Design of Shape-Transforming Canopies for Parachutes

Transcription

1 Design of Shape-Transforming Canopies for Parachutes Amanda L. Pollack 1, Jeffrey S. Moffett, Kyle H. Miller 3 and Casey M. Rogan 4 Worcester Polytechnic Institute, Worcester, Massachusetts, Design of a single-parachute cargo delivery system that can significantly alter its glide slope and descent characteristics via mid-flight shape transformation can reduce current costs and simplify cargo drops. Current systems use multiple canopies to deliver cargo to a predetermined drop zone. Two design concepts were chosen for review based on given constraints and tested through computer simulation and real-world experiments. Developing two parallel transformation concepts has permitted comparison of key performance parameters. In addition to the canopies, a servo-based remote-controlled command system was designed to initiate the transformation. Current tests show that, with further study and research, a single-parachute cargo delivery system could be a viable alternative to the systems currently in use. Nomenclature AGL = above ground level C D = drag coefficient C L = lift coefficient C r = resultant force coefficient CAD = computer-aided design D = drag force g = gravitational acceleration GPS = global positioning system k = 1 air resistance constant ( k = ρs ocd ) L/D = lift-to-drag, glide ratio m = total mass of the system ODE = ordinary differential equation Re = Reynolds number S o = total fabric surface area t = time V = descent velocity V t = trajectory velocity W = total weight of the system WPI = Worcester Polytechnic Institute µ = kinematic viscosity of air ρ = density of air I. Introduction THIS project endeavors to design a viable parachute cargo delivery system with the ability to significantly alter its glide slope and descent characteristics using a mid-air canopy transformation. Systems currently in use, illustrated in Fig. 1, typically employ two separate parachute canopies, the first being a high lift-to-drag ratio (L/D) parafoil that enables the cargo system to steer itself to a predetermined drop zone using GPS. High L/D 1 Student, Aerospace Engineering, WPI Box 399, 100 Institute Rd., Worcester, MA, 01609, Student member. Student, Aerospace Engineering, WPI Box 093, 100 Institute Rd., Worcester, MA, 01609, Student member. 3 Student, Aerospace Engineering, WPI Box 075, 100 Institute Rd., Worcester, MA, 01609, Student member. 4 Student, Aerospace Engineering, WPI Box 549, 100 Institute Rd., Worcester, MA, 01609, Student member. 1

2 also translates to a shallow glide slope, permitting cargo to be deployed many miles from the chosen target, ideally out of range of enemy weapons. After the parafoil approaches its target, a second parachute, usually a round canopy with a low L/D, is deployed while the first deflates. This canopy allows the cargo to descend gently to the ground. Our goal has been to devise a single parachute canopy that could replace and reduce the cost of these current systems. After inventing and reviewing eleven unique concepts for how such a transformation could be undertaken, we selected the two most promising design concepts and sized them to the payload design constraint we had been issued, a maximum cargo weight of five pounds. A five pound payload would be useful in surveillance and reconnaissance, especially in tracking enemy movements. Developing two transformation concepts in parallel has permitted the comparison of canopy flight and performance characteristics, to aid in the ultimate selection of the best design. In addition to our own innovations to permit transformation, canopy design and sizing were based on a literature review of earlier work on parachute design. 1 Two working parachute canopies have been constructed from porous and non-porous rip-stop nylon parachute fabric. Both canopies have been tested in their gliding and vertical descent modes, using high windows in WPI campus buildings as a launch point, and an open wind tunnel made from an adapted industrial fan. Closed wind tunnel testing has also been conducted with a force balance to experimentally determine the drag coefficients of certain canopy designs. A servo-based remote-controlled transformation system has been designed, enabling both canopies to transform on command during testing. The system can reliably effect a major canopy transformation with only a small action at the location of the suspended payload, and thus offers a significant advantage in simplicity and repeatability of operation. The U.S. Army Soldier Systems Center, in Natick, Massachusetts, has provided literature, materials, and funding for this project. Numerous other projects involving parachutes have also been completed at Worcester Polytechnic Institute in conjunction with the Center. Our project is a continuation of this past work, and we have integrated lessons learned into our design. II. Current Systems and Inherent Differences Most modern parachute cargo drop systems have several common features, as illustrated in Fig. 1. After a brief period of freefall, most systems typically first deploy a high-l/d decelerator, the most common being a gliding parafoil canopy. This canopy is often deployed several miles from the designated target. The decelerator is steered to this predetermined point by an on-board guidance control system, which controls actuators and manipulates control lines. As the system nears its target, a high-drag decelerator canopy is deployed, causing the gliding canopy to deflate. The high-drag decelerator then gently lands the cargo at the target. Unfortunately, most cargo deployment systems that operate in this manner are complicated and costly, a fact compounded by an often hurried removal of the cargo on the ground, with little regard to the canopy. Our transforming system differs from standard modern parachute systems in many respects. One key difference is a fundamental simplification of the system. With fewer components to fail, our transforming decelerator should be more reliable, and because canopy fabric from the glide mode is reused in the vertical descent mode, its material costs are also less. Our system will still have the same advantages of a high-glide-to-high-drag descent profile, and full-size versions will be GPSsteerable. Two transitioning canopies of our own design are currently being studied in this project. One consists of a high-glide sailwing that transforms into a high-drag cross parachute, and the other is a parafoil that transforms into a round parachute. Due to the inherent differences in the high-glide portion of the design, the sailwing is rated for one pound Figure 1. Simple schematic of the various stages of while the parafoil is rated for five pounds. current cargo drop systems.

3 III. Alternative Design Concepts As there are no existing examples of a single-canopy parachute system able to transform in the manner required, several weeks were spent inventing and comparing possible methods to effect such a transformation. Early design concepts, illustrated in Fig., examined different ways in which spare fabric could be stored. Due to the way parachutes function, significantly more fabric is required to achieve the same descent velocity in vertical descent as in glide mode, so fabric storage is a requirement. A second round of invention considered a range of spinning designs, which would descend to the ground while rotating over the target to bleed altitude. However, their application would be limited to small payloads (i.e., spinning is not a desirable descent mode for humans nor any other large or unwieldy payload) and the requirement of a rigid frame (as envisioned) led to their quick dismissal from serious consideration. Numerous other design concepts were considered as well. Dismissed concepts are illustrated in Fig. 3. As design iterations progressed, more realistic concepts were considered. In fact, one design, the bottom-most in Fig. 3, was almost identical to a real-world system already in use, despite being devised by this Figure. Theoretical fabric storage methods. group independently. Finally, the consensus was reached that, rather than try to "reinvent the parachute," it would be more sensible to adapt two functional, standard canopies into a single one that could transform. Many combinations of compatible gliding and vertical-descent designs were considered, and two final design concepts were settled on, as illustrated in Fig. 4. The first, in Fig. 4a, transforms from a high-l/d parafoil, one of the best and most popular gliding canopies available today, to a simple round parachute, which is one of the best vertical-descent canopies. 1 The parafoil is an Figure 3. Dismissed design concepts. Rotating designs are on row 1, with parafoil-based designs on rows and 3. 3

4 airfoil-like inflatable canopy (hence its name), requiring some forward velocity to take its shape and fly as intended. The round parachute is a much larger canopy, requiring the storage of large amounts of fabric prior to transformation. Of the two final design concepts chosen, this one is heavier, requiring more fabric for the double-surfaced parafoil, and a significant amount of posttransformation canopy fabric as well. The second final design concept, shown in Fig. 4b, incorporates a Barish sailwing3 and a cross parachute. Both are poorer performers than their counterparts in the first design, but there are nonetheless some advantages to this design. The sailwing is a single-surface canopy, requiring less fabric, and all of the sailwing's surface area is reused in the post-transformation mode. As a result, this system is lighter and would be theoretically less expensive. Transformation is accomplished by unrolling the two arms of the cross parachute from under the leading and trailing edges of the sailwing. a) b) Figure 4. Selected transforming design concepts. IV. Canopy Transformation Mechanism Several design iterations based upon initial fabric storage concepts shown in Fig. produced a reliable method for initiating transformation. Figure 5 illustrates the final version of this design. When the grey servo disk rotates, the servomechanism and attached payload will drop downward. It is predicted that this force, transferred to the overhead canopy with auxiliary lines, will be sufficient to separate magnets holding rolled-up post-transformation fabric in place, effecting a reliable transformation. The servomechanism support bracket and control disk are made of ABS plastic and were produced using a Dimension SST 100es 3D printer in-house at Worcester Polytechnic Institute. Figure 6 shows CAD renderings of the completed servo base and control disk, made in PTC ProEngineer. Figure 5. Illustration of servo mechanism. Figure 6. CAD renderings of servo base and disk. 4

5 Transformation will be triggered using a two-channel remote control transmitter/receiver/servo system. Because it is outside the scope of this project, no current plans exist to monitor our canopies' flights quantitatively, but several still and video cameras are used to capture images during drop tests, and data can be gleaned from these visual records. A final test, wherein each system will be dropped at 400 feet above ground level (AGL) from a Black Hawk helicopter only once, is currently being planned. For this crucial test, many checks of the transformation mechanism's functionality will be conducted prior to the actual event. V. Parachute Sizing and Simulation Parachute behavior is governed by a few simple equations. 1 In steady, vertical descent (i.e., post-transformation mode), drag force can be determined from Eq. (1). 1 D = ρv CDSo (1) D is the drag force (and consequently the weight of the payload), ρ is the density of air, V is the descent velocity, C D is the parachute's experimentally determined drag coefficient, and S o is the canopy's total fabric surface area. This equation allowed us to size our post-transformation canopies. The round parachute was sized at 1.6 m, while the cross parachute had an area of 0.73 m. In gliding mode, a key parameter is the "resultant" force coefficient, given in Eq. (). r D L C = C + C () Lift and drag being related by known L/D ratios for each gliding canopy 3, C r was computed as 0.46 for the parafoil and 1.10 for the sailwing. Eq. (3) permits the calculation of the gliding canopies' trajectory velocity, V t. V t W 1 = (3) S ρ C o r In Eq. (3), W is the total weight of the system. With design constraints considered and geometric properties of the canopies known, the total surface area, S o, of each gliding canopy could be computed. For the parafoil S o = 1.34 m, and for the sailwing, m. The known geometry of each system was then used to construct functional models of each parachute from real porous and non-porous canopy fabric. The descending motion of the canopies has also been examined using an ordinary differential equation (ODE), m & y = mg + ky& (4) where m is the total mass of the parachute and payload, g is the acceleration of gravity, k is a constant relating to the 1 force of air resistance ( k = ρs ocd ), and y and its derivatives refer to motion in the vertical axis only. 4 Transforming canopies have three descent modes: free-fall (phase I), glide (phase II), and vertical descent (phase III). Each mode is governed by the same non-linear differential equation, Eq. (4), the only difference between them being the value of the air resistance coefficient, k. Exact solutions to this ODE were obtained using the software package Maple, and the expressions for canopy altitude and velocity were, respectively: 5

6 (5) The input values listed in Table I were used in applying the differential equation. Some approximations have been made: the free-falling, unopened parachute is approximated as a smooth sphere 30 centimeters in diameter, and all drag coefficients are based on historical literature, not experiments at WPI (except the cross parachute's, which was measured during wind tunnel experiments). Solutions to this ODE can be used to determine a number of properties of transforming parachute systems, as will be seen below. The theoretical terminal velocities for each mode can be determined by examining the value of v(t) as t, yielding the values in Table II. Discontinuities exist when a parachute transforms from one mode to another. These can be reconciled by setting the new mode's conditions at the time of transformation to the old mode's final values at that same time. With this theory in place, the systems' expected behavior can be modeled. In particular, one can examine our planned drop test from a Black Hawk helicopter. Each parachute will be dropped from roughly 400 feet above ground level (AGL), and to maximize the time the canopy is inflated, we assume, based on drop test observations, that the system spends seconds in freefall before the gliding canopy deploys. After seconds of freefall from 400 feet AGL, both systems will have a descent velocity of roughly 18 m/s and will be 340 feet A.G.L. Assuming transformations occur instantaneously, the time to glide to 100 feet AGL can be found, at which point the transformation to vertical descent mode will be triggered. Table III contains the times each canopy must spend in gliding mode before transforming to vertical descent mode, and the predicted time at which it will touch down. Table I: ODE parameter input values mass m 3 lb (1.4 kg) gravitational acceleration g 9.81 m/s Air resistance constants: free-fall k f 0.01 sailwing k s 0.6 parafoil k p 0.36 cross parachute k c 0.5 round parachute k r 0.8 Table II: Theoretical terminal descent velocities Free-fall 35.7 m/s 80 mph Sailwing glide 7.0 m/s 16 mph Parafoil glide 5.9 m/s 13 mph Cross parachute 7.1 m/s 16 mph Round parachute 4.0 m/s 9 mph Table III: Gliding times in seconds Sailwing 11.9 Parafoil Glide 13.8 Cross parachute 16. Round parachute 1.3 6

7 Figure 7. Predicted descent velocity as a function of time for each design. From Table II and Fig. 7, one notices that the parafoil/round parachute system has a lower predicted impact velocity, and that it experiences a more significant difference in its descent velocity after transformation. The sailwing/cross parachute system's descent velocity actually increases slightly after transformation, an undesirable condition resulting from the cross parachute's relative poor performance compared to the round parachute, and a reflection of compromises we had to make in the design of a functional transforming system. The parafoil, however, reduces its descent velocity by 33% after transforming to the round parachute. Further insight can be gained by examining the parachutes' motion in two dimensions, as illustrated in Fig. 8. It is assumed that each system is thrown clear of the helicopter horizontally at 10 m/s and that the system s horizontal velocity is correlated to its vertical velocity using the designed L/D in the glide phase. Removing the effects of gravity, the same differential equation, Eq. (4), can be used to determine how the systems' horizontal motion decays during free-fall and vertical descent modes. As illustrated in Fig. 8, for a given drop altitude, the parafoil/round parachute system is predicted to glide 43% farther than the sailwing/cross parachute system. This is largely due to the parafoil's higher L/D ratio. Figure 8. Altitude as a function of horizontal distance travelled. 7

8 VI. Wind Tunnel Testing To ensure that an historically determined CD for our cross parachute was accurate, the parachute was placed in WPI's closed circuit wind tunnel for testing. The wind tunnel has a ft x ft x 10 ft test section, a contraction ratio of 6:1, and a maximum speed of 55 m/s. The force balance system used was an Aerolab Sting Balance, with a maximum axial force load rating of 10 lbf, and a measurement resolution of 0.01 lb. The force balance was set up facing the oncoming wind with the parachute trailing behind, as illustrated in Fig. 9. This was done in order to obtain positive drag force readings. The opened parachute had a cross-sectional area of 0.84 ft, which gave our experiment a blockage ratio of 1%. The ideal value for blockage is less than 10%, but practical blockage values often range above this number in parachute experiments.5 The parachute inflated mid-experiment can be seen in Fig. 10. The parachute's measured CD varied with increasing wind speed. Several factors accounted for this. The cross parachute did not fully inflate until the air velocity reached 4.9 m/s, and the parachute exhibited some tendencies to bounce off the bottom of the wind tunnel test section after fully inflating. The parachute also showed some tendency to oscillate vertically about its center point. This behavior ceased when the air velocity reached 7.3 m/s. After the drag-reducing oscillation ceased, CD could be accurately measured. A plot of CD as a function of air velocity can be seen in Fig. 11. Figure 9. Diagram of cross parachute on force balance in wind tunnel. Figure 10. Testing the cross parachute in WPI's closed-circuit wind tunnel. Once the air velocity for the parachute reached 6.4 m/s (corresponding to a Reynolds number, based on parachute diameter, of Re = 1.1 x 105), CD values started to plateau, finally stabilizing around V = 8. m/s (Re = 1.4 x 105). Taking the average of the values on the plateau, we calculated a CD of for our cross parachute, which is slightly lower than the lowest "historical" value of 0.6 as given in Ref. 1. The model parachute we tested in the wind tunnel had a total surface area of 0.31 m and an inflated diameter of 0.8 m. The convention devised for parachute engineering in Ref. 1 is to use the total surface area of the parachute (So) in calculating the coefficient of drag. For parachutes at terminal velocity, the descent velocity is given by W=D= 1 V So C D (6) where W, the weight of the system, is equal to D, the drag produced by the parachute, in steady descent. Using this equation in combination with the principle of Reynolds number similarity, we were able to compare the measured descent velocity of the model cross parachute and the predicted descent velocity of the larger prototype sailwing (post-transformation) as a function of payload weight, as seen in Fig. 1. Reynolds number is defined as Re = VD µ where µ is the kinematic viscosity of air. 8 (7)

9 Figure 11. Drag coefficient for model cross parachute as a function of air velocity and Reynolds number. Figure 1. Graph of descent velocity as a function of payload weight for model cross parachute and fullsized prototype sailwing (post-transformation). 9

10 For parachutes, it is acceptable to equate the Reynolds numbers of models and prototypes in order to predict the behavior of the full-sized parachute. For the sailwing in post-transformation mode, the inflated diameter was m (surface area S o = 0.73 m ). As shown in Fig. 1, for a given payload weight, the transformed sailwing is predicted to descend considerably more slowly than the model cross parachute illustrated in Figs. 9 and 10, because its increased surface area produces more drag. VII. Expected Results Preliminary testing has revealed both qualitative and quantitative results pertaining to our canopy designs. First, a generally good agreement between theory and experimental behavior has been observed to date. Drop testing experiments were conducted to determine the descent characteristics of the model cross parachute, and to compare its real-world performance to that predicted by theory. The cross parachute had an area of 48 in (0.311 m ), which would give a predicted descent velocity, with a payload of 1.3 lb (5.8 N) and drag coefficient as determined in the wind tunnel, of 7.3 m/s (3 ft/s) by way of Eq. (1). Drop tests for the cross parachute have shown that descent velocities with different payload weights have reasonably corresponded to predicted values, with descent velocities of to 5 ft/s with a 1.3-lb payload. Figure 13 compares theory to observed results, while Fig. 14a shows an experimental drop test being conducted.other testing has been done using a large industrial fan and cardboard baffle to control flow dispersion. Results from these tests have been purely qualitative, but the fan flow of relatively constant velocity has permitted the setting of line lengths and other significant aspects of the canopies' configuration that would be difficult to accomplish otherwise. Figures 14b and 14c show the pre-transformation parafoil and sailwing in this fan flow, while Fig. 14d shows the posttransformation parafoil (round parachute) inflated over the fan. A third type of testing has occurred in a windy area of the WPI campus, where the flow, while not strictly of constant velocity, was much more steady than that from the industrial fan. Testing of this variety mostly permitted the observation of round/cross parachute behavior in the final vertical-descent mode. Figure 14e shows the sailwing, in post-transformation mode as a cross parachute, in this outdoor flow. The final planned test for our systems will be a drop from approximately 400 feet AGL. Both systems will be dropped from a UH-60 Black Hawk helicopter, providing the opportunity for an assessment of each system's flight characteristics in conditions closely approximating the canopies' real-world applications. Due to logistic and safety concerns, weight will be added to each system to increase inertia and prevent interference with helicopter rotor blades. Causing a more rapid descent in both canopy modes, added weight will also have the benefit of reducing the potential landing area on the ground. Our work to date indicates that, with further research and testing, a cost-effective single-canopy cargo drop system could replace current cargo drop systems. Further testing with larger models, ideally constructed by professional parachute-makers, is recommended. Figure 13. Descent velocity, predicted and measured, as a function of payload weight. 10

11 a) b) d) c) e) Figure 14. Experimental canopy testing on the WPI campus. a) Drop test of small cross parachute. b) Fan test of parafoil. c) Fan test of sailwing. d) Fan test of post-transformation parafoil (round parachute). e) Outdoor wind test of post-transformation sailwing (cross parachute). Acknowledgments We would like to thank Professor David Olinger for serving as faculty advisor to the project. We also wish to thank Justin Riley at the U.S. Army Soldier Systems Center for his advice, guidance, and support throughout this project. The project has been partially funded by the U.S. Army Soldier Systems Center in Natick, Massachusetts. References 1 Knacke, Theo W., Parachute Recovery Systems Design Manual, Para Publishing, California, 199. Screamer Precision Cargo Delivery System Parachute, Strong Enterprises, [Cited 6 February 009]. Orlando, 006, URL: 3 Mort, K. W. and Weiberg, J. A., "Wind-tunnel tests of a series of parachutes designed for controllable gliding flight," NASA-TN-D-3960, Meade, Douglas B., "ODE Models for the Parachute Problem," SIAM Review, Vol 40., June 1998, pp Forostoski, M. F., Riley, J. G., Vaillancourt, V., and Wilfong, J. J., "Investigation of Variable-Glide Parafoils," Worcester Polytechnic Institute, Proj. ME-HJ-0501, Worcester, MA,