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Trade Study Two

Operation Burnout (Team 4)

AE 442 S1

November 3rd, 2019

Member Responsibility Aidan Dreher GNC

Destiny Fawley GNC Conor Hershey Avionics Elena Kamis Flight Software

Austin Lindell Structures Damian Markiewicz Propulsion

Adrian Metcalf Flight Software Aldo Montagner Structures

Joshua Super Avionics Jie Yang Propulsion

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1. MISSION OBJECTIVE/SCOPE The goal of this mission is to vertically land a model rocket stage dropped from a UAV.

The scope of this trade study was to simulate the thrust of a chosen rocket motor and its ability to counteract the force of gravity to reach a velocity of 0 m/s at an altitude of 0 m. All simulations were done in MATLAB and used the thrust curve of either the Aerotech E30, Cesaroni E31, Aerotech E18, and Estes F15, gravity, and drag of a flat circular plate. Due to the results in Trade Study One, it was determined the Aerotech F22 engine provided too much thrust for the masses assumed. Therefore, for Trade Study Two, the team chose engines with lower average thrust values than the Aerotech F22. Values of rocket mass, length and diameter were given and are listed in sections 2.1 through 2.4. Rocket body inertias were also calculated. All results were checked using a “sanity check” to ensure values and results were physically possible.

2. ASSUMPTIONS The goal of these assumptions is to provide the simulation with parameters allowing the team to properly calculate the effects of each.

2.1 Altitude The rocket will be dropped from 20 meters above the landing pad.

2.2 Rocket Mass The rocket mass shall be evaluated at 1.25 kg. This mass value shall be concentrated in the bottom 10 cm of the rocket body.

2.3 Rocket Length The rocket length shall be evaluated at 60 cm.

2.4 Rocket Diameter The rocket diameter shall be evaluated at 7.6 cm.

2.5 Thrust Curve Comparison The intention of this trade study is to help determine which engine will be chosen as the final design. The following sections define the engines tested and their appropriate thrust curves used in the simulation. These thrust curves were taken from thrustcurve.org and confirmed using the motor’s individual data sheets.

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2.5.1 Thrust Curve of Aerotech E30 The thrust curve used in the simulation for the Aerotech 30 is as seen in Figure 1: Aerotech E30 Thrust Curve.

Figure 1: Aerotech E30 Thrust Curve

2.5.2 Thrust Curve of Cesaroni E31 The thrust curve used in the simulation as a test case for the Cesaroni E31 is as seen in Figure 2: Cesaroni E31 Thrust Curve.

Figure 2: Cesaroni E31 Thrust Curve

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2.5.3 Thrust Curve of Aerotech E18 The thrust curve used in the simulation as a test case for the Aerotech E18 is as seen in Figure 3: Aerotech E18 Thrust Curve.

Figure 3: Aerotech E18 Thrust Curve

2.5.4 Thrust Curve of Estes F15 The thrust curve used in the simulation as a test case for the Estes F15 is as seen in Figure 4: Estes F15 Thrust Curve

Figure 4: Estes F15 Thrust Curve

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2.6 External Forces There will be no other aero or body forces applied other than drag and gravity.

2.7 Ignition Time Accuracy All ignition times chosen in the simulation are only given to an accuracy of two decimal places. This is due to the assumption that the onboard computing system will be unable to handle an accuracy greater than this. Thus, to prevent inaccurate simulations the ignition times used in our MATLAB simulation are kept to two significant figures.

2.8 Moment of Inertia The rocket body axes were created with the z axis in the axial direction and x and y axes in in the transverse directions. The rocket body consists of a thin-walled cylindrical body tube.

3. ANALYSIS The table below breaks down the sixteen separate simulations completed per the assumptions listed previously.

Table 1: Case Breakdowns

Case # Altitude (m) Rocket Mass (kg)

Rocket Length (cm)

Rocket Diameter (cm)

Thrust Curve Forces

1 20 1.25 60 7.6 E30 Aerotech Drag only 2 30 1.25 60 7.6 E30 Aerotech Drag only 3 20 1.25 60 7.6 E30 Aerotech Drag only 4 20 1.25 60 7.6 E31 Cesaroni Drag only 5 15 1.25 60 7.6 E31 Cesaroni Drag only 6 15 1.25 60 7.6 E31 Cesaroni Drag only 7 20 1.25 60 7.6 E18 Aerotech Drag only 8 20 1.25 60 7.6 E18 Aerotech Drag only 9 17 1.25 60 7.6 E18 Aerotech Drag only 10 20 1.25 60 7.6 F15 Estes Drag only 11 20 1.25 60 7.6 F15 Estes Drag only 12 11 1.25 60 7.6 F15 Estes Drag only

Each of these cases were completed using a Matlab simulation. This simulation takes in four easily changeable parameters including mass, altitude, length and diameter as can be seen in Figure 5: Code Inputs. In this trade study all values were adjusted as listed in Table 1: Case Breakdowns.

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Figure 5: Code Inputs

The motor thrust curve can also be adjusted, but for this simulation was kept to either the Aerotech E30, Cesaroni E31, Aerotech E18, or Estes F15. In order to find the necessary ignition time, the team manually inputted values of ignition time in seconds out to two significant figures, rerunning the simulation until a velocity of 0 m/s was achieved at 0 m altitude. An example can be seen below in Figure 6: Ignition Time Input.

Figure 6: Ignition Time Input

The simulation then was set to print a graph relating velocity and altitude. The goal was to achieve 0 m/s at 0 m, but the team had varying levels of success achieving this. The graphs, resulting ignition times, and inertias were then saved off and are described further in the following sections.

The moments of inertia about the principle axes of the rocket were calculated with the assumptions stated in Section 2.8 Moment of Inertia. The rocket body was assumed to be a thin-walled cylinder with a 1cm thickness with the moment of inertia given by Eqs. (1) and (2):

𝐼 = 𝐼 =1

12𝑚(3(𝑟 + 𝑟 ) + ℎ ) (1)

𝐼 =1

2𝑚(𝑟 + 𝑟 ) (2)

where 𝐼 , 𝐼 , and 𝐼 are the moment of inertias about the body X, Y, and Z axes, m is the mass of the body tube, 𝑟 is the inner radius, 𝑟 is the outer radius, and h is the height of the length of the body tube. The rocket rotates around the center of gravity (c.g.), which is located in the center of the tube along the z axis by symmetry; therefore, the body inertias are simply the value calculated with Eqs. (1) and (2).

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3.1 Case One

Figure 7: Case One Results

For Case One, the engine chosen has the capability of coming very close to zero, but that the ignition time occurred too early, launching the rocket back into the air up to 8 m and then falling down to the ground without active thrust, resulting in a speed of approximately 12 m/s. Therefore, case one is not an optimal set up of assumptions.

3.1.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.1.2 Ignition Delay for v=0 and alt=0 The ignition for Case One occured 1.4 seconds after rocket release.

3.1.3 Rocket Drop Altitude The optimal altitude that rocket is dropped at for Case One is 20 meters above the landing pad.

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3.2 Case Two

Figure 8: Case Two Results

Case Two is an iteration of Case One with an adjusted ignition time and drop altitude. For Case Two, the engine chosen has the capability of coming very close to zero, but that the ignition time occurred too early, launching the rocket back into the air up to 2 m and then falling down to the ground without active thrust, resulting in a speed of approximately 5 m/s. Therefore, case two is not an optimal set up of assumptions.

3.2.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.2.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Two is 1.7 seconds after rocket release.

3.2.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Two is 30 meters above the landing pad.

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3.3 Case Three

Figure 9: Case Three Results

For Case Three, ignition time occurs at 2.05 seconds, resulting in the simulation reaching 0 m at approximately -1 m/s, which is a manageable velocity for landing. Therefore, case three is the optimal set up of assumptions for the Aerotech E30 engine.

3.3.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.3.2 Ignition Delay for v=0 and alt=0 The optimal time of ignition for Case Three is 2.05 seconds after rocket release.

3.3.3 Rocket Drop Altitude The optimal altitude that rocket is dropped at for Case Three is 20 meters above the landing pad.

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3.4 Case Four

Figure 10: Case Four Results

For Case Four, the engine chosen has the capability of coming close to zero, but that the ignition time occurred too early and the engine fails to provide enough thrust to slow the rocket to 0 m/s. The motor burns out at approximately 3 m above the ground resulting in a speed of approximately 7 m/s. Therefore, case four is not an optimal set up of assumptions. The rocket needs to be dropped from a lower height and ignite later to achieve the desired landing state.

3.4.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.4.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Four is 1.5 seconds after rocket release.

3.4.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Four is 20 meters above the landing pad.

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3.5 Case Five

Figure 11: Case Five Results

For Case Five, the engine chosen has the capability of coming very close to zero, but that the ignition time occurred too early and the engine fails to provide enough thrust to slow the rocket to 0 m/s. The motor burns out at approximately 1 m above the ground resulting in a speed of approximately 4 m/s. Therefore, case five is not an optimal set up of assumptions.

3.5.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.5.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Five is 1.35 seconds after rocket release.

3.5.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Four is 15 meters above the landing pad.

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3.6 Case Six

Figure 12: Case Six Results

For Case Six, the engine chosen has the capability of landing the rocket with a 1 m/s vertical velocity. Since the rocket comes very close to the desired landing state, this is an optimal set of assumptions for this motor; however, the drop height is very low. A stronger motor would be required to achieve a drop height above 15 m.

3.6.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.6.2 Ignition Delay for v=0 and alt=0 The optimal time of ignition for Case Six is 1.39 seconds after rocket release.

3.6.3 Rocket Drop Altitude The optimal altitude that rocket is dropped at for Case Six is 15 meters above the landing pad.

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3.7 Case Seven

Figure 13: Case Seven Results

For Case Seven, the engine chosen is unable to slow the rocket to 0 m/s resulting in a speed of approximately 6 m/s. Therefore, case seven is not an optimal set up of assumptions.

3.7.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.7.2 Ignition Delay for v=0 and alt=0 Thetime of ignition for Case Seven is 1.56 seconds after rocket release.

3.7.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Seven is 20 meters above the landing pad.

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3.8 Case Eight

Figure 14: Case Eight Results

For Case Eight, the engine chosen has the capability of coming very close to zero, but the ignition time occurred too early and the engine fails to provide enough thrust to slow the rocket to 0 m/s. The motor burns out at approximately .5 m above the ground resulting in a speed of approximately 2 m/s. Therefore, case eight is not an optimal set up of assumptions.

3.8.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.8.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Eight is 1.48 seconds after rocket release.

3.8.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Eight is 20 meters above the landing pad.

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3.9 Case Nine

Figure 15: Case Nine Results

For Case Nine, the engine chosen has the capability to slow the rocket to about 2 m/s at 0 m altitude. This is very close to the desired state, and the ignition is within 0.01 s of the optimal ignition time. However, the drop height had to be lowered to 17 m, which is lower than the desired 20 m or higher. Therefore, case nine is an optimal set up of assumptions, but is the best set up for this engine.

3.9.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.9.2 Ignition Delay for v=0 and alt=0 The optimal time of ignition for Case Nine is 1.37 seconds after rocket release.

3.9.3 Rocket Drop Altitude The optimal altitude that rocket is dropped at for Case Nine is 17 meters above the landing pad.

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3.10 Case Ten

Figure 16: Case Ten Results

For Case Ten, the engine chosen has the capability of coming very close to zero, but the engine fails to provide enough thrust to slow the rocket to 0 m/s resulting in a speed of approximately 3 m/s. Therefore, case ten is not an optimal set up of assumptions. Since the motor did not finish burning out, the ignition time should be earlier.

3.10.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.10.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Ten is .90 seconds after rocket release.

3.10.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Ten is 20 meters above the landing pad.

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3.11 Case Eleven

Figure 17: Case Eleven Results

For Case Eleven, the engine chosen has the capability of coming very close to zero, but that the ignition time occurred too early and the engine fails to provide enough thrust to slow the rocket to 0 m/s. The motor burns out at approximately 9 m above the ground resulting in a speed of approximately 14 m/s. Therefore, case eleven is not an optimal set up of assumptions. To achieve 0 m/s velocity at 0 m, the rocket must be dropped closer to the ground.

3.11.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.11.2 Ignition Delay for v=0 and alt=0 The time of ignition for Case Eleven is .6 seconds after rocket release.

3.11.3 Rocket Drop Altitude The altitude that rocket is dropped at for Case Eleven is 20 meters above the landing pad.

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3.12 Case Twelve

Figure 18: Case Twelve Results

For Case Twelve, the engine chosen has the capability of landing with less than 1 m/s velocity. The drop altitude had to be lowered to 11 m due to a low average thrust, which is very low. Therefore, case twelve is not an optimal set up of assumptions, but is the best set up for this engine.

3.12.1 Rocket Body Inertias The moment of inertias in the xx, yy, and zz directions using the simulation are 0.0348 kgm2, 0.0348 kgm2, and 0.0016 kgm2, respectively.

3.12.2 Ignition Delay for v=0 and alt=0 The optimal time of ignition for Case Twelve is .62 seconds after rocket release.

3.12.3 Rocket Drop Altitude The optimal altitude that rocket is dropped at for Case Twelve is 11 meters above the landing pad.

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4. FINDINGS 4.1 Impact of Motor Selection on Altitude The trend observed through these cases with respect to the motor selection of the rocket is the following: The Aerotech E30, which has an average thrust of 33.9 N and burn time of 1 s, was able to slow the rocket to nearly 0 m/s at 0 m in Case Three with a drop altitude of 20. The Cesaroni E31, which has an average thrust of 30.7 N and burn time of 0.9 s, was able to slow the rocket to 0m/s at 0 m with a drop altitude of 15 m. The Aerotech E18, which has an average thrust of 17.1 N and burn time of 2.1 s, came very close to slowing the rocket to 0 m/s in Case Nine with a drop altitude of 17 m. The Estes F15, which has an average thrust of 14.4 N and burn time of 3.5 s, achieved 0 m/s at 0 m with a drop altitude of 11 m. In other words, the average thrust has a large effect on optimal drop altitude. Lower average thrust signifies the drop altitude will generally be lower. The Aerotech E18 is the exception to this because it dropped from higher than the Cesaroni E31 with lower average thrust. This occurred because the burn time was longer, so the extra time required a higher drop altitude.

4.2 Impact of Drop Altitude on Ignition Timing The trend observed through these cases with respect to the altitude the rocket is dropped the following: The Aerotech E30 dropped from 20 m and ignited the motor at 2.05 s after release. The Cesaroni E31 dropped from 15 m with an optimal ignition time of 1.39 s. The Aerotech E18 dropped from 17 m with an optimal ignition time of 1.37 s. The Estes F15 dropped from 11 m with an optimal ignition time of 0.62 s. In general, as drop altitude decreases, the optimal ignition time also decreases. However, this is also a function of the burn time because shorter burning motors should be ignited close to the ground to allow deceleration to 0 m/s at 0 m.

5. TRADE STUDY CONCLUSION Based on the simulation one can see that overall, the best case to use would be Case Three or Case Nine where the motor selected is the Aerotech E30 and Aerotech E18, respectively. Both were able to achieve the desired state with the highest drop altitudes and relatively high ignition times around 2 s. This is ideal because a longer fall time will give the rocket more time to sense the free fall and figure out how to react accordingly.

From this case study our team will continue to design according to the results found in Cases Three and Nine focusing on a weight of approximately 1.25 kgs, an altitude of 20 m, and an E rated engine with a thrust curve like these two.