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1 Design of a Four-Seat, General Aviation Electric Aircraft 2 3 Financial and environmental considerations continue to encourage aircraft 4 manufacturers to consider alternate forms of aircraft propulsion. On the financial 5 end, it is the continued rise in aviation fuel prices, as a result of an increasing demand 6 for air travel, and the depletion of fossil fuel resources; on the environmental end, it is 7 concerns related to air pollution and global warming. New aircraft designs are being 8 proposed using electrical and hybrid propulsion systems, as a way of tackling both the 9 financial and environmental challenges associated with the continued use of fossil 10 fuels. While battery capabilities are evolving rapidly, the current state-of-the-art 11 offers an energy density of ~ 250 Wh/kg. This is sufficient for small, general aviation 12 electric airplanes, with a modest range no more than 200 km. This paper explores the 13 possibility of a medium range (750 km) electric, four-seat, FAR-23 certifiable general 14 aviation aircraft, assuming an energy density of 1500 Wh/kg, projected to be available 15 in 2025. It presents the conceptual and preliminary design of such an aircraft, which 16 includes weight and performance sizing, fuselage design, wing and high-lift system 17 design, empennage design, landing gear design, weight and balance, stability and 18 control analysis, drag polar estimation, environmental impact and final specifications. 19 The results indicate that such an aircraft is indeed feasible, promising greener general 20 aviation fleets around the world. 21 22 Keywords: General aviation aircraft, electric aircraft, aircraft design 23 24 25 Introduction 26 27 The main source of energy in aviation today is fossil fuels. As our energy 28 consumption increases exponentially, it leads to a corresponding rise in the 29 demand for these fuels, which will persist in the next few decades. This 30 increased demand causes an increase in fuel prices, which in turn increases the 31 operating cost for airlines, business flying, and general aviation. More 32 importantly, the increasing use of fossil fuels in aviation results in increasing 33 CO2 emissions, as well as increasing noise levels around airports. There are, of 34 course, other ways to produce energy for airplanes, without using fossil fuels. 35 Many of these are currently being explored but they are not, at the moment, 36 close to their full potential (Riddell, 2004). Electric aircraft offer lower 37 emissions, lower noise levels during taxing, takeoff and landing, lower 38 operating costs, and improved overall efficiency. This paper explores the 39 possibility of an electric four-seater aircraft, as an alternative to conventional 40 gasoline-powered aircraft. 41 The paper presents the preliminary design of a four-passenger, electric, 42 general aviation aircraft, with a range of 750 km, a cruise speed of 270 km/hr 43 at a cruising altitude of 3000 m, a takeoff field length of 760 m and a landing 44 field of 600 m. The main challenge currently associated with electric aircraft is 45 the low specific energy density of the batteries, which results in prohibitive 46 levels of battery weight for typical power requirements. This paper examines 47 possible design solutions that would meet the mission specification of a general 48 aviation aircraft, as described above.
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1 Comparative Study of General Aviation Electric Aircraft 2 3 This section presents a review and comparison of electric general aviation 4 aircraft with a similar mission specification. 5 6 Bye Aerospace eFlyer 4 7 8 The eFlyer (Figure 1) was developed from the smaller two seat Bye 9 Aerospace aircraft and is made of composite materials. It features a cantilever 10 low wing with a fixed landing gear, a single engine tractor configuration, with 11 four-seats enclosed under a bubble canopy. The low wing configuration offers 12 greater fuselage volume for passengers, makes it easier to refuel, and easier to 13 retract the landing gear inside the wing. A single electric motor capable of 14 producing 105 kW (141 hp) is powered by ten batteries, which provide an 15 endurance of four hours. 16 17 Figure 1. Bye Aerospace eFlyer 4 (Bye Aerospace, 2020)
18 19 Pipistrel Panthera 20 21 The Pipistrel Panthera (Figure 2) is a lightweight, all-composite, highly 22 efficient, four-seat aircraft, which is currently under development. The 23 Panthera electro features a cantilever low wing arrangement, similar to eFlyer 24 4. The four-seater aircraft is powered by a Siemens 200 kW electric motor and 25 is intended to achieve a 400 km range with a cruise speed of 218 km/hr. The T- 26 tail configuration offers a simple design, low empennage weight, better tail 27 efficiencies, while at the same time reducing the interference from the wake of 28 the wing and the propeller slipstream.
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1 Figure 2. Panthera Electro (Panthera, 2020)
2 3 4 Yuneec International E430 5 6 Yuneec E430 (Figure 3) is a two-seater electric aircraft with a cruise speed 7 of 100 km/hr, designed for commercial production. It has a V-tail and a high 8 wing made of composites with a high aspect ratio. The high wing makes 9 loading and unloading easier, provides better visibility towards the ground and 10 good ground clearance. The aircraft is powered by 3 to 5 packs of Yuneec 11 OEM lithium polymer rechargeable batteries, which provide 2.5 hours 12 endurance. The batteries can be recharged in 3 to 4 hours from a 220-volt 13 outlet. 14 15 Figure 3. Yuneec E430 (Yuneek, 2020)
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1 Pipistrel Taurus Electro G2 2 3 The Taurus Electro G2 (Figure 4) is a two-seat glider with a range of 600 4 km. It features a low wing configuration with a T-tail and has replaced the old 5 gasoline-powered engine with a high-performance electric power train and Li- 6 Po batteries. 7 8 Figure 4. Taurus Electro G2 (Taurus Electro, 2020)
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10 11 12 Airbus Vahana 13 14 The Airbus Vahana is an electric-powered eight propeller VTOL personal 15 air vehicle prototype by Airbus. It is a self-piloted vehicle with a capacity of 16 two passengers for a range of 100 km cruising at 140 miles/hr. It uses the 17 distributed electric propulsion (DEP) concept on eVTOL aircraft. DEP allows 18 for quickly changing the speed of each propeller independently to compensate 19 for gusty winds, keeping the aircraft stable during flight. 20 21 Figure 5. Airbus Vahana (Airbus Vahana, 2020)
22 23
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1 Preliminary Sizing 2 3 The preliminary sizing of the proposed aircraft consists of weight sizing 4 and performance sizing, as described below (Roskam: part I, 1985). 5 6 Weight Sizing 7 8 The method below estimates the mission takeoff weight (WTO), the empty 9 weight (WE), and the battery weight (WBAT) of the airplane for the mission 10 specification given in the introduction. 11 12 Table 1. Takeoff and Empty Weight of Similar Electric Airplanes Takeoff Weight Aircraft Empty Weight (WE) lbs (WTO) lbs
Pipistrel Taurus Electro G2 1212 674 (Wikipedia)
Lange Antares 23E (Wikipedia) 1873 1124
Extra 330 LE (Wikipedia) 2094 1455
Sunflyer 4 (Bye Aerospace) 2700 1900
Airbus Vahana (Airbus) 1797 1532
Pipistrel Panthera (Wikipedia) 2645 1764
Silent 2 Electro 6482 4321 (Alisport Swiss)
Electrolight 2 6805 4062 (Siegler, 2011)
NASA Scuba Stingray (Banke, 3195 1438 2015)
13 14 Figure 6 shows a regression plot of takeoff versus empty weight for the 15 airplanes listed in Table 1.
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1 Figure 6. Regression plot of takeoff versus empty weight for the airplanes in 2 Table 1
3 4 5 The line in Figure 6 is described by: 6 7 y= 0.9652x + 0.3143 (1) 8 9 while the relationship between takeoff weight and empty weight is given by: 10 11 Log WTO= A + B log WE (2) 12 13 A comparison of equations (1) and (2) gives the regression coefficients A and 14 B for the relationship between takeoff and empty weight of electric, general 15 aviation aircraft: A = 0.3143 and B = 0.9652. The mission weights of the 16 airplane are now calculated as follows. 17 Payload Weight 18 Using an average weight of 175 lbs per passenger plus 30 lbs of baggage 19 (Roskam, part I, 1985) the payload weight is WPL = 4 x (175 + 30) = 820 lbs. 20 Battery Weight 21 Hepperle (2012) gives the following empirical formula for the range of electric 22 aircraft: 1 퐿 푊퐵퐴푇 23 푅 = 퐸∗ ∗ ∗ ( ) ∗ ( ) ∗ ( ) (3) g 퐷 푊푇푂 24 25 Thus, aircraft range depends on lift-to-drag ratio, specific energy density 26 of the battery, total system efficiency, and takeoff weight. Table 2 shows 27 theoretical values of specific energy predicted for the near future (Hepperle, 28 2012).
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1 Table 2. Specific energy density for various types of batteries Battery Theoretical Value Expected in the next 5-10 years Li-Ion 390 Wh/kg 250 Wh/kg Zn-air 1090 Wh/kg 400-500 Wh/kg Li-S 2570 Wh/kg 500-1250 Wh/kg
Li-O2 3500 Wh/kg 800-1750 Wh/kg 2 3 Using the data in Table 2, a Li-O2 battery with an energy density of 1500 4 Wh/kg is used in the proposed design. The battery-powered propulsion system 5 offers the highest efficiency compared to conventional turboprop, turbofan and 6 fuel cell systems (Abdel-Hafez, 2012). The takeoff weight for the mission is 7 calculated from equation (4) and the weight breakdown is shown in Table 3. 8 9 WTO = WE + WPL + WBAT (4) 10 11 Table 3. Summary of mission weights
Take-off weight WTO (lbs) 3980
Payload weight WPL (lbs) 820
Operating empty weight, WE (lbs) 2523
Battery Weight, WBat (lbs) 637
12 13 Takeoff Weight Sensitivities 14 15 Take-off weight sensitivities are obtained using the regression coefficients 16 A = 0.3143 and B = 0.9652 calculated above and coefficients C and D 17 calculated below (Roskam, part I, 1985): 18 19 푊퐸 = 퐶푊푇푂 − 퐷 (5) 20 21 For fully electric aircraft C = 1 and 22 23 퐷 = 푊푃퐿 + 푊퐵퐴푇 = 1457 푙푏푠 (6) 24 25 The equations below describe various sensitivities. 26 Takeoff weight with respect to payload: 27 훿푊푇푂 퐵∗푊푇푂 28 = (7) 훿푊푃퐿 퐷−퐶(1−퐵)∗푊푇푂 29 30 Takeoff weight with respect to empty weight: 훿푊푇푂 퐵∗푊푇푂 31 = 퐿표푔10푊 −퐴 (8) 훿푊퐸 𝑖푛푣.퐿표푔10[ 푇푂 ] 퐵
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1 Range with respect to takeoff weight: 훿푅 WBAT 2 ∗ = −퐸 ∗ 푡표푡 ∗ (L/D) ∗ (1/g) ∗ ( 2 ) (9) 훿푊푇푂 WTO 3 Range with respect to the lift-to-drag ratio: 훿푅 4 = (1 − 푓 − 푓 ) ∗ 퐸∗ ∗ ∗ (1/g) (10) 훿(퐿/퐷) 푒 푝 푡표푡 5 Range with respect to battery energy density: 훿푅 6 = (1 − 푓 − 푓 ) ∗ (퐿/퐷) ∗ ∗ (1/g) (11) 훿퐸∗ 푒 푝 푡표푡 7 8 The sensitivities calculated from the equations above are shown in Table 4 9 and plotted in figures 7, 8 and 9. 10 11 Table 4. Takeoff weight and range sensitivities Sensitivity Parameters Sensitivity Values
훿푊푇푂/훿푊푃퐿 2.92 lbs/lb
훿푊푇푂/훿푊퐸 1.515 lbs/lb
훿푅/훿푊푇푂 -0.188 km/lb 훿푅/훿(퐿/퐷) 74 km 훿푅/훿퐸∗ 0.50 km/Wh/kg 12 13 Figure 7. Takeoff weight vs. payload weight
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1 Figure 8. Range vs. specific energy density
2 3 4 Figure 9. Range vs. lift-to-drag ratio
5 6 7 As expected, range depends strongly on the lift-to-drag ratio but also on 8 the specific energy density of the batteries. This is because the takeoff weight 9 of electric aircraft tends to be higher than conventional aircraft due to the 10 weight of the batteries. Hence, improving battery energy density is paramount 11 in helping increase the range of electric aircraft. 12 13 Performance Sizing 14 15 The proposed aircraft has a takeoff weight less than 6000 lbs, hence it falls 16 under the FAR-23 certification regulations. A performance constraint analysis 17 is used to determine the design point of the aircraft, namely the combination of 18 wing area and power required to meet all the mission and FAR 23 19 requirements. Each requirement is plotted as a relationship between wing 20 loading (W/S) and power loading (W/P), as shown in Figure 11. To meet 21 takeoff and landing requirements an assumption must be made about the 22 maximum lift coefficient of the aircraft in each of the two configurations. The 23 matching graph of the aircraft is presented in figures 11 and 12.
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1 Stall Speed Requirement 2 3 The stall speed requirement is set at 60 knots and relates to wing loading, 4 density altitude and maximum lift coefficient as shown in equation (12). 5 Single-engine airplanes have a range of maximum lift coefficients between 1.3 6 and 1.9 (Roskam, part I, 1985). A density altitude of 10,000 ft is assumed 3 7 (0.0056 lb/ft ). 1 푊/푆 2 8 푉푠푡푎푙푙 = (2 ∗ ) (12) 휌∗퐶퐿푚푎푥 9 10 Takeoff Distance Requirement 11 12 The takeoff distance requirement is 푆푇푂 = 2500 푓푡. 13 Takeoff distance relates to wing loading, power loading, density ratio and 14 maximum lift coefficient as shown in equation (13), using the takeoff 15 parameter defined in equation (14). 16 2 17 푆푇푂 = 8.134 푇푂푃23 + 0.0149 푇푂푃23 (13) 18 (푊/푃)푇푂 19 푆푇푂퐺∞ ((푊/푆)푇푂 ∗ ) = 푇푂푃23 (14) 휎∗퐶퐿푚푎푥 20 21 The density ratio at 10,000 feet is: 휎 = 0.7386 22 while the takeoff parameter is (Roskam, part I, 1985): 23 푙푏푠2 24 푇푂푃 = 220 (15) 23 푓푡2∗ℎ푝 25 26 Hence, the takeoff distance requirement may be expressed as: 27 푊 ( ) 2 푊 푃 푙푏푠 28 ( ) ∗ 푇푂 < 162 (16) 푆 퐶 푓푡2∗ℎ푝 푇푂 퐿푀퐴푋푇푂 29 30 Landing Distance Requirement 31 32 The landing distance requirement is 푆퐿 = 2000 푓푡 at sea level. 33 Landing weight is heavier for electric aircraft since battery weight stays 34 the same throughout the flight unlike the reduction in fuel weight in 35 conventional aircraft. Hence: 36 푊퐿/푊푇푂 = 1 (17) 37 38 The landing distance relates to stall speed by: 39 2 40 푆퐿 = 0.5136 ∗ 푉푆퐿 (18) 41 42 Relating stall speed to wing loading and maximum lift coefficient yields:
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1 2∗(푊/푆)퐿 2 2 = (푉푆 ∗ 1.688) (19) 0.002049∗퐶퐿푚푎푥퐿 3 4 from which we get the relationship for the wing loading as a function of the 5 maximum lift coefficient in the landing configuration. 6 푊 푊 7 ( ) = ( ) = 11.36 ∗ 퐶퐿푚푎푥 (20) 푆 퐿 푆 푇푂 퐿 8 9 Drag Polar Estimation 10 11 To size the aircraft according to climbing requirements, it is necessary to 12 estimate first the drag polars (Roskam, part I, 1985). The drag coefficient is 13 given by: 14 퐶2 15 퐶 = 퐶 + 퐿 (21) 퐷 퐷0 휋∗퐴∗푒 16 17 The low speed drag coefficient can be expressed as a function of the 18 equivalent parasite drag area: 19 20 퐶퐷0 = 푓/푆 (22) 21 22 The equivalent parasite area is estimated from similar aircraft using the 23 takeoff weight as follows: 24 25 퐿표푔10푓 = 푎 + 푏 ∗ log10 푆푤푒푡 (23) 26 where a = −2.0458 and b = 1.00 27 28 퐿표푔10푆푤푒푡 = 푐 + 푑 ∗ log10 푊푇푂 (24) where c = 1.0892 and d = 0.5147 29 2 30 From which we get: 푆푤푒푡 = 875 푓푡 푎푛푑 푓 = 7.9 (25) 31 32 Assuming an aspect ratio A = 10 and an Oswald efficiency factor e = 0.85 33 for the clean configuration, the drag polars are shown in Table 5. 34
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1 Table 5. Drag polars for the proposed aircraft Oswald Zero-Lift Drag Flight Condition Efficiency Drag Polar Coefficient (C ) D0 Factor (e)
2 Clean 0 0.85 0.0407 + 0.0374퐶퐿
2 Takeoff flaps 0.0165 0.80 0.0572 + 0.0397퐶퐿
2 Landing flaps 0.0615 0.75 0.1022 + 0.0424퐶퐿
2 Landing gear 0.0215 no effect 0.1237 + 0.0424퐶퐿
2 3 Climb Requirements 4 5 The rate of climb in fpm is expressed as (Roskam, part I, 1985): 6 7 푅퐶 = 푑ℎ/푑푡 = 33,000 ∗ 푅퐶푃 (26) 8 9 where the rate-of-climb parameter is given by: 10 1/2 푝 (푊/푆) 11 푅퐶푃 = − (27) 푊/푃 1/2 3/2 19∗휎 ∗퐶퐿 /퐶퐷 12 13 The airplane must meet the climb requirements under FAR 23.65 and FAR 14 23.77, as listed below. 15 16 FAR 23.65 17 The minimum rate of climb at sea level must be at least: RC = 300 fpm 18 This gives a rate-of-climb parameter: RCP = 0.0091 hp/lbs 19 20 Using the drag polar for the clean aircraft from Table 5 we get the 21 following relationship between wing loading and power loading: 22 23 208/(2.3 + (W/S) 1/2) = 푊/푃 (28) 24 25 The minimum climb gradient for land planes is 1:12. Using: 26 휎1/2 {퐶퐺푅+(퐿/퐷)−1} 27 퐶퐺푅푃 = 18.97 ∗ ∗ = (29) 푝 (푊/푃)∗(푊/푆)1/2 1/2 퐶퐿 28 29 we get the relationship between wing loading and power loading: 30 31 (푊/푃) ∗ (푊/푆)1/2 = 110.3 (30) 32 33 FAR 23.77 34 The climb gradient must be at least: 퐶퐺푅 = 1/30 = 0.0333
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1 from which we get: 2 3 (푊/푃) ∗ (푊/푆)1/2 = 113 (31) 4 5 Cruise Speed Requirement 6 7 The cruise speed for propeller-driven aircraft is calculated at 70% to 80% 8 of total power. At this power setting, the profile drag is higher than the induced 9 drag, which is approximately: 10 11 퐶퐷𝑖 = 0.1퐶퐷0 (32) 12 13 Cruise speed is proportional to the power index, defined as: 14 푊/푆 1/3 15 푉 ∞ 퐼 = ( ) (33) 푐푟 푝 휎∗(푊/푃) 16 17 For a cruise speed of 150 knots (172 mph) the power index is 퐼푝 = 1.0 18 (Roskam, part I, 1985). Hence equation (33) yields: 19 푊/푆 1/3 20 ( ) = 1 (34) 휎∗(푊/푃) 21 22 It is now possible to determine the best combination of wing loading and 23 power loading by plotting all requirements in the matching graph, as shown in 24 Figure 10 and assuming appropriate values for the maximum lift coefficients. 25 A clean version of this graph is reproduced in Figure 11. Table 6 summarizes 26 the results from these studies. 27 28 Figure 10. Matching graph for the proposed aircraft
29 30 31
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1 Figure 11. Matching graph including only the three critical requirements, 2 which define the design point
3 4 5 The design point shown in Figure 11 results in a wing loading of 20.5 psf 6 and a power loading of 20 lbs/hp. The various design parameters that 7 correspond to these values are summarized in Table 6. 8 9 Table 6. Design parameters Clean 1.5 Maximum lift coefficient, CLmax Takeoff 1.6
Landing 1.8
Aspect ratio 10
Wing loading, W/S 20.5 psf
Takeoff power loading, (W/P)TO 20 lbs/hp
Wing area, S 194 ft2
Take-off power, PTO 199 hp 10 11 12 Preliminary Design 13 14 The following subsections present the preliminary design of the proposed 15 aircraft (Roskam, part II, 1985). 16 17 Configuration 18 19 The proposed configuration is shown in Figure 19. It features a low, 20 cantilever wing with zero sweep for better aerodynamic performance at low
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1 speeds. The T-tail was chosen to increase the effective aspect ratio of the 2 vertical stabilizer, while keeping the horizontal stabilizer outside the wing 3 wake. Finally, a conventional tricycle landing gear offers fewer parts, lower 4 weight, lower cost, is easier to design, and most importantly, provides for good 5 ground stability. 6 7 Propulsion System 8 9 The electric engine chosen is a Siemens brushless motor-SP 260D. It 10 features a double winding motor with a 95% efficiency at 2500 rpm and is 11 lightweight. Energy density, safety, cost, reliability and maintainability were 12 all considered in the selection of rechargeable, lithium-air batteries with an 13 energy density of 1500 Wh/kg, expected to be available in 2025 (Hepperle, 14 2012). 15 The propulsion system is integrated in the fuselage with the electric motor 16 placed at the front and the batteries placed in the wing as well as in the aft 17 fuselage section. The propeller diameter is obtained from equation (35) 18 (Raymer, 2012): 19
1/2 20 퐷푝 = (4 ∗ 푃푚푎푥 ∗ 푛푝 ∗ 푃푏푙) = 5.50 ft (35) 21 22 Fuselage Design 23 24 Fuselage design parameters were calculated using the aerodynamic 25 considerations and definitions in Roskam (part II, 1985) and are shown in 26 Table 7. 27 28 Table 7. Fuselage design parameters Fuselage Parameters Dimension
Length (푙푓) 29.40 ft
Inner diameter (푑푓) 4.5 ft
Fineness ratio (푙푓/푑푓) 6.53 ft
Rear fuselage angle (휃푓푐) 5 deg
Cabin length 10.4 ft
Nose length 5 ft
Tail cone length 14 ft
29 30
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1 Figure 13. Isometric view of fuselage
2 3 4 Wing and Lateral Control Surface Design 5 6 A NASA LS-0417/13 airfoil is selected because of its superior 7 aerodynamic characteristics (McGhee, Beasley & Whitcomb, 1979). From the 8 design wing loading of 20.5 psf, the wing area is: 9 2 10 푆 = 푊푇푂/(푊/푆) = 194 푓푡 (36) 11 12 while the wingspan is found from: 13 14 푏 = √퐴 ∗ 푆 = 44 푓푡 (37) 15 The root, tip, and mean aerodynamic chords are found as follows: 16 푐푟 = 2푆/(푏 ∗ (1 + 푤) (38) 17 푐푡 = 푤 ∗ 푐푟 (39) 2 2 1+푤+푤 18 푐̅ = ( ) ∗ 푐푟 ∗ (40) 3 1+푤 19 while the spanwise location of mean aerodynamic chord is given by: 푏 1+2푤 20 푦̅ = ( ) ∗ (41) 6 1+푤 21 The wing parameters are summarized in Table 8.
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1 Table 8. Wing parameters Wing area (S) 194 ft2
Aspect ratio (A) 10
Wingspan (b) 44 ft
Sweep angle (Λ) 0 deg
Airfoil thickness at the wing centerline (t/c)r 0.14
Airfoil thickness at the wing tip (t/c)t 0.12
Taper ratio (λ) 0.50
Dihedral (Γ) 7 deg
Root chord (cr) 5.87 ft
Tip chord (ct) 2.90 ft
Mean aerodynamic chord (푐̅) 4.57 ft
Spanwise location of mac (푦̅) 9.75 ft
Wing Aerodynamic Center, (χac) 1.14 ft
Aileron Chord Ratio (ca/c) 0.25
Aileron Span Ratio (ba/b) 0.60 2 3 Empennage, Directional and Longitudinal Control Surface Design 4 5 The main objective of the horizontal stabilizer is to counter the pitching 6 moments produced by the wing. This must be accomplished, of course, with 7 the smallest possible empennage area. The location of the empennage amounts 8 to estimating the necessary moment arms 푥푣 푎푛푑 푥ℎ, as defined in Roskam 9 (figure 8.1, part II, 1985). For the proposed aircraft we find: 10 푥푣 = 13.5 푓푡; 푥ℎ = 11.5 푓푡 (42) 11 12 Using the tail volume coefficients, we can now calculate the required area 13 for the horizontal and vertical stabilizers. 14 15 푉ℎ = 푥ℎ ∗ (푆ℎ/(푆 ∗ 푐̅)) (43a) 16 푉푣 = 푥푣 ∗ (푆푣/(푆 ∗ 푏)) (43b) 17 Assuming 푉ℎ = 0.50 푎푛푑 푉푣 = 0.04 (43c) 2 2 18 we find 푆ℎ = 46.25 푓푡 푎푛푑 푆푣 = 26 푓푡 (44) 19
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1 Table 9. Empennage design parameters Design Parameters Horizontal Stabilizer Vertical Stabilizer Aspect Ratio 5 1.6 Taper Ratio 0.5 0.4 Wingspan 15.20 ft 6.44 ft Root Chord 4.05 ft 5.76 ft Tip Chord 2.02 ft 2.3 ft Mean Aerodynamic Chord 3.15 ft 4.27 ft Sweep 10 15 Airfoil NACA 0012 NACA 0012 Dihedral 0 90 Incidence 0 0 2 3 Figure 14. Isometric view of the empennage with respect to the wing
4 5 6 Landing Gear Design & Weight and Balance Analysis 7 8 To size the landing gear, the center of gravity must first be determined 9 through a weight and balance analysis. Since the weight of the landing gear 10 itself must be included in the weight and balance analysis, an iteration is 11 required to finalize the size and disposition of the landing gear as well as the 12 center of gravity location of the aircraft. 13 14 Weight and Balance Analysis 15 16 The initial center of gravity location is determined through a Class-I 17 weight fraction analysis of the major subgroups of the aircraft, using the 18 takeoff weight (Roskam, part II, 1985). Each component weight is expressed as 19 a fraction of the takeoff weight (WTO) or the empty weight (WE), as shown in 20 Table 10.
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1 Table 10. Component weight fractions for similar airplanes and the proposed 2 aircraft Proposed Type Cessna 210 Beech J-35 Cessna 210 J Electric Aircraft
Wing Group /WTO 0.09 0.131 0.099 0.106
Emp. Group 0.024 0.02 0.025 0.023 /WTO
Fuselage Group /WTO 0.109 0.069 0.12 0.099
Landing Gear 0.071 0.071 0.056 0.066 /WTO
Fixed equip. 0.199 0.201 0.171 0.190 /WTO
WE /WTO 0.094 0.115 0.099 0.103 3 4 Using the average weight fractions from Table 10, the Class-I component 5 weights are obtained as shown in the second column of Table 11. The mission 6 weights from weight sizing are included in the third column. The sum of the 7 weights in the first column yields an empty weight of 2342 lbs, which is 8 slightly lower than the value estimated in weight sizing (2535 lbs). The 9 difference is due to round-off errors in the weight fractions used. This 10 difference is redistributed among all the components in proportion to their 11 weights. 12 13 Table 11. Subgroup component weight summary for the proposed aircraft Component Class-I Estimation (lbs) Adjustments Class-I Weight (lbs)
Wing 425 35 460
Empennage 92 8 99
Fuselage 395 33 428
Landing Gear 263 22 285
Powerplant 758 63 821
Fixed Equip. 409 34 443
Empty Weight 2342 195 2535
Payload 820
Battery Weight 637
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Takeoff Weight 3980
1 2 The location of the center of gravity for each of the major airplane 3 components is calculated using the geometric definitions in Roskam (Table 4 10.2, part II, 1985). 5 6 Table 14. Center of gravity location of major aircraft components cg location cg location w.r.t. cg location w.r.t. component w.r.t. Component Length (ft) component leading aircraft nose length edge/nose (ft) (ft)
Fuselage 29.4 0.39 ∗ 푙푓 11.466 11.466
Wing 4.57 0.40 ∗ 푐푤 1.828 11.758 Vertical 4.27 0.30 ∗ 푐 1.281 26.411 Stabilizer 푣
Horizontal 2.56 0.30 ∗ 푐 0.768 27.608 Stabilizer ℎ
Empty Weight 29.4 0.45 ∗ 푙푓 13.23 13.23 7 8 Landing Gear Design 9 10 The maximum static load per strut is calculated from the following 11 equations: 12 푙푚 13 Nose wheel strut: 푃푛 = 푊푇푂 ∗ = 1053 푙푏푠 (45) (푙푚+푙푛) 푙푛 1 14 Main wheel strut: 푃푚 = 푊푇푂 ∗ ∗ = 1465 푙푏푠 (46) 푙푚+푙푛 푛푠 15 where, 푙푚 = 2.7 푓푡 푎푛푑 푙푛 = 7.5 푓푡 16 17 where the geometry for the static load on the tricycle gear is defined in Roskam 18 (figure 9.2a, part II, 1985). Here ns = 2, as there are two main gear struts. One 19 nose gear strut is used based on the maximum static load calculation. The gear 20 ratios are determined as follows: 21 푃푚 22 푛푠 ∗ = 0.74, Main gear tire: 퐷푡 ∗ 푏푡 = 16.5 ∗ 6 𝑖푛푐ℎ푒푠 (47) 푊푇푂 푃푛 23 = 0.26, Nose gear tire: 퐷푡 ∗ 푏푡 = 14 ∗ 5 𝑖푛푐ℎ푒푠 (48) 푊푇푂 24 25 The general arrangement of the landing gear is determined using two 26 geometric, tip-over criteria: 27 28
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1 Longitudinal tip-over criterion 2 3 The main landing gear must be behind the aft center of gravity location 4 and the angle between this location and the main landing gear should be 15 5 degrees as shown in Figure 15. 6 7 Figure 15. Longitudinal tip-over criterion for the proposed aircraft
8 9 10 Lateral tip-over criterion 11 12 The lateral tip-over criterion (Figure 16) requires that 휓 ≤ 550. 13 14 Figure 16. Lateral tip-over criterion (Roskam, part II, figure 9.1a, 1985)
15 16 17 Longitudinal ground clearance criterion 18 19 The longitudinal ground clearance criterion requires that the angle defined by 20 the ground contact of the main landing gear and the fuselage tail is greater than 0 21 the airplane liftoff angle (typically 15 ). As shown in Figure 17, the proposed 22 configuration clearly exceeds this value. 23
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1 Figure 17. Longitudinal ground clearance criterion
2 3 4 Lateral ground clearance criterion 5 6 The lateral ground clearance criterion requires that the angle defined by 7 the ground contact of the main gear and the lowest parts of the wing is at least 0 8 5 with tires and struts deflated. Figure 18 shows that the proposed 9 configuration exceeds this value. 10 11 Figure 18. Lateral ground clearance criterion
12 13 14 As mentioned earlier, an iterative process is required to determine the 15 disposition of the landing gear, as we need to estimate first the center of gravity 16 location of the airplane, which must include the weight of the landing gear 17 itself. As a result of this process, the main landing gear was moved 1.5 ft 18 forward to meet the two geometric criteria mentioned above. A CAD model of 19 the proposed aircraft configuration is shown in Figure 19. 20
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1 Figure 19. Proposed aircraft configuration
2 3 4 Weight and Balance Analysis 5 6 Table 15 shows the component weight breakdown and the center of 7 gravity coordinates of each component, using the final disposition of the 8 landing gear. 9 10 Table 15. Component weights and center of gravity coordinates Weight 풙 푾 ∗ 풙 풛 푾 ∗ 풛 Airplane Component (푙푏푠) (푓푡) (푓푡 ∗ 푙푏푠) (푓푡) (푓푡 ∗ 푙푏푠)
Wing 460 11.76 5408.68 5 2300
Empennage 99 27.01 2673.94 16.4 1623.6
Fuselage 428 11.47 4907.45 6.5 2782
Nose landing gear 57 5.88 335.16 1.5 85.5
Main landing gear 228 14.70 3351.60 2.5 570
Powerplant 800 4.41 3528 6 4800
Fixed equipment 443 11.47 5079.44 6.5 2879.5
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Empty weight 2535 13.23 33538.05 7.38 18708.3
Front row passengers: 350 10 3500 6.5 2275
Rear row passengers: 350 12 4200 6.5 2275
Luggage 120 15 1800 6 720
Batteries 620 11.758 7289.96 5.2 3224
Takeoff Weight 3872
1 2 Center of Gravity Location for Various Loading Scenarios 3 4 Table 16 and Figure 20 show respectively the center of gravity locations 5 and excursion diagram for different loading scenarios. 6 7 Table 16. Final center of gravity location for different loading scenarios CG locations from nose Loading scenarios Weight(lbs) (ft)
Empty Weight 13.23 2535
Empty Weight + Front Row passengers 12.84 2885
Empty Weight + Rear row passengers 13.08 2885
Empty Weight + Passengers 12.75 3235
Empty weight + Baggage 13.31 2655
Empty Weight + Passengers + Baggage 12.83 3355
Empty Weight + Passengers + Baggage + 12.65 3872 Batteries
8
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1 Figure 20. Center of gravity excursion diagram
2 3 4 The center of gravity travel is 0.13 푐̅, well within the range for single 5 engine propeller-driven aircraft, which is between 0.06 푐̅ 푎푛푑 0.27 푐̅ 6 (Roskam, part II, 1985). The most forward and the most aft center of gravity 7 locations are12.64 ft and 13.31 ft respectively from the fuselage nose. The 8 stability and control analysis carried below may require additional iterations to 9 obtain the final center of gravity location of the airplane. 10 11 Stability and Control Analysis 12 13 The static longitudinal and directional stability of the proposed 14 configuration is established through a Class I stability and control analysis. The 15 longitudinal and directional χ-plots will determine any changes needed in the 16 horizontal and vertical tail areas. 17 18 Static Longitudinal Stability 19 20 The two lines in Figure 21 represent respectively the rates at which the 21 center of gravity and the aerodynamic center move as we change the horizontal 22 tail area. The aft center of gravity location was obtained earlier in the weight 23 and balance analysis. The weight of the empennage is known (100 lbs). The 2 24 horizontal tail weight is 49.95 lbs for a planform area of 46.25 ft . Assuming 25 that the weight of the horizontal stabilizer is independent of surface area, the 26 location of the aerodynamic center is found from equation (49). The 27 longitudinal stability parameters are summarized in Table 17. 28 푑휀 푆 푋 +{퐶 ∗(1− ℎ)∗( ℎ)∗푋 } 푎푐푤푓 퐿훼 푑훼 푆 푎푐ℎ 29 ℎ 푥푎푐퐴 = 푑휀 푆 (49) 퐶 ∗(1− ℎ)∗( ℎ) 퐿훼 푑훼 푆 1+ ℎ 퐶퐿 훼푤푓
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1 Table 17. Static longitudinal stability parameters Parameters Values
푥푎푐푤푓 0.091
퐶퐿 훼푤푓 0.095 per deg
퐶퐿 0.069 per deg 훼ℎ
푑휀ℎ/푑훼 0.4
푥푎푐ℎ 3.61 2 3 In Figure 21 the 푥푎푐 and the 푥푐푔 are plotted as functions of the horizontal tail 2 4 area, which varies from 0 to 60 ft . The aircraft needs to be inherently stable 5 with a static margin of 5%, hence: 푑퐶푚 6 = 푥푐푔 − 푥푎푐 = −0.05 (50) 푑퐶퐿 7 8 Figure 21. Longitudinal stability χ-plot
9 10 11 In Figure 21, the horizontal stabilizer area corresponding to the minimum 2 12 static margin of 5% is 50.50 ft , while the horizontal stabilizer area obtained 2 13 through the tail volume coefficient method was 46.25 ft .The difference is 14 within the allowed margins of error for Class-I preliminary design. Hence, the 15 proposed configuration is longitudinally statically stable, and no iteration is 16 required. 17 18 Directional Stability 19 20 The static directional stability is determined using a directional χ-plot with 21 the side slip moment coefficient plotted as a function of vertical tail area. 22 The Cn leg of the χ-plot follows from equation (51):
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1 푆푣 푋푣 2 퐶푛 = 퐶푛 + 퐶퐿 ∗ ∗ (51) 훽 훽푤푓 훼푣 푆 푏 3 4 The wing-fuselage contribution 퐶푛 is calculated from equation (52): 훽푤푓 5 6 퐶푛 = −퐾푛 ∗ 퐾푅퐼 ∗ 푆푓푠 ∗ (푙푓/푆푏) (52) 훽푤푓 7 8 Table 18. Static directional stability parameters Parameters Values 퐶푛 훽푤푓 -0.000341 per deg 퐶 퐿훼푣 0.035 per deg
퐾푛 0.0011
퐾푅퐼 1.5 9 10 The directional χ-plot of the aircraft is shown below. 11 12 Figure 22. Directional stability χ-plot
13 14 15 The proposed design is directionally stable with a vertical tail area of 25.2 2 16 ft obtained from Figure 29 at Cn = 0.001. The value obtained from the tail 2 17 volume coefficient method was 26 ft . The difference between the two values 18 is 3%, which falls within the acceptable limits of accuracy for a Class I 19 preliminary design.
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1 Drag Polars 2 3 The drag polars were estimated in the performance sizing. The objective of 4 this section is to recalculate these drag polars using the actual geometric 5 characteristics of the airplane. 6 Airplane Total Wetted Area 7 The wetted area for the wing, horizontal and vertical tail can be calculated 8 from: 0.25(푡/푐)푟∗1+ 9 푆 = 2 ∗ 푆 ∗ 1 + (53) 푤푒푡푝푙푓 푒푥푝푙푓 1+ 10 11 while the wetted area of the fuselage can be calculated from: 2 2 3 1 12 푆푤푒푡푡푒푑푓푢푠푒 = 휋 ∗ 퐷푓 ∗ 푙푓 ∗ (1 − ) ∗ (1 + 2 ) (54) 푓 푓 13 14 Table 19 shows the wetted areas of the main aircraft components 15 calculated from equations (53) and (54). 16 17 Table 19. Wetted area of main aircraft components Component Wetted Area (풇풕ퟐ)
Wing (푆푤푒푡푤) 406.18
Vertical stabilizer (푆푤푒푡푣) 53.56
Horizontal stabilizer (푆푤푒푡ℎ) 96.28
Fuselage (푆푤푒푡푓) 437.93 Total (푆푤푒푡) 963.00 18 19 Airplane Zero-Lift Drag 20 21 Using the total wetted area from Table 19 in figure 5.20 of Roskam (part 22 VI, 1987) the equivalent parasite area of the airplane is: 23
24 푓 = 9푓푡2 (55) 25 26 from which we can calculate the zero-lift drag coefficient: 27 28 퐶퐷0 = 푓/푆 = 0.046 (56) 29 30 Low speed drag increments 31 32 Using the drag increments due to flaps and the landing gear for the takeoff 33 and landing configurations from Table 5, the revised drag polars are shown in 34 Table 20 for various flight configurations. Table 21 compares the lift-to-drag 35 ratios assumed in preliminary sizing with those calculated through the actual 36 drag polars of the aircraft. The differences in values are within 5%, hence 37 resizing of the aircraft is not necessary.
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1 Table 20. Airplane drag polars
Flight Condition CD
2 Clean 0.0460 + 0.0374퐶퐿
2 Takeoff flaps 0.0625 + 0.0397퐶퐿
2 Landing flaps 0.1075 + 0.0424퐶퐿
2 Landing gear 0.1290 + 0.0424퐶퐿
2 3 Figure 23. Drag polars for cruise, takeoff and landing configurations
4 5 6 Table 21. Comparison of the lift-to-drag ratios from preliminary sizing (assumed) 7 and preliminary design (calculated) L/D L/D Flight Condition difference (preliminary sizing) (preliminary design) Cruise 11.72 11.50 2% Takeoff 10.0 9.70 3% Landing 7.50 7.35 2% 8 9 10 Environmental and Safety Considerations 11 12 The environmental issues associated with the proposed design is the use of 13 lithium-O2 batteries in electric design. Even though the electric aircraft requires 14 no fuel and produces less noise than conventional aircraft, it is clearly not a 15 zero-emission aircraft. The process associated with the production of these 16 batteries emits air pollutants that affect air quality and health. Moreover, the 17 lifetime of these batteries is still short and induces battery waste containing 18 toxic or corrosive materials such as lithium. This hazardous waste could pose
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1 additional threats to health and the environment if improperly disposed. 2 Rechargeable batteries will address to a large extent the disposal issue. 3 4 5 Conclusions 6 7 The paper demonstrated that a fully electric, four passenger, FAR-23 8 certifiable, general aviation airplane with a 750 km range is feasible, assuming 9 an energy density of 1500 Wh/kg. Clearly, it will take significant improvements in 10 battery technology to allow for an aircraft, such as the one proposed in this 11 paper. Nevertheless, as research continues to push the limits of this technology, 12 it is not unlikely to have these batteries available as early as 2025. 13 14 15 References 16 17 Abdel-Hafez, A. (2012). Power generation and distribution system for a more electric 18 aircraft-a review. Recent advances in aircraft technology. pp. 289-308. 19 Airbus. Airbus Vahana.
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1 Roskam, J. (1985). Airplane design part II: Preliminary configuration design and 2 integration of the propulsion system. DARcorporation, Lawrence, Kansas 66046, 3 USA. 4 Roskam, J. (1986). Airplane design, part III: Layout design of cockpit, fuselage, wing 5 and empennage: Cutaways and inboard profiles. DARcorporation, Lawrence, 6 Kansas 66046, USA, 85-122. 7 Roskam, J. (1985). Airplane design, part V: Component weight estimation. 8 DARcorporation, Lawrence, Kansas 66046, USA. 9 Roskam, J. (1987). Airplane design, part VI: Preliminary calculation of aerodynamic, 10 thrust and power characteristics. DARcorporation, Lawrence, Kansas 66046, 11 USA. 12 Sigler, D. (2011). Going vintage electrically.
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