P14651: Drop Tower for Microgravity
Simulation
Adam Hertzlin
Dustin Bordonaro
Jake Gray
Santiago Murcia
Yoem Clara
Pros and Cons of Project Types
Vacuum Tube and
Continuous Lift
+
-
Easy approval
for location
High cost
Museum
functionality
Long completion
time
(>2 Semesters)
Not Feasible
Vacuum Tube
+
Continuous Lift
-
+
-
Satisfies majority of
Baseline for "both" Does not satisfy
Slow cycle time
current requirements
operation
current requirement
Approval by dean
Fast, but useless
Simplicity of design
for certain
cycle time
locations
Requires
continuation by
another SD group
Limits Teams
Vision
forunreliable
Completion
in 2 Possibly
semesters
due to complexity
Project
Educational and
fun for all
Completion in 2
semesters
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
1 Tower
 Reduced price due to less parts.
Vs.
2 Towers
 Increase in price due to all
infrastructure materials multiplied by
2.
 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.
 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
 Costly
 The air needed to be taken out of
 Disrupts view of items falling
the pump is independent of tower
height Can use less costly pump
(Lower pump speed)
 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 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
Engineering Analysis
 Tower Height
Free Fall – No Air Resistance
(Vacuum Conditions)
Applies to All Objects:
 𝑉𝑓 =
 ∆𝑡 =
2 ∗ 𝑔 ∗ ∆𝑦 + 𝑉𝑖 2
𝑉𝑓−𝑉𝑖
𝑔
 Vi=0
 g=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)
 𝑉∞ =
2 ∗ 𝑚 ∗ 𝑔/(𝜌 ∗ 𝐶𝐷 ∗ 𝐴)
 ρ is the Density of Air
 𝐶𝑑 is the Drag Coefficient
 A is the Projected Area of the Falling Object
 ∆𝑡 = 𝑐𝑜𝑠ℎ−1 𝑒
∆𝑦
−𝑔∗𝑉
∞
 𝑉𝑓 = −𝑉∞ ∗ tanh(𝑔 ∗
http://en.wikipedia.org/wiki/Free_fall
2
𝑡
)
𝑉∞
∗ 𝑉∞ /𝑔
Free Fall –Air Resistance
(Atmospheric Conditions)
Results
 Assumptions
 0.5 – 1.0 drop time difference is adequate
 Steel Ball Bearing vs. Feather
 Result
 10 – 15ft Tower Height
Engineering Analysis
 Ultimate Pressure
Gravity Calculation with 1% Error
 Constant Acceleration Equations
 Assumes no air resistance / perfect vacuum
 𝑥 = 𝑥0 + 𝑣0 𝑡 + 0.5𝑎𝑡 2
𝑔 =
2𝑥
𝑡2
, where x is position and t is time
 Error in Gravity
 Assume x.xx% Error due to pressure
 1% 𝐸𝑟𝑟𝑜𝑟 𝑔 = % 𝐸𝑟𝑟𝑜𝑟 𝑥 + 2 % 𝐸𝑟𝑟𝑜𝑟 𝑡 + 𝑥. 𝑥𝑥%
Free Body Diagram of Object
 Force Balance
 𝐹𝑦 = 𝑚𝑎
 𝐹𝐷 − 𝑚𝑔 = 𝑚𝑎
 At Terminal Velocity, acceleration = 0
 𝐹𝐷 = 𝑊
 At Vacuum Pressure, drag force = 0
 −𝑚𝑔 = 𝑚𝑎, where a is downward (negative)
Drag Force (Air Resistance)
 𝐹𝐷 = 0.5𝜌𝑉 2 𝐶𝐷 𝐴
 FD = Drag Force
 ρ = Air Density
 V = Velocity of Object
 CD = Drag Coefficient (Fudge Factor)
 A = Projected Area of Object
𝑃
𝑅𝑇
 P = Air Pressure (Pa)
 R = Specific Gas Constant = 287.05 J/kg*K
 T = Air Temperature = 21°C = 274K
𝑘𝑔
−5
 𝜌 = 1.185 ∗ 10
∗𝑃
𝐽
 𝜌=
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
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
Drag Coefficient, CD
Projected Area, A (m^2)
Mass, m (kg)
m/(CD*A)
1"
Steel Ball
1.625"
Steel Ball
Ping Pong
Ball
Feather
Coffee Filter
0.47
0.47
0.47
1.00
0.75
0.0005
0.0013
0.0013
0.0026
0.0127
0.067
0.289
0.003
0.001
0.001
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.
𝐷4
𝐹1 Ṗ
𝐿
 𝐶𝑉 =
 Viscous Flow: Pressure (micron) * Diameter (in) > 200
𝐷4
𝐹1 Ṗ
𝐿
𝐷3
𝐹2
𝐿
 𝐶𝑇 =
+
 Transitional Flow: 6.0 < Pressure (micron) * Diameter (in) < 200
𝐷3
𝐹3 ,
𝐿
 𝐶𝑀 =
 Molecular Flow: Pressure (micron) * Diameter (in) < 6.0
 C = Conductance (cfm)
 Ṗ = Average Pressure(microns) =





𝑃1 −𝑃2
2
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 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 + ….
Effective Pump Speed
 SEff for each flow regime
 Viscous, Transitional, & Molecular

1
𝑆𝐸𝑓𝑓
=
1
𝑆𝑃
+
1
𝐶𝑛
+
1
𝐶𝑛−1
+ ⋯+
1
𝐶2
+
1
𝐶1
 n = number of pipe diameters or actual lengths
 C = Conductance (cfm)
 𝑆𝑃 = Given Pump Speed (cfm)
 𝑆𝐸𝑓𝑓 = Effective Pump Speed for Tube Dimensions
Evacuation Time
 𝑡=
𝑉
𝑆𝐸𝑓𝑓−𝑉
ln
𝑃0
𝑃1
+
𝑉
𝑆𝐸𝑓𝑓−𝑇
l𝑛
 𝑃0 = 760 Torr (Atmospheric)
 𝑃1 = Viscous–Transitional Pressure
 𝑃2 = Transitional-Molecular Pressure
 𝑃3 = Ultimate Pressure
𝑃1
𝑃2
+
𝑉
𝑆𝐸𝑓𝑓−𝑀
l𝑛
𝑃2
𝑃3
VP6D CPS
Vacuum Pump
• Example: Single 8” x 15’ Tube
 𝑡 = 9. 24 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
 Pump used on left
 See Spreadsheet for:
• Fittings
• Individual conductance
• Individual flow regime time
2 Stage Rotary Pump
15 micron Ultimate Vacuum
Pump Speed – 6.25 cfm
Price: $241.15
Results
 For the tube and pump size listed,
the evacuation time is 9.24 minutes
 This will increase if:
 Tube diameter increases
 Tube length increases
 Pump speed decreases
 Ultimate pressure decreases
Note: The pressure is suitable for most objects, based on slide 18
Engineering Analysis
 Critical External Pressure
Pipe Critical Pressure Calculations
Critical Pressure Calculations for Clear PVC
P
14.7 psi
v
0.37
E
429000 psi
Formula
PCrit=(2*E/(1-v^2))*(1/((OD/t)-1)^3)
SCH 40 Pipe Maximum Pressure
Size (in)
OD (in)
Thickness (in)
Max Pressure (psi)
Factor of Safety
6
6.625
0.28
85.43
5.81
8
10
12
8.625
10.75
12.75
0.322
0.365
0.406
57.98
43.16
35.37
3.94
2.94
2.41
 Desired Factor of Safety = 3-4
Max Pressure Rating of Schedule 40 PVC*, from HARVEL
Size (in)
6
8
10
12
Pipe Dimensions Courtesy of Engineeringtoolbox.com
Max Pressure (psi)
90
58
49
42
*Specifications for white PVC
Factor of Safety
6.12
3.95
3.33
2.86
Summary
 Proposed Requirement Metrics










Tower height: 5 meters
Tower size: 8” Diameter
Number of Towers: 2 (if budget allows)
Pump Speed: 6.25 cfm (2 tubes)
Pump Type: 2 stage Rotary (mechanical roughing pump)
Evacuation Time: 9.24 mins
Ultimate Pressure: 15 microns (0.015Torr or 2Pa)
Negative (Critical) Pressure – Factor of Safety: 3.94
No Isolation Valves
Manual Object Lifting
Concept Designs
Bill of Materials
Preliminary Bill of Materials
Item
Material
Rating
Size
Quantity Total Price ($)
Tube
Clear PVC
SCH40
8inOD x 10ft
3
$1,846.20
Reducing Tee SCH40 PVC Slip x Slip x FPT White PVC SCH40
8in x 8in x 4in
2
$621.20
PVC FPT Plug
White PVC SCH40
8in
4
$707.80
Female Adapter Slip x FIPT
White PVC SCH40
8in x 8in
4
$422.80
Laser Distance Sensor
2
$1,960.00
Pressure Gage
2
$200.00
2 Stage Rotary Pump
2
$352.34
DAQ
1
$99.00
PVC Glue
1 quart
2
$76.04
Polystyrene Beads
1
$40.00
Thermocouples
3
$90.00
Bulk Head Fittings
2
$26.32
U-Bolts
316 Stainless 3,230 lbs
8in
6
$653.10
Total
$7,094.80
 NOTE: This Bill of Materials does not include the pipe, valves, and fittings that
connect the pumps to the tube.