Parachute Suspension Line Drag Analysis1 Dir, Modeling and Simulation Research Center, Dept of Aeronautics, 2410 Fairchild Dr, Member AIAA
2 Cadet, Dept of Aeronautics, 2410 Fairchild Dr
3 Chair, Mechanical Engineering Dept, 18111 Nordoff Street, Associate Fellow, AIAA
Parachute Suspension Line Drag Analysis
K. Bergeron 1
T. Curlett 2 , D. Ecklebe
2 , K. McClure
H. Johari 3
California State University at Northridge, CA 91330
A team of researchers experimentally investigated the drag of several components of
parachute suspension systems commonly used for personnel and cargo airdrops.
Specifically, the team determined drag coefficients for Type III nylon cord, 1000 lb
spectra, and Type VII nylon webbing between Re = 400 to Re = 7,000, and tensions
varying between 10 lbs and 55 lbs. All tests were conducted at an angle of attack of 90 o .
The momentum deficit method was used to determine the drag for each test
configuration, and these were compared against baseline measurements of a 1/8 in
diameter right circular cylindrical rod and a 2 in wide metal band. Close control of the
pitot-static system yielded an uncertainty of approximately 10% for the calculations.
The for the Type III nylon cord ranged from .78 to 1.22, while for the spectra
values remained close to a mean value of .70 over the range of tested conditions.
Coefficient of drag data for the Type VII webbing closely matched the
corresponding values for the metal band. A vortex shedding analysis did not
indicate any synchronization with the natural frequency of the suspension lines, and
the characteristic vortex shedding.
Nomenclature
= coefficient of drag per unit length S = reference surface area, h d
d = diameter of line St = Strouhal Number
D = drag T = line tension
f = frequency of vortex shedding u = mean velocity in wake
h = reference height V∞ = freestream Velocity = characteristic length y = y-location in tunnel
qi = dynamic pressure at location i in wake υ = velocity of the fluid
q∞ = freestream dynamic pressure ρ = density
Re = Reynolds Number
Recent experiences with the Joint Precision AirDrop System have rekindled interest in more precise
characterization of parachute drag and the parachute systems’ many components. Optimization of
parachute performance has relied mostly on the use of empirical methods and general rules-of-thumb.
Lingard 1 documents the range of drag contributions for several ram-air parachute systems, and this work
reflects the wide range of contributions associated with each component. For example, the line drag for a
300 m 2 canopy is reported to contribute approximately 30% of the total drag while line drag for a 36 m
2
contributes as little as 13% of the total drag. Scaling factors are not well understood and are often
complicated by the different systems designs used for different applications. In general, suspension lines
20th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar<BR> 4 - 7 May 2009, Seattle, Washington
AIAA 2009-2982
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
2
and webbing have numerous features that distinguish them from one another including diameter, shape,
coarseness, porosity, rigidity, and strength. All of these features serve to affect the drag that each line will
experience during the flight of the parachute system. It is important to understand how to quantify this
drag in order for the system to accurately determine the system’s performance envelope.
Many round parachutes use Type III nylon cord which is also known as “550.” It is constructed in
accordance with MIL-C-5040, and has a weight of 3 oz/yd. Ram-air chutes often use a braided
polyethylene known as spectra or microline. Spectra is produced in a variety of tensile strengths, and
1000 lb test was chosen for this study. It weighs approximately 2 oz/yard. A third suspension component
was also tested—Type VII nylon webbing. This component has a 6000 lb tensile strength, and is built to
MIL-W-4088 specification, and is on average .08 in thick. Type VII is often used to build harnesses and
provide an intermediary link between the harness and the suspension lines via additional hardware.
II. Background
A. Drag on a Cylinder
The following discussion serves to introduce the various effects and parameters which make this
particular study distinctive from the traditional studies of smooth rigid cylindrical shapes. In particular,
the flow generated by the suspension lines at the low velocities tested is expected to maintain a mostly
laminar boundary layer, experiencing early separation. The expected flow over a cylinder for different
Reynolds Number regimes is shown in Figure 1.
Figure 1: Comparison of wakes of a smooth, rigid, circular cylinder
3
1. Effects
Previous research 4 has established a plot (Figure 2) of expected values of the drag coefficient and
categorized ranges of qualitative changes with respect to the Reynolds Number, . The
subcritical range will be the focus of this effort as varies between approximately 400 and 7,000 for the
reported tests. A closer look at the subcritical range with attention to the interval 100 < Re < 10,000 is
shown in Figure 3. A fine scale dip in can be seen in the region of interest.
3
Figure 2: Cd versus Re for smooth right circular cylinders
Figure 3: Adapted from Hoerner 4 page 3-9.
Of particular note for this experiment is the sensitivity on accurate measurement of the diameter, d, for
the derived valued of . This affect will be addressed below, but due to the fabric nature of both the
suspension line and the webbing, accurate measurement of d was relatively limited.
2. Shape
Figure 4 below illustrates the three general profiles to be analyzed and their respective orientations to
the flow.
Figure 4: Suspension component profiles tested.
In addition to circular cylinders, Hoerner 4 documents the constant for “elliptical” shapes, with
an aspect ratio of (2:1), in the range 10,000 < Re < 100,000. Alternatively, the for a long flat
plate oriented perpendicular to the flow.
Flow Direction
3. Coarseness
Jung et al 3 have run several experiments to compare the drag effects of a rope versus a cylinder. For
their drag experiments, ropes with a 2 inch diameter of varying porosity and roughness were analyzed.
The large diameter of the rope yields a Reynolds Number in the supercritical range of drag. Their results
showed that the additional roughness of the rope caused a more turbulent boundary layer that delayed
separation. While that experiment showed roughness can drastically influence the flow, the suspension
lines chosen for this experiment, have minimal coarseness and thin braiding. Therefore, little influence is
expected for these factors.
However, for the webbing component of the parachute, the diameter more closely represents the
experiments of Jung et al and the influence of roughness and porosity may be significantly greater and
drastically alter the flow characteristics.
4. Porosity
Component porosity measurements were not performed for these tests. However, the effect of
porosity was noticed. Any increase in material porosity equates to a lower pressure downstream of the
material, and thus a lower pressure differential with respect to the freestream flow. A key element of the
current tests which served to counteract this material property was the testing of components under
various tensile loads. As the tension on a line is increased the fibers tend to compress and thus reduce the
material porosity. Additional tensile load also reduces the diameter of the suspension components as the
air gaps between fibers are removed.
5. Synchronization(line “rigidity” and “strength”)
A closely related phenomenon that is associated with increased tensile load is the effect on cylinder
motion due to vortex shedding. If the shedding frequency synchronizes with the oscillations of cylinder,
increases linearly with the ratio of transverse vibration amplitude, , to cylinder diameter 6 , D, and
may be approximated by:
(1)
Lock-in between the vibration frequency and the stationary shedding frequency of “rods” (including
the webbing configuration) can lead to substantial increases in . Vibrations have been seen in the
suspension lines and webbing components of flight tested parachute systems, and thus may have a
significant contribution to total system drag. The natural frequencies of a suspension line follows:
(2)
where n represents the vibrational mode (n = 1, 2, 3, … ), L is the length of the line, T is the average
tension, and λ is the mass per unit length. When compared with the vortex shedding frequency:
(3)
where St is the Strouhal frequency, and is the freestream velocity, then Blevins’ algorithm 6 may be
followed to determine amplitude and drag in vortex-induced vibration.
5
B. Momentum Deficit Method
The momentum deficit method of determining the drag coefficient has proven to be reliable and
accurate 2,5
.
Downstream of the suspension line, a wake is created. For an incompressible fluid, the
momentum into a given control volume surrounding the suspension line can be measured against the
momentum out of the control volume to obtain a net force acting on the line. The net force acting in the
direction of the flow is the drag, D. A typical set of averaged velocity profiles are illustrated in Figure 5.
Figure 5: Averaged velocity wake profile
For any of the profiles defined at t i , t i+1, and t i +2 one may integrate over the entire wake to obtain a drag
per unit height such that,
(4)
With the dynamic pressure given by and the drag coefficient, , where D is drag and S
is the reference surface area, one can determine the coefficient of drag with respect to a unit height as:
(5)
Δyi denotes the length between measurements taken along the y-axis (spanwise direction) and d represents
the diameter of the line.
C. Objective
The objective of this project is to derive the for: 550 cord, 1000 lb spectra/microline, and Type VII
webbing in orientations and under loads typically associated with parachute suspension systems.
III. Set-up and Procedure
Figure 6 shows the geometry associated with each of the tested components. Each component is
aligned with the flow in the same manner that it is found, on average, for parachute systems. The
diameters chosen for each component were determined based on the typical orientation to the freestream
velocity.
6
Spectra/Dacron d≈.125 in
Nylon Webbing and Flat Plate d≈2 in
Figure 6: View of the orientation of the components and sizing.
A. Axis System
Figure 7 depicts the axis system used for all experiments. The angle of attack, α, is defined as the angle
between the freestream velocity, V∞ and the longitudinal axis of the suspension line. This definition for α
differs from the ram air parachute angle of attack which is measured with respect to the canopy chord
line. The x-axis is defined as parallel to the freestream velocity, the y-axis is perpendicular to the
freestream, into the page, and the z-axis is the vertical axis, toward top of the page. Drag, D, is defined as
the aerodynamic force acting parallel to freestream velocity along the x-axis, and lift, L, is defined as the
aerodynamic force perpendicular to the freestream velocity in the z-axis. A third force, the side force, is
present within the system and acts in the y-direction. The respective definitions for side force, L, and D,
again, as mentioned earlier with respect to angle-of-attack, differ with respect to the traditional airfoil
definitions for ram air canopies.
Figure 7: Wind Tunnel Axis System
2
B. Wind Tunnel Set-Up
These tests were conducted in the South Low Speed Wind Tunnel at the United States Air Force
Academy Aeronautics Laboratory. With a test section measuring 3 feet by 3 feet by 7 feet, the tunnel was
within the required parameters for the project purpose. The open-return tunnel uses a fan in the diffuser
to generate the tunnel’s velocity and achieve speeds between 5 and 100 ft/s within the test section. Flow
quality has a turbulence intensity of less than .05% at all speeds. Flow stability over a 30 minutes test
period varies less than .5%. To ensure consistent and accurate tunnel velocities, MKS 223bd differential
pressure transducers (error of 0.15% of reading) were used to measure the total pressure in the tunnel’s
nozzle and compare it to the static pressure measured in the test section. A 1 torr transducer was used for
Flow Direction
7
the 550 cord tests, and a 10 torr transducer was used for all other tests. This change allowed for more
accurate measurements based on tested Re. A schematic of this set-up is in Figure 8.
Figure. 8: Side profiles of wind tunnel configuration.
C. Baseline
Two tests were run to determine a baseline estimate of the drag given shapes. The two different
porosity ropes were compared to a 1/8 inch diameter smooth cylinder bolted on the outside of the wind
tunnel. The drag on the cylinder was expected to be approximately 1.2, and the difference between the
expected value of the cylinder will serve as a calibration of the testing facility and equipment, and also
help determine the difference in drag, if any, of the suspension line versus a smooth surface. The second
baseline test used a 1.8 in wide, smooth, .04 in thick, flat, steel band. These tests were used to baseline the
webbing tests. Both the webbing component and the plate were secured with a clamp within the wind
tunnel. The plate provided a baseline comparison to the rope and cylinder, in addition to a comparison to
the webbing component of similar shape and size.
D. Suspension Line Shedding Test
The suspension lines were secured in the tunnel by a bracket on top of the tunnel and threaded through
a hole in the tunnel where it was secured to a load of known weight underneath the test section.
Measurements were then taken to determine the shedding frequency and momentum deficit downstream
of the rope. To analyze unsteady effects of suspension line drag due to vortex shedding, the flow
downstream from the line was tested with X-wire and single-wire constant temperature hot wire
anemometers. These two probes were mounted in the wind tunnel directly behind the line on a traverse to
move laterally (spanwise) through the flow. Specifically a TSI 1750 X-wire and a TSI single wire (model
7474) were used. Both the X-wire and the single-wire were calibrated in the wind tunnel. No calibration
data existed so calibration was completed with an open-tunnel configuration to obtain a calibration curve
for use throughout the remainder of the experiment. In addition, error data was gathered during this
calibration process.
The probe traversed across the wind tunnel spanwise at a constant height and constant 3-diameter
distance to the rear of the line (0.42 inch). Preliminary testing determined that a span of 2 inches (1 inch
either side of center) was wide enough to capture the entire wake created by the suspension lines. The
probe moved at intervals of 0.01 inches during the traverse across the wake to ensure that the increment
was small enough to show the wake of a diameter as small as 1/8 inches. A delay of three seconds
between intervals was introduced prior to measurements being taken in order to avoid the disturbances
caused by movement of the hotwire. The data was recorded at 1000 Hz for four seconds, output to
Tunnel Vision (a Mainframe data computer that is configured for the proper traverse location) which then
averaged the samples. The data acquisitions equipment used for this configuration was the Agilent
E1421B mainframe.
E. Webbing Component and Flat band
The webbing and flat plate connection required a different set-up for the wake measurement due to its
larger diameter. Due to mounting constraints, a set-up using 10 diameters downstream of the webbing
and flat plate was used, and this configuration resembled the large diameter rope testing of Jung et al.
While 30 diameters is optimal 7 for the length behind the suspension lines, the Fast Rope study has shown
that 10 diameters downstream (18 in. downstream for the flat band) still gave an accurate model of the
wake deficit 3 . Additionally, due to the larger diameter, the measurements were taken at spanwise
increments of 0.5 in for a total span of 15 inches (7.5 inches either side of center), as determined by
previous experiments to capture the full wake. Tunnel blockage was corrected for these measurements.
F. Drag Measurement
A pitot static pressure probe with 1 port was used to measure the speed of the flow. Measurements
were made at a distance of 30 line diameters downstream, a distance determined by previous studies to be
optimal (4.2 inches for this test). 3 This ensured the instruments would not experience any of the vortices
formulated directly aft of the line; instead, the flow would be more consistent, and reliable measurements
could be obtained to determine the momentum decrease of the flow. The data taken from this device
were recorded and averaged by a locally developed software program known as Tunnel Vision. The
experiment takes data 200 times at a rate of 1000 Hz, the software averages every two measurements,
thus generating 100 averaged values. Prior to the first measurement being taken, 10 seconds was given to
negate any disturbances in the flow due to movement of the equipment. Subsequent readings were
delayed 8 seconds to allow the flow in the tubes of the pressure probe to settle; this was referred to as the
dwell time.
No significant effects of twist were noted on the lines tested, therefore, the gage was placed
horizontally to traverse the width of the tunnel to take measurements in pressure variation. Testing
showed the width of the wake region to be relatively small, approximately 20 diameters, and
measurements needed only be taken in the area behind the rope, with one or two data points taken outside
the wake as a freestream velocity measurement. Thus, fine resolution in the line’s wake allowed for more
accurate and timely results of the drag to be produced. As with the webbing and flat plate tests, the data
recording was delayed 8 seconds to allow flow disturbances associated with the rake’s change in position
to subside. After all data was collected at a given tunnel velocity, the next velocity and tension weight
were modified to reflect a new flight regime. The 550 cord was tested at tensions of 10, 38, and 55
pounds which represented the loads experienced by the suspension lines of a typical G-11 canopy. After
traversing the wake of the 550 cord at the three different tensions, the velocity was increased. The 550
was tested at flow velocities of 10, 17, and 25 ft/s. Approximate Reynolds numbers, Re * , of 440, 775, and
1140 respectively were used to report the results as individual tests varied depending on atmospheric
conditions during the tests.
Similar procedures were repeated with the 1,000 lbs spectra. The only modifications were the tunnel
velocities since the spectra line, however, supports the square, ram air chute that is designed to fly
relatively fast. Thus, to determine the correct drag created by the line, it was necessary to test it at 51, 76,
and 93 ft/s. Approximate Reynolds numbers, Re * , of 3530, 5400, and 6600 respectively were used to
report the results as individual tests varied depending on atmospheric conditions during the tests. The
traverse spanned 3 inches. Table 1 summarizes the test matrix.
9
Test Component Cylinder 550 Spectra Plate Webbing
V∞ (ft/s) 20, 30, 45 10, 17, 25 51, 76, 93 17, 51 17, 51
α (deg) 90 90 90 90 90
T (lbs) N/A 10, 38, 55 10, 38, 55 10, 38, 55 10, 38, 55
G. Electrical Systems
As depicted in Figure 9, the MKS 223bd pressure transducers are connected to Agilent 34405A digital
multimeters, allowing for the reading of the transducers’ output to set the correct tunnel speed.
Figure 9: Electrical Component arrangement during momentum deficit testing 3
The data obtained from the pressure transducers was averaged and saved in a usable output format in
Excel via the Tunnel Vision software. This program operated on the Agilent E1421B mainframe. This
machine’s error is negligible in comparison to the other error sources. 5 In addition to recording and
formatting data, Tunnel Vision is capable of automating the tests. See Table 2 for a summary of the bias
and precision errors associate with each component.
Table 2: Uncertainties summary for equipment.
Device or Result Bias Error Precision Error Total Error
MKS 223D 0.15% of reading 0.1154% of reading Test dependent
Traverse 0.0001 in. Immeasurable 0.0001 in.
Diameter 0.000083 in. 0.0000391 in. 0.0000921 in.
223
IV. Results and Discussion
A typical wake profile is shown in Figure 10. Each run took approximately 20 minutes to complete.
Figure 10: Wake profile for metal rod at 45 ft/s.
Figure 11 gives an overview of all suspension line tests in addition to the calibration data for the
cylindrical rod tests and the data presented by Cantwell and Coles 6 . Qualitatively and quantitatively, the
data agree very well with previous results 4 and expected differences. Additional detail will be discussed
in the subsections for each of the parachute components.
Figure 11: Comprehensive Plot
A. System Calibration
The cylinder pressure tests were performed 10 times each at 20, 30 and 45 ft/s to compare to existing
data on the coefficient of drag for a circular smooth cylinder. Past experiments have shown values for the
coefficient of drag between .850 and .898 for a Reynolds number of approximately 5600. Figure 12 and
Table 3 show the setup and equipment configuration are validated for these tests.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
C'D
Re
Rod
550
Spectra
Velocity Re Uncertainty (%)
20 ft/s 1083 0.8956 8.13
30 ft/s 1629 0.8240 8.90
45 ft/s 2462 0.8177 8.95
Figure 12: Comparison of measured to previous experiments for metal rod.
B. 550 and Spectra
The experiment yielded results for the coefficient of drag ranging from 0.74 to 1.25 as averaged over 5
runs for each configuration. The trend shown in the T = 38 lbs and T = 55 lbs data to a possible
asymptotic value of near 1.0. The large uncertainty error during the 550 test runs (and later spectra
test runs) is likely attributed to the inaccuracy of the diameter measurements.
Table 4: Average (5) for 550 rope tests.
Re * T =10 lbs (% unc) T =38 lbs (% unc) T =55 lbs (% unc)
440 1.25 (6.53) 1.04 (7.98) 1.12 (7.39)
775 0.89 (9.49) 1.03 (8.52) 1.19 (7.40)
1140 0.74 ( (10.99) 1.02 (8.64) 0.98 (9.06)
0
0.2
0.4
0.6
0.8
1
1.2
Figure 13: 550, measured for different tensions.
The spectra line pressure tests were completed at 51, 76, and 93 ft/s for line tensions of 10, 38, and 55
lbs. For these runs, the wake curve was much smoother, with considerably less data scatter, reference
Figure 14. The increase uncertainties may be attributed to the higher velocities associated with these
tests. The spectra line showed a much lower with values ranging from 0.64 to 0.75. These results
correlate well with previous experimental data, and the progression of to a constant value at Re = 6600
indicates the dominant effect of geometry for this configuration.
Table. 5. Average (5) for Spectra rope tests.
Figure 14: Spectra, measured for different tensions.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
C'D
Re
(((Re)(Re)
5400 0.67 (12.44) 0.68 (12.33) 0.65 (13.15)
6600 0.66 (12.67) 0.65 (12.85) 0.69 (12.29)
13
Figure 15: Spectra, measured for different Re.
The results from the spectra line runs show that the drag is considerably lower due to the aerodynamic
shape of the spectra as opposed to the 550. Much of the most recent research has focused on the critical
and supercritical regions of cylindrical rods. However, in these cases, all values are in the subcritical
range and rather than the approximated value of 1.2, the coefficient of drag actually has a linear trend in
the much lower Reynolds Numbers.
C. Hotwire
Hotwire tests for computing the shedding frequency, and thus account for any additional contributions
to drag, were only completed for the suspension line tests. Figure 16 shows typical power spectrum
density results. Both sets of data indicate a peak near 350 Hz, and the most notable difference is in the
relative strength of the two spectra: maximum 550 = .345 dB and maximum spectra = .078 dB
Figure 16: Example 550 and Spectra PSDs.
No visible vibrations were seen in any of the tests, including the flat plate and webbing runs, so it was not
anticipated that the hotwire data would show any significant contributions to the drag. Indeed the overall
trends seen in the tested configurations also supported this hypothesis. When compared to the
fundamental natural frequencies for the 550 and spectra, 12 Hz and 33 Hz respectively for the tested
tensions, no synchronization was predicted. A more detailed accounting of the tests will be presented
elsewhere.
0.55
0.6
0.65
0.7
0.75
0.8
0.85
D. Flat Plate and Webbing
Similar to the cylinder runs, the flat plate pressure test was conducted to perform a baseline run to
compare to the webbing component of similar size and shape and determine the effects of the porosity of
the rope and other material factors. The flat plate was run at speeds of 17 and 76 ft/s. See Figure 16 for a
view of a typical wake behind the flat plate. The figure shows that a much wider, but still bell shaped
curve across the wake.
Figure 16: Wake profile for Flat Plate at 76 ft/s, T = 55lbs.
A small amount of twisting occurred with the flat plate testing. The twisting was not present in all test
runs and before each run, the plate was oriented perpendicular to the flow. The averaged results for the
coefficient of drag are presented in Table 6 and Figure 17. The flat plate was tested at various “tensions”
since the plate was relatively flexible as compared with the cylindrical rod used for calibrating the
suspension lines. As Re increased, the data converged to a constant value of .
Table 6: Average (5) for Flat Plate.
Re * T =10 lbs (% unc) T=38 lbs (% unc)
(((Re)(Re)
2660 1.69 (2.39) 1.69 (2.48) 1.68 (2.50)
15
Webbing Pressure Test
The webbing pressure tests were conducted at 17 and 76 ft/s to determine its performance at the
average speed for each suspension line type. Because the webbing component is used to connect the
loads on the parachute to both different rope types, it was necessary to determine its influence on the drag
during both flight regimes. See Figure 18 for a view of the typical wake behind the webbing. The
webbing wake at 17 ft/s showed a more discontinuous profile and lack of resolution near the centerline of
the webbing. was fairly smooth, especially at the higher velocities and closely resembled the wake of the
flat plate.
Fig. 18. Wake profiles for webbing at 17 ft/s and 76 ft/s.
The webbing component experienced significantly less twisting than the flat plate, likely due to the
tension weights attached to the component. See Table 7 for a comparison of the coefficient of drag for
each test condition. The data show the webbing closely matched the results of the flat plate tests. This
correlation is more apparent in Figure 19. Due to the number of configurations shown, uncertainty bars
were not included. The results also show that Reynolds number did not play as important a role in the
drag of the flat plate and webbing component at these speeds.
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
V. Conclusion
The similar results of the smooth cylinder runs to previous research validated the setup of the wind
tunnel and testing procedures. For the flight regimes usually experienced by the 550 a = 1.05 may be
used as a good approximation while for spectra a = 0.68 is appropriate. The webbing component
showed similar drag characteristics to a flat plate of the same shape, but a more detailed study with finer
spanwise spacing between test points may lead to more accuracy. However, using a = 1.65 is a good
first characterization. Specifically, these data have established an initial database to show a more detailed
analysis of the coefficient of drag at lower Reynolds numbers
A more thorough analysis of the shedding frequency should be conducted to determine if the
differences in this area account for additional drag. Past experiments in marine cable applications have
shown that in some cases, the shedding frequency can double or triple the amount of drag on the line.
This phase of testing would include a precise mass per length analysis of each component to quantify the
frequency and effect of the flexible structure in comparison to a cylinder. Additional effort should also
focus on the affect of tension on the porosity and accurate measurement of line “diameter”.
Acknowledgements
The research team would like to acknowledge the assistance provided by SSgt Church-O’Brien and
TSgt Chris Campbell who were pivotal to the project with many long hours helping complete tests.
1.5
1.55
1.6
1.65
1.7
1.75
1.8
(((Re)(Re)
2660 1.61 (2.86) 1.70 (2.58) 1.67 (2.64)
17
Throughout the project, assistance from Lt Col Tim Jung proved to be very helpful and insightful and for
that we owe him our thanks. Finally, the team is also grateful for the funding and support provided by the
Natick Soldier Research Development and Engineering Center for their support of this project.
References
1 Lingard, S., “Precision Aerial Delivery Seminar Ram-Air Parachute Design,” 13
th AIAA
Aerodynamic Decelerator Systems Technology Conference, May 1995, Clearwater Beach. 2 Jung, T., “Drag Model for Fast Rope,” Kuchera Defense Systems, Inc., United States Air Force
Academy, CO, Sep. 2007.. 3 Schlicting, H. and K. Gersten, “Boundary Layer Theory,” 8
th Revised and Enlarged Edition,
Springer-Verlag, 2003. 4 Hoerner, S., “Fluid-Dynamic Drag,” Published by Author, 1958.
5 Jung, T., Gilbert, N., Hickerson, C, Russell, J., Paul, M., “Drag Analysis of a Variety of Rope
Weaves,” AE 471 Report, May 2008. 6 Cantwell, B. and C. Coles, “An experimental study of the entrainment and transport in the
turbulent near wake of a circular cylinder,” J. Fluid Mech. (1983), vol 136, pp 321-374. 7 Antonia, R. and S. Rajagopalan, “Determination of Drag of a Circular Cylinder,” AIAA J. 28,
October 1990.