Aerodynamic Analysis using XFLR-5Aditya Kotikalpudi, Brian Taylor, Claudia Moreno, Harald Pfifer, and Gary J. Balas

Aerospace Engineering and Mechanics

University of Minnesota

Contact: Aditya Kotikalpudi (kotik001@umn.edu)UAV lab (http://www.uav.aem.umn.edu), phone: 612-626-3549

In order to estimate the aerodynamic stability derivatives and control derivatives of the BFF aircraft,aerodynamic analysis was carried out using an open source software, XFLR-5 [7]. The analysis wascarried out using the Vortex Lattice Method (VLM). Since the analysis assumes inviscid flow, the totaldrag estimate is not reliable. It can also carry out dynamic stability analysis, given the mass properties(total mass, location of center of gravity, moments of inertia about X, Y, Z and XZ plane) which weredetermined via inertia swings [2]. Inertia about XZ plane (Ixz) was determined from inertia estimatorprovided by XFLR-5. The stability and control derivatives extracted from the analyses were used toconstruct a nonlinear simulation for the rigid body dynamics of the BFF vehicle.

Aerodynamic Design Realization

The airfoil cross-section used for constructing the model in XFLR-5 was extracted from the point clouddata generated via laser-scan of the aircraft, carried out by The QC Group, based out of Minnetonka,MN [6]. Fig. 1 shows the airfoil extracted from the point cloud (normalized to unit length). It hasbeen verified that the airfoil cross-section remains constant across the entire aircraft except along thecenter line, which incorporates the motor mount, GPS hood and the keel/landing skid. The geometricproperties of the airfoil are listed in table 1.

Figure 1: Airfoil cross-section of BFF

Table 1: Airfoil Geometric Properties

1. Maximum thickness 9.47%Max. thickness location 25.89%

2. Maximum camber 1.69%Max. camber location 24.09%

The model constructed in XFLR-5 does not incorporate the landing skid, the GPS hood and themotor mount. The modelling of control surfaces is close to the actual model, although it is not exact.

1

The deflections are simulated in a streamwise, rather than hingewise, sense. For comparison withfuture flight data, the measured hingewise deflections can be converted to streamwise with equation1.

SW = tan−1(tan(HW ) cos(χ)) (1)

where SW is streamwise deflection, HW is hingewise deflection and χ is the hingeline angle of thecontrol surfaces. Trailing edge downward deflection is considered positive. The model constructed isshown in Fig. 2. Figure 3 depicts the control allocation for the BFF aircraft, surfaces L2 and R2on the wing are used as elevators while surfaces L3 and R3 are used as ailerons. Table 2 summarizesthese definitions.

Figure 2: XFLR-5 Model of BFF

Figure 3: Control surface locations

Table 2: Virtual Control Surfaces

1. Virtual elevator (δe) (L2 + R2)/22. Virtual ailerons (δa) (L3 −R3)/2

2

Figure 4: Comparison of BFF airfoil with NACA 23010

An effort was made to match the given airfoil to a standard NACA airfoil. The closest match was theNACA 23010 but it had a sharper leading edge compared to the extracted airfoil (Fig. 4). Also, NACA0010 was tried as a substitute for the given airfoil, in an effort to reduce the manufacturing costs ofreplicas of the aircraft. However the pitch stability characteristics could not be matched accurately,and since absence of empennage results in sensitivity in pitch stability, it was decided that the originalairfoil extracted will be retained in all the future aircraft built based on the BFF aircraft’s design.The XFLR-5 file (.wpa extension) containing all the analyzed airfoils and wing-body design describedabove has been provided on the UAV lab’s website for users to download. It also has three pre-definedanalyses set up for aerodynamic, longitudinal and lateral stability analyses. Also, a text file containingthe coordinates of the airfoil is provided on the website.

Lift and Pitching Moment Characteristics

The lift coefficient (CL) vs. angle of attack (α) curve and pitching moment coefficient (Cm) vs. αcurve are shown in Fig. 5. The airspeed is fixed to 67.5 ft/s (40 KEAS) which is the airspeed for thefirst linear model out of the 26 linear models which were published by Lockheed Martin for the flexibleBFF vehicle [5]. The X intercept of the Cm vs. α curve determines the trim angle of attack for thegiven airspeed. As seen from the Fig. 5, trim α is around 3.5 degrees. The corresponding coefficientof lift is 0.195. The slope of the Cm − α curve is negative (-0.4166/rad), indicating static stability ofthe aircraft.

Figure 5: Cm vs α & CL vs α graphs

3

Shown in Fig. 6 is the variation of trim elevator deflection with change in angle of attack. Trailingedge downward deflection is considered positive.

Figure 6: elevator deflection vs angle of attack

Stability and Control Derivatives

XFLR-5 is capable of dynamic stability analysis of an aircraft if the mass properties are provided.These values were estimated from inertia swing tests [2] and center of gravity estimation test [1]carried out in the Aeromechanics laboratory of the department and are listed in table 3. Owing to thesymmetry of the aircraft, the lateral and vertical coordinates of center of gravity are assumed to lieon their respective center lines of the aircraft body. The stability and control derivatives were takenfrom the log files generated by the software during the analysis. These derivatives were obtained fora range of trim angles of attack (α) and the acquired data was plotted out. An approximate functionwas then generated for each of these derivatives in terms of α from these plots. The functions areprovided in tables 4 and 5 while the plots are given in appendix A. All the functions are either linearor quadratic and are represented in the following form:

Y = Aα2 +Bα+ C (2)

where Y represents a derivative and α is the angle of attack in radians. The derivatives which varylinearly have a zero value for A.Table 6 lists the derivatives at the trim airspeed of 40 KEAS and an angle of attack of 3.5 degrees,just as an example case. All derivatives are in rad−1. The variation of all control derivatives exceptCmδe was found to be quite small and hence was averaged over the interval of α considered. Also,the side force and sideslip derivatives (CY β , CY p, CY r, Clβ , Cnβ) vary within a very small range dueto lack of a large vertical fin. Hence these values were averaged over the interval as well. All thesederivatives therefore have the values A and B to be zero. A more sophisticated analysis would berequired in order to accurately capture the variations of these derivatives.CLδe derivative is calculated from the CZδe derivative which is actually the output from the analysis.Z axis in XFLR-5 is not the body fixed axis. It refers to the stability Z axis of the aircraft, pointeddownward (i.e. opposite to direction of lift). Similarly, drag derivatives are calculated from the CXderivatives where X axis is pointed along the velocity vector in absence of sideslip. All the coefficientsare calculated in stability axes.

4

Table 3: Mass Properties

Property ValueTotal Weight 11.99 lbC.G. Location 23.2585 inches (from nose)Pitching moment of inertia 1245.83 lb− in2

Rolling moment of inertia 8529.45 lb− in2

Yawing moment of inertia 8118.42 lb− in2

Product of inertia Ixz (estimated) -0.296 lb− in2

Table 4: Longitudinal Aerodynamic Stability and Control Derivatives

Derivatives A B C

CD0 0 0 0.00056CDα 0 -0.2875 -0.1154CDδe 0 0 -0.0313CL0 0 0 -0.0238CLα -7.4785 0.3521 4.5461CLq -7.3119 0.5846 4.4078CLδe 0 0 0.7600

Cm0 0 0 0.0188Cmα 0.8488 -0.0888 -0.4145Cmq 1.5488 -0.0463 -1.9074Cmδe 0.3029 -0.0379 -0.0924

Table 5: Lateral-Directional Aerodynamic Stability and Control Derivatives

Derivatives A B C

CY 0 0 0 0CY β 0 0 -0.0138CY p 0 0 0.0353CY r 0 0 0.0418CY δa 0 0 -0.044

Cl0 0 0 0Clβ 0 0 -0.0153Clp 0.249 -0.0211 -0.5613Clr 0 0.7450 0.0077Clδa 0 0 0.1764

Cn0 0 0 0Cnβ 0 0 0.0196Cnp 0 -0.4555 -0.004Cnr 0.0398 -0.0023 -0.0056Cnδa 0 0 -0.0006

5

Table 6: Aerodynamic Stability and Control Derivatives

Longitudinal lateralCDα -0.1364 CY β -0.1324CLα 4.539 CY p 0.0508CLq 4.414 CY r 0.0391Cmα -0.4166 Clβ -0.0165Cmq -1.904 Clp -0.5613CLδe 0.7645 Clr 0.054CDδe 0.0066 Cnβ 0.0185Cmδe -0.0933 Cnp -0.0325

Cnr -0.005625CY δa -0.0044Clδa 0.1765Cnδa 0.0006

From tables 4, 5 and 6 some observations have been made:

1. The pitching moment coefficient derivatives are seen to be smaller compared to a conventionalstatically stable aircraft with tailplane like the Ultra Stick 25e (data available in the nonlinearsimulation provided on the laboratory website), AMT-200S motor glider [3] and Navion aircraft[4]. However, the values of lift coefficient derivatives are comparable. This is due to lack of ahorizontal stabilizer which plays a major role in defining the pitching moment characteristics ofany aircraft.

2. The β derivative of the side-force coefficient (CY β) is also on the smaller side. This is due tolack of a large vertical fin which is a common feature for conventional aircraft configurations.

3. Control derivatives show a similar trend, where pitching moment coefficient derivative (withrespect to elevator, Cmδe) is small, while lift coefficient derivative (CLδe) and rolling momentcoefficient derivative (with respect to ailerons, Clδa) are comparable to standard values.

Conclusion

The aerodynamic analysis carried out using XFLR-5, although basic in nature, provides a good startingpoint for contructing a nonlinear model simulation. Although the drag model is inacurate, thisprimarily affects the estimation of thrust requirements only and can be improved using flight datafrom glide tests. Overall, the values of the aerodynamic derivatives obtained seem to be reasonableand agree with the physics of flight dynamics. The data estimated through this analysis will beupdated after obtaining flight data from flight testing and carrying out system identification.

References

1. Brian Taylor, ‘BFF Center of Gravity Testing’

2. Aditya Kotikalpudi, ‘Swing Tests for Estimation of Moments of Inertia’

3. Brian Taylor, ‘AMT-200S Motor Glider Parameter and Performance Estimation’, NASA/TM-2011-215974

6

4. E. Seckel and J. J. Morris, ‘The Stability Derivatives of the Navion Aircraft Estimated by VariousMethods and Derived from Flight Test Data’

5. Burnett E., Atkinson, C., Beranek, J., Sibbitt, B., Holm-Hansen, B. and Nicolai, L., “NDOFSimulation model for flight control development with flight test correlation,” AIAA Modelingand Simulation Technologies Conference, Vol. 3, Toronto, Canada, 2010, pp. 7780-7794.

6. Brian Taylor, ‘BFF Laser Scan and Outer Mold Line’

7. Website for download: http://www.xflr5.com

7

Appendix A

Graphs here show the data used to generate the functions for stability and control derivatives, alongwith the curve generated by the functions. Only those graphs are shown which have non-zero slopesi.e. derivatives which were found to be constant across α are not shown. All the derivative valuesalong Y axis are in rad−1.

8

9

10

11

12