Lift and Drag of a Finite Wing

Lift and Drag of a Finite Wing Mishaal Aleem, Tom Esser, Nick Harvey, Brandon Hu AA 32 Aerospace Laboratory I, Section AC William E. Boeing Department of Aeronautics & Astronautics University of Washington, Seattle, WA 9895-24 24-2-2 A finite wing with NACA 232 airfoil and an aspect ratio of 5.6 was tested at the Kirsten Wind Tunnel. The wing was tested with baseline rounded wingtips and circular endplates. Runs were conduced at q = psf and q = 35psf at various angles of attack, approached both increasing and decreasing. The maximum lift for the baseline wing was achieved at 6. Force and moment data, corrected for balance interactions, weight induced moments, and strut drag, showed that the endplates increased the lift curve slope of wing. The test corroborated theoretical data for the lift curve slope, based on the infinite wing slope, for the baseline wing within 3.6%. The wing was found to exhibit flow separation and hysteresis effects near the stall region. China clay flow visualization showed a reduction of wingtip vortices with the use of endplates. a 3-D Lift curve slope ( degrees ) a 2-D Lift curve slope ( AR b c C D C Dp C L C M D DRAG DRAGR e L LIF T Aspect Ratio Span (ft) Chord length (in) Coefficient of Drag degrees ) Coefficient of Parasitic Drag Coefficient of Lift Coefficient of Pitching Moment Drag force (lb) Nomenclature Drag force corrected for balance interactions (lb) Raw Drag force (lb) Span efficiency factor Lift force (lb) Lift force corrected for balance interactions (lb)

LIF T R M Raw lift force (lb) Pitching moment (lb in) NDRAG Normalized Fork Strut Drag (ft 2 ) P M P M R P MW T q QA Re Pitching Moment corrected for balance interactions (lb in) Raw Pitching Moment (lb in) Pitching moment weight tare correction factor (lb in) Dynamic Pressure (psf) Actual Dynamic pressure (psf) Reynolds Number V Airflow Velocity ( ft ) s α Angle of Attack ( ) α max Maximum Lift Angle of Attack ( ) ψ Side-sweep Angle ( ) I. Introduction The purpose of this experiment was to examine the lift, drag, and pitching moment of a finite, or 3-D, wing. A NACA 232 wing model was tested in the Kirsten Wind Tunnel (KWT) at dynamic pressures of psf and 35psf. An external balance collected the force and moment data of the wing at various angles of attack. Flow visualization tests were also conducted by painting china clay on the wing while it was pitched to an angle near the maximum lift angle, and running the tunnel at the aforementioned dynamic pressures to visually see the flow patterns in the resulting china clay pattern. The wing was tested with both standard rounded wingtips and with circular endplates. Using results from the wind tunnel test and applying appropriate balance, strut, and weight tare corrections, various coefficients of lift, drag, and pitching moment curves were produced for each wing configuration and compared to published airfoil data. The span efficiency factor and parasitic drag were also calculated for the wing model. II. Theory At subsonic speeds the viscosity of the airflow gives rise to a boundary layer over a wing, which produces pressure drag and skin friction drag. The boundary layer effects the performance of the wing depending on its state, either laminar, turbulent, or separated. When the boundary layer is laminar it has the lowest energy, but does not stay attached at high angles of attack. The turbulent boundary layer flow stays attached but produces larger drag. Finally, the boundary layer separates, at a unique angle for each airfoil and wing, at which point the wing stalls and lift is decreased. For a 3-D wing, compared to its 2-D counterpart, there is also an induced drag and a change in its lift 2

curve slope, due to its finite geometry. Wind tunnel testing is a powerful and practical way to study the aerodynamics of a wing. The following equations have been compiled in order to reduce and analyze the wind tunnel test force and moment data collected for a finite NACA 232 wing model. When analyzing aerodynamic data, it is often preferable to use force and moment coefficients. These are unitless properties which normalize forces and moments by the dynamic pressure, q, the reference area of the model, S, and, for moments, a reference length, which for a wing is the chord-length, c. The calculations for the lift, drag, and moment coefficients are given by Eqs., 2, and 3, where L, D, and M are the lift force, drag force, and pitching moment, respectively []. C L = L qs () C D = D qs (2) C M = M qsc The aspect ratio, AR, of a wing is defined as the ratio of its span, b, to its chord, c. For a rectangular wing, where the reference area, S, is a product of the span and chord length, the aspect ratio can be given simply by Eq. 4 []. AR = b2 S The span efficiency factor, e, is a way to characterize a 3-D wing as compared with a 2-D of the same aspect ratio with an elliptical lift distribution. Therefore, it is dependent on the lift-to-drag relationship of the wing, specifically dc2 L dc D, and the aspect ratio of the wing, AR. For an elliptic wing, e =. For all others, e <. The span efficiency factor can be calculated as per Eq. 5 []. (3) (4) e = dcl 2 (5) πar dc D The total drag on a wing is the sum of the parasitic and induced drag. Parasitic drag includes the skin friction drag and the form drag. Form drag is a result of the inherent shape of the wing and skin friction drag is a inherent to the fluid interaction between the air and the wing, thus parasitic drag is constant. For a finite wing, the higher pressure on the lower wing surface tends towards the upper surface where pressure is lower. This induces vortices at the wingtips that have a negative angle of attack, reducing the effective angle of attack of the wing and contributing a lift-induced drag component. The total drag coefficient can therefore be presented in the sum in Eq. 6, where the first term is the parasitic drag coefficient and the second is the induced drag coefficient []. C D = C Dp + C2 L πear (6) 3

A 2-D wing with a given airfoil has a given lift curve slope, a. A 3-D wing has a finite aspect ratio and alters this to a different, 3-D lift curve slope, a, for a wing with the same airfoil. The 3-D lift surge slope is dependent on the efficiency factor and aspect ratio of the particular finite wing. The 3-D lift curve slope can thus be found as per Eq. 7 []. a = a + a πe AR (7) When wind tunnel test data is collected it has inherent flaws associated with balance interactions. These balance interactions can be corrected for using data from a corrective balance interactions matrix, which is calculated during a full balance calibration. For the KWT balance, Eqs. 8, 9, and give a simplified version of the matrix equations, where raw lift, drag, and pitching moment, LIF T R, DRAG, and P MR respectively, are corrected for balance interactions to LIF T, DRAG, and P M.[]. LIF T =.994623 LIF T R +.372 DRAGR +.9 P MR (8) DRAG = (.99) LIF T R +.992637 DRAGR + (.2) P MR (9) P M =.7482 LIF T R + (.527) DRAGR +.99458 P MR () Drag tares are applied to account for the drag of the strut below the model. Strut tare data is typically pre-determined by the wind tunnel. A dynamic pressure-normalized drag, N DRAG is calculated from the tare for various side-sweep angles and the correction for drag after strut tares is given by Eq., where QA is the actual dynamic pressure []. DRAG(AFTER TARES) = DRAG(BEFORE TARES) N DRAG QA () As a model moves in a wind tunnel, its center of gravity also moves and induces moments on the model. Weight tares are done for each major model configuration during which the model is yawed and pitched to its most extreme positions. From weight tare data the pitching and rolling moment at any given angle of attack and side-sweep angle can be interpolated for any major model configuration. The weight tare moment is then subtracted from the wind-on collected moment data so that only moments due to aerodynamic phenomena are analyzed. This correction is given for pitching moment by Eq. 2 []. P M (AFTER WEIGHT TARE) = P M (BEFORE WEIGHT TARE) P MW T (2) Flow visualization is another useful type of wind tunnel test. Tufts, china clay, oil, and smoke flow are all methods employed for flow visualization in wind tunnels. For china clay flow visualization, colored china clay is painted onto the wing model. When the tunnel runs, the kerosene 4

dries, leaving china clay dust patterns of the airflow pattern and allowing for visual observation of the aforementioned wingtip vortices. In this experiment the wing is based off of the NACA 232 airfoil. The nomenclature of this indicates that the airfoil has a maximum thickness of 2% of its chord length. Figure shows various theoretical data curves for a 2-D NACA 232 airfoil. This figure is for the 2-D wing s performance at particular Reynolds numbers, Re. Reynolds number is the ratio of inertial forces to viscous forces, thus the performance of the wing varies with Reynolds number. Fig. Theoretical L D, C L, and C D curves for a 2-D NACA 232 airfoil [] From the linear region of the published C L plot, the 2-D slope for a NACA 232 airfoil can be approximated as a =.8. For this experiment, the NACA 232 wing was also tested degrees with circular endplates which theoretically increase the effective span. The the endplates block the wingtip vortices and should produce a larger lift curve slope than the baseline rounded wingtips, as well as higher maximum C L. 5

III. Experimental Apparatus The finite wing experiment was conducted at Kirsten Wind Tunnel (KWT) at the University of Washington, Seattle, Washington. KWT is a subsonic, double return, closed circuit wind tunnel. The test section is 8ft tall by 2ft wide by ft long, with windows available at each side and wind flowing from north to south. Two 5 horsepower engines each run a 7-blade propeller in the wind tunnel circuit. The revolutions per minute (RPM) of the fans are controlled at the test control and acquisition and module (TCAM) in the control room. The propeller RPM are adjusted to control the wind speed. The wind tunnel upflow is.2 and crossflow is.. The turbulence intensity is.72%. Fig. 2 shows an overhead schematic of the wind tunnel, with the red arrows indicating the airflow path. Fig. 2 Overhead schematic of the Kirsten Wind Tunnel [] KWT has an external balance which acquires force data of lift, drag, side force, and moment data of pitch, yaw, and roll. The balance uses mechanical connections and separates each of the 6 degrees of freedom into very small displacements which are transferred to the Eastman Pots that effectively measure the forces and moments acting on the model. A finite wing with NACA 232 airfoil was mounted in the center of the KWT test section onto the balance strut with KWT s 4-H Fork Strut and Pitch Arm #2. Trip dots lined the upper surface of the wing near the leading edge. Measuring tape and calipers were used for wing geometry measurements. The baseline configuration had rounded wingtips, and the wing was also tested with circular endplates. For flow visualization, the wing was painted with china clay, which is a mixture of Kentucky Ball Clay, kerosene, and DayGlo powder. An inclinometer and laser pointer used to do model position calibrations. Metal tape was used to tape over bolt holes on the fairing and the wing, as well as to temporarily mount the inclinometer. Figure 3 shows the fully installed wing model in the KWT test section. 6

Fig. 3 Northeast view of NACA 232 wing model, with baseline rounded wingtips, in KWT IV. Procedure Model Installation and Calibration. Strut Installation and Tare: A long inner strut was lowered into the balance. An outer strut was then placed onto the balance, around the inner strut, and bolted to the top of the balance. A fairing was placed around the outer strut and bolted down to the test section floor. The KWT 4-H Fork Strut and Pitch Arm #2 were attached to the strut. Prior to the lab experiment, a strut drag tare rune (i.e. the the strut with no model installed at various dynamic pressures) was conducted by the KWT employees. A flat-plate wing mount was attached to the fork strut and pitch arm. 2. α-calibration: An angle of attack, α, calibration was conducted by metal taping a mechanical inclinometer to the flat plate. The wing was pitched using an encoder controlled by TCAM. The inclinometer was read at various pitch angles. These angles as read by the inclinometer were recorded and the α-calibration program equated encoder values with the angle of attack of the wing. 3. ψ-calibration: A side-sweep angle, ψ, calibration was conducted by placing a laser pointer on the center-line of the flat-plate wing mount. The south wall of the wind tunnel circuit has a line which marks ψ =. The model was yawed till the laser was pointing at that line and this was set as the ψ = model position. 4. Wing Installation and Measurements: After the model position calibrations, each half of the wing model was bolted to the flat-plate mount and the baseline rounded wing tips were attached. Measurements were taken of the wing span, chord length, maximum thickness, and distance from the leading edge to the trip dots. 7

Wind Tunnel Test. Weight Tare: A weight tare run was done for the baseline configuration. With the wind-off, the model was pitched and yawed to each of its extreme positions, as well as to its homed position, α = ψ =, and a data point was collected by TCAM at each position. 2. α-flags: With the dynamic pressure set at q = psf, the the model was pitched from 6 to + by steps, then to +6 by.5 steps, then to +2 by steps. Force, moment, model position, temperature, and actual dynamic pressure data was collected at each angle. Data was also collected on steps going back to 6 in the same increments. This was then repeated for the baseline configuration at q = 35psf 3. Flow Visualization: Using the real-time data plotting software to find an approximate α max, it was decided that the flow-visualization would be conducted at α = 5.5. China clay was painted onto the pitched wing. The wind tunnel was then turned on to q = psf. The tunnel ran for about minute, after which the wind was brought down and pictures taken of the china clay flow patterns. The china clay was wiped off the wing and the flow visualization test was done again at q = 35psf. 4. Endplates: The standard wing tips were removed and the circular endplates attached to the wing. A weight tare, the α-flags, and the flow visualization runs were each done again with the new, endplates configuration. V. Discussion of Results Various measurements were taken of the NACA 232 wing model s geometry. These measurements are presented in Table. From the measurements of b and c, whose product is S, and Eq. 4, the aspect ratio of the wing was found to be AR = 5.6. Table. Measurements of various wing parameters Parameter Measurement (in) Chord Length 5.5 Span 87 Maximum Thickness.63 Leading Edge to Trip Dots.25 Plate Thickness.238 Plate Diamater 7.5 The maximum thickness of the wing was measured to be % of the chord length, which is just a 9% difference from the theoretical 2% value. The minimal error may be a result of estimating the location of the maximum thickness as well as manufacturing imperfections of the wing model. 8

The trip dots were used to trip the flow over the wing and induce turbulent flow over a majority of the wing s span. Wind tunnel data was collected at q = psf and q = 35psf at various angles for the NACA 232 wing model (see Appendix A for raw test-point data and KWT reduced data). The raw wind tunnel data from the test-point corresponding to α = at q = psf was corrected for balance interactions using Eqs. 8, 9, and. Using the corrected lift force and Eq., the lift coefficient was calculated. The appropriate strut tare was then applied to the drag as per Eq. (see Appendix A for strut tare data) and the appropriate weight tare to the pitching moment as per Eq. 2. Using the corrected drag force and pitching moment, coefficients of drag and pitching moment were found as per Eqs. 2 and 3. Table 2 shows the corrected values compared to the KWT calculations (see Appendix B for MatLab code of all calculations). Table 2. Lift, Drag, and Moment coefficients of the wing at q = psf and α = Coefficient Corrected KWT Corrected Difference C L.83.883.64% C D.458.527 3% C M -.5 -. 72% The errors in C L and C D corrections compared to those from the KWT corrections are within reason when considering that KWT applies additional corrections for wall effects, blockage, and upflow, as well as applying more thorough balance interaction corrections. The large error in C M is a result of the manual data reduction being for the moment coefficient about the balance moment center, whereas the KWT data transfers the moment coefficient to the model moment center at the quarter-chord of the wing. From the wind tunnel data at q = psf, the maximum lift occurs at approximately α max = 6, where the coefficient of lift is.887. This is the stall angle of the wing, after which point the flow over the wing separates. This separated flow causes a divergence from a linear lift curve slope to a decreasing, unpredictable stall region. Figures 4 7 show various plots, including C L vs α, using KWT reduced data for each configuration and dynamic pressure. Part (a) of each figure shows the C L and C D curves as a function of α. The linear region of the C L plot shows the constant lift curve slope as well as the general stall region for each case. The drag coefficient increases with increasing α prior to stall. While C L decreases after stall, C D still increases, at a faster rate, due to separation drag. Part (b) is a zoomed in view near the stalling region of the C L plot. In this zoomed view the principles of hysteresis can be seen in how the wing exhibits different C L values depending on whether it was increasing or decreasing its angle of attack. This phenomena, known as hysteresis, is further discussed on page 6. Part (c) shows the moment coefficients about the quarter-chord of the wing and the lift-to-drag ratio of the wing, each as a function of α. The liftto-drag ratio decreases dramatically after the stalling point. Finally, part (d) of each figure shows 9

the lift coefficient as a function of the drag coefficient..5.2.2..5.8 Increasing Angle Decreasing Angle.6 C L.5. C D C L.4.5.2.5 5 5 5 2 25 Angle of Attack (deg) (a) C L and C D vs. α.98 3 4 5 6 7 8 9 Angle of Attack (deg) (b) C L vs. α - Near the stall point.2 2.2.8.6 C M.2 L/D C L.4.2.4.2.6 5 5 5 2 25 2 Angle of Attack (deg).4.2.4.6.8..2.4.6.8.2 C D (c) C M and L/D vs. α (d) C L vs. C D Fig. 4 Properties of NACA 232 wing with rounded wingtips at q = psf From Fig. 4 it can be see that the baseline wing at q = psf achieves a maximum lift-todrag ratio of approximately 7 at 7.The lift-to-drag ratio increases till this point and then slowly decreases, and drops at a much faster rate after the visible stalling point of 5. As expected, C L increases linearly till stall, while drag increases steeply even after stall. The effects of hysteresis are visible in Fig. 4b. The C L vs C D plot in Fig. 4d is highly non-linear; for positive C D, C L first increases with C D before reaching a relatively constant (though slightly decreasing) value near C D =.9. The coefficient of moment has a small range, and expectedly increases with increasing lift. The behavior of C M also changes drastically, specifically it begins decrease, due to decreasing C L after the stall point when the lift forces on the wing become unpredictable. The stall angle from these plots is at α = 5 for the baseline wing at q = psf.

.5.2.25.2.5.5 Increasing Angle Decreasing Angle. C L.5. C D C L.5.5.95.5 5 5 5 2 25 Angle of Attack (deg).9 3 4 5 6 7 8 9 2 2 Angle of Attack (deg) (a) C L and C D vs. α (b) C L vs. α - Near the stall point.2 2.2.8.6 C M.2 L/D C L.4.2.4.2.6 5 5 5 2 25 2 Angle of Attack (deg).4.2.4.6.8..2.4.6.8.2 C D (c) C M and L/D vs. α (d) C L vs. C D Fig. 5 Properties of NACA 232 wing with rounded wingtips at q = 35psf Figure 5 of the baseline wing at q = 35psf again shows the expected C L, C D, and hysteresis behaviors. The C M plot is again nearly constant though increasing, and again expectedly shows great change after stall. The maximum lift-to-drag ratio of the wing is approximately 8 at an α of 6. The C L vs C D plot shows behavior similar to Fig. 6b where, for positive C D, C L increases non-linearly at first before reaching a slowly decreasing value beyond C D =.9. The general plot trends in Fig. 5 and Fig. 4 are very similar, showing the consistency of the wing s behavior at varying dynamic pressures. The stall angle from these plots is at α = 6 for the baseline wing at q = 35psf.

2.2.6.4.2..8 C L. C D C L.6.4 Increasing Angle Decreasing Angle.2 2 5 5 5 2 Angle of Attack (deg) (a) C L and C D vs. α.98 3 4 5 6 7 8 9 Angle of Attack (deg) (b) C L vs. α - Near the stall point.2 2.2.8.6.4 C M.2 L/D C L.2.4.2.4.6 5 5 5 2 2 Angle of Attack (deg).6.2.4.6.8..2.4.6.8.2 C D (c) C M and L/D vs. α (d) C L vs. C D Fig. 6 Properties of NACA 232 wing with endplates at q = psf Figure 6 shows the plots of the wing with endplates at q = psf. The maximum lift-to-drag ratio is 8 at a higher α (than without endplates) of. The trends of the C L, C D, C L vs. C D curves are the same, though the lift curve slope reaches noticeably larger values of C L than for the baseline wing. The larger lift coefficients result from the endplates physically reducing the wingtip vortices. With these wingtip vortices reduced, there is less don wash, or induced negative α, and therefore improved performance of the wing in generating lift. Hysteresis is again visible in Fig. 6b. Again, C M is small and slightly increasing, and then sharply decreasing after stall. The stall angle from these plots is at α = 4.5 for the wing with endplates at q = psf. 2

2.2.25.2 Increasing Angle Decreasing Angle.5 C L. C D C L..5 2 5 5 5 2 Angle of Attack (deg) 3 4 5 6 7 8 9 Angle of Attack (deg) (a) C L and C D vs. α (b) C L vs. α - Near the stall point.2 2.4.2.8.6 C M.2 L/D C L.4.2.4.2.4.6 5 5 5 2 2 Angle of Attack (deg).6.2.4.6.8..2.4.6.8.2 C D (c) C M and L/D vs. α (d) C L vs. C D Fig. 7 Properties of NACA 232 wing with endplates at q = 35psf Figure 7 shows the plots of the wing with endplates at q = 35psf. The maximum lift-to-drag ratio is 9 at 9. Again, the plots follow the same trends as in the figure before, i.e. increasing C L till stall, increasing C D, constant C M till stall, non-linear C L vs C D, and noticeable hysteresis. The stall angle from these plots is at α = 5.5 for the wing with endplates at q = 35psf. Figures 4 7 show that the overall plot trends of the wing do not change noticeably from the baseline to the endplate case, though there are key differences. With endplates, the lift curve slope was higher and the wing reached increased C L values, as expected due to the wingtip vortices being reduced by the endplates. However, this was at the expense of slightly higher C D values. According to Eq. 6, the parasitic drag occurs when the lift coefficient is zero. This is because when C L =, there is no lift and thus there is no lift-induced drag. The C Dp values for each case were calculated using this information and are presented in Table 3. 3

Table 3. Coefficient of Parasitic drag for NACA 232 wing model Configuration q (psf) C Dp Baseline.22 Baseline 35.73 Endplates.282 Endplates 35.233 The CL 2 vs C D plot of Fig. 8 represents these C Dp values as the horizontal axis intercept of each line. Both Table 3 and this figure show how the parasitic drag increases noticeably, at either dynamic pressure, when the endplates are added. Additionally, within each configuration, C Dp increased with dynamic pressure...9.8.7 Baseline q=psf Baseline q=35psf Endplates q=psf Endplates q=35psf.6 C L 2.5.4.3.2..6.8.2.22.24.26.28.3 C D Fig. 8 C 2 L vs. C D for NACA 232 wing The span efficiency factor of the wing, with and without endplates at each dynamic pressure, was calculated using Eq. 5 and the slope of the CL 2 as a function of C D plot. From this calculation, e for the baseline case was.342 and for the endplate configuration was.532. The expected e was less than because this is a non-elliptical wing. This deviation from theory is a result of the approximations of the wall corrections. Downwash and wingtip vortices contribute to the calculation of e. With wind tunnel testing, however, the walls obstruct these vortices and increase the span efficiency factor. While wall corrections were applied by KWT, these are approximate and for larger models (as in the case of this wing, which had a span just 4.75ft smaller than than the test section width) these approximations are more prone to error due to the tips being closer to, and thus vortices being blocked by, the wall. Additional error can arise from the imperfections of the strut tare such as the strut tare run set-up of the strut and pitch arm being slightly different that the experimental set-up. Expectedly, however, the endplates, which reduce wingtip vortices, 4

caused a higher e., AR, and e, Eq. 7 was From the theoretical 2-D wing lift curve slope of a =.8 degrees used to calculate the 3-D wing slope for the baseline NACA 232 wing to be a =.797 degrees. Experimentally, it was found to be a =.79 degrees, the average of the lift curve slopes of baseline runs at each q value. These values correspond to a difference of just 3.9%. These differences are likely a result of estimating the 2-D slope based off the published graph as well as the fact that the published graph was for 2 particular Reynolds numbers which this experiment did not match exactly. Flow visualization tests were also conducted, near the stall angle, using china clay. The china clay flow visualization showed unique behavior of the flow near the wingtips with and without the circular endplates. This flow visualization corroborated the numeric aerodynamic data. Without endplates, wingtip vortices are prominent and caused large curving patterns near the tips of the wing, as can be seen in Fig. 9. These vortices resulted from higher pressure flow on the bottom surface of the wing tip tending towards the lower pressure flow on the upper surface. Fig. 9 Curved china clay pattern of near the right tip of wing with baseline rounded wingtips With endplates, the the china clay patterns showed much less curvature, visually representing loss of vortices. This is a result of the endplates forcing the higher pressure air to flow straight over the wing edges, leading to a straighter china clay pattern.this flow behavior can be seen in Fig. of circular endplate china clay pattern. Fig. Straight china clay pattern near the left tip of wing with circular endplates Increasing the aspect ratio can reduce the induced drag on a wing, as per Eq. 6. However, the trade-off in this scenario means that the wing must become longer, which leads to its own problems. Issues surrounding the structural strength and vibration of the wing would become more prominent with a longer wing. Additionally, longer wings corresponds to increased cost of materials. Wings 5

must be designed, therefore, with aspect ratios low enough to meet structural integrity standards and be manufactured affordably, but as high as possible to minimize drag and maximize efficiency. Winglets are used on some commercial aircraft to reduce the aircraft s drag by reducing vortices. Circular endplates were tested to show the substantial effect that wingtip vortices have on a wing. By using circular endplates that force the flow straight and reduce vortices, the wing model simulated a 2-D wing of the NACA 232 airfoil. The endplate configuration achieved a higher C L than the baseline and it also had a higher lift curve slope of.784. The particular circular endplates used in this lab would be impractical for real aircraft application, however, because of the substantial additional drag they generated. However, the theoretical principal observed of how endplates on a wing reduce vortices can be used in winglet design. As shown in Figs. 4 7, after the wing stalled, when it returned to an angle near stall that previously had high C L values, the new, decreasing α value of C L was lower. The tendency of the wing to have higher C L when increasing α rather than decreasing is due to airflow separation. When the wing approaches the stall angle, the initially attached air detaches upon stall. However, if the air is starting at an angle higher than stall, the flow is initially separated and continues to stay separated, even below stall, until an α is reached that the allows the flow to re-attach. This phenomena, known as hysteresis, could have a dangerous impact on real aircraft during takeoff and landing. If an aircraft is taking off or landing at high angles and begins to stall, the aircraft would have to lower its angle of attack to below the stall angle to allow the flow to re-attach. If the aircraft is too close the ground however, this large of a decrease in the angle of attack may cause the aircraft to crash into the ground. Understanding aircraft and airflow behavior near the flow separation region is critical. VI. Conclusions In this experiment the a NACA 232 airfoil finite wing model was tested in the Kirsten Wind Tunnel. Force and moment data were collected which allowed for analysis of the lift and drag of the wing. Manually reduced data closely matched the corrected data from Kirsten Wind Tunnel, with the exception of the pitching moment which was calculated about a different point. The wing was found to stall near an angle of α max = 6, after which point the linear lift curve slope decreased. The wing was shown to exhibit hysteresis in the form of different values of lift coefficient depending on whether it was increasing or decreasing its angle of attack. The drag coefficient was found to increase with angle attack before and after the stall point. The finite wing model, which had an aspect ratio of 5.6, had a lift curve slope of.79 which was within 4% of the predicted value based upon from the 2-D slope of the same airfoil. The lift curve was shown to increase with the addition of circular endplates, because they decreased wingtip vortices. However, drag was also shown to increase with these endplates. Flow visualization using china clay provided visual observation of flow patterns and the vor- 6

tices that formed over the wing. Large vortices formed at the wingtips for the baseline configuration as a result of higher pressure flow on the lower surface of the wing tending towards the lower pressure flow on the upper surface. The flow visualization with endplates showed that the endplates substantially reduce these vortices, visually verifying the numeric force coefficient data. These vortices interacting with the wind tunnel walls lead to calculating span efficiency factors that were greater than, where e =.342 for the baseline configuration and e =.532 for the endplate configuration. This experiment may be expanded upon by testing various types of wing tip designs, included drooped and upswept, to see the variation of the vortices with multiple different wingtip shapes. An additional suggestion for improvement would be to run this experiment with and without trip dots to see how they affect the boundary layer and subsequently the lift and drag. The key findings of this experiment support the greater lesson of lift and drag of finite wings, and how they differ from infinite wings. Hysteresis observation provided insight into the safety precautions that need to be taken at landing and take-off. Endplate testing was a useful lesson in the effects of winglets and how they can, if properly designed, improve aircraft performance. Overall this experiment provided quality data about lift and drag of a finite wing that verified theoretical principles and practical applications. References [] Bruckner, A. P., AA 32-Finite Wing Lecture-24, University of Washington, Seattle, WA 9895, 24. 7

Appendix A Raw data from KWT for the for wing at α = and q = psf is presented in Table A Table A. Raw wind tunnel data for wing at α = and q = psf Parameter Unit Value AlphaEnc degrees 9.988 Psi degrees. QNOM psf QA psf 9.978 LIFTR Lb 76.3354 DRAGR Lb 5.52 PMR inlb -8.8596 YMR inlb -.365 RMR inlb 2.297 SFR Lb -.838 TEMPTS degf 6.574 PRESSTS psi 4.74 Time 24hr 3:5:28 PMWT inlb -.5926 RMWT inlb Strut tare data for the KWT 4-H Fork Strut is presented in Table. A2. Table A2. Strut Tare data for 4-H Fork Strut CLW -3.8-2 -.5 - -.8 -.7 -.6 -.5 -.4 -.3 NDRAG (ft 2 ).542.39.244.84.6.48.38.28.8.8 CLW -.2 -...2.4.6.8.6 3.8 NDRAG (ft 2 )..93.87.82.78.69.62.58.56.56 Corrected data from KWT for the NACA 232 test 294 Lab Section AC is presented in Tables A3-A6 A

Table A3. Baseline wing configuration at q = psf QC PSI ALPHAC CLWA CDWA CMWA25 RE MAC.8-6.5 -.36842.374.9876 73526 9.992-5.45 -.29896.2845.8227 732.8-3.985 -.22323.264.64624 73668.22-3.27 -.58.245.4874 73255.5 -.985 -.788.2268.357 7352.5 -.9 -.539.222.556 732365.4 -.2.688.223 -.858 73448.53.996.439.2293 -.7559 732575.96.993.2665.24 -.33775 73496.6 3.3.29523.2555 -.537 73496.4 3.944.3654.275 -.65273 73597.69 5.24.44674.396 -.83345 73333.6 5.949.5329.347 -.97936 73577. 7.36.59663.3786 -.552 734922.49 7.968.6625.489 -.333 732688.85 8.959.73392.4699 -.4686 73428.29 9.976.883.527 -.645 7324.4.58.84448.558 -.769 73682.5.97.87427.5787 -.7784 73648.7.52.9242.638 -.8598 737264.42.982.9426.6457 -.9392 7369.34 2.444.9736.688-2.32 735928.9 3.8.95.7272-2.55 73544.39 3.433.28.7553-2.66 73636.4 3.96.532.7934-2.2532 735245.9 4.54.769.835-2.3426 734424.27 5.29.887.8855-2.459 735758.92 5.499.4.846-2.544 734485.74 5.966.35.634-2.5943 733847.44 6.979.35.3238-2.7646 732767.6 8.3.9858.542-2.988 73532.95 8.964.9534.788-3.464 73827.276 2.4.9576.8926-3.853 7427 A2

Table A4. Baseline wing configuration at q = 35psf QC PSI ALPHAC CLWA CDWA CMWA25 RE MAC 34.947-6.4 -.37396.268.26899 36695 35.24-5.7 -.29622.2357.2942 37228 35.366-4.22 -.22296.2.7355 37444 35.597-2.994 -.4623.92.2592 37846 35.486-2.5 -.74.787.86 37622 35.495 -.33 -.34.729.3753 37654 35.462 -.24.7296.733 -.827 375378 35.475.978.48.79 -.5374 375533 35.579 2.5.22658.9 -.9 377439 35.458 3.7.355.279 -.467 3752 35.432 3.986.3769.233 -.983 374348 35.43 4.988.45235.2599 -.23682 37372 35.56 5.983.52678.2956 -.2844 375749 35.679 6.952.5987.3345 -.3242 37886 35.765 8.39.687.3833 -.3722 3837 35.75 8.98.7489.432 -.4476 385 35.724 9.975.8958.493 -.468 37933 35.5.58.85869.5238 -.48734 37568 35.57.958.88888.5524 -.5633 37678 35.472.472.92522.5864 -.5386 37456 35.57 2..96.6244 -.55332 375996 35.54 2.472.999.6576 -.57469 374799 35.528 3.24.239.78 -.59892 374977 35.476 3.47.59.737 -.6949 373897 35.43 4.3.88.7788 -.6448 37258 35.323 4.439.33.846 -.66499 37757 35.43 5.37.345.8635 -.68929 372755 35.345 5.483.526.98 -.763 374 35.24 5.933.678.9448 -.73355 36847 35.66 7.54.576.3682 -.8545 36559 35.27 7.975.39.538 -.8588 36939 35.363 8.94.9587.7227 -.9989 377 35.59 2.36.9292.972 -.95957 375447 A3

Table A5. Endplate wing configuration at q = psf QC PSI ALPHAC CLWA CDWA CMWA25 RE MAC.47. -6.25 -.48.3799 -.88 73658 9.979. -5.8 -.335.344 -.67 7358 9.952. -4.9 -.24669.3239 -.442 729684.42. -3.27 -.775.35 -.35 7335.96. -.99 -.8668.2869 -.9 73566.5. -.24 -.423.289 -.8 73566.9..9.84.2825 -.47 73628...962.667.2868 -.984 73569.63..969.2425.332 -.96 73437.4. 2.989.32797.36 -.833 73587.83. 3.983.424.335 -.759 73546.2. 5.5.49352.3596 -.679 736585.43. 5.95.56938.3874 -.6 737467.96. 7.47.6566.4222 -.59 73579.33. 7.986.73244.456 -.448 73778.. 8.984.832.496 -.426 73639.5. 9.957.8847.5428 -.342 73786.74..488.92576.567 -.282 73534.5...96254.598 -.27 73667.74..54.9974.626 -.22 73526.36..943.28.6452 -.42 733847.42. 2.488.64.6842.53 7348.77. 3.3.94.772.93 73544.7. 3.483.73.7466.37 7354.5. 3.998.394.7836.454 734434.54. 4.59.57.82.563 7346.64. 4.933.59.96.33 734977. 5.55.28.24 -.325 73265.69. 5.9.45.572 -.584 73572.26. 7..95.3597 -.237 742.95. 8..9895.5767 -.3977 73983.65. 8.993.9474.7635 -.4854 738743.229. 9.977.9925.9287 -.5534 7476 A4

Table A6. Endplate wing configuration at q = 35psf QC PSI ALPHAC CLWA CDWA CMWA25 RE MAC 35.335. -5.99 -.4796.326 -.577 376557 35.425. -5.53 -.3329.296 -.464 37835 35.568. -4. -.24695.275 -.332 38762 35.388. -3.2 -.6269.259 -.27 3777 35.387. -2.48 -.85.2396 -.4 376943 35.37. -.996.64.233 -.3 376496 35.393..28.8645.2333 -.935 376797 35.633..974.6472.238 -.857 38333 35.595..976.2555.2479 -.776 38498 35.542. 2.979.33448.2626 -.698 37937 35.532. 3.994.493.2837 -.622 37897 35.692. 4.996.5343.393 -.553 3896 35.39. 6.3.586.344 -.484 37443 35.47. 6.989.66464.3756 -.43 377399 35.554. 7.97.74326.453 -.336 37892 35.397. 9.5.82562.463 -.247 37573 35.475. 9.995.978.537 -.28 37789 35.43..456.9369.5362 -.67 37584 35.43..999.9754.5669 -.9 37634 35.42..52.44.597 -.6 375774 35.373..97.454.6258 -. 374742 35.334. 2.48.8.6578.69 373838 35.37. 3.2.37.6927.45 373276 35.239. 3.468.427.7256.29 37847 35.68. 4..736.7623.295 37379 35.256. 4.522.23.7963.369 37986 35.83. 4.954.2233.834.425 37482 35.8. 5.48.2452.876.475 37328 35.74. 5.993.343.854 -.95 368226 35.. 6.964.85.3637 -.274 36862 35.399. 8.37.34.62 -.43 374363 35.625. 8.98.95343.7526 -.4848 378625 35.578. 9.95.92.98 -.55 377665 A5

Appendix B The MatLab code of calculations and plot generation for this report is presented following. clear all close all clc %% %Data Loading %%Wing Data b = 87/2; %[ft] c = 5.5/2; %[ft] S=b*c; %[ftˆ2] AR=bˆ2/S; % %%Load Wind Tunnel Data baselineq=xlsread('aa32 Thurs Data (AC).xlsx','Wing Only q = psf'); baseline35q=xlsread('aa32 Thurs Data (AC).xlsx','Wing Only q = 35 psf'); epq=xlsread('aa32 Thurs Data (AC).xlsx','Wing with Endcaps q = psf'); ep35q=xlsread('aa32 Thurs Data (AC).xlsx','Wing with Endcaps q = 35 psf'); %Baseline Data alpha_base_q=baselineq(:,6); CL_base_q=baselineq(:,7); CD_base_q=baselineq(:,8); CM_base_q=baselineq(:,9); alpha_base_q35=baseline35q(:,6); CL_base_q35=baseline35q(:,7); CD_base_q35=baseline35q(:,8); CM_base_q35=baseline35q(:,9); %Endplate Data alpha_ep_q=epq(:,6); CL_ep_q=epq(:,7); CD_ep_q=epq(:,8); CM_ep_q=epq(:,9); alpha_ep_q35=ep35q(:,6); CL_ep_q35=ep35q(:,7); CD_ep_q35=ep35q(:,8); CM_ep_q35=ep35q(:,9); %% B

%Part : Manual DR for q=psf alpha=deg, psi=deg %Load Raw Data alpha_a=9.988; %[deg] QA=9.978; %[psf] QC=.4; %[psf] LIFTR=76.3354; %[lb] DRAGR=5.52; %[lb] PMR=-8.8596; %[lb] PMWT=-.5926; %[lb] %Balance Interactions LIFT=.994623*LIFTR +.372*DRAGR +.9*PMR; DRAG=(-.99)*LIFTR +.992637*DRAGR + (-.2)*PMR; PM=.7482*LIFTR + (-.527)*DRAGR +.99458*PMR; %Coefficient of lift C_L=LIFT/(QA*S); C_Lerror=(C_L-.883)/((.883+C_L)/2)*; %Drag Tare NDRAG=.57979675; %Interpolated NDRAG based on CLW DRAG=DRAG - NDRAG*QA; %[lb] %Weight Tare PM=PM-PMWT; %[lb] %Coefficients of drag and pitching moment C_D=DRAG/(QC*S); C_M=PM/(QC*S*c*2); %[lb] %[lb] %[lb] %% %Part 2: Curves for Baseline at q %C_L and C_D vs Alpha figure; [AX,H,H2] =... plotyy(alpha_base_q(::33),cl_base_q(::33),alpha_base_q(::33),cd_base_q(: set(get(ax(),'ylabel'),'string','c_l', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','c_d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hold off print -depsc CLandCDqbase %C_L vs Alpha Zoom figure(2); plot(alpha_base_q(24::3),cl_base_q(24::3), 'blue') hold on plot(alpha_base_q(36::43),cl_base_q(36::43), 'red') ylabel('c_l', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hlegend=legend('increasing Angle', 'Decreasing Angle'); B2

set(hlegend,'fontsize',4, 'location', 'Best'); hold off print -depsc CLzoomqbase %C_M and L/D vs Alpha figure(3); [AX,H,H2] =... plotyy(alpha_base_q(::33),cm_base_q(::33),alpha_base_q(::33),cl_base_q(: set(get(ax(),'ylabel'),'string','c_m', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','l/d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) print -depsc CMandLDqbase %C_L vs C_D figure(4); plot(cd_base_q(::33),cl_base_q(::33)) xlabel('c_d', 'fontsize', 6) ylabel('c_l', 'fontsize', 6) print -depsc CLvsCDqbase %% %Part 3: Curves for Baseline at 35q %C_L and C_D vs Alpha figure(5); [AX,H,H2] =... plotyy(alpha_base_q35(::33),cl_base_q35(::33),alpha_base_q35(::33),cd_base_q35(: set(get(ax(),'ylabel'),'string','c_l', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','c_d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hold off print -depsc CLandCDq35base %C_L vs Alpha Zoom figure(6); plot(alpha_base_q35(25::33),cl_base_q35(25::33), 'blue') hold on plot(alpha_base_q35(33::43),cl_base_q35(33::43), 'red') ylabel('c_l', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hlegend=legend('increasing Angle', 'Decreasing Angle'); set(hlegend,'fontsize',4, 'location', 'Best'); hold off print -depsc CLzoomq35base B3

%C_M and L/D vs Alpha figure(7); [AX,H,H2] =... plotyy(alpha_base_q35(::33),cm_base_q35(::33),alpha_base_q35(::33),cl_base_q35(: set(get(ax(),'ylabel'),'string','c_m', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','l/d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) print -depsc CMandLDq35base %C_L vs C_D figure(8); plot(cd_base_q35(::33),cl_base_q35(::33)) xlabel('c_d', 'fontsize', 6) ylabel('c_l', 'fontsize', 6) print -depsc CLvsCDq35base %% %Part 4: Curves for Endplates at q %C_L and C_D vs Alpha figure(9); [AX,H,H2] =... plotyy(alpha_ep_q(::33),cl_ep_q(::33),alpha_ep_q(::33),cd_ep_q(::33)); set(get(ax(),'ylabel'),'string','c_l', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','c_d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hold off print -depsc CLandCDqep %C_L vs Alpha Zoom figure(); plot(alpha_ep_q(24::3),cl_ep_q(24::3), 'blue') hold on plot(alpha_ep_q(36::43),cl_ep_q(36::43), 'red') ylabel('c_l', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hlegend=legend('increasing Angle', 'Decreasing Angle'); set(hlegend,'fontsize',4, 'location', 'Best'); hold off print -depsc CLzoomqep %C_M and L/D vs Alpha figure(); B4

[AX,H,H2] =... plotyy(alpha_ep_q(::33),cm_ep_q(::33),alpha_ep_q(::33),cl_ep_q(::33)./cd set(get(ax(),'ylabel'),'string','c_m', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','l/d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) print -depsc CMandLDqep %C_L vs C_D figure(2); plot(cd_ep_q(::33),cl_ep_q(::33)) xlabel('c_d', 'fontsize', 6) ylabel('c_l', 'fontsize', 6) print -depsc CLvsCDqep %% %Part 5: Curves for Endplates at 35q %C_L and C_D vs Alpha figure(3); [AX,H,H2] =... plotyy(alpha_ep_q35(::33),cl_ep_q35(::33),alpha_ep_q35(::33),cd_ep_q35(::33)); set(get(ax(),'ylabel'),'string','c_l', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','c_d', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hold off print -depsc CLandCDq35ep %C_L vs Alpha Zoom figure(4); plot(alpha_ep_q35(24::3),cl_ep_q35(24::3), 'blue') hold on plot(alpha_ep_q35(36::43),cl_ep_q35(36::43), 'red') ylabel('c_l', 'fontsize', 6) xlabel('angle of Attack (deg)', 'fontsize', 6) hlegend=legend('increasing Angle', 'Decreasing Angle'); set(hlegend,'fontsize',4, 'location', 'Best') hold off print -depsc CLzoomq35ep %C_M and L/D vs Alpha figure(5); [AX,H,H2] =... plotyy(alpha_ep_q35(::33),cm_ep_q35(::33),alpha_ep_q35(::33),cl_ep_q35(::33)./cd set(get(ax(),'ylabel'),'string','c_m', 'fontsize', 6) set(get(ax(2),'ylabel'),'string','l/d', 'fontsize', 6) B5

xlabel('angle of Attack (deg)', 'fontsize', 6) print -depsc CMandLDq35ep %C_L vs C_D figure(6); plot(cd_ep_q35(::33),cl_ep_q35(::33)) xlabel('c_d', 'fontsize', 6) ylabel('c_l', 'fontsize', 6) print -depsc CLvsCDq35ep close all %% %Part 6: e and C_D_p %Parasitic drag CDp_base_q=CD_base_q(6); CDp_base_q35=CD_base_q35(6); CDp_ep_q=CD_ep_q(6); CDp_ep_q35=CD_ep_q35(6); %Plot for CLˆ2 vs CD figure(7); box on hold all xlabel('c_d', 'fontsize', 6) ylabel('c_lˆ2', 'fontsize', 6) ylim([.]); plot(cd_base_q(:6),cl_base_q(:6).ˆ2) plot(cd_base_q35(:6),cl_base_q35(:6).ˆ2) plot(cd_ep_q(:6),cl_ep_q(:6).ˆ2) plot(cd_ep_q35(:6),cl_ep_q35(:6).ˆ2) hlegend=legend ('Baseline q=psf', 'Baseline q=35psf', 'Endplates... q=psf', 'Endplates q=35psf', 'location', 'Best'); set(hlegend,'fontsize',4, 'location', 'Best'); print -depsc CL2vsCD e_base_q=2/(pi*ar); e_base_q35=2/(pi*ar); e_ep_q=27/(pi*ar); e_ep_q35=27/(pi*ar); B6

%% %Part 7: Lift-curve slope a=.75;%2d slope a_calc=a/(+a/(pi*e_base_q*ar));%3d slope slope=(cl_base_q(25)-cl_base_q())/(alpha_base_q(25)-alpha_base_q()); slope2=(cl_base_q35(25)-cl_base_q35())/(alpha_base_q35(25)-alpha_base_q35()); a_exp=(slope+slope2)/2; %mean of experimental slope a_error=abs(a_exp-a_calc)/((a_exp+a_calc)/2); %slope error slope3=(cl_ep_q(25)-cl_ep_q())/(alpha_ep_q(25)-alpha_ep_q()); slope4=(cl_ep_q35(25)-cl_ep_q35())/(alpha_ep_q35(25)-alpha_ep_q35()); a2_exp=(slope3+slope4)/2; close all B7