P14651: Drop Tower for Microgravity Simulation

1. P14651: Drop Tower for Microgravity Simulation Adam Hertzlin Dustin Bordonaro Jake Gray Santiago Murcia Yoem Clara

2. Pros and Cons of Project Types Limits Teams Vision for Project Not Feasible

3. 1 Tower Vs. 2 Towers • Increase in price due to all infrastructure materials multiplied by 2. • Smaller diameter piping. • 1 objects dropping, 1 position sensor and smaller release system per tower. • 2 Vacuum pumps. • Less volume to evacuate. • Two different environments can be created, which means that the 2 objects can be drop at different pressures. • More interactive to public. • Lasers are independent from each other. • Reduced price due to less parts. • Larger diameter tube. • 2 objects dropping, 2 position sensors and larger release system. • 1 Vacuum pump. • Larger volume to evacuate. • Only one environment can be created. The two objects must be drop at same pressure. • Occupies less space at location. • Lasers can conflict with each other.

4. Isolation Valve – Cost vs. Time • Assumptions: No losses due to connection points, 10 cubic foot per meter pump, 15 micron ultimate pressure, 2ft above & below valves, single tower

5. - Isolation Valves Pros and Cons + Quicker cycle time The air needed to be taken out of the pump is independent of tower heightCan use less costly pump (Lower pump speed) • Our Conclusion: Although isolation valves would save a substantial amount of time, the time benefit does not outweigh the cost for the tower height we are considering. At this scale it would be more beneficial to increase the pump size instead. • Costly • Disrupts view of items falling • Can not alter for a continuous system in the future • More pipe / pump sections  need more parts • More chance of pressure leak

6. List of Experiments • Dropping two objects simultaneously • Measure Gravity • Measure Drag • Balloon Expansion • Marshmallow Expansion • Sound Insulator • Plastic Bottle Compression Note: The following slides will attempt to justify the required tower pressure and size to complete these experiments

7. Engineering Analysis Tower Height

8. Free Fall – No Air Resistance (Vacuum Conditions) Applies to All Objects: • Vi=0 • g=32.2ft/s2

9. Free Fall –Air Resistance (Atmospheric Conditions) • Fall Time Differs Per Object; Depends on Drag Coefficient, Projected Area and Mass of Object Dropped. • Equations Dependent on Terminal Velocity (Vterm or V∞); The Highest Velocity the Object Reaches, at the Point Downward Acceleration Becomes Zero http://en.wikipedia.org/wiki/Free_fall

10. Free Fall –Air Resistance (Atmospheric Conditions) • ρ is the Density of Air • is the Drag Coefficient • A is the Projected Area of the Falling Object http://en.wikipedia.org/wiki/Free_fall

11. Free Fall –Air Resistance (Atmospheric Conditions)

12. Results • Assumptions • 0.5 – 1.0 drop time difference is adequate • Steel Ball Bearing vs. Feather • Result • 10 – 15ft Tower Height

13. Engineering Analysis Ultimate Pressure

14. Gravity Calculation with 1% Error • Constant Acceleration Equations • Assumes no air resistance / perfect vacuum • , where x is position and t is time • Assume x.xx% Error due to pressure

15. Free Body Diagram of Object • Force Balance • At Terminal Velocity, acceleration = 0 • At Vacuum Pressure, drag force = 0 • , where a is downward (negative)

16. Drag Force (Air Resistance) • FD = Drag Force • ρ = Air Density • V = Velocity of Object • CD = Drag Coefficient (Fudge Factor) • A = Projected Area of Object • P = Air Pressure (Pa) • R = Specific Gas Constant = 287.05 J/kg*K • T = Air Temperature = 21°C = 274K

17. Objects to calculate gravity • Based on a certain vacuum pressure and other parameters, center objects will be suitable of calculations while others are not • Objects vary by their mass, projected area and drag coefficient • Assumptions: • Allowable Error in Gravity due to Pressure = 0.01% • This can increase if the error from the position and time measurements are minimized • Pressure = 0.015 Torr = 2 Pa • This can be decreased if a more efficient pump is available (cost / benefit) • Max Tube Height = 5 meters • Constant Acceleration • Ideal Gas • Room Temperature • Standard Gravity

18. Results • For the assumptions on the previous slide the following equation must be satisfied: • m/(CD*A) >= 1.19 kg/m^2 Where: m = mass (kg) CD = Drag Coefficient A = Projected Area Note: Error % and Pressure can be adjusted to change this threshold

19. Engineering Analysis Evacuation Time

20. Conductance • The flow of air in a tube, at constant temperature, is dependent on the pressure drop as well as the cross sectional geometry. • Viscous Flow: Pressure (micron) * Diameter (in) > 200 • Transitional Flow: 6.0 < Pressure (micron) * Diameter (in) < 200 • , • Molecular Flow: Pressure (micron) * Diameter (in) < 6.0 • C = Conductance (cfm) • F1 = Viscous/Transitional Flow Scale Factor = 0.52 • F2 = Transitional Flow Scale Factor = 12.2 • F3 = Molecular Flow Scale Factor = 13.6 • D = Pipe Diameter (in) • L = Pipe Length (ft) Viscous Molecular

21. Equivalent Pipe Length • Pipe fittings can cause losses within a piping system • These include: elbows, tees, couplings, valves, diameters changes, etc. • Tabulated values for Le/D can be used to adjust L in the conductance equations • D = Diameter of Pipe • Le = Equivalent Length • Total Length = L + Le1 + Le2 + Le3 + ….

22. Effective Pump Speed • SEff for each flow regime • Viscous, Transitional, & Molecular • n = number of pipe diameters or actual lengths • C = Conductance (cfm) • = Given Pump Speed (cfm) • = Effective Pump Speed for Tube Dimensions

23. Evacuation Time • = 760 Torr (Atmospheric) • = Viscous–Transitional Pressure • = Transitional-Molecular Pressure • = Ultimate Pressure • Example: Single 8” x 15’ Tube • Pump used on left • See Spreadsheet for: • Fittings • Individual conductance • Individual flow regime time VP6D CPS Vacuum Pump 2 Stage Rotary Pump 15 micron Ultimate Vacuum Pump Speed – 6.25 cfm Price: $241.15

24. Results • For the tube and pump size listed, the evacuation time is 9.24 minutes • This will increase if: • Tube diameter increases • Tube length increases • Pump speed decreases • Ultimate pressure decreases Note: The pressure is suitable for most objects, based on slide 18

25. Engineering Analysis Critical External Pressure

26. Pipe Critical Pressure Calculations • Desired Factor of Safety = 3-4 *Specifications for white PVC Pipe Dimensions Courtesy of Engineeringtoolbox.com

27. Summary • Proposed Requirement Metrics • Tower height: 5 meters • Tower size: 8” Diameter • Number of Towers: 2 (if budget allows) • Pump Speed: 6.25 cfm (2 tubes) • Pump Type: 2 stage Rotary (mechanical roughing pump) • Evacuation Time: 9.24 mins • Ultimate Pressure: 15 microns (0.015Torr or 2Pa) • Negative (Critical) Pressure – Factor of Safety: 3.94 • No Isolation Valves • Manual Object Lifting

28. Concept Designs

29. Bill of Materials • NOTE: This Bill of Materials does not include the pipe, valves, and fittings that connect the pumps to the tube.