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EVALUATING THE IMPACT OF PARASITIC DRAG ON THE ACCURACY OF ENDURANCE PREDICITIONS Leonid Heide, Chris Regan, Demoz Gebre Egziabher University of Minnesota: Twin Cities August 26, 2018
Abstract
The cost-effectiveness and versatility of electric unmanned aerial vehicles (UAVs) has led to an increase in demand for efficient payload-carrying aircraft [4]. Many project criteria require an endurance prediction based on a specific mission profile. Current methods for determining the endurance of fixed-wing UAVs involves estimating the key variable of parasitic drag using empirical equations and approximated drag values. This study seeks to evaluate the impact of estimating parasitic drag using conventional methods on the accuracy of endurance predictions for UAVs. Using glide tests, drag is measured for a small electric aircraft, and compared to predictions made using the component drag build up-method for conventional aircraft. It is demonstrated that the parasitic drag generated by small UAVs is sufficiently large to invalidate endurance predictions based on coefficients of drag calculated with the standard component drag build up method developed for fixed wing aircraft.
Background
The endurance of electric unmanned aerial vehicle (UAV) can be predicted using the drag and the power system characteristics of an aircraft. Total drag consists of drag caused by the generation of lift 2 (푘퐶퐿 ) and a lift-independent component (퐶퐷0) [6]. This relationship is shown in the expression used to calculate the drag coefficient (퐶퐷):
2 (1) 퐶퐷 = 퐶퐷0 + 푘퐶퐿 .
Drag caused by the creation of lift, known as induced drag, can be reliably estimated since the coefficient of lift (퐶퐿) is typically easy to calculate using aircraft characteristics or wind-tunnel data. However the lift-independent component of drag, known as parasitic drag, is difficult to extrapolate analytically as it includes complex factors such as skin friction, pressure drag, and interference drag [2]. 2
In order for an aircraft to maintain steady flight, sufficient thrust must be generated by the power system to overcome the total drag force [1]. In the case of un-accelerated flight thrust must equal drag [6] and the power required is the cross-product of the aircraft’s velocity and drag. In the case of electric aircraft, power is provided by a battery pack. The time over which the battery can reliably output the necessary current can be calculated using the characteristics of the battery, the discharge rate, and the power system’s efficiency (which can be accurately estimated for electric UAVs) [10]. By combining the required power and battery equations, the endurance of an aircraft in hours (E) can be determined by the equation [10]:
푛 1−푛 휂푡표푡푉×퐶 (1) 퐸 = 푅푡 [1 2푊2푘 ] 휌푈3푆퐶 +( ) 2 퐷0 휌푈푆
Equation 1 demonstrates the relationship between the endurance and the coefficient of parasitic drag
(퐶퐷0). An accurate drag prediction is therefore essential to predict endurance, and to maximize an aircraft’s flight time and range (since drag must be minimized) [4].
The quickest method to the estimate parasitic drag coefficient is by using aircraft surface area and estimated skin friction coefficients [5]. The skin-friction method is based on the assumption that the parasitic drag for “clean” aircraft is primarily skin-friction drag [7],[3]. However this method only provides a rough estimate of the minimum coefficient of drag. A more accurate drag prediction can be made with the component drag build-up method (CDBM). The CDBM estimates parasitic drag by using modified skin friction coefficients and component “form factors” that estimate the pressure drag due to viscous separation [7], [3]. Effects due to component interference and special features can also be accounted for using the component build-up method. Empirical equations utilized for the CDBM are derived from analyses of full-scale aircraft designs with high Reynolds numbers. The Reynolds number is used as a scaling factor for calculations in aerodynamic, and represents the ratio of the inertial forces to the viscous forces experienced in motion as a body moves through a fluid [2]. The small size of electric UAVs coupled with their lower operational velocities results in them having significantly smaller Reynolds numbers and higher drag relative to their size [9]. The purpose of this study is to demonstrate that estimating drag of a small electric UAV using the component drag build-up method developed for conventional aircraft causes significant inaccuracies in endurance predictions. It is proposed that accurate drag coefficients are necessary to make valid endurance predictions.
To demonstrate that parasitic drag on small UAVs is high enough to cause a significant divergence from aircraft endurance predictions, an Eflite Ultra-Stick 25e belonging to the University of Minnesota Uninhabited Aerial Vehicle lab was equipped with an airspeed sensor, GPS, and the Goldy-III 3
flight controller. The aircraft was put through a series of glide tests during which descent rates and true airspeeds were recorded by the Goldy-III flight controller. Using the collected data and standard atmospheric conditions, the glide-angle, lift, and drag equations, the parasitic drag curve was determined for the aircraft. The real drag was then compared to a prediction made using the component drag build up method. It was concluded that the parasitic drag on a small UAV is higher than a prediction made using assumptions that hold for conventional aircraft, thereby invalidating endurance predictions made using coefficients derived from the standard CDBM.
Prediction
The coefficient of induced drag (퐶퐷푖) was calculated using the equation [6]:
퐶2 (2) 퐶 = 퐿 푑푖 휋퐴푅푒
Where (퐴푅) is the wing’s aspect-ratio. The coefficient of lift (퐶퐿) was calculated using the aircraft’s parameters [6]:
2푊 (3) 퐶퐿 = 2 휌푈 푆푟푒푓
Where (푊) is the aircraft’s weight in, (𝜌) is density of the free-stream, (푈) is the airspeed, and (푆푟푒푓) is the aircraft’s reference area. Oswald’s efficiency factor (푒) was calculated using the equation provided by Raymer [7]:
(4) 푒 = 1.78(1 − 0.0045퐴푅0.68) − 0.64
The coefficient of parasitic drag (퐶퐷0) was calculated using the equation [7]:
Σ(푄푐퐶푓퐹퐹푐푆푤푒푡푐) (5) 퐶푑0 = 1.05 [ + 퐶푑0 + 퐶푑0 ] 푆푟푒푓 푝푟표푝푒푙푙푒푟 푙푎푛푑푖푛푔 푔푒푎푟
Where 퐶푓 is the skin friction coefficient, and 퐹퐹푐, 푆푤푒푡푐 represent form factor, and wetted area of a given component respectively. Contributions due to interference drag are represented by 푄푐, which was assumed to be one due to the aircraft being high-wing [7]. The additional 5% accounts for any additional protrusions, such as the pitot-static tube mount. For the wing and the horizontal and vertical stabilizers, the form factor (퐹퐹) was calculated using the following [7]:
4 0.6 푡 푡 0.18 (6) 퐹퐹푤푖푛푔 & 푠푡푎푏푖푙푖푧푒푟푠 = [1 + ( ) + 100 ( ) ] ∗ [1.34푀 ] (푥⁄푐)푚 푐 푐
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푡 Where (푥⁄푐) is the chord-wise location of the airfoil’s maximum thickness, ( ) is the airfoil thickness 푚 푐 divided by chord, and (푀) is the Mach number. The fuselage’s form factor was calculated using [7]:
60 푓 (7) 퐹퐹 = 1 + + 푓푢푠푒푙푎푔푒 푓3 400
푙 (8) 푓 = 4 √( )퐴 휋 푚푎푥
Where (푙) is the maximum thickness, and (퐴푚푎푥) is the maximum frontal area (assuming a smooth surface). The skin friction coefficient (퐶푓) was calculated using a method from “Boundary Layer Theory” by Hermann Schlichting [8]:
0.455 퐴 (9) 퐶푓 = 2.58 − (푙표푔10푅퐿) 푅퐿
Where the Reynold’s number (푅퐿 ) is based on the wing chord length [2], The constant (A) was determined using a table provided in “Boundary Layer Theory”[8]. A linear fit was assigned to the provided values of (A) and the critical Reynold’s numbers. Variable A was then found for the lower critical Reynold’s number for the NACA 0012 airfoil [11].
To account for a wind-milling prop, an additional factor (퐶푑0푝푟표푝푒푙푙푒푟) was factored on, calculated using:
0.8휎퐴푝푟표푝푒푙푙푒푟 푑푖푠푘 (10) 퐶푑0 = 푝푟표푝푒푙푙푒푟 푆푟푒푓
푛 (11) 𝜎 = 푏푙푎푑푒 퐴푅푏푙푎푑푒휋
Where (푛푏푙푎푑푒) is the number of blades, (퐴푝푟표푝푒푙푙푒푟 푑푖푠푘) is the frontal area of the propeller disk, and
(퐴푅푏푙푎푑푒) is the blade aspect ratio. Additionally, the landing gear was accounted for:
0.25퐴푡푖푟푒+0.05퐴푠푡푟푢푡 (12) 퐶푑0 = 1.2 [ ] 푙푎푛푑푖푛푔 푔푒푎푟 푆푟푒푓
Where (퐴푡푖푟푒) and (퐴푠푡푟푢푡) are the frontal cross-sectional areas of the tire and strut respectively. An additional 20% was added to account for interference drag between the components and the fuselage.
Using the coefficients, the induced, parasitic, and total drag curves could then be plotted using the drag equation [6]:
1 (13) 퐷 = 𝜌푈2푆 퐶 2 푟푒푓 퐷 5
Methodology
An Ultra-Stick 25e, a single engine electric aircraft with a 1.25 meter wingspan, was equipped with an airspeed sensor, GPS, and the Goldy-III flight controller and data collector. The aircraft made several controlled glides, where the airspeed was adjusted using through deflection of the elevator. The aircraft altitude and airspeed was recorded by Goldy-III throughout the flight. Using the data, the descent rate (퐻̇ ) and average airspeed (푉퐴푉퐺) was determined over various ranges throughout the glides. Drag was then obtained by first solving for the glide angle (훾) [6]:
퐻̇ (14) 훾 = sin−1 [ ] 푉퐴푉퐺
(15) 퐷 = 푊 sin 훾
Figure 1: “Thor”, the Ultra-Stick 25e used for the glide tests, with the Goldy III flight controller on board
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Results
Figure 2: The bottom graph shows altitude throughout the flight (glides correspond to downward slopes), and the corresponding airspeed on the top graph.
Figure 3: A sample range from the third glide test, showing the steady glide descent and the stable velocity 7
Measured Drag 12
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7 Drag Drag (N)
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3 10 12 14 16 18 20 22 24 26 Airspeed (m/s)
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Figure 4: The total drag values determined by the glide tests. The standard deviation of the average airspeed is (0.4397).
Discussion
In order to isolate real parasitic drag, the calculated induced drag was subtracted from the real total drag values shown in figure 4:
(16) 퐷푟푒푎푙 푝푎푟푎푠푖푡푖푐 = 퐷푟푒푎푙 푡표푡푎푙 − 퐷푝푟푒푑푖푐푡푒푑 푖푛푑푢푐푒푑
As induced drag is marginal at higher velocities, and all collected data was for velocities above 10 m/s, any inaccuracies in the predicted induced drag are negligible in the scope of this operation. A quadratic best-fit line was applied to the real parasitic data points, with an R2 values of 0.9856 (figure 5). 8
14 Measured vs. Predicted Parasitic Drag
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10 Experimental: y = 0.0224x2 - 0.0859x 8 R² = 0.9856
Drag Drag (N) 6
4 Predicted: y = 0.0054x2 - 0.0044x
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0 0 5 10 15 20 25 Airspeed (m/s) Experimental Parasitic Drag Experimental Parasitic Drag Fit Predicted Parasitc Drag
Figure 5: The experimental parasitic drag values, its quadratic fit, and the predicted parasitic drag curve.
The parasitic drag calculated using the component drag build up method had an average percent error of 71%. The significant difference between the predicted and actual drag curves confirms the hypothesis that the methods employed for conventional aircraft provide unreliable estimates for small electric UAVs. The inaccuracy can be attributed to a variety of potential factors. The described empirical equations (such as those for calculating form-factor) are developed from aircraft with large Reynolds numbers, and therefore may not be suited for aircraft with small Reynolds numbers. Furthermore, assumptions reasonably made for a large aircraft regarding about the “cleanliness” of the body, low interference drag, and uniformity of dynamic pressure, may not be made for a small aircraft. Although the resistance caused by externally mounted components (such as a pitot-static probe or antennae) is negligible on conventional aircraft, the large relative size of these devices on small UAVs means that they contribute a significant amount of pressure and interference drag. In addition, since the square fuselage of the Ultra-Stick 25e has un-filleted edges and a flat front, the assumption of a relatively smooth, rounded surface cannot be made. The fuselage’s form would generate a large amount of turbulence, thereby having a much larger drag coefficient than predicted. 9
The drag inaccuracy of the parasitic drag prediction has a significant impact on the endurance prediction. As the power required to overcome drag is given by the cross product of drag and velocity, power curves for both the predicted and measured drag were created.
Figure 6: Graph showing the predicted amount of power required to overcome the drag force and the experimentally determined power required to overcome the drag force vs. airspeed.
Figure 6 demonstrates that the power necessary to overcome drag is noticeably higher than what was predicted. The significant difference in the power curves confirms that making drag predictions using the component build up method (developed from conventional aircraft) is not a viable method to predict a UAV’s endurance.
To accurately predict endurance of small UAVs analytically, the component drag build up method must be adjusted. Further research can be done to determine whether conventional empirical equations (such as the form-factor) are viable for low Reynolds numbers. Methods can be developed to better account for drag caused by exterior components, and un-rounded bodies (like the fuselage of the Ultra-Stick 25e). The effect of interference drag on small aircraft, and how to better determine the interference factor for various scenarios can also be studied. 10
Conclusion
Accurate drag coefficients are essential to making valid endurance predictions for fixed-wing aircraft. Parasitic drag predictions were made for an Ultra-Stick 25e using the components build up method. A series of glide tests were performed in order to back-out the actual parasitic drag curve of the aircraft, and the values compared to the predictions. It was demonstrated parasitic drag predictions made using the component drag build-up method (with assumptions based on conventional aircraft), do not reflect real drag values and therefore cannot be used to make accurate endurance predictions.
Acknowledgments
This research was financed by the University of Minnesota’s undergraduate research opportunities program (UROP).
I am grateful to my mentor Dr. Demoz Gebre Egziabher for giving me the opportunity to conduct this research, and providing invaluable advice.
I am very thankful to Chris Regan from the University of Minnesota Unmanned Aerial Vehicle lab for his crucial support and advice throughout the research process.
I also wish to thank Curtis Olson from the University of Minnesota Unmanned Aerial Vehicle lab, who piloted the Ultra-Stick 25e during the glide tests.
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Work Cited
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