The Dynamics of Inflatable Space Structures
Final Report
16.622
Spring 2003
Authors:
David A. Broniatowski
Christopher Graff
Advisor: Prof. Raul Radovitzky
Tuesday, May 14, 2003
Abstract
Inflatable space structures, which hold promise to increase efficiency and economy, have
not been put in widespread use due to problems associated with modeling and accurately
predicting the inflation dynamics of the systems. This project attempts to characterize a set of
thermodynamic process parameters that will show repeatability in the interim dynamics and
reliability in the final state of system for the inflation of inflatable tubular structures. In order to
achieve this, an experiment was devised to inflate sets of tubes and to measure the internal
pressures and tip trajectories of the tubes through the inflation process. The set of parameters
investigated included the tube folding or initial packing configuration, the inflation pressures, the
aspect ratio and the material thickness of the tube. The results of the experiment showed that for
the given range tested, steady state reliability was prevalent in smaller tubes (lower aspect ratio)
or rolled tubes (packed in a rolled configuration). With regards to transient dynamic
repeatability, the data indicated that rolled, thin tubes seem to be more repeatable than other
configurations. The conclusions resulting from the data collected tended to show that rolled
tubes, with higher inflation pressures produced better repeatability results, at the expense of
reliability – where there was a problem of many tubes failing due to material and seal failures.
Reliability could be enhanced by producing smaller aspect ratio tubes, or as suggestions for
future work, to improve the material and sealing techniques.
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Table of Contents
Abstract……………………………………………………………………………………. 1
Table of Contents………………………………………………………………………….. 2
List of Figures ………………………………………………………………………………3
List of Tables………………………………………………………………………………. 3
1.0 Introduction…………………………………………………………………………… 4
1.1 Background and Motivation………………………………………………….. 4
1.2 Hypothesis……………………………………………………………………. 5
1.3 Objectives…………………………………………………………………….. 5
1.4 Success Criteria……………………………………………………………….. 6
1.5 Strategy and Value to Technical Community………………………………… 6
2.0 Previous Work and Literature Review………………………………………………… 7
2.1 Background Research…………………………………………………………. 7
2.2 Analysis of Previous Work…………………………………………………… 8
2.3 Summary and Conclusion of Literature Review……………………………… 9
3.0 Technical Approach…………………………………………………………………… 10
3.1 Experimental Overview……………………………………………………….. 10
3.2 Experimental Design………………………………………………………….. 11
3.3 Hardware, Assembly, and Facilities……………………………………………14
3.4 Tube Manufacturing ………………………………………………………….. 15
3.5 Software and Data Collection…………………………………………………. 15
3.6 Testing Matrices and Aging Tests……. ……………………………………… 16
3.7 Experimental Errors and Error Mitigation…………………………………….. 19
3.8 Data Collection Procedures and Calibration …………………………………. 19
4.0 Results…………………………………………………………………………………. 20
4.1 Qualitative Assessment……………………………………………………….. 20
4.2 Data Analysis Technique Assessment………………………………………… 20
4.3 Reliability Results……………………………………………………………... 22
4.4 Repeatability Results………………………………………………………….. 23
5.0 Discussion and Analysis………………………………………………………………. 25
5.1 Reliability Analysis……………………………………………………………. 25
5.2 Repeatability Analysis………………………………………………………… 26
5.3 Assessment of Hypothesis…………………………………………………….. 31
6.0 Summary and Conclusions……………………………………………………………. 32
6.1 Summary……………………………………………………………………… 32
6.2 Suggestions for Future Work…………………………………………………. 33
7.0 Acknowledgements…………………………………………………………………… 35
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8.0 List of References…………………………………………………………………….. 36
9.0 Appendices ……………………………………………………………………………. 37
Appendix A: Data Collection Procedures and Calibration Checklist……………… 37
Appendix B: Table of Reliability Results Analysis……………………………….. 38
Appendix C: Relevant Formulae…………………………………………………... 40
Appendix D: Table of Hardware for Experimental Set-up………………………… 41
List of Figures
Figure 1: Diagram of Experimental Set-up………………………………………………… 12
Figure 2: Sample deployment of a Z-folded tube structure. Picture sourced from
Jet Propulsion Laboratories..……………………………………………………..13
Figure 3: Sample deployment of a rolled tube structure. Picture sourced from
Jet Propulsion Laboratories………………………………………………………14
Figure 3: Comparison of Pressure History Curves for Data Analysis Evaluation…………. 21
Figure 4: Distance traveled vs. time for 40”, thick, 3psi rolled configuration…………….. 27
Figure 5: Distance traveled vs. time for 40”, thin, 3psi rolled configuration……………… 28
Figure 6: The first 4 seconds of a sample inflation of a thick, 12” V-folded tube
inflated at 1 psi………………………………………………………………….. 29
Figure 7: Sample inflation of 40”, thick, rolled tube inflated at 3 psi and experiencing
tape-failure due to re-use……………………………………………………...... 30
List of Tables
Table 1: Experimental Test Matrix………………………………………………………… 18
Table 2: Deviation Comparison of Data Analysis Techniques ……………………………. 21
Table 3: Reliability results configuration………………………………………………….. 22
Table 4: Dynamic Repeatability results for each test configuration. “I/D” stands
for insufficient data and indicates that the camera’s buffer filled before
the inflation finished……………………………………………………………… 24
Table 5: Listing of each repeatable configuration with its associated reliability………….. 30
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1.0 Introduction
1.1 Background and Motivation
Research on inflatable space structures has shown promise in developing low mass and
space efficient structures, which can greatly reduce the launching costs. Certain space structures,
such as antennas or reflectors, do not require a large mass to maintain their structural integrity
since they operate under a micro-gravity environment. As such, the only large loads these
structures see are generally during a launch. Developing inflatable space structures is one
solution to reducing launch mass, and thus cost, of putting the structure in orbit. Inflatable space
antennas can be made of lightweight, flexible material, pre-folded on the ground, and then
inflated and expanded into the appropriate structural configuration.
If successful in the
deployment, these structures can reduce the mass and volume required over conventional space
structures, which translates to more efficiency and economy.
The idea of inflatable structures dates back to the 1960’s, but a lack of understanding of
the dynamics of deployment has precluded their widespread use.
Specifically, no reliable
method exists for predicting the deployment dynamics of a complex, multi-tubular, inflatable
space structure. A common approach is to recourse to structural finite element analysis, which
ignores some potentially important phenomena, such as the dynamics of the pressure and gas
flow inside the inflatable structure and the coupled interactions with the dynamic structural
response. The interaction between the gas flow and the structure’s membrane has not been very
well studied, even though it has a great effect on the inflation dynamics and possible chaotic
behavior of inflating structures.
The National Aeronautics and Space Administration (NASA) ran the Inflatable Antenna
Experiment (IAE)1 on board a space shuttle in 1996 to test the deployment of a reflector antenna.
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One of the goals was to gather data on the dynamics of the deployment in a rarefied and minimal
gravity environment. Although the deployment was considered an overall success, the dynamics
of the deployment itself were not well predicted or controlled1, and there are no new data or
other experiments to show how a different structure would behave under similar conditions.
The motivation for the project is to increase the base of knowledge about inflatable
structures.
Examining the effects of the geometry, folding configuration, and the inflation
pressures on the structure would help towards a better understanding of the dynamics of
inflatable structures and the effects that gas flow and pressure have on the flexible membrane of
the inflatable structure. This research will help in developing the validation tools needed for
models that predict the inflation dynamics of inflating structures, and thus help in developing,
engineering, and implementing successful inflatable space structures that are more efficient and
reduce costs over more conventional structures.
1.2 Hypothesis
There exists a range of parameters under which the inflation process of an inflatable
structure will occur in a predictable, repeatable and consistent manner.
1.3 Objectives
The goal of this project is to determine via experimentation the role of various parameters
(e.g. pressure, aspect ratio of tube, thickness of tube material, deflated structure fold pattern, etc.)
in the dynamics of an inflatable tube structure. The project will investigate the behavior of the
inflation process by examining the repeatability of the inflation (studying the dynamics of the
process), and the reliability of the inflation (by looking at the final state of the process).
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1.4 Success Criteria
Success would be reached in the attainment of a range of process parameters, such as
inflation pressures and geometric configurations, under which the repeated inflation of an
inflatable space structure could be reliably estimated. Demonstrating a lack of repeatability
within our range of test parameters would also constitute success.
1.5 Strategy and Value to Technical Community
In order to assess the hypothesis, an experiment was devised in order to test inflatable
tubes, varying the inflation pressures, the aspect ratio of the tubes, the folding pattern of the tube,
and the thickness of the material of the tube. Analysis of two folding patterns, a V-folded
configuration and a rolled configuration, (See Figure 2 and Figure 3), would allow for a
comparison of tubes with a single V-fold and what is effectively a continuous distribution of
small-angle folds that make up the coils of the rolled configuration. The different inflation
pressures would demonstrate the effect that flow and pressure have on the flexible membrane.
Mylar, a polyethylene film, was adopted as the base material out of which the tubes were
constructed, with two different thickness values tested. The other geometric configuration that
was tested was the aspect ratio, or the ratio between the length and the diameter of the tubes.
Inflatable space structures are seen as a solution to the problem of making deployment of
space structures more economical and efficient. Yet, even with numerous studies and research in
this area, the engineering problems associated with complex inflation processes have not been
solved. This project attempts to contribute to the characterization—and, therefore, to the better
understanding—of the dynamics of the deployment process of an inflatable structure. In
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particular, the collected data will be useful in the future as a validation tool for models
attempting to predict the inflation dynamics of structures.
2.0 Previous Work and Literature Review
2.1 Background Research
Six papers were provided as research for the project by Prof. Raul Radovitzky. The first
paper was written by Namiko Yamamoto under Prof. Radovitzky’s supervision in the summer of
20022. Their paper reviews a set of experiments of inflating tubes, summarizing the results, and
analyzing the pressure history results for repeatability. The second paper, by Miyazaki and Uciki
of the University of Nihon, Japan, contained the research on which Yamamoto and Radovitzky
based their experimentation. This article summarizes Miyazaki’s and Uchiki’s development of a
numerical method for modeling the deployment motion of inflatable membrane structures3. This
method is based on a finite element analysis that takes into account the deformation of the
flexible structure material and the pressure of the inflation gas.
Researchers at L’Garde, Inc. and JPL (Jet Propulsion Laboratory) have conducted
studies and experiments regarding inflatable structures4,5. They also designed, built and tested the
inflatable space structure that was used in the Inflatable Antenna Experiment launched on NASA
mission STS-77 on May 19,1996. In their paper, Freeland and Veal discuss the deployment of
an inflatable space antenna on a space shuttle mission and investigate the development of new
materials and controls for inflatable structures4. Other authors have published work regarding
the computer simulation of the deployment of structures, and new materials and designs for use
with inflatable structures. Salama, Kuo, and Lou have developed a simplified inflation model,
allowing for gas flow, pressure variation, and large deformations5. Guidanean and Williams have
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described new components developed by L’Garde for use with inflatable truss structures to
control inflation and help to develop more complex structures6.
2.2 Analysis of Previous Work
The numerical method proposed in the paper by Miyazaki and Uchiki was based on an
energy-momentum method, with the model being incremented over time by equalizing the
amount of work done by the static pressure inside the membrane to the mechanical energy of the
membrane during the inflation process. Essentially, the model looked at the interaction between
the geometrically nonlinear deformation of the tube and the static pressure of the injected gas.
The model accounted for aspects of the deployment process such as the wrinkling or folding of
the membrane, any contact that the membrane may have when packaged, and the interaction
between the geometrically non-linear deformation of the membrane and the inflation gas. This
model assumes negligible dynamic pressure and discounts the higher frequency deformation
arising from it, and it thus may not be valid for faster inflation rates of tubes 3. This study also
neglects the details of the gas flow, as well as its coupled interaction with the deforming
structure. In other words, the gas in this model acts as a mere loading device. The study states
that such fast deployments can be analyzed by commercial software like that used to analyze the
inflation of air bags in cars. Also, the flexible tubular structure used in the experiment carried
out in a drop tower was relatively small – the radius was only 12mm and the length only 200mm
– which could lead to scaling problems when applied to larger structures3.
Guidanean and Williams’s paper discusses the results of the IRSS II project (Inflatable
Rigidizable Space Structure, Phase II)6. The main objectives of this project were to develop
structural trusses using more complex joint structures, and to examine deployment in a vacuum
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environment. Secondary objectives to the program were to investigate the issues of
environmental testing and the effects the environment has on the structure and packaging.
It was noted in the paper that L’Garde has developed a material for an inflatable structure
that consists of a fabric and water-soluble resin, which when dehydrated becomes rigid6. The
strength of this type of material is greater than other flexible membranes like Mylar or other
plastics used in testing inflatable structures. Also, L’Garde has developed a complex joint, which
can join multiple fabric tubes to form large, complex truss structures. This joint was simpler in
design and cheaper to fabricate than previous attempts, specifically the joints developed for the
Phase I part of the Inflatable Rigidizable Space Structure program6.
JPL and L’Garde’s paper on inflatable antenna technology and a preliminary review of
the shuttle experiments contained an overall summary of the Inflatable Antenna Experiment
(IAE) flown on the space shuttle, STS-77 4. The paper summarized the experiment set-up by
L’Garde on the space shuttle, defined the objective of the experiment, and stated the preliminary
findings. Most important for our purposes was the demonstration of deployment reliability of a
space antenna structure in orbit. The inflation of the experimental antenna structure was
controlled through the use of sensors, valves, and regulators. However, the inflation of the
structure was significantly affected by residual air stored within the structure and the release of
strain energy in the structure as it was expanding. Although the structure did eventually reach its
final shape, it did not do so in the manner or on the time-scale predicted.4
2.3 Summary and Conclusions of Literature Review
All of the previous research and proposed models for the inflation of structures fail to
adequately address the dynamics of how the pressure and flow of gas affect the deformable
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material of the inflatable structure. The models used to analyze the inflation processes are based
on numerical or Finite-Element analyses of the structural problem with the gas playing the role
of a loading device. These tools, up to now, have given accurate estimation of the steady-state
dynamics, but there is still no accurate method to predict the transient dynamics, as evidenced by
the Inflatable Antenna Experiment results on the Space Shuttle. In order to better develop and
implement future inflatable structures, it is necessary to better understand the transient dynamics
of the inflation process. Some of the experiments described in the papers also do not reflect the
effects of size and how scaling can affect the deployment process of various structures.
Additionally, more research is needed into the instability of inflating the structure with a highspeed flow or at higher pressures, rather than just lower pressures or lower speed flows, possible
chaotic behavior, and what parameters may affect that type of deployment.
3.0 Technical Approach
3.1 Experimental Overview
The experiment was designed to test the deployment of an inflatable tube structure and to
gather pressure history data and visual deployment and point-tracking data. These data would
then be analyzed to derive results that would be used to assess the hypothesis. The testing set-up
consisted of a compressed gas tank supplying air to inflate the tube, appropriate sensors (pressure
transducers) to measure the pressure of the tube, a computer controlled solenoid to switch the air
supply on and off, calibration equipment, a computer-controlled high speed video camera, and a
computer that collected all the data. The testing apparatus was made in such a way to allow for
quick changes of the inflation tubes between trials, and a dark background was set-up for greater
contrast in the video data. The basic approach in our experimental setup was to adopt Namiko
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Yamamoto’s setup as a baseline and then to propose and integrate technical enhancements
geared towards improving the precision, scope and quality of the experimental data and reducing
sources of error.
3.2 Experimental Design
The testing equipment consisted of the following items: a compressed air tank; a pressure
regulator to calibrate the inflation stagnation pressure; a Setra meter for measuring the inflation
stagnation pressure; a computer actuated solenoid; two pressure transducers; an amplifier for the
pressure transducers’ signals; an inflating tube assembly; a computer with HP Data Logger and
MiDAS video software; and a high-speed video camera (see Figure 1). The compressed air tank
was connected first to the pressure regulator, which allowed for controlling the pressure within
the system, with the Setra pressure meter measuring the stagnation pressure within the system.
The computer-actuated solenoid was then connected in-line, and was used to shunt the air to the
rest of the inflation apparatus. Pressure transducers were then connected up- and downstream of
the tube inflation assembly, and measured the static pressure at each point. The sensors were
wired into an amplifier, and the signals then sent to the computer to be recorded by the HP Data
Logger software. The voltages measured by the pressure transducers were calibrated to the
actual pressure in PSID, as obtained by the Setra meter. The task of obtaining, installing, and
operating pressure sensors within an inflating tube is a complex procedure that was beyond the
scope of this experiment. Thus, only measurements of the static pressure directly upstream and
downstream of the base of the tube were used to collect pressure history data.
The computer controlled a solenoid that was plumbed in-line to shunt the air from the
Setra meter to the rest of the set-up, thus allowing for the execution of the experiment. The same
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signal that actuated the solenoid also cued the camera to start recording; thus synchronizing the
video data with the start of the inflation process. The high-speed camera was used to film the
inflation of the tube structure with frame rates ranging between 60 to 250 frames per second
(fps), depending on the time-length of the video data (a maximum of 512 frames could be
captured at 640x480 pixel resolution per experiment). To calibrate distances in the MiDAS
software for data analysis, an 18-inch ruler was clamped to the base of the inflation apparatus
that was visible within the camera’s field of view.
Figure 1: Diagram of Experimental Set-up
The measurements taken for each experimental trial included the tracking of the tip end
of the tube and the pressure histories during the inflation process.
There were two main
geometrical folding patterns tested. The first was a rolled pattern, which was a flattened tube,
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rolled into coils, held together with double-sided tape, and inflated from one end (see Figure 3).
The second type was a V-Folded pattern, which was a flattened tube that was folded at the midpoint (see Figure 2). The initial orientations of the tubes were all pointed upwards, such that the
V-folded configuration initially looked like an inverted “V”, and the rolled tube would unroll
upwards.
Figure 2: Sample deployment of a V-folded tube structure. Picture sourced from Jet Propulsion
Laboratories3.
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Figure 3: Sample deployment of a rolled tube structure. Picture sourced from Jet Propulsion
Laboratories3.
For the tube structures, the variables to be tested were different geometric configurations,
different packaging, different material thicknesses, and different inflation pressures. The
parameters of the configurations include changing the aspect ratio of the tube, the folding pattern
of the tube, the inflation stagnation pressure and the material type.
3.3 Hardware, Assembly, and Facilities
The hardware and assembly considerations necessary to build the testing apparatus are
summarized in Appendix D: Table of Hardware for Experimental Set-up.
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3.4 Tube Manufacturing
Tubes were manufactured out of Polyethylene Terephthalate Film (PET Polyester, with
UL 94HB Rating), or more commonly referred to as Mylar. Rolls of Mylar were ordered in
0.002 inch and 0.005 inch thicknesses. The rolls were marked and cut to the appropriate sizes,
then folded over length-wise and sealed at the edges and at one end to form tubes. The impulse
heat sealers were common, commercially available items. However, the largest sealer was only
15.5 inches long, and many tubes were longer than the tray of the sealer, which meant that the
tubes had to be repositioned and resealed to form a longer, continuous seal. Each tube took
between 5 and 10 minutes to build, with larger tubes requiring more time due to the multiple
seals. The manufacturing process was accurate to within the measuring capabilities of hand tools
used, but quality was heavily influenced by the impulse sealers used, the procedure needed to
seal longer tubes, and the human operator. Overall, the tubes were accurate enough for the
purposes of the project without requiring a large investment of time and effort to develop other,
more complex manufacturing processes.
3.5 Software and Data Collection
The data collection was facilitated by HP Data Logger software and MiDAS video
software. The HP Data Logger was set-up to record the pressure history data of the two static
pressure transducers, and to output the data (pressure readings) onto spreadsheets for data
analysis. The MiDAS software available with the high-speed video camera was set-up to record
8 seconds of video data, at 60 to 250 fps. The viewing area included a set of mirrors, angled
such that all three dimensions (depth, height, and breadth) could be viewed and analyzed within
a single camera’s frame. The point-tracking feature of the software was used to track the tip end
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of the tube through the inflation for the purposes of determining the dynamic repeatability. Use
of the mirrors allowed the point-tracking feature to determine all three coordinates of the tube
end through the inflation process using only one video camera recording.
Analysis of the trajectories of the tracking points was done on the computer using the
MiDAS video software, and then output to a spreadsheet. This output (the coordinate values of
the tip end of the tube with respect to the base of the tube) was then pasted into the pressure
history spreadsheet output for comparison. Since the computer controls the opening of the
solenoid to inflate the tubes, as well as the start signal for the video recording, overlaying the
output spreadsheet data only required a small time stamp adjustment, which consisted of
subtracting the solenoid starting time-stamp from that corresponding to the beginning of
pressure-recording. The data analysis could then be done by using these spreadsheets and
formulas outlined in Appendix C.
3.6 Testing Matrices and Aging Tests
The baseline testing matrix is divided into blocks representing individual combinations of
geometric configuration (aspect ratio), folding pattern, material thickness, and inflation
pressures.
The geometric configurations include three different aspect ratios in order to
investigate behavior of the tube as a function of its slenderness.
There were two different material thicknesses tested:

Thicknesses: 0.005 in.; 0.002 in.
Aspect ratios were defined as the ratio of the length of the tube to its diameter:

Aspect Ratios: 12:1, 20:1, 40:1
There were two different folding patterns tested:
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
Folding Patterns: Rolled, V-Folded
The testing consisted of inflating the tubes at 3 different pressures (relative to atmospheric
pressure).

Inflating Pressures: 1 psi, 2 psi, 3 psi
Tests for aging effects followed the same procedure as for each of the experimental data
sets. Initially, the repeatability of 5 2-psi, 20”, V-folded inflations of each thickness was to be
compared to 5 separate inflations of a single tube. Since most tubes burst after their first full
inflation, it was concluded that 5 separate tubes must be used for each test configuration due to
this material constraint.
Since aging was determined to be significant for both material thicknesses, each material
was only tested extensively for 8 parameter sets. These 8 sets are located at the extremes of each
parameter’s range as shown in the following test matrix. The other 10 parameter sets were tested
only once to assure that the experiment did not exceed the scope for the 16.62X courses. Thus, a
maximum of 50 tubes per material were tested in addition to the 6 needed to test for aging. This
brought the maximum tube manufacturing count up to 112.
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The baseline testing matrix is shown below, where the highlighted portion illustrates a
single trial per testing configuration (see Table 1: Experimental Test Matrix).
Table 1: Experimental Test Matrix
V-Folded
Rolled
12 inches
Rolled
V-Folded
Rolled
V-Folded
1 Trial for each
highlighted block in the
matrix.
• 5 Trials otherwise.
•
20 inches
40 inches
50 Total Tubes
=> 50 Trials
1 Psi
2 Psi
x2 material thicknesses
=> 100 tubes & 100 trials
3 Psi
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3.7 Experimental Errors and Error Mitigation
The most significant source of error that could occur in this experiment was due to
variability in the quality of the tubes.
The sealers used to manufacture the tubes are
commercially available impulse sealers, which were not long enough to produce one continuous
seal in the larger tubes. This allowed larger tolerances and error in aligning the multiple seals
needed to completely seal a large tube. Human error in measuring, cutting, and actually sealing
also affected the quality of the tubes. The sealing effects, as well as material limitations, were
evident in the aging tests (Section 3.6), where the majority of the tubes failed after a single
inflation trial.
Other sources of error from the testing equipment were mitigated by using a Setra meter
to calibrate the initial inflation pressures to within 0.01 psi, with the meter itself having a
measuring accuracy to within 0.001 psi. The amplifier used for the pressure transducer signals
was calibrated to measure 1 Volt per 1 psi of differential pressure. Also, the pressure transducer
signals were calibrated to read within 1 mV for an actual pressure of zero with a measurement
capacity on the order of mvolts. The accuracy of this equipment allowed for measurement errors
to be below 1%.
3.8 Data Collection Procedures and Calibration
The Data Collection procedure is outlined as a checklist in Appendix A: Data Collection
Procedures and Calibration Checklist.
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4.0 Results
4.1 Qualitative Assessment
Qualitative assessments of the experiment results show that the major distinction in the
dynamic behavior can be attributed to the folding configurations of the tubes. The dynamics of
the rolled configuration were more constrained due to its packaging, and appeared to be more
repeatable than the V-folded counterparts. The tape used to package the rolled tubes also seemed
to have a controlling effect of the inflation, allowing only one or two coils to unroll at a time,
which appeared to result in more predictable inflations. Another assessment was that the greater
inertia of the larger tubes affected the dynamics of the inflation by allowing more overshoot in
the unrolling of a coil or the unfolding process. Also, V-folded tubes seemed to be more affected
by aerodynamic disturbances, from the surroundings or from the actual velocity of the tube
inflating, than the rolled tube configurations.
As expected, the human factor in tube manufacturing proved to be a major issue. There
were a large number of tube failures from poor seals. The sealing problems appeared to be
mainly caused by the variation of temperature of the impulse sealer, which allowed weak spots
and pinholes to develop in and around the seals. When the tubes were then inflated, they failed
at these weak points.
4.2 Data Analysis Technique Assessment
Two forms of data analysis were compared for one of the data sets in order to assess their
validity compared to the observed data. The Thick, V-folded, 40” tubes failed to fully inflate for
the inflation pressures tested. Instead, these tubes inflated only half-way without having air enter
the second, upper chamber, effectively acting as simple, flat tubes. The pressure history data for
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these tubes was analyzed for the Root Mean Square (RMS) deviation from the mean pressure
curve, and the RMS deviation of the time integral of the pressure curves from the time integral of
the mean pressure curve. The following table shows the deviation of these curves:
Table 2: Deviation Comparison of Data Analysis Techniques
Thick, V-folded, 40” Tubes
RMS Deviation of Pressure
History Curves
RMS Deviation of Integral
Curves
1 PSI
5.4%
3 PSI
3.4%
4.8%
1.6%
Also shown below are the plots of the actual data.
3.00E+00
1.00E+00
2.50E+00
8.00E-01
101-1
101-1
105-1
101-2
105-1
2.00E+00
101-2
105-2
6.00E-01
105-2
101-3
101-3
105-3
101-4
for
105-3
1.50E+00
101-4
105-4
105-4
101-5
4.00E-01
101-5
105-5
101-Mean
105-5
1.00E+00
101-Mean
105-Mean
105-Mean
2.00E-01
5.00E-01
0.00E+00
-1
0.00E+00
1
3
5
7
9
11
13
Thick, 40”, 1 psi, V-folded
15
-1
1
3
5
7
9
11
13
15
17
Thick, 40”, 3 psi, V-folded
Figure 4: Comparison of Pressure History Curves for Data Analysis Evaluation. 101
corresponds to downstream pressure and 105 corresponds to upstream pressure in the legend for
each graph.
A comparison of the deviation results of the two analyses shows that the integral analysis
will tend to show less deviation in a system that has very little observational deviation. Here, the
integral analysis of the pressure history curves gave a 95.2% and 98.4% confidence level of
repeatability of the 1 psi and 3 psi tests, whereas the RMS deviation of pressure curves gave only
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
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94.6% and 96.6% confidence level, respectively.
These data also show confidence in the
relatively small level of internal variability of a repeatable inflation system, even with the errors
associated with the experiment.
4.3 Reliability Results
Data sets were assigned into three categories based on their reliability. The results of this
categorization are listed in Table 3: Reliability results configuration.
V-folded
Thick 12”
Tubes
40”
Thin 12”
Tubes
40”
Rolled
1 PSI
3 PSI
1 PSI
3 PSI
Full
Full
Full
Full
Partial
Partial
Many
Leaks
Full
1
Full
Kinked
Partial, Many
Bursts Bursts
Mostly
Full
Full
Mostly
2
Full
Ripped
Table 3: Reliability results configuration.
Those sets that consistently provided a full or mostly full1 inflation for each tube were
categorized as reliable for the purposes of this experiment. Note that this category includes all of
the rolled tubes that were inflated at 3 psi as well as most of the rolled 1 psi inflations. There
An inflation is characterized as “mostly full” when all but the final coil of a rolled tube inflates and both pressure
sensors read stagnation pressure. This is considered variability due to tape effects.
1
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
22
were a number of data sets in which the tubes burst or developed leaks and kinks with a
frequency that prevented gathering five full inflations within the time-scope of this project.
Since this is considered to be an artifact of the sealing process rather than an effect of the
inflation process, these data sets are categorized as having indeterminate reliability.
This
category includes thin 40” tubes inflated at 3 psi as well as rolled 1psi thick 40” tubes and 12” Vfolded thin 1psi inflations. In the case of each of the V-folded tubes of indeterminate reliability,
leaks and kinks tended to form directly under the fold. In the case of the thin, 40” rolled tubes
that were inflated at 3 psi, there were two tube failures due to the tube material tearing at
locations where the Mylar had formed kinks during the folding process. Thus, the lack of
reliability is considered to be a constraint on the material rather than on the inflation or sealing
processes. Finally, there were two data sets in which none of the tubes achieved full inflation.
Since these tubes all behaved in the same manner (their only motion was due to external
aerodynamic disturbance), the data gathered from these 40” thick V-folded inflations were used
to get a rough idea of the internal variability in the experiment as previously described in Section
4.2.
4.4 Repeatability Results
For the purposes of this experiment, a data set is considered to be repeatable if at least
one of the two statistical analyses run on the point tracking data for that set indicate a
significance level of 90% or more.
The most repeatable data set was the thin, 40” rolled 3 psi tube configuration, which
demonstrated a 93% confidence level in repeatability based on the RMS data analysis and a 94%
confidence level in repeatability based on the time-integral data analysis. This was the only set
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
23
for which the time-integral data analysis provided conclusive results, therefore, this set is
considered more repeatable than the thin, 40” rolled 1 psi tube configuration, which
demonstrated a 94.6% confidence level in repeatability in the RMS data analysis but a 73%
confidence level using the time-integral test.
The repeatability results for each tested configuration are listed below in Table 4. Note
that the six most repeatable configurations possess at least two values of the test variables under
which the most repeatable data set was conducted (i.e. thin, rolled, 3 psi & 40” long).
Thick, V-folded tubes
12 inch
40 inch
1 PSI
RMS Test
I/D
3 PSI
Integral Test
RMS Test
Integral Test
15%
49%
18%
29%
I/D
I/D
I/D
Thin, V-folded tubes
RMS Test
12 inch
40 inch
24%
Integral Test
RMS Test
Integral Test
27%
14%
22%
I/D
9%
34%
18%
Integral Test
RMS Test
Integral Test
59%
8%
23%
I/D
10%
29%
I/D
Thick, Rolled tubes
RMS Test
12 inch
40 inch
I/D
Thin, Rolled tubes
RMS Test
12 inch
40 inch
Integral Test
RMS Test
14%
27%
5%
27%
Integral Test
8%
27%
7%
6%
Table 4: Dynamic Repeatability results for each test configuration. “I/D” stands for insufficient
data and indicates that the camera’s buffer filled before the inflation finished.
Due to the nature of confidence testing, an assertion cannot be made that a given
configuration is not repeatable, as that would constitute acceptance of the null hypothesis. Some
conclusions can be drawn from comparison of the repeatable data sets to all other data sets.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
24
Rolled thick tubes, for example, tend to be less repeatable on average than their thin
counterparts. Similarly, tubes inflated at 3 psi tend to be more repeatable on average than those
inflated at 1 psi. Note that those tubes that did not inflate have indeterminate repeatability due to
a lack of any data.
Although repeatability tests were also run on the pressure history data, analysis shows
that pressure repeatability does not correspond to dynamic repeatability and is therefore not
useful towards proving or disproving the hypothesis of this experiment. Despite the fact that the
pressure data is not useful towards directly inferring dynamic repeatability, it allows for a more
in-depth examination of the behavior of the tube inflations (for more detail, please refer to
Section 4.2).
5.0 Discussion and Analysis
5.1 Reliability Analysis
Trends may be observed with regards to the way in which test parameters affect the
reliability of a given inflation set. For example, it is notable that all of the reliable configurations
used either rolled tubes or 12” V-folded tubes. The inability to judge reliability of the long Vfolded tubes is due to the frequency of burst failures that occurred under the V-fold in these
configurations. An explanation of this phenomenon can be found upon examination of the
pressure data for V-folded tubes. As the tube inflates, the downstream and upstream air pressure
both increase, implying a similar build-up of equal or greater magnitude occurring inside of the
tube. As the pressure builds, a large amount of force is exerted at the V-fold due to its small area
as compared to that of the surrounding walls. Since the folding process often weakens the seal at
the fold location (perhaps causing small cracks or holes), the combination of large forces and a
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
25
weak seal leads to material or seal failure in the form of a tube burst. This problem is aggravated
in larger tubes when the increased weight of the top half of the V-folded tube begins to put
further stress on the seal.
The least reliable configurations were those for which all tubes failed to inflate, namely
the two 40”, thick, v-folded tube data sets. In each of these cases, the pressure of the air coming
through the inflation apparatus was insufficient to force the v-fold open, thus inflating only the
bottom portion of the tube. This is due to the larger stiffness of the tube, which with the
increased weight of the entire tube structure, required more force to achieve full-inflation. This
configuration was also tested once at 5 psi, yielding the same results. Similar results occurred
for some of the thin tubes at 1psi, whereas at 3 psi most of the thin tubes burst.
In summary, although a sufficiently high pressure is necessary for the full inflation of Vfolded tubes, pressures that are too high tend to cause bursts. Thus, if reliability is to be
guaranteed, the tube material’s stiffness and weight as well as the strength of the seals place
fundamental limits on the inflation stagnation pressure. A corollary to this statement is that tubes
tend to inflate more reliably if they are flexible and have small moment arms.
5.2 Repeatability Analysis
As commented in section 4.3, there is a set of parameters that is shared among all of the
most repeatable configurations. The data indicates that for rolled tubes, thin tubes seem to be
more repeatable than thick tubes. From these data, it is hypothesized that a high initial potential
energy for the tube in its packaged state tends to act as a disturbance to repeatability. The effects
of this potential energy in a rolled tube can be seen upon comparison of Figure 5 and Figure 6,
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
26
which show the distance traveled vs. time for the 40-inch, 3psi, thick and thin rolled inflations
respectively.
Distances
30.00
25.00
Distance (inches)
20.00
Distance 1
Distance 3
15.00
Distance 4
Distance 5
Mean Curve
10.00
5.00
0.00
0
1
2
3
4
5
6
7
8
9
Time (seconds)
Figure 5: Distance traveled vs. time for 40”, thick, 3psi rolled configuration. Note the
overshoots present in two of the inflation specimens.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
27
Distances
25.00
Distance (inches)
20.00
Distance 1
Distance 2
Distance 3
Distance 5
Mean Curve
15.00
10.00
5.00
0.00
0
1
2
3
4
5
6
7
8
Time (seconds)
Figure 6: Distance traveled vs. time for 40”, thin, 3psi rolled configuration. Note the stepwise
motion of each inflation with little or no overshoot.
Note the overshoot of the thick tube for some of the unrolling stages. This corresponds to the
rolled part of the tube recoiling as energy is released in the unrolling process. This effect is not
as visible in the thin tubes due to the smaller energy input required to roll them and hold them in
their packaged shape.
Similar considerations must be taken into account for the V-folded tubes, for which
inertia effects become significant for heavier tubes. Note the oscillatory motion of the tube tip in
Figure 7.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
28
Total Distance Moved, Pt. 1
1.40
Distance (units)
1.20
1.00
0.80
0.60
0.40
0.20
3.896
3.680
3.464
3.248
3.032
2.816
2.600
2.384
2.168
1.952
1.736
1.520
1.304
1.088
0.872
0.656
0.440
0.224
0.008
0.00
Seconds
Figure 7: The first 4 seconds of a sample inflation of a thick, 12” v-folded tube inflated at 1psi.
These oscillations correspond to the upper section of the tube partially unfolding and
then falling, thus re-closing the tube at the V-fold. This effect is a result of low pressure
combined with a large moment arm of the upper section of the tube. As the pressure builds up,
the tube begins to unfold, increasing the volume and thus resulting in an overall pressure drop
within the tube. With a high pressure no longer present to maintain the tube’s inflation, the
significance of the effects of gravity increases until the fold closes sufficiently to allow another
pressure buildup. Such oscillatory behavior adversely affects repeatability since it does not
occur on a consistent basis within a given test configuration.
Furthermore, the number,
frequency, and amplitude of these oscillations seem highly influenced by un-modeled dynamic
effects, such as air leakage.
Another conclusion that may be drawn from the repeatability data is that rolled tubes tend
to be more repeatable than V-folded tubes. The tape that holds the rolled tube together acts as a
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
29
constraining factor on the motion of the tube such that it may only unroll in one direction,
namely along the major axis of the tube. V-folded tubes do not have this property since they are
unconstrained in their motion. It is notable that in the case of a tape-failure (as would sometimes
occur on thick rolled tubes that were experiencing aging effects) the sudden lack of constraint on
the rolled tube would allow for the conversion of potential energy into kinetic energy, thus
resulting in large motions and a loss of repeatability (see Figure 8).
Tape-Failure
30.00
Distance Travelled (inches)
25.00
20.00
15.00
Tape-Failure
10.00
5.00
0.00
0
1
2
3
4
5
6
7
8
9
Time (seconds)
Figure 8: Sample inflation of 40”, thick, rolled tube inflated at 3psi and experiencing tapefailure due to re-use. Note the steps followed by the large oscillation.
Finally, higher stagnation pressure values tended to yield more repeatable results for
rolled tubes. This is due to the fact that the overall inflation process happens with more force,
thus overcoming many of the tape-effects inherent in the rolled-tube structure. If the stagnation
pressure is too high, however, there is a risk of material failure in the tube thus negatively
impacting reliability.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
30
Although pressure history repeatability does not serve as a metric for overall dynamic
repeatability it does provide insight into the forces driving those dynamics. For example, a sharp
drop in pressure corresponds with the sudden increase in available un-inflated tube volume. This
implies, in the case of a V-folded tube, that the tube has unfolded. In the case of a rolled tube,
this indicates that a coil has just unrolled. Since each successive drop in pressure tends to
adversely affect pressure repeatability, pressure repeatability may be used as a metric for the
overall speed of the inflation process. A rolled tube, which inflates in multiple quick bursts, will
have lower pressure repeatability than a V-folded tube, which tends to inflate in a single,
continuous motion.
This assertion is supported by the pressure repeatability data, which
indicates that the four most repeatable pressure history data sets are the four 12” V-folded
configurations. This implies that these smaller tubes inflate in a more continuous fashion than
their larger counterparts. More specifically, they are less prone to system disturbances that scale
with size and those that can adversely affect pressure flow such as mass/gravity effects.
5.3 Assessment of Hypothesis
This experiment hypothesized the existence of a range of thermodynamic process
parameters for which an inflatable structure deployed in a repeatable and reliable manner. The
following Table 5 lists the 4 configurations that have demonstrated both repeatability and
reliability within a 90% confidence level, as well as the two remaining repeatable inflation sets
that have indeterminate reliability.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
31
Table 5: Listing of each repeatable configuration with its associated reliability.
Configuration
Reliability level
Thick, rolled, 12”, 3psi
RMS Confidence in
repeatability
8%
Thin, rolled, 40”, 1psi
5%
Mostly Full
Thin, rolled, 12” 3psi
8%
Full
Thick, rolled, 40”, 3psi
10%
Full
Thin, rolled, 40”, 3psi
7%
Indeterminate
Thin, v-folded, 40”, 3psi
8%
Indeterminate
Full
The hypothesis is therefore proven.
6.0 Summary & Conclusions
6.1 Summary
It was determined that reliability was achieved for 9 of 16 test configurations, barring
tape effects. Of the remaining 7 configurations, 5 were of indeterminate reliability due to
insufficient seal strength, tube kinking, and other material failures.
The remaining 2
configurations, both 40” long, thick and v-folded were determined to be unreliable since they
never achieved full inflation. These two configurations were used to provide a rough idea of the
internal variability of the system.
Of the 16 configurations tested for dynamic repeatability, 6 data sets yielded repeatable
results (a significance level of 90% or more) on the RMS data analysis test. The most repeatable
configuration, which yielded significant results on both statistical analysis tests, was the set of
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
32
thin, rolled, 40” tubes inflated at 3 psi. Each of the other 4 repeatable data sets utilized at least
two of the above test parameters.
An examination of the repeatability data yields that a high initial potential energy in a
given tube’s packaged form will adversely affect the repeatability of the system. In the case of a
rolled tube, a higher initial potential energy (e.g. from a stiff tube) results in a larger overshoot
each time a coil unrolls. Similarly, in a V-folded tube, a larger moment arm above the v-fold
tends to result in tube oscillations and a less repeatable inflation. Other sources of disturbance
include aerodynamic effects that scale with tube surface area and are more likely to affect Vfolded tubes than rolled tubes. The effects of these disturbances may be overcome with a higherpressure input at the risk of decreased reliability due to a higher likelihood of leaks and material
failures at higher pressures.
6.2 Suggestions for Future Work
Recommendations for future work include multiple improvements to the tube-making
process. A large source of variability in the data was due to the lack of standardization for the
inflation specimens, since each one of them was hand-made. A number of specimens had kinks
or holes that had to be resealed or patched with packing tape, thus providing a source for pinhole
leaks and other un-modeled effects. For future versions of this experiment, it is recommended
that a more uniform method of tube manufacturing be used.
Reliability analysis was restricted on many of the tubes that had leaks and bursts. Many
of these leaks formed in places where two tube seals had to be joined together due to the impulse
sealer’s restricted size. Similarly, leaks often formed in 40” tubes where the tube had to be
folded over to permit the full sealing of the tube within the impulse sealer’s tray, thus creating a
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
33
kink. Furthermore, bursts often occurred directly next to the seal on the tube wall. This was due
to material weakening caused by excessive heat in the sealing process. Future experiments
should make use of a longer impulse sealer with finer heat control to alleviate these problems.
Lapses in reliability that were not caused by seal failure were often caused by kinks in the
Mylar that arose from the folding process. This problem became especially noticeable in the
thicker rolled tubes. A proposed solution to this problem would be to use a material that is
softer, more elastic, and more fabric-like that would be able to fold without kinking. This
material would have the added advantage of a smaller strain potential energy when folded.
Some aspects of the experimental set-up could also be improved upon. For many of the
larger inflations, eight seconds was not enough time for a full inflation to occur. This resulted in
a loss of valuable point-tracking data that could have been avoided if more memory had been
available for the data acquisition board.
It is recommended that future iterations of this
experiment ensure that a full inflation can be captured at the desired resolution in the allotted
time. The placement of the experimental setup next to an air vent and a wind-tunnel inlet in the
Newman Lab also caused some aerodynamic disturbance that would ideally be removed in the
future.
So as to better simulate inflations in the micro-gravity environment of space, it may
eventually be necessary to test these, and other, configurations in a vacuum chamber and/or on a
drop tower. Although both of these suggestions greatly exceed the scope of the 16.62X courses,
they may be considered for future tests.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
34
7.0 Acknowledgements
We would like to acknowledge the following people for providing advice, information,
assistance, and feedback throughout the design and implementation process of the project:
Course Advisor: Professor Raul Radovitzky.
Course Professors and Staff: Earll M. Murman, Edward M. Greitzer, John J. Deyst, Paul
H. Bauer, John J. Kane Jr., Jennifer Pixley, David Robertson, E. Donald Weiner,
and Richard F. Perdichizzi.
Course Teaching Assitants: Daniel Craig and Gregory Mark.
Namiko Yamamoto.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
35
8.0 List of References
1) Freeland, Robert; Bard Steven; Veal, Gordon; Bilyeu, Gayle; Cassapakis, Costa; Campbell,
Thomas and Bailey, M.C., “Inflatable Antenna Technology with Preliminary Shuttle Experiment
Results and Potential Applications,” presented at the 18th Annual Meeting and Symposium of the
Antenna Measurement Techniques Association, September 30 – October 3, 1996, Seattle,
Washington.
2) Yamamoto, Namiko; Radovitzky, Raul, “Setting up an experiment for verification of a
calculation method for inflatable tube structure,” Massachusetts Institute of Technology,
Cambridge, MA, Aug. 2002.
3) Miayazaki, Yasuyuki; Uchiki, Michiharu, “Deployment Dynamics of Inflatable Tube,”
presented at the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference, Denver, CO, Apr. 22-25, 2002.
4) Freeland, R. E.; Veal, G. R., “Significance of the Inflatable Antenna Experiment
Technology,” presented at the AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics,
and Materials Conference and Exhibit, 39th, and AIAA/ASME/AHS Adaptive Structures Forum,
Long Beach, CA, Apr. 20-23, 1998, Collection of Technical Papers. Pt. 4 (A98-25247 06-39),
Reston, VA, American Institute of Aeronautics and Astronautics, Inc., 1998, p. 2789-2796.
5) Salama, Moktar; Kuo, C.P.; Lou, Michael; Jet Propulsion Lab, “Simulation of
Deployment Dynamics of Inflatable Structures,” presented at the
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and
Exhibit, 40th, St. Louis, MO, Apr. 12-15, 1999, Collection of Technical Papers. Vol. 4 (A9924601 05-39), Reston, VA, American Institute of Aeronautics and Astronautics, 1999, p. 25242534.
6) Guidanean, Koorosh; Williams, Geoffrey T., “An Inflatable Rigidizable Truss Structure With
Complex Joints,” presented at the AIAA/ASME/ASCE/AHS/ASC Structures, Structural
Dynamics, and Materials Conference and Exhibit, 39th, and AIAA/ASME/AHS Adaptive
Structures Forum, Long Beach, CA, Apr. 20-23, 1998, Collection of Technical Papers. Pt. 4
(A98-25247 06-39), Reston, VA, American Institute of Aeronautics and Astronautics, Inc., 1998,
p. 2797-2806.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
36
Appendix A: Data Collection Procedures and Calibration Checklist
Before a set of tube inflations could begin, a number of calibrations had to be made. The
following checklist describes experimental procedure directly prior to the inflation of the first
tube of a given data set.


















Shut down the computer.
Attach the high-speed camera to the computer using the supplied cable.
Reboot the computer into Windows.
Zero the Setra stagnation pressure meter. (Press the “zero” button)
Open the pressure regulator on the compressed air tank.
When the pressure value on the Setra meter has reached its steady state value (after
approximately 5 minutes), adjust the external pressure-regulator to achieve the pressure
desired for the experiment.
Load the HP Data-Logger software and open the experimental test setup configuration.
Turn on data-logging. If the pressure transducers do not read 0 volts, turn the offset knobs
on the amplifier until the transducer offset is calibrated to 0.
Seal the metal inflation apparatus with hand and turn on the pressure switch. If the
recorded upstream and downstream pressure values do not read stagnation pressure use
the gain knobs on the amplifier to calibrate the pressure transducers to the stagnation
pressure.
When the transducers are calibrated, turn off the pressure switch, turn off the data-logger.
Slide the Mylar tube over the metal tube in the inflation apparatus.
Secure the Mylar tube with duct tape, making sure that no leaks are visible.
Using a pair of pliers, tighten the hose clamp around the end of the Mylar tube to further
prevent leaks.
Load the MiDAS software and open the camera for viewing.
Set the camera to record at 640x480 resolution. Pick the desired frame rate (usually 60
frames per second).
Adjust the camera’s position so that it is as close as possible to the tube while still
allowing for the video capture of the full inflation and the reflection in the mirror.
Focus the camera’s lens to achieve as sharp a picture as possible.
Adjust the aperture opening and the location of the halogen lamps so as to provide
adequate lighting for the experiment. The reflective tape should contrast strongly with the
rest of the tube. This will aid in point tracking.
Each tube in the data set must then execute the following procedure to collect experimental data.




Press the “Record” button in the MiDAS window to prepare the camera for a trigger.
Start data-logging. Turn on the pressure switch to initiate the experiment. The camera
will stop taking data after it has captured 512 frames.
Stop the data-logger after the experiment is finished. Turn off the pressure switch.
Save the data.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
37
Appendix B: Tables of Reliability Results Analysis
Thick, V- Folded Tubes
Pres. Hist. RMS
12 Inch
Dynamics
Pres. Hist. Integrals
Pres. Hist. RMS
40 Inch
Dynamics
Pres. Hist. Integrals
Upstream
Dn-stream
Upstream
Dn-stream
15.8%
15.6%
9.3%
9.0%
Secant
Arc-length
Secant
Arc-length
15%
49%
18%
29%
Upstream
Dn-stream
Upstream
Dn-stream
5.9%
5.8%
3.7%
3.4%
Upstream
Dn-stream
Upstream
Dn-stream
5.4%
5.1%
3.6%
3.4%
Secant
Arc-length
Secant
Arc-length
NA
NA
NA
NA
Upstream
Dn-stream
Upstream
Dn-stream
4.8%
4.5%
1.7%
1.6%
Thin, V - Folded Tubes
Pres. Hist. RMS
12 Inch
Dynamics
Pres. Hist . Integrals
Pres. Hist. RMS
40 Inch
Dynamics
Pres. Hist . Integrals
3 PSI
1 PSI
1 PSI
3 PSI
Upstream
Dn -stream
Upstream
Dn-stream
9.5%
9.1%
8.9%
8.7%
Secant
Arc-length
Secant
Arc-length
24%
27%
14%
22%
Upstream
Dn -stream
Upstream
Dn-stream
8.8%
8.3%
11.0%
10.6%
Upstream
Dn -stream
Upstream
Dn-stream
25.3%
25.3%
14.4%
13.8%
Secant
Arc-length
Secant
Arc-length
6%
58%
8%
34%
Upstream
Dn -stream
Upstream
Dn-stream
41.2%
30.7%
23.8%
19.6%
*The Dynamics analyses for the 40”, 1 psi only consisted of 3 trials, and video data could only
be compared up to the first 2 seconds of inflation.
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
38
Appendix B: Tables of Reliability Results Analysis
Thick, Rolled Tubes
Pres. Hist. RMS
12 Inch
Dynamics
Pres. Hist . Integrals
Pres. Hist. RMS
40 Inch
Dynamics
Pres. Hist . Integrals
1 PSI
3 PSI
Upstream
Dn -stream
Upstream
Dn-stream
30%
30%
17.5%
17.2%
Secant
Arc-length
Secant
Arc-length
18%
59%
8%
23%
Upstream
Dn -stream
Upstream
Dn-stream
16.2%
16.0%
16.8%
15.1%
Upstream
Dn -stream
Upstream
Dn-stream
20.2%
19.7%
12.9%
12.3%
Secant
Arc-length
Secant
Arc-length
NA
NA
10%
29%
Upstream
Dn -stream
Upstream
Dn-stream
26.7%
24.9%
29.8%
23.9%
*The Dynamics analyses for the 40”, 3 psi had numerous tape failures.
Thin, Rolled tubes
Pres. Hist. RMS
12 Inch
Dynamics
Pres. Hist . Integrals
Pres. Hist. RMS
40 Inch
Dynamics
Pres. Hist . Integrals
1 PSI
3 PSI
Upstream
Dn -stream
Upstream
Dn-stream
15.1%
15.1%
22.5%
21.1%
Secant
Arc-length
Secant
Arc-length
14%
27%
8%
27%
Upstream
Dn -stream
Upstream
Dn-stream
19.4%
18.8%
37.7%
24.9%
Upstream
Dn -stream
Upstream
Dn-stream
22.9%
22.3%
12.6%
12.1%
Secant
Arc-length
Secant
Arc-length
5.4%
27%
7%
6%
Upstream
Dn -stream
Upstream
Dn-stream
7.8%
7.7%
36.9%
23.3%
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
39
Appendix C: Relevant Formulae
The formula used to solve for the normalized RMS deviations in the statistical analyses is
described below:
  x in  m n 2 
 n


i 
n




iK
0.5
Normalized RMS Deviation

Where:
n = data point number
i = inflation trial
m = mean
x = pressure or trajectory data point of sample
K = normalization constant (tube length)
The data points for the pressures and point tracking were saved onto spreadsheets, where
the formula for deviation was then applied to calculate the percent deviation for the data sets.
The results of the percent deviation for each configuration are shown in Appendix B.
For each given inflation, the integral percent deviation was given by the following
formula:
 x t
n
n
 tn 1   M
n
Integral Percent Deviation =
Where:
M=

M
  x n t n  t n1  i
n
, where i is inflation trial
i
t = time stamp of data point x
x = pressure data point or arc-length of sample
n = data point number
i
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
40
Appendix D: Table of Hardware for Experimental Set-up
Part/Description
High Speed Video Camera (Redlake
MASD, Inc.), and MiDAS Video
Software
Mirror Stands
Source
MIT Aero/Astro
Department
Amount
1
Student Expense
$0
MIT Aero/Astro
4
$0
Department
10”x 40” Door Mirrors
Economy Hardware,
4
$40 – (reimbursed by
Cambridge, MA
Deptartment)
HP Data Logger Software
MIT Aero/Astro
1
$0 – (available for student
Department
use on lab computers)
Personal Computer (for data gathering), MIT Aero/Astro
1
$0 – (available for student
includes Data Acquisition card
Department
use)
Flexible Hose Piping, Fittings, Hose
MIT Aero/Astro
X
$0 – (dept. stock, avail.
clamps
Department
for student use)
Model 2100 Strain Gage Conditioner
MIT Aero/Astro
1
$0 – (available for student
and Amplifier System, 2 Channel
Department
use)
System; Instruments Division,
Measurements Group, Inc.
Wiring, connections
MIT Aero/Astro
X
$0 – (stock)
Department
Pressure Transducers
MIT Aero/Astro
2
$0 – (available for student
Department
use)
Computer Actuated Solenoid Switch
MIT Aero/Astro
1
$0 – (available for student
Department
use)
Pressure Regulator
MIT Aero/Astro
1
$0 – (available for student
Department
use)
SETRA air pressure meter
MIT Aero/Astro
1
$0 – (available for student
Department
use)
Tube Inflating Assembly, T-fitting
MIT Aero/Astro
1
$0 – (stock suuplies)
Department
Background, matt black cloth and
MIT Aero/Astro
X
$0 - (stock supplies)
cardboard
Department
Measuring/Cutting Equipment
MIT Aero/Astro
X
$0 - (stock supplies)
(straightedge, scissors)
Department
Mylar rolls; Clear Polyethylene
McMaster-Carr
1 roll of $17.19 (.002”), $38.67
Teraphthalate Film – Part No.:
each
(.005”)
8567K24, 8567K54
thickness
Gelb Machine Lab, Newman Lab and
MIT Aero/Astro
X
$0 – (avail. For students)
Hanger
Department
Impulse Sealers, 12” and 15-1/2”, Part Harbor Freight Tools 1 each $39.99 (15-1/2”), $29.99
No.: 43477-2VGA, 43476-2VGA;
(12”)
Distributed by Harbor Freight Tools
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
41
Broniatowski, Graff – The Dynamics of Inflatable Space Structures
42