Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Development of a Parachute Deployment Model for Airdrop Simulations
Joseph Mudrak
Wyle
Dayton, OH
joseph.mudrak.ctr@us.af.mil
ABSTRACT
Appropriate trajectory modeling of airdropped, uncontrolled-parachute-decelerated payloads has presented a
challenge to the airdrop community for decades, from operators and planners to analysts and developers. A range of
approaches have become available as computers have become more portable and powerful, but there are still
significant gaps to be filled in airdrop modeling.
At the extremely computationally expensive end are techniques such as fluid-structure interaction modeling, which
can provide a detailed characterization of the physics of parachutes during their deployment. At the simpler end,
empirical ballistic approximations are still in widespread use during airdrop operations. Complicating the issue is the
nature of parachute deployment itself—an uncontrolled piece of fabric, violently unfurling in a heavily turbulent
environment, exhibits behavior which is crucial to analyzing a system’s performance but which is equally difficult to
predict.
The Precision Air Drop (PAD) modeling and simulation team at the Air Force Research Laboratory (AFRL) has
attempted to strike a balance between oversimplification and futile complexity, developing a matrix of simulation
options, each providing their own balance between complexity and resource economy. This paper discusses the issues
and motivations for the development of the current AFRL parachute deployment model and its phases and options.
This model includes two options and phases to cover the motion between egress from an aircraft and parachute
inflation, as well as four distinct options for the inflation phase. The models have been informed by and evaluated
against both video evidence and video-based position tracking, providing a layer of validation and verification. They
have added fidelity to the trajectory simulations, but they also offer many avenues through which probabilistic
simulations can be carried out. Thus, the underlying models now contain a level of detail and flexibility which allows
for reasonable answers and valuable information for the analyst.
ABOUT THE AUTHOR
Joseph Mudrak is an aeronautical engineer at Wyle, working to meet the modeling, simulation, and analysis needs
of AFRL under the Precision Air Drop project. Joseph is one of two developers of the Weather Integrated Stochastic
Simulation (WISS), an airdrop simulation owned by AFRL and centered on the analysis needs of AFRL and its fellow
airdrop stakeholders. He has been employed in this capacity since 2013. Joseph holds a B.S in Aeronautical and
Astronautical Engineering from The Ohio State University.
2016 Paper No. 16133 Page 1 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Development of a Parachute Deployment Model for Airdrop Simulations
Joseph Mudrak
Wyle
Dayton, OH
joseph.mudrak.ctr@us.af.mil
DIFFICULTIES IN THE MODELING OF AIRDROP
Airdrop is a deceptively complicated problem. On the surface, airdrop may appear to be a simple task: identify the
needs and location of a group under duress, navigate to that location, and release appropriate supplies near the party
in need. Of course, it is rarely that straightforward. Airdrop, to be clear, is a term which can be used to refer to many
different situations, all of which vary on the theme of navigating an aircraft near a target and deploying a payload in
the hopes that it will reach that target by the time it encounters terrain. Personnel airdrop refers to the operation wherein
parachutists jump from aircraft and often are able to steer toward their destination. Cargo airdrop can itself be split
into multiple dimensions. Precision cargo airdrop at its most accurate uses parafoils attached to a guidance and control
unit to steer the payload as a parachutist might. The subset discussed here, however, is totally passive.
Mass supply via uncontrolled airdrop is a frustrating task, and often can only generously be referred to as a science.
The variability of the process can be of the order of hundreds of yards. This originates from multiple sources, but
heretofore unpublished Air Force Research Laboratory (AFRL) research has suggested the error sources tend to fall
into three major groups: aircraft state, wind forecast quality, and parachute modeling.
An aircraft in airdrop configuration slows to a calibrated airspeed (CAS) in excess of 130 knots, typically unchanging
with drop altitude. Traveling just above the ground at sea level would yield a ground speed over 65 meters per second
(m/s), or nearly 220 feet per second (ft/s). For high altitude missions intended to reduce the risk of detection and attack
by adversarial forces, the low air density at altitude can push this ground speed for the same CAS over 100 m/s (330
ft/s)—and this 130-knot case only describes a low-speed scenario. Perhaps in other environments this ground speed
would still be trivial, but airdrop is often a largely manual process, subject to human variation. Airdrop operations
training can perpetuate informal and inconsistent “rules of thumb,” further increasing this variation. As a result,
standard deviations in payload release time are on the order of at least a second, so in many cases the battle over
impact location accuracy is lost before the payload even leaves the aircraft.
If the payload release problem has a silver lining, it is that it is relatively straightforward to identify and break down.
In understanding the wind field which affects the trajectory post-release, the complexity and difficulty shifts to the
other end of that scale. Wind is less discrete, and of course is invisible to the human eye and so is tougher to observe.
Even LiDAR and RADAR wind sensing devices rely on particles blown by wind to estimate its character. Its turbulent
nature leaves it theoretically daunting and computationally impractical for use in an accessible airdrop simulation.
Somewhere in the middle ground between these contributors is the parachute performance. A commonly recited
complaint is that parachutes rarely open consistently. Intangible variations in parachute packing (also a manual
process), parachute manufacture, and the effects of turbulent air on a flexible canopy-and-suspension-line system can
all affect the way a parachute deploys and inflates. In this way, deployment resembles the wind itself—chaotic, of
very limited predictability, and difficult to observe. Via tracking cameras at locations such as the U.S. Army Yuma
Proving Ground (YPG), the state of the parachute and the location of the bundle in space can be determined and
analyzed, bringing the observability of parachute deployment closer to that of payload release.
Parachute deployment, then, is a daunting but more manageable topic of study. A thorough description of the
deployment may help illustrate the depth of the analysis problem, and will introduce vocabulary for the description of
the attempts to solve the problem.
Parachute Deployment
Restrained in the aircraft, each 4-foot-by-4-foot (1.2 meters per side) payload bundle sits on steel rollers and is
equipped with a parachute packed into a small deployment bag strapped to the top surface of the bundle. Attached to
2016 Paper No. 16133 Page 2 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
the deployment bag is a cable called a static line. The other end of the static line is connected to a more substantial
cable, named the anchor cable. The anchor cable is suspended in the aircraft above the bundles and runs the length of
the cargo bay. The aircraft is flown to the designated release point at an angle of attack around 7°, which is enough
tilt to facilitate unassisted bundle rollout.
Once the tethers restraining the bundles to the aircraft have been released, the bundles slide aftward, each one dragging
its static line along the anchor cable. The bundle accelerates steadily toward the end of the cargo loading ramp and
tips over the edge, static line still attached. This is where the deployment physics begin to take effect.
Within a second after bundle tip-off, the static line pulls taut against the end of the anchor cable, breaking the straps
binding the deployment bag to the bundle. The deployment bag is held momentarily by the static line while the bundle,
still in free-fall, unreels the suspension lines and bridle of the parachute from the deployment bag. Soon the bundle,
having pulled the suspension lines taut in addition to the static line, is able to wrest free the parachute from its
deployment bag. The furled parachute then enters the freestream in its own right and is whipped behind the bundle. It
is not until this point that the parachute is able to begin inflation.
With the parachute no longer forced flat by the whipping motion, air begins to enter the canopy. This inflation happens
slowly at first, but as air enters the geometry, pressure builds within the parachute, expanding its diameter, allowing
more air to enter, which expands the diameter further until, eventually, the parachute reaches its maximum radius,
growing the drag force on the canopy as it does so. This process is necessarily turbulent due to the wake from the
bundle itself, and is very dependent on conditions following the elongation of the suspension lines. It represents the
final piece of the parachute deployment, and is the most physically dramatic part of the deployment process.
MODELING
Inflation modeling continues to receive academic attention, often in the context of discrete methods such as
computational fluid dynamics or, more recently, fluid-structure interaction modeling. These methods are invaluable
to programs which need to design decelerator systems, especially when testing opportunities are limited. They are,
however, very computationally expensive, and not suitable for a simulation which may need to quickly assess the
effects of stochastic input distributions on broader operations.
On the other end of the spectrum, current operational tools for parachute inflation modeling often rely on empirical
point-to-point approximations to model the deployment phase. While this does present a more inexpensive route in
terms of calibration and computation, it risks oversimplifying the representation of the process, and is inflexible to
changes made to the airdrop environment. The goal of the deployment simulation, then, has been to find a balance
between simple but less informative empirical modeling and resource-consuming but detailed discrete modeling.
The models and equations of motion within the Weather Integrated Stochastic Simulation (WISS) have gone through
several incarnations since their initial derivation. Because quantitative analysis throughout the development process
has been motivated by evolving issues and stakeholders’ requirements, the qualitative process will comprise the bulk
of this discussion, although data will be provided to illustrate the efficacy of the simulation.
Initial Deployment Model Incarnation
At the beginning of the effort described in this paper, the simulation was created solely to further understanding of
wind effects on airdrop impact points and so did not include a physical rollout or parachute deployment model; bundles
were effectively given an initial position and released into the atmosphere. As a first approximation to an aircraft-toground bundle simulation, a spreadsheet (Jim Warrick, Wamore, Inc., 2012) was provided which used a simple Euler
method scheme to advance the bundles through space and which assumed immediate parachute inflation.
This method was a valuable starting block, but significant disparities between it and real-world data were evident.
Using a sample of airdrop tests at YPG, analysis showed the simulated forward throw was far too short. This difference
was attributed to the immediate inflation assumption.
Multiple sources of information were considered in rectifying this issue. Data from YPG included manual selection
of timestamp data on four relevant events: exit, activation, elongation, and inflation. A decision was made to use these
same events in the deployment model. Bundle exit was associated with bundle tip-off and was apparent in testing
video. Activation was defined as the breaking of the ties between the bundle and the deployment bag. Elongation
2016 Paper No. 16133 Page 3 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
consisted of the phase between activation and the beginning of parachute inflation. Inflation was defined as beginning
at the moment the parachute began to enlarge and ending at the moment it began to show signs of oscillation.
Activation particularly affected high-altitude, low-opening (HALO) airdrop systems, which consist of two stages: a
low-drag drogue and a high-drag recovery parachute. The act of breaking the ties between the drogue parachute
deployment bag and the bundle “activated” the timer device used to release the drogue parachute and deploy the
recovery parachute. Modeling of this event was vital for analyzing full HALO trajectories.
The next event, elongation, covered the period of time between activation and the start of bundle inflation and was
considered important, but no variables appeared to correlate well with event timing. The most substantial revelation
from empirical data consisted of drogue parachutes elongating slightly more quickly (1.3 seconds compared to 1.4) at
15,000 feet (4572 meters) above mean sea level than at 10,000 (3048 meters). An empirical value of 1.4 seconds was
chosen for both parachutes.
The simulation also saw its first inflation model, described by earlier U.S. Navy research (Ludtke, 1988). This model
was based on the “filling distance” concept, an idea rooted in conservation of mass and which suggests that a parachute
expands in volume as a function of the mass of the air traveling into and through it. Such methods present an “inflation
time” as a function of the airspeed at inflation initiation.
The Ludtke model as it is used within the simulation involves four common equations and seven additional equations
to handle the special infinite-mass case. One produces a constant, K1, as a function of gravity, air density ρ, steadystate parachute volume V0, steady-state drag area cDS0, rigged mass m, steady-state parachute mouth area AM0, steadystate parachute pressurized area AS0, cloth permeability constants k and n, and a mean coefficient of pressure cp:
K1=
V0 gρi (cD S)0
cP ρ n
2mg (AM0 -AS0 k ( i ) )
2
(1)
K1 then feeds into a second equation which produces the time 𝜏 required for the parachute to open fully for the first
time (i.e. not considering unsteadiness caused by breathing or instabilities) which itself is also a function of rigged
mass, gravity, air density, and steady-state drag area, as well as the velocity magnitude at elongation ‖v‖i :
τ=
14mg(eK1 -1)
gρi ‖v‖i (cD S)0
(2)
The opening time is then adjusted as a function of initial and steady-state drag area, as well as j, a curve-fit-derived
power factor introduced by Pflanz to account for parachute types and the unique influence of their geometric porosities
on drag area growth during inflation. Ludtke’s assumption of a geometrically non-porous parachute requires a value
of 6 for j. The instantaneous drag area (cDS)i can be calculated as a function of time, steady-state drag area, the Pflanz
factor j, and the ratio η between the area of the canopy opening at line snatch and the same area at full open:
2
1 ⁄𝟑
(cD S)i = ((1-η) (ti⁄τcorr ) +η) (cD S)0
(3)
Ludtke’s research also produced specific relations for a case called “infinite-mass” inflation, where the parachute does
little work in decelerating the bundle, but still reduces its terminal velocity. This only affected the deployment of
drogue parachutes, but the phenomenon was mentioned often and so its inclusion was considered a valuable feature.
This model required the use of canopy elasticity information, which incidentally became useful as higher fidelity
elongation calculations came into use.
The principal infinite-mass equation produces a ballistic mass ratio M, which is more commonly used to aid a
parachute system design process by helping determine the maximum shock force experienced by the parachute. While
shock force is useful in these calculations, its desired purpose here is to indicate whether the parachute will undergo
an infinite-mass deployment with temporary over-inflation, or a finite-mass deployment to be capped at the steadystate drag area. The ballistic mass ratio is used to determine the threshold between finite- and infinite-mass inflation,
2016 Paper No. 16133 Page 4 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
and is a function of rigged weight, gravity, air density and velocity at line stretch, corrected finite-mass opening time,
and steady-state drag area:
M=
2mg
gρi |v|i (cD S)0 τcorr
(4)
While Ludtke’s model is more robust than a more empirical implementation and considers parachute permeability, air
density, and dynamic pressure, issues were observed. Low-weight bundles transitioning to their second parachute
frequently experienced unrealistically long inflation times on the order on tens of seconds, apparently owing to their
lower drogue descent rate. This was improved by making compromises against high-weight bundles whose inflation
times were lower to begin with and so were affected minimally by the changes.
These compromises collapsed when an alternative recovery parachute option was added to the simulation. Modeling
of this new parachute also suffered from inflation time overshoot at low weights, but was more difficult to correct.
While it was possible to force both parachutes to exist harmoniously within the simulation, it was clear that the
inflation model would need adjustments to appropriately model the full range of parachutes and bundle weights.
First Revision: Physics-Based Separation and Elongation
The addition of a physics-driven elongation model was motivated by transition elongation data, where disparities
between simulation and reality appeared at low bundle weights. It was clear that real-world recovery parachutes under
lighter bundles took longer to elongate—at odds with the empirical constant value.
In HALO operations, the recovery parachute is deployed when the drogue parachute is cut from the bundle. The
discarded drogue parachute pulls on the recovery parachute deployment bag from above, and the free-falling bundle
pulls on the recovery parachute from below. Elongation requires spatial separation between the drogue parachute and
the bundle, and because lighter bundles descend and free-fall at slower rates, elongation simply takes more time.
A general solution was found in previously published work (Haak & Hovland, 1966) which used simplified, algebraic
equations for elongation and separation. These equations treated the solution in iterative and more detailed terms,
albeit still simplified, and so were a good choice for the next step of model development:
2
L1 =√(
gt21
1
) + [Vt1 - ln(1+J1 Vt1 )]
2
J1
(5)
ρ(cD S)b
2mb+c
(6)
1
1
ln(1+Jb Vt2 )- ln(1+Jc Vt2 )
Jb
Jc
(7)
J1 =
Ls =
2
J=
ρ(cD S)
2m
(8)
L1 describes the length of the static line during activation, and Ls describes the length of the suspension lines during
elongation. Once enough time t has elapsed to eclipse the reference lengths in each part, the deployment segments are
deemed complete. Variables denoted with the subscript b refer to the bundle and c refers to the parachute canopy. The
velocity V for each phase refers to the velocity at the start of that phase.
The new elongation approach provided a convenient opportunity to overhaul parachute elongation for both phases,
and yielded a definite improvement in modeling the recovery chute deployment. While timing for drogue elongation
was well-approximated, it was obvious that certain drogue-specific phenomena, including the whipping effect, were
not being modeled, and there were concerns that the empirical solution could be invalid across different flight regimes.
2016 Paper No. 16133 Page 5 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Second Revision: Filling-Time Inflation
With elongation addressed, the inflation process was targeted for improvement. A decision was made to use a simpler
model, still based on the filling-time concept, but relying on a single per-chute empirical constant. This model was
less detailed than the Ludtke model, but was less likely to diverge from reality at the edges of the airdrop envelope.
tf =
nD0
V
(9)
In this equation, D0 refers to the constructed parachute diameter, V is the freestream velocity scalar, and n is a chutedependent, empirical constant. Older tables provide standard n values for ringslot, cross, and solid flat parachutes
(Knacke, 1992), but a formula has been presented (Potvin, 2012) based on the opening characteristics of the chute,
which was modified to make use of variables already introduced by Ludtke’s model:
n=
V0
ηAM0 D0
(10)
Potvin describes a term AM,early as the early mouth area, taking the place of AM0. AM,early can be split into two preexisting parts: the steady-state parachute mouth area and the mouth area ratio, both available from the Ludtke model.
This simpler inflation estimator removed some of the physics-driven relationships, but counterintuitively resulted in
more consistent and reliable output. Elastic over-inflation from Ludtke’s inflation model could be retained.
Third Revision: Elastic Elongation
The second major change to the elongation model involved introducing the drogue parachute whipping motion which
was missing from the simpler elongation model. This required a change from an algebraic elongation solution to one
estimated via finite differential equations representing a simplification of the standard physics. This also carried the
benefit of modeling the effect of the changing trajectory angle, which was neglected by the simpler formulation.
The drogue whipping motion was accomplished via a tension force between the parachute and the bundle. Initially a
centripetal force was used, but resulted in the parachute position drifting further from the bundle than the suspension
lines should have allowed. Another issue was that simulated elongation time frequently overshot the true data. These
issues prompted further development.
To provide a low-order estimate of the process of the elongation and stretch of the parachute lines, Hooke’s law was
applied to approximate a spring-like tension force. Conveniently, the elastic material properties originally intended
for the Ludtke inflation model were already available and could be used:
k=-
Fmax
εmax rchute/bundlemax
T=-krchute/bundle
(11)
(12)
This method required a finer simulation time-step but did not suffer from parachute drift. The centripetal tension
calculation was retained, but only to be used in the absence of parachute material data. Minor tweaks and calibration
have been carried out on this method, but the physics-based option has retained this general methodology, leaving
only it and the fully empirical method for parachute elongation.
Fourth Revision: Radial-Force Inflation
Following the early successes but limitations of Ludtke’s inflation model, interest still existed in an inflation model
which could provide insight into the effects of not only altitude and airspeed, but also finer, more parachute-specific
variables. One key assumption made by the inflation models used to this point had been that the deployment and
inflation was occurring vertically. Although later stages in multi-stage systems do inflate during vertical descent, much
of the inflation of a drogue parachute or a single-stage system occurs at an angle closer to horizontal.
Brief experimentation with a filling-distance method derived from the filling-time method showed good potential, but
indicated a need for different empirical constants compared to filling-time inflation for larger parachutes. Because of
2016 Paper No. 16133 Page 6 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
this apparent incompatibility, development of the filling-distance method has been suspended, but the model itself
remains a potential empirical alternative to a complex physics-based inflation model.
For that physics-based model, development turned to a model published by Wolf (Wolf, 1973). This model made use
of flight-tangential force, a quantity the simulation was already calculating, and radial force. This was also the first
inflation solution introduced to the simulation which required the use of differential equations for parachute radius.
The original paper states four total governing equations for flight path and canopy radius, but the simulation only
makes use of a modified version of the equation for radial growth, the final equation of the four:
2
(mci +mr )
d Rc
dt
2
=2cR qc Sc sin θ -Fx tan θ - (
dmci dmr dRc
+
)
dt
dt
dt
(13)
The subscripts c and f refer to the canopy and the forebody, or in this case the bundle, while ci refers specifically to
the portion of the canopy which has inflated. R is the inflated radius of the canopy, x and r refer to flight-tangential
and canopy-radial action, and θ represents the angle of the suspension lines from the parachute centerline. The variable
q is the dynamic pressure 1/2ρV2, and cR is a radial force coefficient found by experiment and testing.
Previous models produced an inflation time, and the drag area grew as a function scaled to that time. This meant
changes in trajectory angle or external perturbations had no effect of the inflation process. With this model, however,
a parachute’s radius became an implicit function of its bundle’s motion, and the perturbations in the environment
could adversely affect inflation quickness. The Wolf model is currently the favored inflation model by the simulation
development team, and sits alongside the Ludtke and filling-time methods as an inflation option. Unlike Ludtke’s
model, it does not support canopy elasticity in its current form. An update to this model was later published, and may
be included in a future update.
MODEL SUMMARY AND DATA
Event duration (s)
Development Example: Event Timing
It is difficult to find a single metric which effectively compares all of the different phases of parachute deployment.
Real-world velocity at parachute elongation—the start of parachute inflation—is useful, although it cannot be
described as an independent variable. This “snatch” velocity is historically linked to parachute inflation time through
the filling-distance concept, but it is itself dependent on additional variables such as bundle mass and drop altitude.
Figure 1 and Figure 2 were produced in the analysis of modeled trajectories of HALO bundles, which were the focus
of analysis through most of the simulation’s development. They represent the model state after the third revision. Data
labeled YPG was generated from observation of video from at YPG, while WISS data was generated by the simulation.
2
1.5
1
0.5
0
0
10
20
30
40
50
60
70
Bundle velocity at full elongation (m/s)
YPG Activation
YPG Elongation
YPG Inflation
WISS Activation
WISS Elongation
WISS Inflation
Figure 1. High-Altitude Drogue Parachute Deployment
2016 Paper No. 16133 Page 7 of 11
80
90
100
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Event duration (s)
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
30
35
40
45
50
Bundle velocity at full elongation (m/s)
YPG Elongation
YPG Inflation
WISS Elongation
WISS Inflation
Figure 2. Low-Opening Recovery Parachute Deployment
Treating the comparison chronologically, focus should first fall to the drogue parachute. The drogue parachute system
is displayed in Figure 1. The drogue activation model is a piece which has not been modified since its initial inclusion.
The activation event remains very straightforward—the bundle simply falls off the ramp and eventually breaks its
restraints—and the model reflects this. Small model inconsistencies are evident, however, and their sources have not
yet been identified. Mean modeling error for this event was calculated at 0.16 seconds, not negligible at the high
groundspeeds immediately following tip-off.
Elongation can account for half of the total deployment time of small parachutes. Accuracy is especially critical in
this phase, as the bundle still possesses a large portion of its initial groundspeed, and variation in event duration can
be higher than with activation. As can be seen in Figure 1, elongation time can correlate inversely with snatch velocity.
For the fully empirical elongation model, the pre-set elongation time was usually a rough average of recorded values,
which would have been around 1.37 seconds for the displayed data. This would have resulted in errors of roughly 0.2
seconds for lengthy events and -0.3 seconds for brief events, and the average error would have been 0.11 seconds.
Near the edges of the operational envelope this time error could result in a distance error on the order of tens of yards.
While in the totality of errors this contributor is relatively minor, it is worth addressing because a clear opportunity
for improvement can be observed. The newer elongation model yields a mean error of just 0.067 seconds, an
improvement of 40% from the previous iteration.
For this snatch-velocity metric, the inflation model appeared to perform well, but a small number of drops (outlined
in black for a little more clarity) appeared to force the average error higher. Without those two drops, inflation model
error would have averaged a scant 0.08 seconds, but their inclusion raises the average error to a still-helpful 0.115
seconds. Errors on the order of 0.3 seconds should not be ignored, and so work continued on a model which might
provide yet more information.
An important element of the then-current filling-time inflation model is that it is a very easy model to set up. Some of
this is illustrated in Figure 1 and the variables which were chosen. Recall that this semi-empirical inflation model only
takes in three variables at its most basic level: an empirical parameter, diameter, and snatch velocity. Effective
diameter is explicitly defined for every type of parachute, and snatch velocity can be identified via data from tracking
cameras. Ergo, the empirical parameter is the only unknown, and the filling-time theory is sound enough that good
results do tend to arise from it. Although it may not have all of the detail or precision as the Ludtke or Wolf inflation
models, it is still the quickest and easiest way to simulate inflation. This suggests that it is still the best available option
for estimating new systems with limited data, especially while the inclusion of the Wolf method continues to go
through a period of refinement.
2016 Paper No. 16133 Page 8 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Next, attention can fall to the second, recovery stage. Because activation is an instantaneous event for HALO transition
events, only the elongation and inflation need to be represented.
Simulated recovery parachute elongation was a consistent underestimation of the real-world event. This appears to be
related to some limitation of the model. (Recall that transition elongation is simulated fully physically, with the
parachutes and the bundle described separately from each other. The pre-inflation drag parameter for the recovery
parachute was reduced to the unrealistic value of 0, and the real-world durations still could not be obtained.) The result
is an average elongation error of 0.22 seconds; however, using an empirical mean of 1.30 seconds would have still
resulted in an average error of 0.26 seconds. This indicates that while the physics-based elongation model may be
encountering its limits, it has still maintained or improved the accuracy of the simulated event.
It may be noted that lower snatch velocities correspond to longer elongation times in both reality and in the simulation.
Because transition events happen around the same altitude for a given location, snatch velocity tends to be a function
of only bundle mass. The physical estimation of this phenomenon provides the analyst with better awareness of the
variation and its causes than a single empirical value might. In this sense, although the mean error for the prior data is
not significantly improved, the model has better predictive ability.
Recovery parachute inflation will be the last event in the simulation. Recovery parachute inflation, like drogue
parachute inflation, matched well with reality, with a mean error below 0.08 seconds. As with the drogue parachute,
the success of the inflation prediction is due in large part to the simplicity of the process of setting up and calibrating
a filling-time inflation model.
Development Example: Trajectory Data
Since these findings, other, single-stage parachute systems have been modeled effectively with this simulation as well.
For these comparisons, event timing was not made available, forcing comparisons against recorded position data
instead of parachute state information. Table 1 through Table 4 show the accuracy of the simulation after the third
major revision compared to the accuracy in its current fourth-revision state, calibrated and with better outlier detection
and removal. Throw and fall are convenient metrics of trajectory model accuracy, splitting the deployment into vertical
and horizontal components. The parachutes are the G-12E model recovery parachute, the 26-foot-diameter ringslot
(26’ RS) parachute, and the LCADS-LV (low-cost aerial delivery system, low-velocity) and LCADS-HV (highvelocity) cruciform systems.
Table 1. Forward Throw Error, Pre-Fourth-Revision
Parachute
G-12E
26' RS
LCADS-LV
LCADS-HV
5 seconds
10 seconds
15 seconds
Average Delta (m)
18
-14
3
9
Average Delta (m)
18
-17
22
18
Average Delta (m)
14
-17
36
30
Table 2. Forward Throw Error, Post-Fourth-Revision
Parachute
G-12E
26' RS
LCADS-LV
LCADS-HV
2016 Paper No. 16133 Page 9 of 11
5 seconds
Average Delta (m)
0
-3
5
1
10 seconds
Average Delta (m)
-1
-2
12
6
15 seconds
Average Delta (m)
-1
-2
20
11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
Table 3. Fall Error, Pre-Fourth-Revision
Parachute
G-12E
26' RS
LCADS-LV
LCADS-HV
5 seconds
Average Delta (m)
-31
6
-31
35
10 seconds
Average Delta (m)
-33
-2
-39
30
15 seconds
Average Delta (m)
-31
-4
-34
47
Table 4. Fall Error, Post-Fourth-Revision
G-12E
26' RS
LCADS-LV
5 seconds
Average Delta (m)
0
1
1
10 seconds
Average Delta (m)
-1
-1
3
15 seconds
Average Delta (m)
-1
-1
4
LCADS-HV
-1
0
0
Parachute
First, a disclaimer is necessary. It must be made clear that this is not a fair, “apples-to-apples” comparison between
simulation revisions. Improvements in data post-processing have made it easier to calibrate the models. In addition,
the statistics for Table 2 and Table 4 are calculated with outliers and aberrations automatically removed. These appear
to be legitimate outliers in most cases, but the previous data in Table 1 and Table 3 did not have this luxury.
Clearly, the LCADS-LV model warrants additional improvement, especially in comparison to the other parachutes
studied here. Those other simulated parachutes, however, perform very well on average. There is still strong variation
in each of these parachutes, but the ability to approach the mean displacement of each parachute will in time allow the
analysts to accurately determine the variability in the input parameters to the models.
Model Options
Although the relative merits of each method have been discussed in some detail throughout this discussion, there is
value in explicitly summarizing them and their benefits and drawbacks.
Elongation is served by two models, an empirical option and a physics-based one. The empirical option takes a single
input for elongation time, while the physics-driven option is affected by a multitude of variables, most of which are
parachute-specific, static, and pre-determined. The physics-based option is affected by parachute diameter, suspension
line length, parachute weight, bundle weight, the drag area of the packed parachute, airspeed and air density.
The empirical option is best chosen when little is known about the parachute, but elongation events have been observed
from which to derive a representative average event duration, the single input to the model. The physics-based option
is more sensitive to more variables, and is ideally chosen when the physical parameters of the parachute can be
estimated with some accuracy. The elongation performance of such a well-defined system can then be approximated
simply by adjusting the packed parachute drag area parameter.
Inflation estimation is a more difficult process. This is served by four models. The simplest is the filling-time model,
a function of parachute geometry, line-snatch airspeed, and an empirical input. The simple filling-distance model is
used similarly, but has not been explored in depth. An extension to this theory is available by way of the Ludtke
method, additionally a function of parachute permeability, initial opening conditions, and air density. While all three
of these options compute an inflation time a priori the Wolf model computes inflation as it occurs. The Wolf model
avoids explicit use of parachute permeability but does include added-mass coefficients, a radial force coefficient, and
use of physical parameters such as parachute canopy weight and line length.
2016 Paper No. 16133 Page 10 of 11
Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2016
The filling-time and filling-distance methods are possibly the most reliable and straightforward in the simulation,
although the two are not currently compatible with each other. The filling-distance method requires knowledge of the
path taken by the parachute, while the filling-time method requires only a timer. It may be shown at a later date that
the filling-distance method is the better method for predicting performance in novel flight regimes, but the minimal
data requirements of the filling-time method make it a more preferable option, particularly for systems with little
available test data.
If canopy fabric permeability numbers are available and data is available for numerous drop conditions, the Ludtke
model can be appropriate and informative for systems with medium-to-high descent rates. Low-weight, high-drag
systems with descent rates below around 10 meters per second may not be simulated as accurately. If enough
information is available to the analyst, including not only nominal parachute construction data but also sufficient
inflation timing and trajectory data, the Wolf model appears to consider the greatest number of variables, and should
be the highest fidelity inflation model in the simulation.
CONCLUSION
Identifying and minimizing variability is the key to airdrop. Variability will always exist and will always play a role
in airdrop operations. In addition, aircrews must trust their flight-management or mission-planning systems to provide
them accurate information. They are, by instruction, reliant on this software to know where to release their cargo and
to understand the risks—both to themselves and to receiving parties—associated with a mission. It is vitally necessary
that variability be appropriately modeled, and this requires that the processes themselves be appropriately modeled.
Operational software is rigidly constrained according to the computational limitations inherent in the operational
airdrop environment. Onboard software must perform quickly and its development must be tightly controlled. Outside
the operational realm, however, the opportunity exists to continuously develop alternate, higher-fidelity models which
provide better approximations of real world data. If improvements are indeed discovered, insight gained from them
can in turn improve the operational software. This insight can take the form of updates to the empirical inputs to the
software, or it may even include some form of the models. Thus, the simulation is not simply an extended thought
exercise, but rather an alternate means to the end of improving airdrop operations.
It is clear from the perspective of the analysts that the additions and modifications to the airdrop model have resulted
in a more reliable, higher-fidelity simulation, without resorting to computationally expensive methods. The models
have been adjusted and added in direct response to the data and to the unique requirements of the project, and the
result is a simulation which can provide extensive insight at a sliver of the cost of live testing.
ACKNOWLEDGEMENTS
Thanks are owed to the Air Force Research Laboratory, which has supported this effort as part of the Precision Airdrop
program. Additional thanks go to Amanda Cinnamon of Dayton Analytics, the architect of the WISS airdrop
simulation which houses the models discussed in this paper.
REFERENCES
Haak, E. L., & Hovland, R. V. (1966). Calvulated Values of Transient and Steady State Performance Characteristics
of Man-Carrying, Cargo, and Extraction Parachutes. Wright-Patterson Air Force Base, OH: Air Force Flight
Dynamics Laboratory.
Jim Warrick, Wamore, Inc. (2012, May 18). Ideal CARP Enabled by WGRS and Variable Drogue Fall. Phoenix, AZ,
USA.
Knacke, T. W. (1992). Parachute Recovery Systems Design Manual. Santa Barbara, CA: Para Publishing.
Ludtke, W. P. (1988). Observations on the Inflation Time and Inflation Distance of Parachutes. Naval Surface Warfare
Center, Underwater Systems Department.
Potvin, J. (2012). The Science and Engineering of Parachute Inflation II: Estimators & MI-theorem. H. G. Heinrich
Parachute Systems Short Course.
Wolf, D. (1973). A Simplified Dynamic Model of Parachute Inflation. AIAA Aerodynamic Decelerator Systems
Conference.
2016 Paper No. 16133 Page 11 of 11