U.S. Air Force T&E Days 2009 10-12 February 2009, Albuquerque, New Mexico AIAA 2009-1721 Evaluation of the Drag Reduction Potential and Static Stability Changes of C-130 Aft Body Strakes Heather G. Pinsky 1 and Matthew C. Gray 2, Matthew D. Welch 3 and Dr. Thomas R. Yechout 4 United States Air Force Academy, Colorado Spring, CO, 80840 For the past several years, Lockheed Martin and the United States Air Force Academy have been investigating the drag reduction potential for different variants of the C-130. This investigation was the fourth and final phase of the effort to maximize the drag reduction potential through aft body modifications to the C-130. This phase focused on two objectives involving a beavertail strake modification on the aft body: investigate the drag reduction potential through a representative range of C-130 deck angles, and analyze and define the longitudinal, lateral, and directional static stability implications of the beavertail strake modification. A significant drag reduction potential of 12 drag counts was found for a deck angle of 1.5 degrees which correlated well with results from previous phases. An increase in drag was found at deck angles greater than 4 degrees, but this should not be a concern since a typical C-130 mission spends very little time at these deck angles. The static stability evaluation showed that the addition of beavertail strakes generally increases both longitudinal and directional stability while lateral stability is relatively unchanged. Trim angle changes were identified which will require additional trailing edge up elevator deflection. The addition of C-130 aft body strakes was expected to increase mission radius by up to 18 NM, or loiter time by up to 6 minutes, or result in an overall fuel savings of up to 506 pounds per 6 hour mission. This was projected to an overall fuel savings of approximately 35.5 million pounds per year for the C-130 fleet. It is recommended that the flow characteristics that effect directional stability at a deck angle of 3.7 degrees be investigated since a decrease in directional stability was found at this one condition. This effort was funded by Lockheed Martin Corporation (Marietta). Nomenclature List α = Deck Angle, deg C n = Yawing Moment Coefficient AFSOC = Air Force Special Operations Command ρ = Density, slugs/ft 2 β = Sideslip Angle, deg S = Wing Reference Area, ft 2 b = Moment Arm, in/ft V = Velocity, knots or ft/s C D = Drag Coefficient USAFA = United States Air Force Academy C l = Rolling Moment Coefficient Y = Side Force, lbs C m = Pitching Moment Coefficient I. Introduction he Lockheed Martin C-130 (Fig. 1) is one of the most versatile aircraft on the United States Air Force s flight T lines. This versatility and range of missions has led to the development of variants to the C-130, many of which the Air Force Special Operations Command (AFSOC) employs. The mission requirements of the AC-130 gunship and EC-130 Commando Solo have led to several United States Air Force Academy Department of Aeronautics (USAFA/DFAN) programs which conducted drag reduction studies. One aspect of these programs was mitigation of the vortex characteristics of the airflow behind the aft fuselage. Lockheed Martin first tasked a study 1 Cadet, Department of Aeronautics, PO Box 3549, Student 2 Cadet, Department of Aeronautics, PO Box 4237, Student 3 Cadet, Department of Aeronautics, PO Box 2264, Student 4 Professor, Department of Aeronautics, DFAN, USAFA, CO, Associate Fellow 1 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
of drag reduction methods that could be employed on the aft fuselage of AFSOC C-130 aircraft in June 2005. The aft cargo door area is a source of drag for the C-130 due to vortices that form in this area and associated flow separation. The transport and airdrop mission of the C-130 requires full use of the cargo door whereas the AC-130 and EC-130 missions generally do not involve the aft cargo door. Therefore, the first two phases of research focused on drag reduction methods to improve AFSOC mission capability with different design changes to the aft cargo door area. Phase I 1 of this research focused on evaluating four drag reduction methods and concluded that aft body fairings and beavertail strakes were the most appropriate options. Phase II 2 extensively studied combinations and different configurations of these two approaches and found that the addition of the beavertail strakes was the best option since they could be applied to the entire C-130 fleet and not just AFSOC aircraft. The beavertail strakes, presented in Fig. 2, are thin fences located vertically under the horizontal tail outside of the cargo door. Phase III 3 analyzed these strakes by evaluating the loads placed on them by the vortices forming aft of the fuselage and also looked at various geometric blending techniques. Through use of a water tunnel, dye injection provided a visual understanding of the strakes influence on the vortex structure. Building on these developments, this phase of study (Phase IV) identified the drag reduction potential of the beavertail strakes throughout the available C-130 deck angle range since Phases I-III had focused on the max endurance deck angle of 1.5 degrees. In addition, the longitudinal, lateral, and directional static stability implementation of the strakes were evaluated. BEAVERTAIL STRAKES Figure 1. Generic Lockheed Martin C-130 2 Figure 2. Beavertail Strake on C-130 Model 2 II. Theory The effects of the beavertail stakes on drag reduction potential, longitudinal and lateral-directional stability were determined by wind tunnel testing for the representative range of deck angles and sideslip angles for the C-130 through a comparative analysis between the baseline and strake configuration. The drag reduction was quantified using drag counts where a drag count is defined as 0.0001 of the parasite drag coefficient ( ). Therefore, a C D0 difference of 0.0003 in was defined as 3 drag counts. Three specific stability derivatives were of interest. The longitudinal stability derivative, C mα, represents the change in the pitching moment coefficient about the y body axis with respect to a change in angle of attack 4. The aircraft must have a negative C mα for longitudinal static stability. Therefore, if a gust were to cause a perturbation in trim angle of attack to a slightly lower value, a positive pitching moment would result, causing the aircraft to return to trimmed conditions 4. Lateral stability requires a negative value for C lβ, the change in the rolling moment coefficient about the x body axis with respect to a change in sideslip angle, β 4. This requirement makes an aircraft roll away from the direction of sideslip. Since the strakes are located near the x axis, little effect on C lβ was expected. It is important to note that too much lateral stability is undesirable, as it results in unfavorable dutch roll characteristics. The final derivative for evaluation was C nβ, the change in directional or yawing moment coefficient about the z body axis, with respect to a change in sideslip 4. For directional stability, the slope C nβ must be positive. A positive C nβ causes the aircraft to generate a yawing moment toward the direction of sideslip. The addition of the strakes was expected to increase the value of C nβ, making the C-130 more directionally stable. The effectiveness of the beavertail strakes was related to the vortex strength in the aft cargo door area. To understand how the beavertail strakes influence the aft body flow field, a computational investigation was performed by USAFA in 2006 5. This analysis around the aft section of the fuselage used an unstructured grid with no wings. A Reynolds Averaged Navier-Stokes (RANS) method was applied for turbulent flow inside the boundary layer C D0 2
while a Detached Eddy Simulation (DES) method was utilized for flow outside the boundary layer. Figures 3 and 4 show the two aft body vortices, each forming off one side of the fuselage and continuing under the horizontal tail. Figure 3. C-130 Aft Body Flow 6 Figure 4. Vortex Development Under C-130 Horizontal Tail 6 This analysis showed the ability of the strakes to reduce the strength of the vortices. Figures 4 and 5 compare the vortex strength without and with strakes, illustrating that the strakes reduce the low pressure vortex core. Further study of the physics of the vortex was completed by Wooten and Yechout in 2007 6 through the use of pressure sensitive paint applied to the aft underbelly area of the C-130. Figure 6 again compares the effectiveness of the strakes demonstrating a definite region of higher surface pressure (reduced vortex strength) with the strake. Figure 5. Reduction in Vortex Strength from Figure 6. Pressure Sensitive Paint Results Beavertail Strake Installation 6 (Strake on Right Side) 6 Objectives The overall objectives of this effort were: 1. To investigate the drag reduction potential of beavertail strakes through a representative range of C-130 deck angles and project this to improvements in C-130 operational capability. 2. To analyze and define the longitudinal, lateral, and directional static stability implications of beavertail strakes. 3
III. Set-up and Procedure 1. Wind Tunnel All testing took place in the Subsonic Wind Tunnel at the USAFA Aeronautics Laboratory. The tunnel has a three foot by three foot test section and can attain Mach 0.6. It is a closed circuit, single return wind tunnel. A picture of the tunnel is shown in Fig. 7. Figure 7. USAFA Subsonic Wind Tunnel 6 Figure 8. 1/48 th Scale C-130 model 2. Test Models A 1/48 th scale C-130 model was used for the testing. The model had its wing sections removed to reduce the moment load on the force balance so that the balance limits were not exceeded when tested at high deck angles and Mach numbers (Fig. 8). The previous phases had wings with only the outboard section of the wings removed and tests were run at a constant deck angle of 1.5. Exceeding the balance s limits at the speeds tested for that configuration was not a concern. The same reference dimensions presented in Table 1 were used to provide accurate comparisons among the various phases and to obtain trends from the data. Note that the reference area is for the scaled C-130 wing planform without removal of the wing sections. This allowed an accurate estimate of drag count reduction. The 1/48 th scale model was mounted in the tunnel with a sting and Able Corporation 100 lb internal force balance as shown in Fig. 9. The sting/force balance configuration left the aft fuselage area unobstructed. An arc crescent was used to achieve deck angle sweeps and side slip angle sweeps. Table 1. 1/48 th Scale Model Reference Dimensions Reference Area, S 109 in 2 Reference Length, l 24.4 in Figure 9: 1/48 th scale C-130 model mounted in the USAFA subsonic wind tunnel 4
The strake dimensions are described by Fig. 10. This particular strake design was recommended as the optimum strake design from the prior phases of research. Figure 11 depicts the location of the strakes on the underbelly aft section of the C-130. Figure 10. Dimensions of the studied beavertail strake Figure 11. Underbelly view of strake location 3. Reynolds Number Testing was conducted from Mach 0.3 to Mach 0.45. The Reynolds number for the full-scale C-130 at Mach 0.3 and 10,000 feet is 1.57 x 10 8, and at Mach 0.45 the corresponding Reynolds number is 2.355 x 10 8 based on the fuselage length 9. The Reynolds number for the 1/48 th scale model was approximately 3.266 to 4.898 x 10 6 at 0.45 Mach number. 4. Test Configurations/ Test Matrix The test matrix is presented in Table 2. A baseline test without strakes was compared to a test with the addition of the beavertail strakes for each test condition. An air off test was performed for all test points shown in Table 2. This calculated the gravity loads on the force balance which were then subtracted from the air on test results. After this test, the same deck angle (analogous to angle of attack but referenced to the fuselage water line) and side slip angle conditions were tested at Mach 0.3, 0.4, and 0.45. Accomplishing these tests required a VXI data acquisition system and software to read the data. The Department of Aeronautics wrote two programs for use in the testing facility. The Tunnel Vision program sends commands to the data acquisition system (VXI) to specify the sampling rate and length, along with setting up the test configurations so the data can be collected at a series of sting positions. Tunnel Vision collects and saves the data for the air off and air on tests. The Reduces program takes the data from Tunnel Vision, converts it to engineering units from the application of calibration files, and then calculates the lift, drag, and moment coefficients. Table 2. Test Matrix Configuration Mach Number Deck Angle (α) Sweep Sideslip Angle (β) Sweep Baseline B1 M=0.3,0.4,0.45 α =0.7-10.7 β =-5.32 to 4.68 (2 increments) (2.5 increments) (at α=0.7,3.7,6.7,8.7 ) Beavertail Strakes S1 M=0.3,0.4,0.45 α =0.7-10.7 β =-5.32 to 4.68 (2 increments) (2.5 increments) (at α=0.7,3.7,6.7,8.7 ) 5
5. Uncertainty Analysis The uncertainty was calculated using the AIAA Total Systems Approach 7, which estimates uncertainty in the data by assessing bias error (B i ) and precision error (P i ). An Able Corporation 100lb internal force balance and the pressure instrumentation in the tunnel were the primary sources of bias error, both having a ±0.5% accuracy of the applied load according to the manufacturer. In addition, the various coefficients were derived from measured quantities, so bias error was calculated from the influence coefficient (the derivative of each coefficient with respect to each measured quantity) times the uncertainty in the measured quantity. The precision error is a measure of data repeatability and for this effort, data was sampled at 100 times per second for several seconds and averaged. For a 95% confidence interval, Eq. 1 described the precision error where σ is the standard deviation in the measurements. P i = 2σ (1) Knowing the bias and precision error, the total uncertainty is described by the root mean square of the two errors, presented in Eq. 2. 2 2 U = B i + P i (2) Table 3 illustrates the overall best and worst case uncertainty for each aerodynamic coefficient, indicating that the yawing moment coefficient experienced the highest uncertainty. Table 3: Best and Worst Case Uncertainty C D C m C n C l Best 0.00036 0.00998 0.0093 0.00019 Worst 0.00260 0.05600 0.1400 0.00270 In addition to the uncertainty analysis, hysteresis was also evaluated to assess the repeatability of the data. Hysteresis is the difference in data during an up and down loading or test sequence. Table 4 summarizes the maximum and average hysteresis in the data for the four coefficients evaluated. Figure 12 presents a representative hysteresis plot. For comparison of the baseline and with strakes results, all loadings were obtained during the up cycle to enhance the accuracy of the comparison and minimize the effects of hysteresis. Overall, the hysteresis associated with this evaluation was small. Table 4. Maximum and Average Hysteresis Cn Cl Cm Cd Baseline Strakes Baseline Strakes Baseline Strakes Baseline Strakes Average 0.00015 0.00018 0.00004 0.00005 0.00246 0.00304 0.00024 0.00028 Maximum 0.00059 0.00049 0.00010 0.00023 0.01050 0.00762 0.00050 0.00060 Figure 12. Representative Sample of Observed Hysteresis 6
IV. Results and Discussion 1. Drag Characteristics First, the drag coefficient obtained at all three Mach numbers and various deck angles was graphed to compare the strake configuration to the baseline configuration as shown in Fig. 13. As the deck angle increased, a typical drag polar shape was found. Figure 14 presents the change in drag coefficient at the various deck angles with the addition of the strakes. At 0.7 deck angle, a drag reduction of 12-16 drag counts was found with the strakes. A good correlation with past work on drag reduction (Phases I, II, and III) for 1.5 deck angle was found where a drag reduction of 9 to 12 drag counts was indicated (see dashed lines). It was also found that there was a drag increase with strakes as the deck angle increased beyond 4 but this was not a large concern since the C-130 spends very little time at these large deck angles. Since the maximum range and endurance deck angles are believed to be 0 and 1.5 respectively, the strakes were found to offer a significant drag reduction potential for flight conditions where the aircraft spends the majority of its flight time. Figure 15 presents a drag reduction potential with the strakes as a function of deck angle. Figure 13. Comparison of Drag Coefficient at Mach 0.3 Figure 14. Drag Coefficient Change as a Result of Adding Strakes Figure 15. Drag Count Reduction Potential 2. Pitching Moment Characteristics 7
Next, pitching moment coefficient was graphed versus deck angle to compare the trim angle and longitudinal stability of the C-130 with and without strakes. Figure 16 compares the pitching moment coefficient characteristics of both configurations at Mach 0.4. Figure 16. Comparison of Moment Coefficient at Mach 0.4 At Mach 0.3, only a downward shift in the curve was found with strakes while the slope,, increased slightly. The downward shift was anticipated due to the increase in pressure on the underside of the horizontal stabilizer with the dissipation of the vortices. As a result, more lift is probably produced by the horizontal stabilizer, which probably causes the downward shift and a lower trim angle. At Mach 0.4 and Mach 0.45 there was a downward shift and a noticable decrease in the slope, C mα. The trim angle was again reduced and the C-130 actually became more longitudinally stable at the higher Mach numbers with the addition of strakes. Figure 17 shows how the longitudinal static stability derivative, C mα, changed with Mach number. This suggests that as Mach number, or Reynolds number, increases the strakes provide increasing longitudinal stability to the aircraft. Overall, the longitudinal stability change with the strakes was considered small. Figure 18 shows how the trim angle changed with the addition of strakes, which implies: 1) that higher Mach numbers generate more of a downward shift in the C m versus deck angle graph, and 2) that additional trailing edge up elevator deflection will be required for trim at a given deck angle with the strakes. C mα Figure 17. Change in C mα Figure 18. Change in Trim Angle The decrease in trim angle (for a fixed elevator deflection) should not cause any problems for the aircraft as long as sufficient trailing edge up elevator travel is available to trim the aircraft at high deck angles. 3. Yawing Moment Characteristics 8
The next focus of the stability analysis was to define the effect on directional stability resulting from the addition of the beavertail strakes. This study analyzed the data obtained from sideslip (β) sweeps at deck angles of 0.7, 3.7, 6.7 and 8.7 degrees. Figure 19 presents a representative yawing moment coefficient versus sideslip graph angle at Mach 0.4. Figure 19. Yaw Coefficient at M= 0.4 and deck angle = 3.7 Figure 20. Change in C nβ Recall that directional stability is defined by a positive slope ( ) where a larger positive slope, or steeper line indicates increased stability. For this evaluation, the slopes were negative, indicating that the model was unstable. This was expected for this model since it had no wings and a minimal vertical tail. Even though the resulting slopes are all negative, the important aspect to focus on for stability analysis is the difference in the slope ( C nβ ) between the baseline model and the configuration with strakes. Examining these differences, a less negative slope in this case a shallower line indicates an increase in stability. All deck angles were found to improve directional stability except for 3.7 degrees. Figure 20 summarizes the results for all test Mach numbers by presenting the differences in slope for all the yawing moment coefficients graphs, and displays the significant shift at a deck angle of 3.7 degrees. This graph quantifies the extent to which stability will increase or decrease. The positive differences imply an increase in directional stability and an increase in of up to 0.00005 was found. The decrease in directional stability at 3.7 degrees deck angle may result from a change in the vortex pattern around the aft fuselage when sideslip is present. This change is most likely causing an extra side force on the leeside strake that decreases the restoring yawing moment back to steady flight. This was an unexpected but important result. It is recommended that the unique flow characteristics causing the decrease in directional stability at the 3.7 deck angle be investigated with CFD and/or water tunnel analysis so that the cause of the stability decrease can be understood. This decrease was evident for all three test Mach numbers. Overall, the changes in directional stability with the addition of the strakes were small. C nβ C nβ 4. Rolling Moment Characteristics Another important stability parameter evaluated was lateral stability. By graphing the rolling moment coefficient versus sideslip angle, changes in the slope,, indicate changes in lateral stability with the addition of C lβ the strakes. Recall that a negative slope, C lβ, is required for lateral stability. A graph was created for each test deck angle at each Mach number, evaluating Cl β with and without strakes. There were a total of twelve graphs for deck angles of 0.7º, 3.7 º, 6.7 º, and 8.7 º at M = 0.3, 0.4, and 0.45. Figure 21 illustrates a typical rolling moment coefficient ( C l ) versus sideslip angle (β) graph for 8.7 degrees deck angle at a Mach number of 0.3. The baseline configuration maintained a slightly negative slope indicating positive stability. However, the actual stability of the curve is not critical for these results, since the model had an abbreviated vertical tail and did not have wings. Recall that the objective was to evaluate the changes in lateral stability with the addition of strakes. 9
Therefore, the difference in the slopes of the baseline curve and strake curve was the important observation. A linear trend-line was used to define the slope of each line. This case was the expected result, with both the baseline and strake configurations maintaining a slight negative slope, with relatively no change between the two curves. Figure 21. C L vs. β Curve for deck angle = 8.7º at M = 0.3. Figure 22. Change in C lβ Figure 22 summarizes the change in slope between the lateral stability curves with strakes and without strakes. From Fig. 22, at Mach 0.4, there is little change between the strake and baseline configurations. At Mach 0.3 and 0.45, there is a trend for a slightly negative change in slope, indicating less stability with the addition of strakes. However, for Mach 0.3 at 3.7 degrees and Mach 0.45 and 8.7 degrees, there was little change in slope. It is important to note that the change in lateral stability for all test cases was small ( 0. 0008 ) indicating that the addition of strakes had little effect on the lateral stability. V. Operational Impact To assess the impact that addition of the strake would have on an operational mission, the analysis presented in Reference 8 was used for a typical AFSOC 6 hour gunship mission. Assuming a 12 drag count reduction for a maximum endurance mission and an 18 count drag reduction for a maximum range mission (0 degree deck angle), Table 5 summarizes the potential improvements in mission capability. Table 5. Mission Performance Improvement with Strakes for a 6 hour AFSOC Mission Mission Drag Count Reduction Increased Mission Radius Increased Loiter Time Fuel Savings Maximum Range Maximum Endurance 18 18 NM X 506 lbs 12 X 6 min 338 lbs There are approximately 675 C-130 s of different variants across the Air Force 9 and assuming all fly an average of two missions a week, this would constitute an average of 70,200 missions in year. With a maximum fuel savings of 506 pounds on an average AFSOC mission, this correlates to over 35.5 million pounds of fuel saved per year. VI. Conclusions and Recommendations This effort quantified the drag reduction potential of C-130 aft body strakes through a range of deck angles representative of the C-130 flight envelope. A significant drag reduction potential of 12 drag counts was found for a deck angle of 1.5 degrees which correlated well with results from previous investigations. An increase in drag was found at deck angles greater than 4 degrees but this should not be a concern since a typical C-130 mission spends very little time at these deck angles. The next focus of the evaluation defined the static stability implications of the 10
beavertail strake addition where all the stability changes fund were small. The pitching moment characterization indicated increases in longitudinal stability with the strakes, especially at higher Mach numbers and Reynolds numbers causing a trim angle change that requires additional trailing edge up elevator deflection for trim. Directional stability increased at all deck angles except 3.7. The lateral stability of the C-130 was relatively unchanged with the addition of strakes. With respect to the operational impact, the addition of C-130 aft body strakes was projected to increase mission radius by up to 18 NM, or loiter time by up to 6 minutes, or result in an overall fuel savings of up to 506 pounds per 6 hour mission. This was projected to an overall fuel savings of approximately 35.5 million pounds per year for the C-130 fleet. It is recommended that further investigations, such as CFD and water tunnel analysis, focus on understanding the source of the decrease in directional static stability at 3.7 deck angle. There are probably unique flow characteristics around the strakes which develop from a change in the aft body vortex pattern with sideslip. In addition, repeating selected runs at various configurations would compliment the uncertainty analysis. Acknowledgments The authors would like to thank Mr. Ken Ostasiewski for his many hours of continued assistance and expertise in the operation of the USAFA Subsonic Wind Tunnel as well as Dr. Tom McLaughlin for his guidance in uncertainty analysis. Also, Mr. Jeff Falkenstine s expertise in the machine shop allowed the model to be tested at high deck angles. References 1 Karmondy, M.T., and Yechout, T.R., Phase I Investigation of C-130 Aft Body Drag Reduction Approaches, USAFA DFAN Report 06-01, January 2006. 2 Karmondy, M.T., and Yechout, T.R., Phase II Wind Tunnel Investigation of C-130 Aft Body Drag Reduction, USAFA DFAN Report 06-03, June 2006. 3 Wooten, J.D., and Yechout, T.R., Phase III Wind Tunnel Investigation of C-130 Aft Body Drag Reduction Approaches-Aft Body Strakes, USAFA DFAN Report 06-07, December 2006. 4 Black, B., Schwaab, M., and Yechout T.R., Aerodynamic Evaluation of the MC-130P Combat Shadow and Comparison to the C-130, USAFA DFAN Report 06-06, July 2006. 5 Karmondy, M.T., and Yechout, T.R., Development of Aft Body Drag Reduction Approaches for Special Operations C-130 Aircraft, USAF Academy, April 2006. 6 Wooten, J.D., and Yechout, T.R., Aerodynamic Evaluation of C-130 Aft Body Strakes and In-Flight Loading Prediction, USAFA DFAN Report 07-03, May 2007. 7 Assessment of Experimental Uncertainty with Application to Wind Tunnel Testing, AIAA Standard S-071A- 1999. 8 Dowty, J.C., and Yechout, T.R., Operational Impact Predictions of USAFA Recommended Drag Reduction Modifications for the AC-130U Gunship, USAFA DFAN Report 98-4, October 1998. 9 C-130 Factsheets, URL: www.af.mil/factsheets [cited 8 March 2008]. 11