- Email: [email protected]
Project-based introduction to aerospace engineering course: A model rocket
ARTICLE IN PRESS Acta Astronautica 66 (2010) 1525–1533
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Project-based introduction to aerospace engineering course: A model rocket Sanjay Jayaram a,, Lawrence Boyer a, John George a, K. Ravindra a, Kyle Mitchell b a b
Department of Aerospace and Mechanical Engineering, Saint Louis University, Saint Louis, MO 63103, USA Department of Electrical and Computer Engineering, Saint Louis University, Saint Louis, MO 63103, USA
a r t i c l e in fo
abstract
Article history: Received 20 October 2009 Accepted 30 October 2009 Available online 16 December 2009
In this paper, a model rocket project suitable for sophomore aerospace engineering students is described. This project encompasses elements of drag estimation, thrust determination and analysis using digital data acquisition, statistical analysis of data, computer aided drafting, programming, team work and written communication skills. The student built rockets are launched in the university baseball field with the objective of carrying a specific amount of payload so that the rocket achieves a specific altitude before the parachute is deployed. During the course of the project, the students are introduced to real-world engineering practice through written report submission of their designs. Over the years, the project has proven to enhance the learning objectives, yet cost effective and has provided good outcome measures. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Space education Model rocket
1. Introduction Most undergraduate aerospace engineering curriculums contain an introductory course that introduces sophomore students to the world of aerospace. Generally this course tends to be a broad introduction to terminology, basic aerodynamics, performance, propulsion, structures and a brief introduction to rockets and basic orbital mechanics. In some programs, a hands-on project is assigned to the students to make the course more interesting and provide an opportunity for the students to use the fundamental knowledge they have gained in mathematics and physics in their freshman year. Many of these courses involve providing a hands-on experience, wherein the students build, test and fly concepts developed in the class [1,2]. Several aerospace engineering curriculums have introduced a project based approach to
Corresponding author.
E-mail addresses: [email protected] (S. Jayaram), [email protected] (L. Boyer), [email protected] (J. George), [email protected] (K. Ravindra), [email protected] (K. Mitchell). 0094-5765/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2009.10.038
teach the introductory aerospace engineering course [3–5]. Rojas, et al. [6] the introduced a problem-basedlearning (PBL) concept for undergraduate students in aerospace engineering. Over a number of years, Virginia Tech has introduced several courses in their aerospace engineering program at the beginner’s level to introduce aerospace engineering concepts, by including design concepts for freshmen students [1]. Interdisciplinary design team concepts have also been explored in the past several years [7,8]. Hands-on education of rocket technology using water rockets is discussed in [14]. The project consists of structural study, propulsion system study, aerodynamic study, stability and flight trajectory study. At Saint Louis University’s Parks College of Engineering and Aviation, the aerospace engineering department offers an introductory course entitled ‘‘Introduction to Aeronautics and Astronautics’’ at the sophomore level. In this course, the students are required to form design teams to assemble and test a model rocket to a specified set of constraints. The constraints include that of the payload mass being determined such that the rocket altitude will reach 100 ft. This allows the test firing of the rocket in a relatively small area such as a baseball field.
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S. Jayaram et al. / Acta Astronautica 66 (2010) 1525–1533
Nomenclature CD CDBT CDB CDF Cf d dB g0 Isp ‘ me mprop mpl
initial mass of rocket final mass of the rocket number of fins maximum frontal area of the body wetted area of fins wetted area of the body distance covered during burn total distance covered during coasting distance covered during one iteration of coasting portion total distance covered during all iteration of coasting portion thickness ratio of fins velocity air density at sea level
mi mf n SBT SF SW sb sc Ds
drag coefficient drag coefficient for body and tube base drag coefficient drag coefficient of fins skin friction coefficient body tube diameter base diameter of rocket acceleration due to gravity at sea level specific impulse length of the rocket body empty mass of rocket propellant mass payload mass
SDs t/c V
r
This kind of design oriented project motivates students to the concepts of aerospace engineering and engineering sciences in general. ‘‘Introduction to Aeronautics and Astronautics’’ course is taught in the fall semester (16 weeks) and consists of three 50-min lectures per week. The class size has remained steady over the past decade with an average student enrollment of 30. At Parks College, introduction to modern tools of data acquisition and analysis such as MATLAB and LabVIEW provides an opportunity for more sophisticated methods to be employed that was not possible in earlier years. The uniqueness in the hands-on project adopted in this course is twofold: (1) technical aspects and (2) educational aspects. In general technical aspects, the students are required to learn and implement modern, industry standard tools, such as, experimental data acquisition, industry standard software. Besides introducing newer concepts, the project requirements reinforce several topics that the students have learned in previous classes (for example PRO/E modeling, determination of center of gravity experimentally and moment of inertia).
Some of the specific technical aspects the students are required to learn and perform are shown below:
Assembly of the Model Rocket Kit, and development of a Pro-Engineer (PRO/E) model of the rocket.
Determination of the specific impulse of the rocket
engine through experimental data acquisition using LabVIEW. Aerodynamic drag coefficient estimation, both analytically and by MATLAB simulation. Determination of the size of the payload, both analytically and by MATLAB simulation. Calculation of center of mass and moment of inertia. Mission simulation using MATLAB. Flight test and experimental data acquisition from onboard accelerometer. Analysis through experimental data and numerical simulation.
The educational aspects introduces the students to perform projects in a team setting thus enforcing team work and communication aspects as well as ethics. The
Table 1 Model rocket individual parts dimensions and mass.
1 2 3 4 5 6 7
8
9
Item
Mass (g)
Mass (slug)
Length (in)
Thickness (in)
Diameter (in)
Lg tube Engine Sm blue tube Nose cone Part 1 Nose cone Part 2 Parachute Sm green tube
4.54 18.22 1.11 3.5 3.25 4.04 3.36
0.000311 0.001248 0.0007606 0.000240 0.000223 0.000277 0.000230
7.775 2.75 2.76 0.785 2.75 3.1 1.12
0.0175 0 0.0175 0 0 0 0.1
0.96 0.69 0.72 0.94 0.97 0.94 0.94
Item
Mass (g)
Mass (slug)
Top (in)
Bottom (in)
Balsa x3
2.26
0.000155 Leading edge (in) 3.057
1.235 Thickness (in) 0.39
2.195 Side (in) 2.28
Item
Mass (g)
Mass (slug)
Length (in)
Thickness (in)
Width (in)
Metal hook
1.33
9.11E 05
3.23
0.023
0.123
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students also learn systems engineering process, where design process, test and evaluation and design documentation aspects are covered. This process exposes students to computer aided design, analytical methods numerical simulation, experimental data acquisition and data analysis and relevant academic experience in one single project.
2. Project statement: rules and objectives
desired altitude and perform a controlled descent by parachute deployment. The project is judged on the following criteria: (1) maximum altitude of 100 ft—no more, no less, (2) parachute deployment and controlled descent, (3) experimental data acquisition and data analysis and (4) a detailed written report with software numerical simulation.
3. Hands-on model rocket project
The objective of the project is to assemble a model rocket that is to be launched from ground, achieve a
The following section details the assembly and analysis component of the course, namely the hands-on model rocket project. This project exposes sophomore students to the excitement of the aerospace engineering field and the expectations for future courses. The friendly competition gives the students an opportunity to show their creativity and ingenuity in developing a model rocket. The goal is to achieve an active learning environment for acquiring a conceptual framework as well as problemsolving skills. The connection between theory and practice is vividly demonstrated in the model rocket project. This experience is greatly appreciated by sophomore engineering students deciding whether or not to major in aerospace engineering. Design is an integral part of the practice of engineering and it should be an integral part of students’ education during their entire undergraduate career [10,11].
Fig. 1. (a) Diagram of a typical model and (b) PRO/E model of the rocket.
Static calibration of cantilever balance 0.014 Voltage = 0.0106(Weight) + 0.0001 Voltage (volts)
0.012 0.01 0.008 0.006 0.004 0.002 0 0
0.2
0.4
0.6 0.8 Load (lbs)
1
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1.2
Fig. 2. Static calibration of cantilever ‘‘load cell’’.
1.4
Fig. 3. Rocket motor on test rig.
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3.1. Organization The students in the class are divided into working teams of two to three students to each group. In the middle of the semester, typically after 7 weeks of lecture, one model rocket kit (ESTES ALPHA model) with all relevant accessories is given to each group. Randomizing the teams facilitate the development of teamwork skills, which many of the students lack prior to this course. This process also helps students in establishing teamwork and communication skills. The groups are required to assemble the model rocket, perform experimental tests on the rocket motor, basically following the rules and objectives described in the previous section. 3.2. Model rocket kits Each team is provided with the model rocket kit (ESTES ALPHA model) parts described in Table 1. The total assembled length of the model rocket is approximately 12 in weighing approximately 45 g. The approximate cost of each model rocket kit is $15.00. Each kit includes a rocket motor (Estes B6-4) weighing approximately 18 g. All students will have already completed a one credit machine shop course with lectures on safety and additional machine shop techniques and a two credit
computer aided design course using PRO/E prior to enrolling in this course. ‘‘One credit’’ is equivalent to one contact hour in a week, so a three credit hour course will have a total of 48 contact hours in a semester (with 16 weeks per semester). In comparison to ‘‘Bologna Accord’’, the European University credits are prorated by one-half when compared to a typical American University. Figs. 1a and b show the diagram of the typical model rocket and PRO/E computer aided design sketch. 4. Project tasks First, the teams determine the specific impulse of the rocket motor. This involves acquiring thrust data from the engine using LabVIEW. Second, the teams determine the drag coefficient of the model rocket. Third, the teams estimate the payload. Fourth, the teams calculate center of mass and moment of inertia both analytically and using graphical software. Fifth, the teams conduct a MATLAB simulation. Sixth, the teams perform a flight test by launching the rocket. These individual tasks are described in detail below. 4.1. Determination of specific impulse of rocket motor To determine the specific impulse of the rocket motor, a simple static test rig is used consisting of a cantilever beam (Fig. 3). A strain gage is attached near the fixed end. To calibrate the device, three to four readings of the strain gage are recorded corresponding to static weights hung from the tip of the cantilever beam. It should be noted here that most sophomores may not have had exposure to strain gage techniques but have had enough knowledge from introductory physics course (Wheatstone bridge circuit) to comprehend the experiment. A sample calibration curve is shown in Fig. 2. A regression analysis is performed to obtain the relationship between load and voltage. Students are required to show error bars as well. The rocket assembly is then attached to the cantilever beam load cell. The rocket motor is fired and the output of the strain gage is fed to a data acquisition board to collect
Fig. 4. Wiring diagram in LabVIEW for thrust time history.
Model Rocket Static Thrust Data
Thrust un IbS
3 2.5 2 1.5 1 0.5 0 0
0.2
0.4
0.6
0.8
1
Time in Seconds Fig. 5. Thrust vs. time for rocket motor Estes B6-4.
Fig. 6. Mission profile for the model rocket.
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the time history of thrust from the rocket motor using LabVIEW. A photograph of the rocket attached to the cantilever test rig is shown in Fig. 3. The LabVIEW wiring diagram for acquiring the time history of thrust is shown in Fig. 4. Using numerical data obtained using LabVIEW (Fig. 5), students use either Simpson’s rule or trapezoidal rule to
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calculate the total impulse by estimating the area under the thrust vs. time curve. The average mass flow rate is obtained knowing the mass of the propellant (equal to the mass of the rocket motor before burn minus the mass of the casing after burn) and the duration of the burn. An interesting observation not relevant to the present study is the calculation of the first few resonant frequencies of
Height Vs. Time 110 100 90 80
Height (ft)
70 60 50 40 30 20 10 0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
-10 Time in Seconds Velocity Vs. Time 80 70 60 50 40 30 Velocity (ft/s)
20 10 0 -10 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-20 -30 -40 -50 -60 -70 -80 -90 Time in Seconds Fig. 7. (a) Altitude vs. time and (b) velocity vs. time.
5
5.5
6
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the cantilever beam by a power spectral analysis of the thrust data shown. Based on the numerical calculations, the specific impulse was found out to be 73.71 seconds.
estimated:
4.2. Drag coefficient estimation
Here mi = me + mprop + mpl and mf = me + mpl. Then, writing the equation of motion for the rocket for the coasting portion of the flight (free flight) including the effects of drag is shown below:
By methods outlined in summary equations provided by Gregorek [9] and Shevell [14], the students estimate the drag coefficient for the rocket model. The summary equations outlined by Gregorek are repeated here for reference. The friction coefficient varies with Reynolds number and hence varies with velocity of the rocket. An average estimation of Cf must be determined by the student. CD ¼ 1:05ðCDBT þ CDB þ CDF Þ
ð1Þ
h iS W CDBT ¼ 1:02Cf 1 þ1:5=ð‘=dÞ3=2 SBT
ð2Þ
3 0:029 dB CDB ¼ pffiffiffiffiffiffiffiffiffiffi CDBT d
ð3Þ
t SF n CDF ¼ 2Cf 1 þ 2 c SBT
ð4Þ
vb ¼ g0 Isp ln
mf
mi mf
ð5Þ
dv 1 ¼ mf g0 þ rV 2 SBT CD dt 2
ð6Þ
from which dv 1 rV 2 SBT CD ¼ g0 þ dt 2mf
ð7Þ
From Eq. (7), it can be written 1 Dv ¼ Dt g0 þ rV 2 SBT CD 2mf
ð8Þ
Eq. (8) is used successively after burnout to determine the decrease in velocity Dv in each time interval Dt and thus the incremental distance covered, Ds =V1 Dt (where V1 = Vb Dv for the first step and Vn = Vn 1 Dv for subsequent steps) until the final velocity is zero. If the total distance covered by the rocket (equal to SDs +sb) is Table 2 CG for individual components.
4.3. Determination of payload—method 1 Fig. 6 below shows a typical mission profile for the flight of the model rocket. The height gained by the rocket during burnout, sb is calculated by Newton’s laws of motion. Knowing the average thrust during the burn, and the average mass of the rocket between points 1 and 2, calculating the average acceleration between 1 and 2 and the distance sb as well as the rocket velocity at the end of the burn, vb is completed. Using the rocket equation (see for example, Anderson [12]) given in Eq. (5) the payload mass is
Part
Mass (M) (g)
CG location (in)
M CG
Base Lower body tube Upper body tube Engine mount tube Engine Nose cone Parachute Adapter ring Red coupler Payload
12.7 6.9 6 1.2 18 7.5 3.2 3.8 1.2 100
1.3 5.8 15.55 1.37 1.37 16.5 16.5 2.2 11.7 4.2
16.51 40.02 93.3 1.65 24.73 123.75 52.8 8.36 14.04 420
Payload Vs. Altitude 0.011 0.01 0.009
Payload (slug)
0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0
25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 Altitude in Feet Fig. 8. Sample payload determination chart.
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equal to 100 ft, the payload estimated from Eq. (5) is the appropriate payload. If not, a revised payload is used and the steps repeated until the payload yields the desired height of 100 ft. From these calculations, students observe that the drag force may not be significant in the present study. Nonetheless, this exercise provides them with an appreciation for all the interdependent parameters.
4.4. Determination of payload—method 2— numerical simulation Students use MATLAB to run a time domain simulation of the rocket (see Fig. 7a and b). Gravity, weight reduction
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due to fuel usage, thrust profiles and drag forces were all incorporated into the simulation. This method is preferred to hand calculations due to the time-savings over a closed-form solution due to the increased accuracy due to compensation for time-dependent variables such as drag, thrust and weight. In addition, this exercise provides a useful application of programming in MATLAB that students have been exposed to during their second semester of study. The amount of payload to be carried is decided by running several iterations of the m-file flight simulation program. The maximum altitude achieved with each payload is recorded and arranged into a chart showing payload vs. maximum altitude (see Fig. 8). From this chart, the proper payload to reach a maximum altitude of 100 ft is decided upon.
4.5. Calculation of center of mass and mass moment of inertia Although these quantities are not used in the present project, this exercise is an interesting one for the students to calculate the center of mass knowing the mass of the components and the mass moment of inertia of the model rocket along the longitudinal axis. Students then verify the value of the location of center of mass by balancing the assembled rocket on a knife edge. They also verify the moment of inertia value by suspending the rocket by a long string and measuring the period of torsional oscillations. It is noted here that while students are introduced to the concept of center of mass, moment of inertia in calculus, physics and statics, simple exercises mentioned above reinforce these fundamental concepts.
Fig. 9. Location of CG.
Model Rocket Simulation Inputs Thrust Data Hard-Coded Rocket Data User Defined Inputs
Main Simulation Outer Loop: Payload Inner Loop Thrust Calculation Drag Calculation Mass Calculation Kinematical Calculations Time Increment Payload Increment
Outputs Rocket Data
Fig. 10. Mission simulation layout.
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The mass of various components and the locations of their individual centers of gravity are summarized in Table 2. With a defined central coordinate system, the distances from the coordinate system (Fig. 9) to each component were found.
Based on the coordinate system, the center of gravity of the Alpha Rocket with all of the parts assembled as required was 0 inches in the x-axis, 0 inches in the z-axis, and 5.19 inches in the y-axis. 4.6. Mission simulation using MATLAB
Fig. 11. Experimental and numerical determination of rocket height.
The payload for the Alpha Rocket was calculated through the use of computer simulation using MATLAB. The simulation method for calculation was preferred over hand calculation because the simulation allowed for multiple solutions, data for the theoretical flight of the desired payload, more complicated calculations, and realistic conditions. The program starts by the user inputs; the maximum payload to be calculated, the interval the payload should increase within the simulation and the interval the time that should increase within the simulation; larger intervals in the simulation would produce faster results, but larger error results. Fig. 10 shows the mission simulation layout. 4.7. Flight test
Fig. 12. PCB layout of the accelerometer board and the actual prototype.
The student teams conduct a flight test with the payload (usually either sand or lead pellets) in the rocket model. Two sextants located orthogonally 100 ft apart from the launch pad measure the maximum altitude reached by the model rocket (Fig. 11). The rocket also carries an accelerometer board in its nose cone to collect the acceleration data of the rocket. In the report, students are asked to assess the errors in the analysis and compare to flight test results. Fig. 12 shows the printed circuit board (PCB) layout of the accelerometer board and the actual prototype that was used in flight test.
Acceleration Vs. Time 250
Acceleration (ft/s^2)
200
150
100
50
0 0
0.2
0.4
0.6
0.8
1
1.2
-50 Time in Seconds Fig. 13. Numerical simulation of rocket acceleration vs. time.
1.4
1.6
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of drag coefficient, specific impulse, data acquisition using modern tools, use of Computer Aided Drafting, while reinforcing fundamental concepts such as the rocket equation, center of mass, moment of inertia, numerical integration, statistical analysis and report writing skills. The cost of the project is low enough that one or two students can be assigned to each group even in a relatively large class. Our experience also indicates that the hands-on approach generates more interest in the students and leads to a better appreciation for the material that they learn rather than a typical analytical project.
References
Fig. 14. Accelerometer data from flight test.
The accelerometer board has an onboard micro computer that records the output data of two accelerometers. The accelerometers chosen are the ADXL321 two axis gravity sensitive accelerometer (Analog Devices [13]). The accelerometer is mounted such that one axis measures acceleration in line with the rocket. The axis of the second accelerometer is orientated to measure a change in the gravity vector if the rocket diverges from a vertical trajectory. It is important to know whether the rocket is flying vertical in order to know if gravity is affecting the measurement of acceleration in line with the rocket. The device has a memory for over 100 s and a battery life of a few hours. It has a start/reset button that resets the position the microcontroller is writing into the Serial EPROM to the beginning. The USB interface is used to read the recorded flight data into a PC. Once downloaded to the PC, the student teams evaluate the flight of their rocket using onboard measurements. Fig. 13 shows the acceleration time history from the numerical simulation and Fig. 14 shows the actual flight test results. 5. Summary and future plans The project described in this paper introduces the students to some fundamental concepts such as estimation
[1] W.H. Mason, H. Robertshaw, D.J. Inman, Recent experiments in aerospace and design engineering education, in: 42nd AIAA Aerospace Sciences Meeting and Exhibit AIAA, Reno, Nevada, 2004. [2] D.J. Newman, A.R. Amir, Innovative first year aerospace design course at MIT, Journal of Engineering Education 90 (3) (2001) 375–381. [3] J. Perkins, R. Mitcheltree, R. Vess, Aircraft design education at north carolina state university, AIAA Paper 89-0649, 27th Aerospace Sciences Meeting, Reno, NV, 1989. [4] S.M. Batill, Using prototypes and flight validation in teaching aerospace systems design, 1991 SAE Aerospace Atlantic, Dayton, OH, 1991. [5] E. Livne, Evolution of the capstone airplane design course at the University of Washington, AIAA Paper 99-0570, 37th AIAA Aerospace Sciences Meeting, Reno, NV, 1999. [6] J.I. Rojas, X. Prats, A. Montlaur, E. Garcı´a-Berro, Model rocket workshop: a problem-based learning experience for engineering students, International Journal of Emerging Technologies in Learning 3 (4) (2008) 70–77. [7] J.F. Marchman III, W.H. Mason, Freshman/Senior Design Education, AIAA Paper 94-0857, 1994. [8] J.F. Marchman III, W.H. Mason, Freshman/senior design education, International Journal of Engineering Education 13 (2) (1997) 143–152. [9] G.M. Gregorek., Simplified model rocket drag analysis, IAA Student Journal, December 1973. [10] H. West, W. Flowers, D. Gilmore, Hands-on design in engineering education, Journal of Engineering Education 80 (5) (1990) 560–564. [11] V. Ercolano, Learning Through Cooperation, ASEE Prism, November 1994. [12] J. Anderson, Introduction to Flight, sixth ed., McGraw Hill, USA, 2007. [13] /http://www.analog.com/static/imported-files/data_sheets/ADXL321. pdfS. [14] N. Tomita, R. Watanabe, A.V. Nebylov, Hands-on education system using water rockets, Acta Astronautics 61 (11–12) (2007) 1116–1120.
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Project-based introduction to aerospace engineering course: A model rocket Sanjay Jayaram a,, Lawrence Boyer a, John George a, K. Ravindra a, Kyle Mitchell b a b
Department of Aerospace and Mechanical Engineering, Saint Louis University, Saint Louis, MO 63103, USA Department of Electrical and Computer Engineering, Saint Louis University, Saint Louis, MO 63103, USA
a r t i c l e in fo
abstract
Article history: Received 20 October 2009 Accepted 30 October 2009 Available online 16 December 2009
In this paper, a model rocket project suitable for sophomore aerospace engineering students is described. This project encompasses elements of drag estimation, thrust determination and analysis using digital data acquisition, statistical analysis of data, computer aided drafting, programming, team work and written communication skills. The student built rockets are launched in the university baseball field with the objective of carrying a specific amount of payload so that the rocket achieves a specific altitude before the parachute is deployed. During the course of the project, the students are introduced to real-world engineering practice through written report submission of their designs. Over the years, the project has proven to enhance the learning objectives, yet cost effective and has provided good outcome measures. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Space education Model rocket
1. Introduction Most undergraduate aerospace engineering curriculums contain an introductory course that introduces sophomore students to the world of aerospace. Generally this course tends to be a broad introduction to terminology, basic aerodynamics, performance, propulsion, structures and a brief introduction to rockets and basic orbital mechanics. In some programs, a hands-on project is assigned to the students to make the course more interesting and provide an opportunity for the students to use the fundamental knowledge they have gained in mathematics and physics in their freshman year. Many of these courses involve providing a hands-on experience, wherein the students build, test and fly concepts developed in the class [1,2]. Several aerospace engineering curriculums have introduced a project based approach to
Corresponding author.
E-mail addresses: [email protected] (S. Jayaram), [email protected] (L. Boyer), [email protected] (J. George), [email protected] (K. Ravindra), [email protected] (K. Mitchell). 0094-5765/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2009.10.038
teach the introductory aerospace engineering course [3–5]. Rojas, et al. [6] the introduced a problem-basedlearning (PBL) concept for undergraduate students in aerospace engineering. Over a number of years, Virginia Tech has introduced several courses in their aerospace engineering program at the beginner’s level to introduce aerospace engineering concepts, by including design concepts for freshmen students [1]. Interdisciplinary design team concepts have also been explored in the past several years [7,8]. Hands-on education of rocket technology using water rockets is discussed in [14]. The project consists of structural study, propulsion system study, aerodynamic study, stability and flight trajectory study. At Saint Louis University’s Parks College of Engineering and Aviation, the aerospace engineering department offers an introductory course entitled ‘‘Introduction to Aeronautics and Astronautics’’ at the sophomore level. In this course, the students are required to form design teams to assemble and test a model rocket to a specified set of constraints. The constraints include that of the payload mass being determined such that the rocket altitude will reach 100 ft. This allows the test firing of the rocket in a relatively small area such as a baseball field.
ARTICLE IN PRESS 1526
S. Jayaram et al. / Acta Astronautica 66 (2010) 1525–1533
Nomenclature CD CDBT CDB CDF Cf d dB g0 Isp ‘ me mprop mpl
initial mass of rocket final mass of the rocket number of fins maximum frontal area of the body wetted area of fins wetted area of the body distance covered during burn total distance covered during coasting distance covered during one iteration of coasting portion total distance covered during all iteration of coasting portion thickness ratio of fins velocity air density at sea level
mi mf n SBT SF SW sb sc Ds
drag coefficient drag coefficient for body and tube base drag coefficient drag coefficient of fins skin friction coefficient body tube diameter base diameter of rocket acceleration due to gravity at sea level specific impulse length of the rocket body empty mass of rocket propellant mass payload mass
SDs t/c V
r
This kind of design oriented project motivates students to the concepts of aerospace engineering and engineering sciences in general. ‘‘Introduction to Aeronautics and Astronautics’’ course is taught in the fall semester (16 weeks) and consists of three 50-min lectures per week. The class size has remained steady over the past decade with an average student enrollment of 30. At Parks College, introduction to modern tools of data acquisition and analysis such as MATLAB and LabVIEW provides an opportunity for more sophisticated methods to be employed that was not possible in earlier years. The uniqueness in the hands-on project adopted in this course is twofold: (1) technical aspects and (2) educational aspects. In general technical aspects, the students are required to learn and implement modern, industry standard tools, such as, experimental data acquisition, industry standard software. Besides introducing newer concepts, the project requirements reinforce several topics that the students have learned in previous classes (for example PRO/E modeling, determination of center of gravity experimentally and moment of inertia).
Some of the specific technical aspects the students are required to learn and perform are shown below:
Assembly of the Model Rocket Kit, and development of a Pro-Engineer (PRO/E) model of the rocket.
Determination of the specific impulse of the rocket
engine through experimental data acquisition using LabVIEW. Aerodynamic drag coefficient estimation, both analytically and by MATLAB simulation. Determination of the size of the payload, both analytically and by MATLAB simulation. Calculation of center of mass and moment of inertia. Mission simulation using MATLAB. Flight test and experimental data acquisition from onboard accelerometer. Analysis through experimental data and numerical simulation.
The educational aspects introduces the students to perform projects in a team setting thus enforcing team work and communication aspects as well as ethics. The
Table 1 Model rocket individual parts dimensions and mass.
1 2 3 4 5 6 7
8
9
Item
Mass (g)
Mass (slug)
Length (in)
Thickness (in)
Diameter (in)
Lg tube Engine Sm blue tube Nose cone Part 1 Nose cone Part 2 Parachute Sm green tube
4.54 18.22 1.11 3.5 3.25 4.04 3.36
0.000311 0.001248 0.0007606 0.000240 0.000223 0.000277 0.000230
7.775 2.75 2.76 0.785 2.75 3.1 1.12
0.0175 0 0.0175 0 0 0 0.1
0.96 0.69 0.72 0.94 0.97 0.94 0.94
Item
Mass (g)
Mass (slug)
Top (in)
Bottom (in)
Balsa x3
2.26
0.000155 Leading edge (in) 3.057
1.235 Thickness (in) 0.39
2.195 Side (in) 2.28
Item
Mass (g)
Mass (slug)
Length (in)
Thickness (in)
Width (in)
Metal hook
1.33
9.11E 05
3.23
0.023
0.123
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students also learn systems engineering process, where design process, test and evaluation and design documentation aspects are covered. This process exposes students to computer aided design, analytical methods numerical simulation, experimental data acquisition and data analysis and relevant academic experience in one single project.
2. Project statement: rules and objectives
desired altitude and perform a controlled descent by parachute deployment. The project is judged on the following criteria: (1) maximum altitude of 100 ft—no more, no less, (2) parachute deployment and controlled descent, (3) experimental data acquisition and data analysis and (4) a detailed written report with software numerical simulation.
3. Hands-on model rocket project
The objective of the project is to assemble a model rocket that is to be launched from ground, achieve a
The following section details the assembly and analysis component of the course, namely the hands-on model rocket project. This project exposes sophomore students to the excitement of the aerospace engineering field and the expectations for future courses. The friendly competition gives the students an opportunity to show their creativity and ingenuity in developing a model rocket. The goal is to achieve an active learning environment for acquiring a conceptual framework as well as problemsolving skills. The connection between theory and practice is vividly demonstrated in the model rocket project. This experience is greatly appreciated by sophomore engineering students deciding whether or not to major in aerospace engineering. Design is an integral part of the practice of engineering and it should be an integral part of students’ education during their entire undergraduate career [10,11].
Fig. 1. (a) Diagram of a typical model and (b) PRO/E model of the rocket.
Static calibration of cantilever balance 0.014 Voltage = 0.0106(Weight) + 0.0001 Voltage (volts)
0.012 0.01 0.008 0.006 0.004 0.002 0 0
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Fig. 2. Static calibration of cantilever ‘‘load cell’’.
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Fig. 3. Rocket motor on test rig.
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3.1. Organization The students in the class are divided into working teams of two to three students to each group. In the middle of the semester, typically after 7 weeks of lecture, one model rocket kit (ESTES ALPHA model) with all relevant accessories is given to each group. Randomizing the teams facilitate the development of teamwork skills, which many of the students lack prior to this course. This process also helps students in establishing teamwork and communication skills. The groups are required to assemble the model rocket, perform experimental tests on the rocket motor, basically following the rules and objectives described in the previous section. 3.2. Model rocket kits Each team is provided with the model rocket kit (ESTES ALPHA model) parts described in Table 1. The total assembled length of the model rocket is approximately 12 in weighing approximately 45 g. The approximate cost of each model rocket kit is $15.00. Each kit includes a rocket motor (Estes B6-4) weighing approximately 18 g. All students will have already completed a one credit machine shop course with lectures on safety and additional machine shop techniques and a two credit
computer aided design course using PRO/E prior to enrolling in this course. ‘‘One credit’’ is equivalent to one contact hour in a week, so a three credit hour course will have a total of 48 contact hours in a semester (with 16 weeks per semester). In comparison to ‘‘Bologna Accord’’, the European University credits are prorated by one-half when compared to a typical American University. Figs. 1a and b show the diagram of the typical model rocket and PRO/E computer aided design sketch. 4. Project tasks First, the teams determine the specific impulse of the rocket motor. This involves acquiring thrust data from the engine using LabVIEW. Second, the teams determine the drag coefficient of the model rocket. Third, the teams estimate the payload. Fourth, the teams calculate center of mass and moment of inertia both analytically and using graphical software. Fifth, the teams conduct a MATLAB simulation. Sixth, the teams perform a flight test by launching the rocket. These individual tasks are described in detail below. 4.1. Determination of specific impulse of rocket motor To determine the specific impulse of the rocket motor, a simple static test rig is used consisting of a cantilever beam (Fig. 3). A strain gage is attached near the fixed end. To calibrate the device, three to four readings of the strain gage are recorded corresponding to static weights hung from the tip of the cantilever beam. It should be noted here that most sophomores may not have had exposure to strain gage techniques but have had enough knowledge from introductory physics course (Wheatstone bridge circuit) to comprehend the experiment. A sample calibration curve is shown in Fig. 2. A regression analysis is performed to obtain the relationship between load and voltage. Students are required to show error bars as well. The rocket assembly is then attached to the cantilever beam load cell. The rocket motor is fired and the output of the strain gage is fed to a data acquisition board to collect
Fig. 4. Wiring diagram in LabVIEW for thrust time history.
Model Rocket Static Thrust Data
Thrust un IbS
3 2.5 2 1.5 1 0.5 0 0
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1
Time in Seconds Fig. 5. Thrust vs. time for rocket motor Estes B6-4.
Fig. 6. Mission profile for the model rocket.
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the time history of thrust from the rocket motor using LabVIEW. A photograph of the rocket attached to the cantilever test rig is shown in Fig. 3. The LabVIEW wiring diagram for acquiring the time history of thrust is shown in Fig. 4. Using numerical data obtained using LabVIEW (Fig. 5), students use either Simpson’s rule or trapezoidal rule to
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calculate the total impulse by estimating the area under the thrust vs. time curve. The average mass flow rate is obtained knowing the mass of the propellant (equal to the mass of the rocket motor before burn minus the mass of the casing after burn) and the duration of the burn. An interesting observation not relevant to the present study is the calculation of the first few resonant frequencies of
Height Vs. Time 110 100 90 80
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-20 -30 -40 -50 -60 -70 -80 -90 Time in Seconds Fig. 7. (a) Altitude vs. time and (b) velocity vs. time.
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the cantilever beam by a power spectral analysis of the thrust data shown. Based on the numerical calculations, the specific impulse was found out to be 73.71 seconds.
estimated:
4.2. Drag coefficient estimation
Here mi = me + mprop + mpl and mf = me + mpl. Then, writing the equation of motion for the rocket for the coasting portion of the flight (free flight) including the effects of drag is shown below:
By methods outlined in summary equations provided by Gregorek [9] and Shevell [14], the students estimate the drag coefficient for the rocket model. The summary equations outlined by Gregorek are repeated here for reference. The friction coefficient varies with Reynolds number and hence varies with velocity of the rocket. An average estimation of Cf must be determined by the student. CD ¼ 1:05ðCDBT þ CDB þ CDF Þ
ð1Þ
h iS W CDBT ¼ 1:02Cf 1 þ1:5=ð‘=dÞ3=2 SBT
ð2Þ
3 0:029 dB CDB ¼ pffiffiffiffiffiffiffiffiffiffi CDBT d
ð3Þ
t SF n CDF ¼ 2Cf 1 þ 2 c SBT
ð4Þ
vb ¼ g0 Isp ln
mf
mi mf
ð5Þ
dv 1 ¼ mf g0 þ rV 2 SBT CD dt 2
ð6Þ
from which dv 1 rV 2 SBT CD ¼ g0 þ dt 2mf
ð7Þ
From Eq. (7), it can be written 1 Dv ¼ Dt g0 þ rV 2 SBT CD 2mf
ð8Þ
Eq. (8) is used successively after burnout to determine the decrease in velocity Dv in each time interval Dt and thus the incremental distance covered, Ds =V1 Dt (where V1 = Vb Dv for the first step and Vn = Vn 1 Dv for subsequent steps) until the final velocity is zero. If the total distance covered by the rocket (equal to SDs +sb) is Table 2 CG for individual components.
4.3. Determination of payload—method 1 Fig. 6 below shows a typical mission profile for the flight of the model rocket. The height gained by the rocket during burnout, sb is calculated by Newton’s laws of motion. Knowing the average thrust during the burn, and the average mass of the rocket between points 1 and 2, calculating the average acceleration between 1 and 2 and the distance sb as well as the rocket velocity at the end of the burn, vb is completed. Using the rocket equation (see for example, Anderson [12]) given in Eq. (5) the payload mass is
Part
Mass (M) (g)
CG location (in)
M CG
Base Lower body tube Upper body tube Engine mount tube Engine Nose cone Parachute Adapter ring Red coupler Payload
12.7 6.9 6 1.2 18 7.5 3.2 3.8 1.2 100
1.3 5.8 15.55 1.37 1.37 16.5 16.5 2.2 11.7 4.2
16.51 40.02 93.3 1.65 24.73 123.75 52.8 8.36 14.04 420
Payload Vs. Altitude 0.011 0.01 0.009
Payload (slug)
0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0
25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 Altitude in Feet Fig. 8. Sample payload determination chart.
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equal to 100 ft, the payload estimated from Eq. (5) is the appropriate payload. If not, a revised payload is used and the steps repeated until the payload yields the desired height of 100 ft. From these calculations, students observe that the drag force may not be significant in the present study. Nonetheless, this exercise provides them with an appreciation for all the interdependent parameters.
4.4. Determination of payload—method 2— numerical simulation Students use MATLAB to run a time domain simulation of the rocket (see Fig. 7a and b). Gravity, weight reduction
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due to fuel usage, thrust profiles and drag forces were all incorporated into the simulation. This method is preferred to hand calculations due to the time-savings over a closed-form solution due to the increased accuracy due to compensation for time-dependent variables such as drag, thrust and weight. In addition, this exercise provides a useful application of programming in MATLAB that students have been exposed to during their second semester of study. The amount of payload to be carried is decided by running several iterations of the m-file flight simulation program. The maximum altitude achieved with each payload is recorded and arranged into a chart showing payload vs. maximum altitude (see Fig. 8). From this chart, the proper payload to reach a maximum altitude of 100 ft is decided upon.
4.5. Calculation of center of mass and mass moment of inertia Although these quantities are not used in the present project, this exercise is an interesting one for the students to calculate the center of mass knowing the mass of the components and the mass moment of inertia of the model rocket along the longitudinal axis. Students then verify the value of the location of center of mass by balancing the assembled rocket on a knife edge. They also verify the moment of inertia value by suspending the rocket by a long string and measuring the period of torsional oscillations. It is noted here that while students are introduced to the concept of center of mass, moment of inertia in calculus, physics and statics, simple exercises mentioned above reinforce these fundamental concepts.
Fig. 9. Location of CG.
Model Rocket Simulation Inputs Thrust Data Hard-Coded Rocket Data User Defined Inputs
Main Simulation Outer Loop: Payload Inner Loop Thrust Calculation Drag Calculation Mass Calculation Kinematical Calculations Time Increment Payload Increment
Outputs Rocket Data
Fig. 10. Mission simulation layout.
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The mass of various components and the locations of their individual centers of gravity are summarized in Table 2. With a defined central coordinate system, the distances from the coordinate system (Fig. 9) to each component were found.
Based on the coordinate system, the center of gravity of the Alpha Rocket with all of the parts assembled as required was 0 inches in the x-axis, 0 inches in the z-axis, and 5.19 inches in the y-axis. 4.6. Mission simulation using MATLAB
Fig. 11. Experimental and numerical determination of rocket height.
The payload for the Alpha Rocket was calculated through the use of computer simulation using MATLAB. The simulation method for calculation was preferred over hand calculation because the simulation allowed for multiple solutions, data for the theoretical flight of the desired payload, more complicated calculations, and realistic conditions. The program starts by the user inputs; the maximum payload to be calculated, the interval the payload should increase within the simulation and the interval the time that should increase within the simulation; larger intervals in the simulation would produce faster results, but larger error results. Fig. 10 shows the mission simulation layout. 4.7. Flight test
Fig. 12. PCB layout of the accelerometer board and the actual prototype.
The student teams conduct a flight test with the payload (usually either sand or lead pellets) in the rocket model. Two sextants located orthogonally 100 ft apart from the launch pad measure the maximum altitude reached by the model rocket (Fig. 11). The rocket also carries an accelerometer board in its nose cone to collect the acceleration data of the rocket. In the report, students are asked to assess the errors in the analysis and compare to flight test results. Fig. 12 shows the printed circuit board (PCB) layout of the accelerometer board and the actual prototype that was used in flight test.
Acceleration Vs. Time 250
Acceleration (ft/s^2)
200
150
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of drag coefficient, specific impulse, data acquisition using modern tools, use of Computer Aided Drafting, while reinforcing fundamental concepts such as the rocket equation, center of mass, moment of inertia, numerical integration, statistical analysis and report writing skills. The cost of the project is low enough that one or two students can be assigned to each group even in a relatively large class. Our experience also indicates that the hands-on approach generates more interest in the students and leads to a better appreciation for the material that they learn rather than a typical analytical project.
References
Fig. 14. Accelerometer data from flight test.
The accelerometer board has an onboard micro computer that records the output data of two accelerometers. The accelerometers chosen are the ADXL321 two axis gravity sensitive accelerometer (Analog Devices [13]). The accelerometer is mounted such that one axis measures acceleration in line with the rocket. The axis of the second accelerometer is orientated to measure a change in the gravity vector if the rocket diverges from a vertical trajectory. It is important to know whether the rocket is flying vertical in order to know if gravity is affecting the measurement of acceleration in line with the rocket. The device has a memory for over 100 s and a battery life of a few hours. It has a start/reset button that resets the position the microcontroller is writing into the Serial EPROM to the beginning. The USB interface is used to read the recorded flight data into a PC. Once downloaded to the PC, the student teams evaluate the flight of their rocket using onboard measurements. Fig. 13 shows the acceleration time history from the numerical simulation and Fig. 14 shows the actual flight test results. 5. Summary and future plans The project described in this paper introduces the students to some fundamental concepts such as estimation
[1] W.H. Mason, H. Robertshaw, D.J. Inman, Recent experiments in aerospace and design engineering education, in: 42nd AIAA Aerospace Sciences Meeting and Exhibit AIAA, Reno, Nevada, 2004. [2] D.J. Newman, A.R. Amir, Innovative first year aerospace design course at MIT, Journal of Engineering Education 90 (3) (2001) 375–381. [3] J. Perkins, R. Mitcheltree, R. Vess, Aircraft design education at north carolina state university, AIAA Paper 89-0649, 27th Aerospace Sciences Meeting, Reno, NV, 1989. [4] S.M. Batill, Using prototypes and flight validation in teaching aerospace systems design, 1991 SAE Aerospace Atlantic, Dayton, OH, 1991. [5] E. Livne, Evolution of the capstone airplane design course at the University of Washington, AIAA Paper 99-0570, 37th AIAA Aerospace Sciences Meeting, Reno, NV, 1999. [6] J.I. Rojas, X. Prats, A. Montlaur, E. Garcı´a-Berro, Model rocket workshop: a problem-based learning experience for engineering students, International Journal of Emerging Technologies in Learning 3 (4) (2008) 70–77. [7] J.F. Marchman III, W.H. Mason, Freshman/Senior Design Education, AIAA Paper 94-0857, 1994. [8] J.F. Marchman III, W.H. Mason, Freshman/senior design education, International Journal of Engineering Education 13 (2) (1997) 143–152. [9] G.M. Gregorek., Simplified model rocket drag analysis, IAA Student Journal, December 1973. [10] H. West, W. Flowers, D. Gilmore, Hands-on design in engineering education, Journal of Engineering Education 80 (5) (1990) 560–564. [11] V. Ercolano, Learning Through Cooperation, ASEE Prism, November 1994. [12] J. Anderson, Introduction to Flight, sixth ed., McGraw Hill, USA, 2007. [13] /http://www.analog.com/static/imported-files/data_sheets/ADXL321. pdfS. [14] N. Tomita, R. Watanabe, A.V. Nebylov, Hands-on education system using water rockets, Acta Astronautics 61 (11–12) (2007) 1116–1120.