 Joseph B., Jordan V., Chris M., Nicolas D.

N:lbs. g:lbs. 0.2248 454.4

Engine Specifications Engine Name A8-3 Total Impulse (N-s) 2.5 Thrust Duration (s) 0.5 Delay Time (s) 3 Engine Weight (g) 16.2 Propellant Weight (g) 3.12

Engine Specifications (Alternate Units) Engine Name A8-3 Total Impulse (lb-s) 0.5620

Model Specifications Model Name Rattler-7 Model Weight (g) 42.07

Model Specifications (Alternate Units) Model Name Rattler-7 Model Weight (lbs.) 0.0926

Flight Analysis Liftoff Weight (lbs.) Burnout Weight (lbs.) Thrust (lbs.) Vmax (ft/s) Vaverage (ft/s) Burnout Altitude (ft.) Coasting Distance (ft.) Total Altitude (ft.) Expected Altitude1 (ft.) Expected Altitude2 (ft.) Expected Altitude3 (ft.)

Engine Weight (lbs.) Propellant Weight (lbs.)

g 32.32

0.0357 0.0069

Flight Analysis (Alternate Units) 0.1282 0.1248 1.124 129.38 64.69 32.35 258.97 291.31 174.79 87.39 233.05

Vmax (mi/h)

88.21

Expected Altitude1 (m) Expected Altitude2 (m) Expected Altitude3 (m)

52.52 26.26 70.03

d1 = 0.6 d2 = 0.3 d3 = 0.8

ft.:mi 5280

Constants s:h d1 3600 0.6

d2

d3 0.3

0.8

m:ft. 3.328

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Project 003 – D12-5 Engine Analysis Table 2. Model Rocket Analysis: D12-5 Table. Project 003 - Model Rocket Analysis Project ENGN110 - MON 2:00 PM 4/6/2015 Joseph B., Jordan V., Chris M., Nicolas D.

N:lbs. g:lbs. 0.2248 454.4

Engine Specifications Engine Name D12-5 Total Impulse (N-s) 20 Thrust Duration (s) 1.6 Delay Time (s) 5 Engine Weight (g) 40.9 Propellant Weight (g) 24.93

Engine Specifications (Alternate Units) Engine Name D12-5 Total Impulse (lb.-s) 4.4960

Model Specifications Model Name Quest Big Dog Model Weight (g) 201.98

Model Specifications (Alternate Units) Model Name Quest Big Dog Model Weight (lbs.) 0.4445

Flight Analysis Liftoff Weight (lbs.) Burnout Weight (lbs.) Thrust (lbs.) Vmax (ft./s) Vaverage (ft./s) Burnout Altitude (ft.) Coasting Distance (ft.) Total Altitude (ft.) Expected Altitude1 (ft.) Expected Altitude2 (ft.) Expected Altitude3 (ft.)

Engine Weight (lbs.) Propellant Weight (lbs.)

g 32.32

0.0900 0.0549

Flight Analysis (Alternate Units) 0.5345 0.5071 2.81 234.85 117.43 187.88 853.29 1041.17 624.70 312.35 832.94

Vmax (mi/h)

160.13

Expected Altitude1 (m) Expected Altitude2 (m) Expected Altitude3 (m)

187.71 93.86 250.28

d1 = 0.6 d2 = 0.3 d3 = 0.8

ft.:mi 5280

Constants s:h d1 3600 0.6

d2

d3 0.3

0.8

m:ft. 3.328

m 242.88

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Project 003 – E16-6 Engine Analysis Table 3. Model Rocket Analysis: E16-6 Table. Project 003 - Model Rocket Analysis Project ENGN110 - MON 2:00 PM 4/6/2015 Joseph B., Jordan V., Chris M., Nicolas D.

g:lbs. N:lbs. 454.4 0.2248

Engine Specifications E16-6 Engine Name 33.4 Total Impulse (N-s) 2.1 Thrust Duration (s) 6 Delay Time (s) 81 Engine Weight (g) 40 Propellant Weight (g)

Engine Specifications (Alternate Units) E16-6 Engine Name 7.5083 Total Impulse (lb-s)

Model Specifications Quest Big Dog Model Name 158.93 Model Weight (g)

Model Specifications (Alternate Units) Quest Big Dog Model Name 0.3498 Model Weight (lbs.)

Flight Analysis Liftoff Weight (lbs.) Burnout Weight (lbs.) Thrust (lbs.) Vmax (ft/s) Vaverage (ft/s) Burnout Altitude (ft.) Coasting Distance (ft.) Total Altitude (ft.) Expected Altitude1 (ft.) Expected Altitude2 (ft.) Expected Altitude3 (ft.)

Engine Weight (lbs.) Propellant Weight (lbs.)

g 32.32

0.1783 0.0880

Flight Analysis (Alternate Units) 0.5280 0.4840 3.5754 433.51 216.75 455.18 2907.34 3362.52 2017.51 1008.76 2690.02

Vmax (mi/h)

295.57

Expected Altitude1 (m) Expected Altitude2 (m) Expected Altitude3 (m)

606.22 303.11 808.30

d1 = 0.6 d2 = 0.3 d3 = 0.8

ft.:mi 5280

Constants d1 s:h 0.6 3600

d3

d2 0.3

0.8

m:ft. 3.328

m 242.88

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Analysis of “d” Values The d-values determine the strength of the air resistance acting on the rocket. This value is directly proportional to the expected altitude because the d-value is estimated as a percentage of the expected altitude. This means that the d-value must be inversely proportional to the magnitude of the air resistance, because if a higher percentage leads to a higher expected altitude, then there is less air resistance acting on the model rocket. Paint, Decals Effect on Altitude The use of paint and decals on the model rockets added mass to the entire model rocket system. If an object has a greater mass, it is pulled in more by the force of gravity. Since the force of gravity opposes the force of thrust, the result concludes to a lower expected altitude, due to this greater mass being pulled in by gravity.

Now we are going to conclude and speak about what our group learned from the project.

4.0 Conclusion and Recommendations Conclusion: The model rocket project has taught us many things about the engineering process. We learned that there are four methods to determine apogee: “trigonometry by using a handheld angle measuring tool, use of an onboard altimeter device, simplified analytical calculations based on Newton’s second law, and rocket flight simulation.” [1] Analyzing all four of these areas help us to come up with the most accurate data for our project. We also learned that “engineering data is precious and it must be carefully recorded and saved for future use.” [1] However, a problem arises between the four methods of collecting data. All four methods have their own advantages and disadvantages. We learned that we “need to try various methods to find alternate solutions and that different methods result in different answers. Each method is subject to error due to assumptions and uncontrollable external factors.” [1] Such as analytical and trigonometry is all mathematical and works in theory. This contrasts with using an altimeter, which is a much more precise, real-world way of collecting data. And even to another extent, with simulations, you are relying on a computer model to accurately predict real world phenomena, which may not be reliable. With that said, even the most accurate data collector in theory, the altimeter, may not be as practical as we would like. An altimeter is expensive and the risk of either losing or breaking one must be taken into account. Each altimeter costs around $60 and weighs about 10 grams. [1] In fact, during our own experiment, “almost a third of the team project model rockets were lost due to wind and limited campus launch space availability.” [1] Engineering is not only about improving on a particular project, but also emphasizes cost efficiency. Another important concept we learned was teamwork by working together to build the rocket, paint the rocket, collect data, interpret data, and ultimately put it all together for an easy to read report. We have

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gained spreadsheet skills in Microsoft Office, “while performing data entry and necessary mathematical calculations.” [1] Overall, this project was a great learning experience of how to collect and analyze data as future engineers. Recommendations: For our launch, a parking lot on Old Dominion University’s campus was used. However, on the day of the launches the weather was less than ideal as it was cold and windy. If possible, for future launch dates, a mild day with almost no wind would be the most ideal situation for collecting the most relevant data. Also, the method for collecting data would be at its most accurate if we used altimeter’s on every rocket. If there was a way to ensure the rockets with altimeters would be recovered and the cost of acquiring altimeters was low it would provide use with the most accurate data. [1] A way to ensure the accuracy of an altimeter is to test an altimeter on the top floor of a tall building or by “simply adding additional weight as payload to cause more powerful engines to provide a lower apogee.” [1] For our purposes, a $60 altimeter would work best. [1] However, we made the most of what resources we had at the time.

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Appendix Table of Contents: •

A1

Model Rocket Safety Code

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A2

Forces Acting on a Rocket

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A3

“How High Will the Rocket Go?”

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A4

Engine Specification Charts

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A5

E16-6 Specifications

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A6

Quest Big Dog- Simulation Results

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A7

Altitude Prediction Program

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A8

Ascend Time Calculation

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A9

How to Reference

References: 1.

Sarper, Huseyin, Vahala, Linda, “Use of Single Stage Model Rockets to Teach Some Engineering Principles and Practices to First Year Engineering and Engineering Technology”, Paper AC 2012-1922, ASEE Proceedings, 2015.

2.

http://www.grc.nasa.gov/WWW/k-12/rocket/rktparts.html