Water Bottle Rocket Team 9: Darren Combs, Lauren Darling, Andrew Moorman, Esteben Rodriguez, Amanda Olguin

OVERVIEW Sensitivity Adjustments Modified Rocket Predictions Results Introduction Static Testing Methods Baseline Rocket MATLAB Rocket Design Sensitivity Adjustments Modified Rocket Predictions Results Lessons Conclusions Team 9

Introduction Goal Process model manufacture Fly analyze Apply previous aerodynamic and thermodynamic knowledge to build a bottle rocket trajectory code Process Team 9

Overall Concepts 3 (4) Phases of flight Drag, thrust and weight Depends on model used Drag, thrust and weight The rocket fins will align themselves parallel to free stream Assumption: rocket will point into the wind Team 9

Governing Equations 𝐹=0 𝑚 𝑅 = 𝑚 𝐵 𝐹= 𝑐 𝑑 𝜌 𝑒 𝐴 𝑡 𝑉 𝑒 2 +( 𝑝 𝑒 − 𝑝 𝑎 ) 𝐴 𝑡 Phase 3 Phase 2 𝐹= 𝑚 𝑉 𝑒 +( 𝑝 𝑒 − 𝑝 𝑎 ) 𝐴 𝑡 Phase 1 Team 9

Static Testing Allows measurement of the total force that is exerted throughout firing Load Cells push against a stationary structure with a load cable attached that measure force Long string of data is cut down and then adjusted in order to correctly approximate Isp ∆𝑉= 𝐼 𝑠𝑝 𝑔 0 ln⁡( 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑚𝑎𝑠𝑠 𝑓𝑖𝑛𝑎𝑙 𝑚𝑎𝑠𝑠 ) Team 9

Wind tunnel 𝐷𝑟𝑎𝑔= 1 2 𝜌 𝑉 ∞ 2 𝑐 𝑑 𝐴 𝐵 The wind tunnel allows us to come up with a coefficient of drag for our rocket. Spinning vs. non-spinning rocket: making a rocket spin provides stability. Solve for Cd 𝑐 𝑑 =2∗ 𝐷𝑟𝑎𝑔 𝜌 𝑉 ∞ 2 𝐴 𝑏 Team 9

Baseline Rocket 4 fins Set parallel to the airflow close to the nozzle triangular in shape 3.25 inch base by 3 inch height Set parallel to the airflow close to the nozzle Payload consist of an altimeter and packing peanuts (27 grams) Weight of rocket: 160 grams Payload hub is at the nose of the rocket encapsulated by extra casing (bottom of a 2 liter bottle) Payload nose of rocket included holes for accurate pressure readings Team 9

Thermo Model Pros: Cons: Takes into account most variables So many inputs to keep track Most are variable throughout Team 9

Thermodynamic Matlab modeling Input Values Wind tunnel data Initial conditions Wind conditions ODE 45 Results & Plots Team 9

Isp Model Pros: Cons: Easiest to model Ballistic for majority of launch Cons: Initial ΔV gives rocket initial momentum propelling it to go further. Team 9

Isp MATLAB Modeling Input Values Set Conditions Upload Wind Tunnel Data/ Compute Drag Upload Static Test Data / Compute V Adjust Wind Data ODE 45 Plots/ Angle Computation Outputs Team 9

Interpolation model Pros: Cons: Pulling real thrust values Interpolation/finding values gets tricky Data collection is very sensitive Team 9

Interpolation MATLAB Modeling Input Values Set Conditions Upload Wind Tunnel Data/ Compute Drag Adjust Wind Data Upload Static Test Data / Compute Thrust ODE 45 Plots/ Angle Computation Outputs Team 9

Sensitivity adjustments Exit Area 20.7 ft increase per 1 in decrease of diameter exit 15.5 ft increase per 0.1 decrease in Cd 48.5 ft increase per 1 kg decrease in water mass 0.011 ft increase per 1 kg/m^3 decrease of water density 3.38 ft increase per 1 psi increase of pressure Drag Coefficient Water Mass Water Density Pressure Team 9

Modified Rocket design How did you choose your design? Changing water fraction yielded the highest range change The final design became the base TA rocket with an adjusted water mass of 600 grams. Team 9

Uncertainties Random Gaussian Wind Wind Angle Temperature Air Density Water – 2 grams Pressure – 1 psi Cd – 0.2 Thrust (Interp model) – 10 lbf Launch Stand – 1 degree Initial Velocity (ISP model) – 10 mps Angle Finder – 5 degrees Time of Flight – 1 sec Team 9

Thermodynamic Flight Prediction Semi major Axis: 271 ft Semi minor Axis: 127 ft Data scatter represents 100 runs Team 9

ISP Flight Prediction Semi major Axis: 389 ft Semi minor Axis: 130 ft Data scatter represents 100 runs Team 9

Interpolation Flight Predictions Semi major Axis: 34.4 ft Semi minor Axis: 31.4 ft Data scatter represents 100 runs Team 9

Results from Launches 4/16 Max Height Distance Deflection Duration S1  4/16 Max Height Distance Deflection Duration S1 S2 S3 Actual NA 233’8” 4° Left 4.7 sec 31° 36° 28° Isp 189’10” 323’2” 4.1° Right 5.3 sec 56.7° 30.2° 23.7° Interp 72’8” 199’7” 6.9° Right 3.9 sec 62.9° 16.8° 11.2° Thermo 44’7” 165’ 58° Right 3.1 sec 50.9° 10.5° 6.8° Altimeter   Launch Angle: 45° Pressure: 40 PSI Water: 600g Wind speed: 5 mph from ENE Launch Angle: 45° Pressure: 40 PSI Water: 530g Wind speed: 7 mph from NNE  4/16 Max Height Distance Deflection Duration S1 S2 S3 Actual NA 206’6” 0° 4.54 sec 32° 40° 31° Isp 195’3” 323’10” 6.0° Right 5.3 sec 33.8° 27.6° Interp 95’6” 222’ 9.9° Right 4.3 sec 24.1° 24.2° 16.6° Thermo 64’1” 157’ 39.2°Right 3.6 sec 18.3° 18.4° 11.6° Altimeter   Team 9

Results from Launches Launch Angle: 45° Pressure: 40 PSI Water: 600g Wind speed: 2 mph from S  4/21 Max Height Distance Deflection Duration S1 S2 S3 Actual NA 211’ 0° 4.24 sec 26.5° 28° 36° Isp 186’3” 310’ 0.8° Right 5.2 sec 33.5° 33.6° 27° Interp 29’7” 74’4” 3.5° Right 2.6 sec 10.1° 10.2° 5.3° Thermo 77’8” 140’10” 18.3°Right 3.9 sec 24° 24.1° 14.6° Altimeter 84’   4.64 sec  4/21 Max Height Distance Deflection Duration S1 S2 S3 Actual NA 221’ 4° Left 4.83 sec 35° 32° 23° Isp 192’10” 328’9” .3° Right 5.4 sec 55.4° 29.9° 23.7 Interp 134’5” 268’9” 4.8° Right 4.9 sec 28.8° 28.7° 21.6° Thermo 60’ 162’8” 3.3° Right 3.5 sec 57° 15.2° 9.7° Altimeter 89’10”   4.69 sec Launch Angle: 45° Pressure: 40 PSI Water: 600g Wind speed: 2 mph from NNE Team 9

Altimeter Data Altimeter data Raw Data Adjust and Zero data to flight Pressure Altitude Converter to find height Altimeter data Validation of code comes from comparing it to the data accrued from the various launches the rocket performed. Subtract altitude of launch site to find height of launch Team 9

Lessons learned Parameters that likely had the greatest effect on the flight in our case was water fraction and PSI. Don’t give rockets to small children as it is possible fins will be removed. Rockets that are unstable can be stabilized if fins are oriented to spin the rocket. The process of physically manufacturing and testing a model design. Team 9

Discussion/conclusions Greatest Uncertainty Factors: Wind, Initial momentum, Exit coefficient, integration techniques. Interpolation Model performed most accurately to our launch results Error issues come from the difficulty in modeling each factor and the configuration of air holes for the payload Future Improvements: Find scientific way to determine coefficient of friction on test stand. Soap is rather viscos. Maximize height of rocket along with distance. Team 9

sources Wind Tunnel Rocket Test Procedure. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. Static Test USB VI Procedure. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. Static Test Firing Procedure. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. Launch Pad Procedure. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. TA Rocket Specifications. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. Rocket Lab Presentation Criteria. Boulder: University of Colorado Aerospace Engineering Sciences Department, 27 Apr. 2014. PDF. Team 9