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 š 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 āvāi : τ= 14mg(eK1 -1) gρi āvāi (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 ⁄š (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