Adam HertzlinDustin Bordonaro

Jake GraySantiago Murcia

Yoem Clara

P14651: Drop Tower for Microgravity Simulation

Pros and Cons of Project TypesVacuum Tube and

Continuous Lift Vacuum Tube Continuous Lift

+ - + - + -

Easy approval for location High cost

Satisfies majority of current

requirementsSlow cycle time Baseline for "both"

operationDoes not satisfy

current requirement

Museum functionality

Long completion time

(>2 Semesters)

Simplicity of designApproval by dean

for certain locations

Fast, but useless cycle time

Requires continuation by

another SD group

Educational and fun for all Completion in 2

semesters Completion in 2 semesters

Possibly unreliable due to complexity

Fast cycle time and meets all requirements

Can be done in budget Can be done in

budget

May have time for system design of lift

May have time for system design of

vacuum tube

Larger diameter, possibility of 2 tubes

+ 4 - 2 + 6 - 2 + 5 - 3

Not Feasible

Limits Teams

Vision for Project

1 Tower Vs. 2 Towers

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.

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.

Isolation Valve – Cost vs. Time

Time to Evacuate (min)

No Isolation Valves

Time to Evacuate (min) Isolation

Valves

Price, Single Tower, 2 Isolation

Valves

15ft Tower 40ft Tower 15ft / 40ft Tower 15ft / 40ft Tower

6" Dia. 3.25 8.95 0.86 $4,940.00

8" Dia. 5.72 15.46 1.52 $6,880.00

12" Dia. 12.79 34.25 3.41 $9,984.00

Assumptions: No losses due to connection points, 10 cubic foot per meter pump, 15 micron ultimate pressure, 2ft above & below valves, single tower

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)

- 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

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.

List of ExperimentsDropping two objects simultaneously Measure Gravity Measure DragBalloon ExpansionMarshmallow ExpansionSound InsulatorPlastic Bottle Compression

Note: The following slides will attempt to justify the required tower pressure and size to complete these experiments

Engineering Analysis Tower Height

Free Fall – No Air Resistance (Vacuum Conditions)Applies to All Objects:

Vi=0g=32.2ft/s2

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

Free Fall –Air Resistance (Atmospheric Conditions)

ρ is the Density of Airis the Drag CoefficientA is the Projected Area of the Falling Object

http://en.wikipedia.org/wiki/Free_fall

Free Fall –Air Resistance (Atmospheric Conditions)

ResultsAssumptions

0.5 – 1.0 drop time difference is adequateSteel Ball Bearing vs. Feather

Result10 – 15ft Tower Height

Engineering Analysis Ultimate Pressure

Gravity Calculation with 1% ErrorConstant Acceleration Equations

Assumes no air resistance / perfect vacuum

, where x is position and t is time

Assume x.xx% Error due to pressure

Free Body Diagram of ObjectForce Balance

At Terminal Velocity, acceleration = 0

At Vacuum Pressure, drag force = 0, where a is downward (negative)

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

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

ResultsFor 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

1" Steel Ball

1.625" Steel Ball

Ping Pong Ball Feather Coffee Filter

Drag Coefficient, CD 0.47 0.47 0.47 1.00 0.75

Projected Area, A (m^2) 0.0005 0.0013 0.0013 0.0026 0.0127

Mass, m (kg) 0.067 0.289 0.003 0.001 0.001

m/(CD*A) 280.46 459.63 4.62 0.39 0.14

Engineering Analysis Evacuation Time

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

Equivalent Pipe LengthPipe fittings can cause losses within a

piping systemThese include: elbows, tees, couplings,

valves, diameters changes, etc.Tabulated values for Le/D can be used to

adjust L in the conductance equationsD = Diameter of PipeLe = Equivalent LengthTotal Length = L + Le1 + Le2 + Le3 + ….

Effective Pump Speed SEff for each flow regime

Viscous, Transitional, & Molecularn = number of pipe diameters or actual

lengthsC = Conductance (cfm) = Given Pump Speed (cfm)= Effective Pump Speed for Tube Dimensions

Evacuation Time

= 760 Torr (Atmospheric) = Viscous–Transitional Pressure = Transitional-Molecular Pressure = Ultimate Pressure

• Example: Single 8” x 15’ Tube

Pump used on leftSee Spreadsheet for:• Fittings• Individual conductance• Individual flow regime time

VP6D CPS Vacuum Pump

2 Stage Rotary Pump15 micron Ultimate

VacuumPump Speed – 6.25 cfm

Price: $241.15

ResultsFor the tube and pump size listed, the evacuation time is 9.24 minutesThis will increase if:

Tube diameter increasesTube length increasesPump speed decreasesUltimate pressure decreases

Note: The pressure is suitable for most objects, based on slide 18

Engineering Analysis Critical External Pressure

Pipe Critical Pressure Calculations

Desired Factor of Safety = 3-4

P 14.7 psi

v 0.37

E 429000 psi

Size (in) OD (in) Thickness (in) Max Pressure (psi) Factor of Safety

6 6.625 0.28 85.43 5.81

8 8.625 0.322 57.98 3.9410 10.75 0.365 43.16 2.9412 12.75 0.406 35.37 2.41

SCH 40 Pipe Maximum Pressure

Critical Pressure Calculations for Clear PVCFormula

PCrit=(2*E/(1-v^2))*(1/((OD/t)-1)^3)

Pipe Dimensions Courtesy of Engineeringtoolbox.com

Size (in) Max Pressure (psi) Factor of Safety6 90 6.128 58 3.9510 49 3.3312 42 2.86

Max Pressure Rating of Schedule 40 PVC*, from HARVEL

*Specifications for white PVC

SummaryProposed Requirement Metrics

Tower height: 5 metersTower size: 8” DiameterNumber 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: 3.94No Isolation Valves Manual Object Lifting

Concept Designs

Bill of Materials

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

Item Material Rating Size Quantity Total Price ($)Tube Clear PVC SCH40 8inOD x 10ft 3 $1,846.20Reducing Tee SCH40 PVC Slip x Slip x FPT White PVC SCH40 8in x 8in x 4in 2 $621.20PVC FPT Plug White PVC SCH40 8in 4 $707.80Female Adapter Slip x FIPT White PVC SCH40 8in x 8in 4 $422.80Laser Distance Sensor - - - 2 $1,960.00Pressure Gage - - - 2 $200.002 Stage Rotary Pump - - - 2 $352.34DAQ - - - 1 $99.00PVC Glue - - 1 quart 2 $76.04Polystyrene Beads - - - 1 $40.00Thermocouples - - - 3 $90.00Bulk Head Fittings - - - 2 $26.32U-Bolts 316 Stainless 3,230 lbs 8in 6 $653.10Total $7,094.80

Preliminary Bill of Materials