DESIGN OF AN ALL-ELECTRIC REGIONAL AIRLINER
BEN BRELJE – TEAM LEAD ADAM BYBEE RYAN KITSON ERIC METCALF BEN ROTHACKER
Table of Contents 1 Summary .................................................................................................................................................... 1 2 Introduction ............................................................................................................................................... 4 3 Interior Layout ........................................................................................................................................... 6 4 Aerodynamics ............................................................................................................................................ 8 5 Weights and CG........................................................................................................................................ 16 6 Stability and Control ................................................................................................................................ 21 7 Propulsion Systems .................................................................................................................................. 26 8 Landing Gear ............................................................................................................................................ 30 9 Method Validation ................................................................................................................................... 32 10 Direct Operating Cost............................................................................................................................. 33 11 Design Refinement and Optimization .................................................................................................... 37 12 Structures and Loads.............................................................................................................................. 42 13 Computational Procedure ...................................................................................................................... 46 14 Conclusions ............................................................................................................................................ 49 15 Citations ................................................................................................................................................. 50 16 Appendices ............................................................................................................................................. 53
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1 Summary 1.1 Executive Summary Increasing fuel and carbon prices have sparked interest in hybrid electric propulsion systems. To foster ideas for future design concepts, AIAA has requested proposals for the design of an advanced technology aircraft utilizing hybrid electric propulsion for entry into service by 2030 in the 70-seat regional class. Accelera, to meet the design challenge, performed preliminary design and analysis of three aircraft concepts: a baseline turboprop modeled after the Q400, another aircraft very similar in design to the Q400 but with all electric propulsion, and finally, an unconventional design that combines all-electric propulsion with a double bubble lifting fuselage. After designing and analyzing each aircraft, the all-electric model, named Vision, was chosen for further design and refinement based upon lowest direct operating cost (DOC), operational feasibility, and marketability. The Vision is 25% less expensive to operate than Q400, produces no point-source carbon emissions, and is not subject to fluctuations in the price of jet fuel, presenting huge operational and cost advantages for airlines. The Vision uses a double bubble fuselage, an H-tail, and an aft-mounted propeller configuration. The aircraft has six abreast seating, split forward and aft to allow for battery storage above the wing box area. A hallway is provided between the two passenger compartments, along with full-size exit doors at both front and aft of the passenger cabin. In order to make electric propulsion feasible, we chose to use Lithium-Air (Li-air) batteries in lieu of the AIAA-specified Li-ion batteries. High specific energy is a key enabler of efficient electric-powered flight because of the structural and drag penalty of heavy batteries. Conservative estimates suggest that Li-air will possess 80% higher specific energy compared to future Li-ion cells. The batteries drive stacks of advanced Halbach-array motors for minimum weight. The modular design of the motor provides a breakthrough in safety and redundancy compared to complex, delicate turbine engines. The Accelera Vision incorporates many new technologies to facilitate a cost effective all-electric design. Lithium air batteries power the advanced aft mounted coaxial counter-rotating scimitar propellers. This propeller configuration ingests the bounder layer of the double bubble fuselage. The Vision also utilizes advanced composites on many parts of the aircraft and uses innovative morphing high-lift devices. The Vision’s aerodynamics capitalizes on advances in wing and fuselage technology to increase efficiency and reduce operating costs. The lifting fuselage and ingested boundary layer reduces the lift that must be generated by the wings and reduces overall drag. The revolutionary high-lift devices provide extensive laminar flow capabilities and in-flight aerostructural optimization. In order to optimize the Vision’s design, a multidisciplinary design optimization (MDO) strategy was employed. An optimizer was designed and 10 variables, with corresponding constraints, were chosen in order to balance run time and optimization potential using a vortex lattice code and parametric structural code. In the end, adopting an MDO strategy provided a decrease in DOC of 5%.
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1.2 Three-View Exterior Drawings
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1.3
Comparison Table Table 1: Performance Summary Comparison
Aircraft
Vision
Q400 [1]
MIT D-8.5 [2]
Take Off Weight (lbs) Empty Weight (lbs)
67,245
65,000
101,591
2030 Baseline Turboprop 64,632
30,322
37,717
51,406
41,417
CL (cruise)
0.6346
0.472
--
0.568
CLmax (landing) CLmax (takeoff) L/D (cruise) P/W (hp/lb) W/S (lb/ft^2)
2.89 2.4 22.51 0.164 74.5 (planform), 65 (effective) Composites, Electric prop.,BLI, Advanced Propellers, Double-Bubble Lifting Fuselage, Morphing Flap/Slat/Control Surface Electric Halbach Array
2.8 2.4 18.0 0.27 54.3
3 -25.3 0.083 (T/W) 88
2.8 2.4 22.2 0.25 59
N/A
Composites, BLI, Propellers, Double-Bubble lifting fuselage
Advanced turboprop/prop ellers
Turboprop PW150A
Turbofan
Max Power (hp) SFC DOC (cent/ASnmi) Energy Cons. Pmi/gal Span (ft)
5510 x 2 N/A 9.58 291
5075 x 2 0.459 13.76 67.39
37.7 (kN SLST) 0.174 (TSFC) -315
Turboprop GE CPX38 "Rubber" 8003.2 0.33 17.93 59.5
98.53
95.5
170
114.728
Ref Area (ft^2) AR Avg. t/c (wing) Mach (cruise) Static Margin
902.5 10.76 15% 0.52 17.0%
701 13 15% 0.58 16%
1152 24.85 15% 0.72 10%
1012.5 13 15% 0.55 9.2%
New Technology
Type Model
Figure 1: MIT D-8.5
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Figure 2: Bombardier Q400
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1.4 Photorealistic Rendering
2 Introduction Over the past several years, increases in operating costs, especially fuel, have led to increasingly troublesome times for many airlines. From small regional airlines to large legacy carriers, no one is exempt from the effects of ever increasing fuel prices. The regulatory environment has demanded aircraft that are less harmful to the environment. This has led to a growing interest in the use of hybrid electric propulsion systems. Hybrid electric propulsion systems have the potential to completely redefine air travel by decoupling airline economics from the price of fuel. NASA and the FAA have recently conducted studies that identify the various advances in aircraft design and manufacturing that are expected by the year 2030. These advances include areas such as propulsion, structures, aerodynamics, subsystems, as well as operations technologies. To explore possible applications of these “N+3” technologies, the AIAA has requested proposals for hybrid-electric regional aircraft designs to meet the requirements summarized in Table 2.
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Table 2: Summary of Requirements [3] Requirement
Value
Unit
Note
Crew Passengers Seating Pitch Seating Width Cargo Volume Cargo Weight Revenue Cargo Full Payload Weigth Balanced Field Length Minimum Cruise Speed Initial Cruise Altitude Maximum Cruise Altitude Maximum Range Economic Mission
2 70 32 17.2 280 2,450 0 16,450 4,000 Mach 0.45 >20,000 45,000 1,200 400
Battery Volume Battery Weight Useful Energy
9 360 122
ft^3 lbs kWh
750 Whr/kg
Electric motor power density Electric motor and controller combined system efficiency Generator power density Generator efficiency
3 0.95
hp/lb
Unless supported by outside research
3 0.96
hp/lb
Assumed 2030 Jet Fuel Price Assumed 2030 Electricity Price
5 0.05
$/gal $/kW
Single class (FAR requires 2 flight attendants) in in ft^3 lbs lbs lbs ft ft ft NM NM
4 ft^3/ pax 35 lbs/ pax
Sea Level, Standard Day
Full payload
Including battery rental fee and carbon tax
Accelera initiated this project by designing three distinct aircraft concepts. The first concept, code named Red, is a baseline conventional configuration with engines that provide estimated 2030 performance (Figure 3). Red is inspired by the Bombardier Q400 turboprop aircraft, a widely used regional turboprop. The second concept, code named White, is very similar to the previous design, but utilizes a radical new all electric propulsion system (Figure 4). White retains much of the Red structure except for extensive employment of advanced composites, a stretched fuselage to accommodate batteries, a larger wing to handle the added battery weight, and a slightly larger horizontal tail.
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Figure 3: Red Concept (Baseline)
Figure 4: White Concept
The third and most unconventional design, code named Blue, combines all-electric propulsion with a double bubble lifting fuselage. The aircraft also has a tail mounted propulsion system with advanced coaxial counter-rotating propellers. After designing and analyzing each of the three concepts, Accelera down-selected, choosing only one aircraft as a viable candidate for further refinement based upon direct operating cost (DOC). The aircraft chosen for further design was the Blue concept, which we renamed Vision. The Vision underwent several iterations after down-selection before arriving at the final design. Further refinement was conducted in aircraft weights, interior layout, exterior configuration, wing parameters and location, stability and control, structures and loads and aerodynamics. Aerodynamics was improved using AVL, XFLR5 and XFOIL software. Stability, control and loads analysis was conducted using MATLAB. Interior layout was done in AutoCAD and the exterior configuration was done using SolidWorks. Finally, the design was subjected to multidisciplinary optimization to improve operating cost. The gradient-based optimization resulted in a 5% decrease in DOC and over 2,000 lb reduction in maximum takeoff weight. Optimization for aerodynamic performance and structural weight was also explored. 2.1 Vision Concept Accelera designed the Vision to take advantage of emerging technology in combination with electric propulsion to optimize direct operating cost for the 2030 production date. The result is an unconventional double-bubble lifting fuselage with boundary layer ingestion. Lithium-air batteries power two coaxial counter-rotating propellers mounted in a pusher configuration on the horizontal stabilizer to ingest the fuselage boundary layer. The empennage is configured as an H-tail because the propeller placement is driven by the location of the fuselage trailing edge. In addition to the previously mentioned advanced technologies, Vision takes advantage of recent improvements in composite structure manufacturing and research involving morphing high lift devices. The result of the Vision design is a unique application of advanced technology that promises large reductions in direct operating cost for the 2030 regional aircraft market.
3 Interior Layout The Accelera Vision utilizes an oblong double-bubble fuselage, which allows for six-abreast seating in a single aisle arrangement. The flight deck, galley, lavatory, and entry door are forward of the passenger cabin, with two emergency exit doors at the rear and one more located forward of the cabin to satisfy FAR requirements. ACCELERA
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The battery compartment is located halfway between the passenger seating area on each side of the fuselage. This setup leaves a hallway between the separate seating areas that allows crew and passenger movement. The battery compartment is pressurized along with the fuselage. Figure 5: Battery compartment cross-section
Figure 6: Cabin cross-section
Figure 7: Interior cabin layout
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4 Aerodynamics In order to minimize direct operating cost of the final aircraft, we needed to optimize the tradeoffs between aerodynamic performance and structural weight. With these considerations in mind, we chose a double-bubble lifting fuselage with a low wing and H-tail for our design. 4.1 Aerodynamic Layout and Design Philosophy To improve fuel burn, maximize high-lift performance, and minimize weight, the conventional aircraft configuration was completely reconsidered. To guide the design philosophy, we considered the drag on an aircraft in rough conventional categories of induced drag, separation drag, friction drag, interference drag, and compressibility drag. Based on initial studies of cruise Mach design space, wave drag was assumed negligible to simplify analysis. While induced drag can be minimized through creative wing planform shaping, it is difficult to reduce significantly simply because it is required for lift. Our method for induced drag reduction is reducing overall aircraft weight and lift. Our aerodynamic design therefore concentrated on minimizing the remaining separation, friction, and interference drags. A double-bubble lifting fuselage promised significantly reduced weight through cascading benefits and the opportunity to use electric propulsion to greatest advantage. Direct benefits include slightly smaller required wing area, lower wetted surface area, and reduced induced drag via improved lift distribution over the fuselage. Cascading benefits include a beneficial moment for reduction of trim drag and a slight weight reduction through better co-location of weight and lift. However, the double-bubble fuselage alone has a high frontal area and high rear fuselage base drag, reducing its feasibility. To complement the double-bubble fuselage, we designed a lightweight, clean wing configuration of reasonable aspect ratio to improve high-lift performance and cruise fuel burn. An H-tail empennage was chosen to keep control surfaces in clean air during main wing stall, to minimize structural weight, and to allow our propulsion system to be mounted on the rear fuselage. This synergistic aerodynamic and propulsion combination approach allowed us to take advantage of the full structural weight benefit of the double-bubble fuselage while minimizing the associated aerodynamic disadvantages. Figure 8 and Figure 9 demonstrate a rough 2-dimensional approximation to the 3-dimensonal flow performed for cruise flight conditions with XFLR5 and Xfoil 6.97 software. The large regions of separated flow on the conventional fuselage and typical cockpit design result in little lift and significantly higher drag under cruise conditions (ReynoldsL=163 x 107, Mach = 0.52, angle of attack = 3°). Blue arrows represent normalized pressure magnitude and direction, and red dotted lines represent the boundary layer.
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Figure 8: Viscous flow over a conventional fuselage
Figure 9: Viscous flow over a double-bubble lifting fuselage
It should be noted that the shape of the rear fuselage modeled above does not perfectly represent the fineness ratios achievable with propulsion system active; the favorable pressure gradient provided by the propulsor will allow a lower fineness ratio and therefore lower weight for a given level of drag. In addition, a double-bubble lifting fuselage creates much of its lift on its front surfaces due to the ramplike lower fuselage. This lift also creates a beneficial trim moment in addition to that provided by the negative camber on the rear fuselage. These effects, as discussed above, allow us to significantly reduce the size of our horizontal stabilizer. 4.2 Boundary Layer Ingestion We achieved additional cascading benefits and mitigated the high drag of the fuselage through effective propulsion location. With centrally located propulsion, the propellers ingest the wake of the fuselage, increasing propulsive efficiency, and provide a favorable pressure gradient over the rear fuselage, reducing separation in most flight regimes [2]. This effect is known as boundary layer ingestion and is ACCELERA CRITICAL DESIGN REVIEW 9
illustrated in Figure 10. Centrally located propulsion also eliminates engine-out yaw moment, reducing wetted area and weight of the vertical and horizontal stabilizers, respectively [4]. This location also allows high wing performance by removing the interference and poor lift distribution often caused by engine nacelles. Boundary layer ingestion has two main effects on energy consumption: improved propulsive efficiency and reduced fuselage drag due to separation. We account for both of these effects using an empirical correction factor, λ, following the MIT N+3 configuration studies [2]. In this method, L/D is increased simply by dividing by λ, which is 0.81 in our case (assumes 40% boundary layer ingestion on the top of the fuselage). Equation 1
Figure 10: Boundary layer ingestion schematic
4.3 Wing Design Once we had chosen an overall aerodynamic layout, we needed to perform more detailed design. After initial sizing, we began using Mark Drela’s Athena Vortex Lattice (AVL) panel method code for more refined design. This code, given an input geometry defined by panels, can determine induced drag and perform a variety of stability and trim analyses for refined design. Our parasitic drag was calculated via a component build-up method following Raymer and Kroo, where our fuselage was again modeled as a lifting surface to correctly capture the associated higher form factor [5] [6]. Our configuration required some special considerations when defining geometry in AVL. We modeled our fuselage as a thick wing with appropriate cross-section because it is a lifting surface. The wing also was placed in the same vertical plane as the root section of the wing to best approximate that the fuselage and wing are in fact connected. Separating these surfaces in AVL led to poor simulation of our configuration. We also adopted a paneling similar to that used by Mark Drela in his modeling of the D8.5 aircraft after initial issues with panel spacing [7]. To refine the paneling while maintaining a reasonable computational cost, we assume symmetry in our AVL model. After significant refinement, our AVL model was deemed a reasonable approximation of our actual configuration. This model and its associated paneling are shown in Figure 11.
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Figure 11: AVL panel geometry
Our multi-disciplinary optimizer refined our wing configuration’s overall sizing, aspect ratio, taper ratio, wing root incidence, and linear twist to the values given in Table 3. Table 3: Final design values for wing design parameters Span (ft) 98.53
Ref Area (ft2) 902.5
Aspect Ratio 10.8
Root Chord (ft) 11.54
Taper Ratio 0.50
Root Incidence -2.0°
Twist
Dihedral
-2.2°, linear
5°
With overall wing planform established, we needed to refine the details of our wing, such as high-lift devices and specific airfoils to be used. To appreciably reduce friction, our wing needed a very high degree of laminar flow. Current technology is limited by the relatively rough, gapped upper and lower surface of aircraft wings to unacceptably low laminar flow extents. Therefore, we chose to pursue a new technology to allow an unprecedented smooth upper and lower wing over all but the necessary gaps for rear control surfaces. The wing will be manufactured from composites with special coating to mitigate debris accumulation, and will utilize a novel high-lift configuration currently undergoing testing by SADE, the Smart Single-Slotted Flap. 4.3 High-Lift System Our high-lift system, called the Smart Single-Slotted Flap (SSSF), consists of a morphing leading edge to take the place of a slat and a slotted, morphing flap [8]. This system adapted to our wing is shown in Figure 12.
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Figure 12: Detailed high-lift system, with takeoff deflection in red and landing in blue
The morphing leading edge allowed us to design our wing airfoil’s leading edge primarily with cruise conditions in mind, yielding a smaller leading edge radius and lower drag. The most important feature of this system, however, is that it leads to an unbroken upper and lower wing surface, allowing aggressive laminar flow airfoil design. Detailed design of our airfoils will be discussed later in this report. There are several additional benefits to this system as well; because the leading and trailing edges of the wing can actively change shape, they can deflect in flight. The leading edge can change shape to provide deicing capability, eliminating the de-icing difficulty usually present in composite wings. It can also change shape to avoid stall when significant maneuvers are necessary. The trailing edge can help alter camber and lift distribution, allowing a reduction in induced drag across all flight regimes. According to SADE studies, the smart leading edge provides less high-lift performance than a dedicated leading edge slot, but higher performance than a Krueger slat. Like the Krueger slat, it allows for improved laminar flow over the upper surface of the wing by avoiding the introduction of surface gaps. Unlike the Krueger slat, it also avoids a lower wing surface gap. The cambered trailing edge flap provides performance between a single- and double-slotted Fowler flap. Though this performance did limit our capability, the benefits in cruise drag reduction by improved airfoil design made this limitation acceptable. A sectional Clmax of the SSSF configuration is included as Figure 13.
Cl
Figure 13: SSSF lift curve [8]
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CL, max was determined using values from SADE studies adapted to 3D via methods by Raymer and Jenkinson for an unswept wing, while drag was determined as for a single-slotted flap with Kreuger slat [5] [9]. 4.4 Airfoil Design Taking full advantage of the double-bubble configuration’s fuselage lift and our high-lift system’s smooth upper and lower surfaces required unique airfoil designs. We designed custom airfoils for both our fuselage (the DB-38 airfoil), and for our wing (the BLAM-7 airfoil). 4.4.1 Fuselage Airfoil Our fuselage airfoil required a highly multi-disciplinary design. The airfoil had to meet diverse design goals and constraints, including cockpit viewing angle, rear fuselage fineness ratio, low separation for propulsive performance, trim drag moment, and sufficient lift. All these constraints were in addition to the usual requirements to house the aircraft’s passengers, cockpit, structures and baggage and for low drag. Due to the high number of constraints, our fuselage design necessitated a total of 43 manual design iterations to achieve sufficient performance. To minimize fuselage drag, we concentrated on minimizing separation drag on the rear fuselage, because achieving friction drag reductions through laminar flow is unrealistic on protuberance-littered fuselages. We assumed fully turbulent flow on our fuselage as a result of the gaps and protuberances from doors, windows, pitot probes and antennae, etc. Of the 43 fuselage designs, the 38th provided what we felt was the best compromise between all requirements (Figure 14). Figure 14: The DB-38 fuselage airfoil
This airfoil has a number of notable characteristics separating it from less refined designs. Our airfoil effectively exploits lower fuselage shaping to maximize beneficial trim moment, allowing reduction in the horizontal tail sizing. The leading edge region also creates a majority of the lift on this section, further improving trim drag. The nose leading edge radius is large to allow a reasonably sized cockpit and associated viewing angles, and to avoid stall during takeoff and landing. The trailing edge region does not separate under normal flight conditions even without beneficial pressure gradients provided by the engine, reducing drag over conventional fuselages significantly. All these goals are accomplished while maintaining the space necessary to house the aircraft’s components and payload at a reasonable fineness ratio. Though these accomplishments may seem mundane stated individually, it was a very significant challenge to meet them all simultaneously. 4.4.2 Main Wing Airfoil In order to achieve the low drag necessary for electric propulsion, our main wing required very aggressive laminar flow design. As mentioned previously, our high-lift system allowed such aggressive design.
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Using Xfoil for modeling with reasonable freestream turbulence levels, we achieved laminar flow over roughly 70% of the lower surface and 80% of the upper surface at and around cruise conditions with the design shown in Figure 15 [10]. Figure 15: The BLAM-7 laminar airfoil used on our main wing
We achieved this impressive laminar flow extent through several means. The small leading edge radius afforded by our high-lift system design allowed us to place the point of maximum thickness very far back on the airfoil, giving a highly favorable pressure gradient. Second, we designed the airfoil to recover pressure back to freestream conditions only after transition to turbulence, allowing a very steep rear airfoil surface without fear of unexpected separation. We ensured that this pressure recovery design did not cause unacceptable stall characteristics by designing the recovery region with a monotonically increasing curvature where feasible. This will induce separation to travel slowly forwards on the rear of the airfoil as angle of attack increases rather than occur on the leading edge in flight conditions where stall is unavoidable. As a result, our airfoil should allow extremely docile stall characteristics, an important feature in a commercial aircraft. This would need to be verified by more detailed modeling for further design, however. 4.5 Aerodynamic Performance As summarized in Table 4 through Table 6 our aerodynamic configuration achieved impressive aerodynamic performance at an acceptable cost and structural weight. Table 4: Aerodynamic performance Parameter L/D Cruise Stall speed (kias) (Takeoff, MTOW) Stall speed (kias) (Landing, MTOW)
Vision 22.7 72 79
Table 5: Oswald efficiency factors from AVL Condition Cruise (Clean) Take Off (Flaps) Landing (Flaps)
Oswald efficiency, e 1.1 1.0 0.9
Table 6: Parasitic drag from build-up Condition Cruise (Clean) Take Off (Flaps) Landing (Flaps)
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CD, 0 0.0170 0.0246 0.0887
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Drag polars were calculated using AVL, and are shown below. AVL’s lack of stall modeling limits the usefulness of this data, but is provided here to give an idea of the rough lift-to-drag ratio expected for each flight regime. Figure 16: Cruise drag polar, calculated in AVL
Figure 17: Takeoff drag polar, calculated in AVL
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Figure 18: Landing drag polar, calculated in AVL
5 Weights and CG 5.1 Empty Weight Weight was estimated using Raymer’s detailed component weight equations, which are based on historical data. Correction factors were applied for composite parts as described by Table 20 [6]. Table 7 summarizes the components of the Vision’s empty weight. Table 7: Empty weight components Component Wing Horizontal Tail Vertical Tail Fuselage Electrical Propulsion Nacelle Propellers Landing Gear Avionics, Controls, and Electrical Interior + ECS Empty Weight
Weight (lb) 5,769 518 844 12,268 3,674 212 767 2,631 3,154 3,953 30,322
The wing presents unique opportunities for aerostructural optimization. In order to obtain best MDO results based on reliable analysis methods, we averaged two wing weight formulas. Both formulas take into account design variables of interest, such as taper, sweep, and thickness-to-chord ratio (Figure 19). (
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(
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(
)
Equation 2 [6]
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(
)
(
(
( ) )
( ( )
) ( )
Equation 3 [7]
The two formulas account for geometry slightly differently, as illustrated by Figure 20. Wing weight estimates remain within 12% between the two methods at all reasonable combinations of aspect ratio and taper. The Torenbeek formula doesn’t seem to account as strongly for structural benefits of taper and systematically predicts higher weights at high aspect ratios. Figure 19: Wing weight modeling Raymer formula [6]
Torenbeek formula [7]
Figure 20: Wing weight model variance
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5.2 Payload The payload weight requirements, based on AIAA requirements with the addition of two flight attendants, are summarized in Table 8. Category Passengers Crew Baggage / Person Total
Table 8: Payload Weight Requirement [3] Number Weight / Individual (lb) 70 200 4 200 74 35 74
Total Weight (lb) 14,000 800 2,590 17,390
5.3 Energy Consumption Electric propulsion demands modification to the traditional weight buildup method because the Breguet Range Equation cannot be applied. A standard two-phase mission profile was used for energy consumption analysis as outlined in Figure 21 and Table 9. Figure 21: Mission profile assumptions
Mission
Reserve
Cruise 100 nmi ½ hr loiter
½ hr loiter
Takeoff
Landing
Table 9: Mission parameters Phase
Time/Distance
Altitude (ft MSL)
Takeoff Cruise Loiter Divert Divert Loiter Landing
4000 ft BFL 400 / 1200 nmi 30 minutes 100 nmi 30 minutes 4000 ft BFL
0 24,000 10,000 10,000 10,000 0
Our custom energy code assumes that the mass of the aircraft is constant throughout the entire mission profile. This allows the code to calculate an energy ratio E/WTO using Equation 4 through Equation 6. For cruise conditions, the code replaces the drag polar in Equation 7 with a lift-to-drag ratio taken from the AVL panel code. For takeoff, energy consumed is assumed to be average takeoff thrust integrated over the balanced field length. ACCELERA
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Equation 4
Equation 5 Equation 6 The weight of the batteries depends on the electrical efficiency of the motor and the energy density of the batteries, according to Equation 13. Takeoff weight is subsequently calculated using “zero fuel” weight and the fuel/battery fraction according to Equation 7. Equation 7 (
)
5.4 Center of Gravity A weight and balance code calculates the centroid of each weight component and determines the center of gravity of the aircraft as a combination of point masses. Passengers are assumed to be evenly distributed from the rear seat to the front passenger seats. 50% of luggage weight is assumed to be carry-on and is also distributed through the cabin. Figure 22 and Figure 23 illustrate the change in center of gravity as the aircraft is loaded. It’s important to note that for an electric configuration, the mass of the aircraft does not change during a normal flight. Therefore, as long as the airplane meets the static margin requirement on takeoff, then the constraint is satisfied for the whole flight. The CG excursion plots for the Vision show that at both MTOW and at zero payload, the airplane meets its static margin constraint. The static margin can even be tuned if fewer than normal batteries are required for a particular mission; if a row of batteries is vacant, the entire stack may be slid forward or backward to adjust CG position for the entire mission. More importantly, the Vision is statically stable on the ground for all loading and balance conditions. Figure 22: CG excursion at MTOW mission (1200nmi, 70 pax + cargo)
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Figure 23: CG excursion at zero payload (1200 nmi ferry)
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5.5 Takeoff Rotation Analysis In order to verify that sufficient tail moment is available to rotate the airplane during a takeoff roll, a special control case was set up using AVL. Flaps were set to a nominal 30°, speed was set to the minimum takeoff stall speed of 80 knots, and angle of attack was fixed to zero. The tail was then given authority to fix pitch moment coefficient about the main gear at 0.2 to represent a takeoff rotation and the lift distribution examined for feasibility (Figure 24). Results indicated that the desired takeoff rotation could be achieved with a reasonable elevator deflection of -15°. The tail maintained a Cl margin over stall of about 20% [8]. To verify the tip-back angle required to achieve liftoff, a worst-case scenario of takeoff stall speed (80 kts) and maximum takeoff weight was analyzed in AVL. Flaps were set to 40° and the tail commanded to balance moment about the landing gear. Figure 25 represents the lift distribution at the critical liftoff condition. Trim can be achieved at an elevator deflection of -15° and a rotation angle of 9.6°, which allows 2° of clearance at the tail. These two analyses demonstrate that the Vision design meets all aerodynamic and balance requirements for the takeoff phase. Figure 24: Takeoff Rotation Analysis
Tail Clmin : 20% margin until airfoil stall
Figure 25: Liftoff analysis
Wing Clmax: 10% margin until local stall
Tail Clmin : 40% margin until airfoil stall
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6 Stability and Control 6.1 Static Stability Static stability was verified using previously-calculated cg information and AVL software. AVL contains built-in static stability analysis routines. All of our run cases in AVL fix pitch moment about the center of gravity, Cm , to zero (in order to capture trim drag). Static margin was calculated using the neutral point derived from AVL. Table 10: Summary of stability and control metrics Parameter Static Margin (1200 nmi Cruise) Static Margin (400 nmi Cruise) Static Margin (Empty, 1200 nmi) Wing Incidence Elev. deflection at cruise Cruise angle of attack CVT CHT
Value 17 % 11.9% 9.6% -2.012° 1.00° 1.07° 0.0604 0.6971
Empennage and control surfaces were initially sized based on historical guidelines assembled by Raymer (twin turboprop class). We justified reducing the size of the vertical tail from historical guidelines because of our centerline thrust. No off-axis thrust means that there is no engine out yaw moment, which in most cases is the critical constraint for vertical tail sizing. Tail volumes are summarized in Table 10; control surfaces are summarized in Table 11. Table 11: Control surface sizing Inboard Span Location (% b/2) Outboard Span Location (% b/2) Inboard Chord Fraction (% c) Outboard Chord Fraction (% c)
Flaps Slats 10 10 70 95 30 7 30 7
Ailerons 70 95 30 30
Elevator 40 95 30 30
Rudder 60 95 30 30
In order to verify that the horizontal tail satisfies static stability requirements, tail sectional Cl at the critical trim condition (CLmax and stalled wing) was checked to ensure that tail authority falls within aerodynamic constraints (Figure 26). The tail sectional Cl was only at 50% of stall Clmin, indicating sufficient trim authority even in a worst-case scenario [8].
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Figure 26: Critical trim condition
Cl of tail section well above Clmin
6.2 Dynamic Stability Analysis In order to verify that the empennage sizing is adequate to ensure dynamic stability, a modal analysis was conducted using AVL software. Axis moments of inertia were calculated according to historical data on radius of gyration, according to the following equations: (
Equation 8 [6]
)
Where: Rx = 0.22 , Ry = 0.34 , Rz = 0.38 AVL combines mass matrix information with aerodynamic force calculations to provide information about the dynamic modes of the aircraft in flight, in the form of eigenvalues corresponding to each mode. Acceptable dynamic stability was defined as fulfilling all of the criteria of Level 2 of the MIL-F8785B handling qualities rating scale [9]. Level 2 indicates that an aircraft is capable of fulfilling mission requirements but may require simple controllers or additional pilot attention. Table 12 summarizes the results of the dynamic stability study. Table 12: Dynamic Stability Parameters Mode
Eigenvalues
Parameter
Simulated
MIL-F-8785B Level 2 Criterion
Short Period
-0.691 +/- 1.295i
Phugoid
-0.943 +/- 1.850i
Roll
-2.958
ξ ω ξ ω τ
0.45 1.407 rad /s 0.0274 0.0854 rad/s 0.35 s
0.25 < ξ < 2.0 No requirement 0<ξ No requirement 0 < τ < 1.4
Dutch Roll
-0.002371 +/- 0.0865i
ξ ω ωξ
0.05129 1.852 rad /s .0950 rad / s
0.02 < ξ 0.4 < ω 0.05 < ω ξ
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Figure 27: AVL dynamic stability simulation
Figure 28: Modes in the complex plane
Therefore, the Vision aircraft design meets all Type II handling characteristic requirements and will be stable and safe in flight. 6.3 Control Design and Analysis The eigenvalues examined above reveal Dutch roll and phugoid oscillation with relatively small but still positive damping ratios, as well as small short period oscillations. Our goal in designing a controller was to improve modal damping. In order to increase aircraft dynamic stability, multiple controllers were explored to damp out the phugoid oscillations of the aircraft. The controllers that were explored were proportional, proportional derivative (PD), proportional integral (PI) and proportional integral derivative (PID). The controller that provided the most favorable control response was the proportional integral controller. Output from Vision’s AVL model provided us with the state space matrices of the aircraft. We plotted the eigenvalues (Figure 29), made a Nyquist plot (Figure 30), a root locus (Figure 31), vehicle response plots (Figure 32), and Bode plots (Figure 33) of the system. The eigenvalues showed that the dutch roll, the phugoid oscillation and the short period were near the imaginary axis (lightly damped). The roll mode was much further from the imaginary axis so was more stable. After implementing a PID autopilot scheme, feeding back vertical speed to the elevator control input, the eigenvalues for both the phugoid oscillations and the short period oscillations moved away from the imaginary axis, improving damping of both modes.
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Figure 29: Eigenvalue Plot Eigenvalues 40 30
Phugoid mode improvement from pitch damping
Imaginary Axis (seconds-1)
20 10 0 -10 -20 -30 -40 -14
-12
-10
-8
-6
-4
-2
0
Real Axis (seconds -1)
Figure 30: Nyquist Diagram Nyquist Diagram 4
3
2
Imaginary Axis
1
0
-1
-2
-3
-4 -2
-1
0
1
2
3
4
Real Axis
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Figure 31: Root Locus Plot Root Locus 80
Chosen gain: Kp = 190
60
Imaginary Axis (seconds-1)
40
20
0
-20
-40
-60
-80 -250
-200
-150
-100
-50
0
50
Real Axis (seconds -1)
Figure 32: Vehicle time response (vertical speed) Step Response
Impulse Response 3 2
2
Amplitude
Amplitude
No control
3
1
0
1 0
0
200
400
600
-1
800
0
Time (seconds)
1
1
0.5
100
200
300
8
400
0.5
0
0
Time (seconds)
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Amplitude
Amplitude
PID Control
Step Response
0
4
Time (seconds)
1.5
0
2
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4
6
Time (seconds)
25
Figure 33: Bode diagrams Vertical Speed
Vertical Speed Error Magnitude (dB)
Bode Diagram
0 -100 0
Phase (deg)
Phase (deg) Magnitude (dB)
No Control
Bode Diagram 100
-90 -180 -2 10
0
2
10
10
20 10 0 180 90 0 -2 10
Frequency (rad/s)
Bode Diagram
Phase (deg) Magnitude (dB)
Phase (deg) Magnitude (dB)
PID Control
Bode Diagram
-50 -100 0 -90 -180 0
2
10
2
10
Frequency (rad/s)
0
-270 -2 10
0
10
10
50 0 -50 90 0 -90 -2 10
Frequency (rad/s)
0
10
2
10
Frequency (rad/s)
From the vehicle response plot in particular it is clear that the Phugoid oscillation has been dramatically reduced compared to the uncontrolled system. The controller may be used in level flight as a mode dampening system, or as a vertical speed hold during climb or descent phase.
7 Propulsion Systems The primary design feature involved in the requirements for this project is in the nature of the propulsion system. Particularly, the design challenge is to produce an aircraft that utilizes an electrical or hybrid-electrical system for propulsion. The Vision aspires to be the first production mass transport aircraft to feature a completely electrical propulsion system. To accomplish this goal, the aircraft design incorporates some ingenious emerging technologies for electrical energy storage and transmission. 7.1 Electrical Energy Storage The limiting factor when it comes to electrical propulsion systems has always been specific energy of the energy storage medium. This is of particular importance for aircraft due to induced drag and structural penalties from the added weight. The AIAA competition rules state that the stock batteries available for consideration in submitted designs have an energy density of 750 Whr/kg. After performing simple sizing trade studies involving the max takeoff weight and the required battery energy to fly for the full required range of 1200 nmi, we concluded that batteries of higher energy density would be required in order to make an all-electric design feasible. We decided to pursue alternatives to lithium-ion to enable a path forward in electric propulsion. The most promising battery technology of the near future is known as a lithium-air (Li-air) battery. This “air breathing” battery produces electrical energy by oxidizing lithium metal with ambient oxygen. Such ACCELERA
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a battery allows vast improvement in energy density because it does not include a solid cathode like other batteries (lithium polymer). As such, the Li-air battery has a practical energy density that is projected to reach 1.35 – 1.70 kWhr/kg [10] [11]. For the purposes of our design, a more conservative energy density of 1.35 kWhr/kg was assumed. The energy density of Li-air immediately enabled us to switch to all-electric propulsion and eliminate fuel-burning engines and systems at a tremendous weight, cost and complexity savings. The new batteries were assumed to have the same general dimensions as the AIAA specification and were placed at the midpoint of the main deck. This location was chosen for several reasons. First, given the internal dimensions of our aircraft, the space beneath the main cabin where a traditional cargo compartment would be is of inadequate height to house the batteries. Additionally, several structural benefits are realized as described in the structures and loads section. Since Li-air batteries require ambient oxygen, a system will need to be installed on the aircraft to provide airflow through the battery cores in order for them to discharge power. However, this problem is of low concern because the batteries are projected to require an airflow that is “comparable to the specific airflow of internal combustion engines” [11], much less than that required for a turboprop engine or typical APU, for which the systems challenges have already been solved. Additionally, over the last two years, focused research has resulted in rapid advances in rechargeability and power density of the technology [10]. It is reasonable to expect Li-air batteries will be ready for deployment by 2030. In order to connect the batteries to the motors located into the tail of the aircraft, redundant energy conduits will be laid underneath floor of the aircraft from the compartment location into the rear of the aircraft where the required power control equipment is housed. From here, the conductors will travel through the vertical structural boxes in the vertical tails and into the horizontal stabilizer and engine nacelle. 7.2. Electric Motors. Power density is the figure of merit for aerospace electric Figure 34: Halbach Array motor disc motors. The motor selected for Vision is the Halbach array motor currently undergoing small scale production and testing by LaunchPoint Technologies. This motor is a brushless, permanent magnet motor that is currently able to provide a power density of 5 hp/lb, which nearly doubles the AIAA baseline motor spec of 3 hp/lb [12]. However, we assumed a power density of only 3 hp/lb in order to conservatively account for the added weight of the power transmission system and other peripheral equipment. LaunchPoint Technologies originally developed this motor for use in UAV systems, but already have designs in development for a motor in the 2000 hp range utilizing the same technology. The rapid scaling is due to the modular nature of these motors. With little modification, it is possible to stack as many motor discs as necessary to produce the required power output for a particular application. An added benefit of the stacked module configuration is that a motor is less likely to suffer a catastrophic failure during operation. If one of the modules fails, the engine will be able to continue at a reduced power due to the independent nature of the modules. Figure 35 schematically illustrates such a stacked configuration.
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Figure 35: Stacked Halbach Array Motor Concept [12]
7.3 Propulsion Configuration The Vision produces the necessary thrust for flight using propellers. The reason for this is a simple correlation between propulsive efficiency and Mach number. The aircraft was designed for cruise at a Mach number near 0.5. At this design point, the propulsive efficiency of propellers is vastly superior to turbofan engines (Figure 36). Additionally, propellers are more easily integrated into a fully electrical system as current fan based engines are designed to accommodate a combustor section and extremes of temperature associated with fuel combustion. Propellers are currently designed for a particular mission independent of the energy storage and transmission method. This prevents the large design cost of producing an entirely new engine type. Figure 36: General Propulsive Efficiency [13]
The decision was made early on in the design process to place the propulsion system of the Vision in the rear of the aircraft with the thrust vector directly along the centerline. There are numerous advantages to this location. Firstly, the position of the thrust along the centerline prevents the aircraft from having to fly under a severe yaw moment in the event of an engine out condition. This reduces the weight and size required for the vertical tails. Additionally, the centrally located propeller ingests the boundary layer from the double-bubble fuselage, reducing the impact of the greater associated friction drag area [14]. ACCELERA
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The final propulsion configuration improvement applied to the design is a coaxial, counter rotating pusher style propeller disk. This decision was motivated by the need to locate the propulsion in the boundary layer of the fuselage, yet produce enough power for takeoff. The propeller blades themselves are composite in construction and feature a heavily twisted and swept “scimitar” shape to delay the onset of wave drag on the propeller tips. Each of the paired counter rotating propellers are geared such that if one of the propellers should be damaged, the two independent motor stacks housed in the motor pod may operate the single remaining propeller at increased power. This is another example of the versatility allowed by employing a fully electrical propulsion design. Furthermore, the coaxial propellers serve to increase propulsive efficiency. A single isolated propeller disk observes an inevitable loss of efficiency due to the swirl induced in the airflow by the rotating propeller blades. Inclusion of a second, counter rotating propeller behind the first causes the rotational component of the flow to be canceled out for a gain in efficiency around 8%, as observed in past applications [13]. Figure 37: Counter Rotating Coaxial Propeller Disk
7.4 Propeller Fatigue Due to the location of our propeller disk behind the vertical and horizontal stabilizers, the propeller blades will be exposed to the unsteady wake emanating from the trailing edges of the control surfaces. Research was conducted to ensure that this effect would not cause the propeller blades to be critically loaded in fatigue such that our propulsion configuration was impractical. This research revealed that there are several aircraft currently in operation that utilize a similar propulsion configuration successfully. One such example is the General Atomics MQ-9 Reaper, also features a composite propeller located directly behind its primary tail control surfaces (Figure 38). Figure 38: MQ-9 propeller configuration comparison to Vision [14]
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While the exact fatigue properties of the propellers used on the MQ-9 are not known, the design of the drone for use as a long endurance and low maintenance aircraft supports the conclusion that the operational fatigue on a composite propeller due to tail wake is not a critical concern. Because of the anisotropic nature of composite materials, the characterization of fatigue effects must be done on a part by part basis with an extensive series of test defined by the FAA. If this design was to be submitted for type certification, the propeller blades would undergo many tests to determine their fatigue life in normal operating conditions and ensure that the effect of the wake on the propeller disk did not cause premature fatigue failure of the component. 7.5 Thrust Modeling For the purposes of meeting the takeoff field length constraint, power was converted to an effective takeoff thrust based on a regression model [5, p. 692], which gave us an effective takeoff maximum thrust of 12,100 lbf.
8 Landing Gear 8.1 Landing Gear Tire Sizing The landing gear tires were sized using the method provided by Roskam [16]. This method takes into account the center of gravity excursion of the aircraft, the distance between the nose and main landing gear, and the center of gravity height. This is to develop upper and lower bounds that the landing gear would experience during operation. After applying the Roskam method, the maximum load for each tire was evaluated. A tire from the B.F. Goodrich catalog provided by Roskam was then chosen for the main and nose landing gear that met the load requirements (Table 13).
Table 13: Landing Gear Sizing Count Diameter Width Tire Type Nose gear Main gear
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20 30
5.5 7.7
Type VII Type VII
Max Loading (lbs) 7200 21300
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Predicted Max from Roskam Method (lbs) 6437 16982
Unloaded Inflation Pressure (PSI) 230 360
30
Figure 39: Landing Gear Sizing
8.2 Landing Gear Disposition The nose landing gear will rotate aft and under the cabin floor in order to accommodate the sharp ramp at the nose of the fuselage. The main landing gear will rotate into the wing box fairing. Figure 40 illustrates the configuration of the landing gear before and after deployment. Figure 40: Landing gear disposition
8.3 Longitudinal Tip-Over The longitudinal tip-over criterion was met using the method provided by Roskam [16]. The angle between the vertical gear axial position position and the aft center of gravity line is measured to ensure that the aircraft will not tip backward about the landing gear. The Vision has an angle of 43.94°, which meets the longitudinal tip-over criterion.
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Figure 41: Longitudinal tip-over criterion
8.4 Lateral Tip-Over The lateral tip-over criterion was checked with the method provided by Raymer [6]. The Raymer method is based on geometry as shown in Figure 42. The indicated angle must be less than 63° which the Vision easily meets at an angle of 54.62°. Figure 42: Lateral tip over criterion satisfied [6]
9 Method Validation Method validation for an all-electric airplane is difficult at best. With no analogous historical data with which to check DOC, our approach to method validation involves picking figures of merit from aerodynamics, structures, and cost estimation in order to validate the accuracy of the code for our application.
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Table 14: Method validation Figure of Merit L/D WTO fwE DOC (cents / AS nmi)
Vision 22 – 24 67,245 lb 45% 9.58
MIT D-8 22.1-25.3 101,991 lb 50% N/A
Q400 18.0 65,000 lb 58% 13.76
2030 Baseline (Red) 22.0 64,600 lb 64% 17.93
Our aerodynamic code validates well, with a L/D within the range predicted for the similar MIT D-8 aerodynamic configurations. Takeoff weight is within 3% of the Q400 for the same design range and number of passengers, so the overall weight code produces reasonable values by itself. Empty weight fraction appears to be low at first glance. An explanation for the small structural fraction is heavy energy storage. Since the MIT-D8 concept stores energy-dense fuel, a smaller portion of its payload fraction is devoted to energy. This increases the weight of interiors, seats, ECS, lavatories, and other components which are included in empty weight fraction. The Vision design also takes advantage of electric infrastructure by eliminating an APU, and by removing de-icing equipment from the morphable leading edge. All of these factors directly reduce the empty weight fraction of the airplane. For a discussion of DOC validation, see Section 10.
10 Direct Operating Cost Direct Operating Cost (DOC) is used as the figure of merit for optimization and down selection, so an accurate estimate of DOC was critically important for design decisions. Our strategy for estimating cost involved generating initial estimates for cost components based on historical data, then making adjustments based on engineering intuition about the design of the aircraft. DOC is defined as the cost per available seat distance ($/pax nmi) of expenditures directly related to aircraft operations. Liebeck defines DOC as the combination of the following categories: flight and cabin crew, landing and navigation fees, airframe and engine maintenance, energy, depreciation, insurance, and financing [15]. An explanation of our method for estimating each category follows. All values have been adjusted to reflect 2012 U.S. Dollars. 10.1 Labor Flight and cabin crew costs were calculated according to Equation 9, which determines the cost per individual crew member. (
)
Equation 9
The labor cost fraction due to benefits was assumed to be 30% for all of our cost analyses, except where benefits are already included [16]. Pilot wages were calculated using data on average regional captain salaries from the Airline Pilots Association, based on ½ time flight utilization (80 hours per month) according to Equation 10 [17] Flight attendant data from the Bureau of Labor Statistics was incorporated using the same equation [18]. Equation 10
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Block time was assumed to include both actual time spent in the air (as calculated by the fuel and energy codes based on flight profile and range) as well as Raymer’s estimates for ground maneuver (15 minutes) and in flight maneuver (6 minutes) [5]. 10.2 Energy Cost of fuel and electricity are calculated based on the weight of the energy storage used during flight [19]. Since the price of electricity stipulated by the AIAA competition includes charging and battery maintenance, we neglect to include charging efficiency in our calculation according to Equation 15 [3]. 10.3 Fees Landing fees and navigation fees were calculating using historical regression, using takeoff weight, mission range, and block time according to Equation 16 [19]. 10.4 Ownership The cost of ownership includes financing, depreciation, and insurance, which are tied to the purchase price of the airplane. In order to model the purchase price, we used the DAPCA IV program cost model [5]. The model uses empty weight, maximum design speed, and production run quantity to estimate the number of hours required in design, production, and support. Labor wrap rates are then multiplied by the estimated hours to calculate the total price of the airplane program, which can be converted to unit cost. In order to account for advanced materials and complexity of design, we incorporated a 1.6 cost multiplier to the DAPCA IV price for the Vision program. Cost of power plants was calculated by scaling the total required power by a “cost-per-hp” factor determined from historical data. The electric motor price was hard to determine since no FAR 25certified products are currently available. See 16.4 Motor Price Regression Model for details of our custom electric motor regression model. Table 15 summarizes the components of aircraft unit cost. Table 15: Airplane Unit Cost Acquisition Cost Categories Design and Test Production (Labor + Materials) Propulsion Avionics Interiors Total Flyaway Cost
Vision $2.63 M $17.91 M $754 K $3.19 M $119 K $2.45 M
Depreciation, insurance, and financing are calculated according to standard formulas presented in the class notes [Equation 17 - Equation 19] and the constants in Table 21. 10.5 Maintenance Another key design goal is to reduce maintenance cost. Maintenance can be roughly divided into two components: airframe and engine. To calculate airframe maintenance, we used Equation 20, a historical regression model [19]. Engine maintenance was calculated from the 1967 ATA cost estimating method for turboprops (Equation 21 - Equation 25) [6]. We assume that flight hours are the same as block hours. ACCELERA
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10.5 DOC Results The Accelera Vision concept boasts a 46% reduction in operating costs relative to a baseline hightechnology turboprop under the same cost modeling assumptions, and a 16% decrease relative to Bombardier’s claims about the Q400. Table 16: Operating cost performance (2012 cents / pax nmi)
DOC (cents / pax nmi) % change on baseline
Red (Baseline) 17.93 --
Blue (PDR) 12.09 -32%
Q400 [1]
Vision
13.76 --
9.58 -46%
The Q400 DOC value has been converted to 2012 dollars; it has not been normalized to the cost of fuel. It is included to validate our cost code and illustrate the impact of volatile fuel prices on aircraft DOC. The Vision concept’s outstanding cost performance is achieved by taking advantage of the relative pricing of energy. Figure 44 exhibits the qualitative differences in cost breakdown between the conventional and electric concepts. Vision is more expensive to buy but costs substantially less to operate than the baseline design. Figure 43: DOC components of 2030 baseline (Red)
Figure 44: DOC components of Vision design
10.6 Energy Price Sensitivity To help explain the vast difference in energy cost between Vision and the 2030 baseline design, it is important to consider the relative cost of a unit of energy under the assumptions of the AIAA competition requirements. Under the competition requirements, electricity is priced at $0.05 / kWhr, whereas jet fuel is priced at $5 / gallon. Normalizing both energy rates to a common unit of price per unit energy delivered to the drive shaft, we find that electricity is approximately six times cheaper than the fuel-powered equivalent (Table 17). The biggest cause of the discrepancy, apart from the high cost of jet fuel, is that efficiency losses are taken at the power plant, not at the aircraft . ACCELERA
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Table 17: Energy price arbitrage Competition Price Energy Density Raw Price / MJ Therm/Elec/Mech Efficiency Price / effective shaft MJ Price / effective shaft kWhr
Electricity $0.05 / kWhr
Jet-A $5 / gal 35.3 MJ/L [20] $0.0374 / MJ 45% (thermal)+ 95% (mechanical) $0.0874 / esMJ $0.315 / eskWhr
$0.0138 / MJ 95% (electrical) $0.0145 /esMJ $0.0522 / eskWhr
10.7 Mission Phase Analysis The energy consumption and weight code used to analyze the Vision concept provides fine-grained control over mission parameters and detailed information about the relative contribution of each mission phase to energy consumption. Figure 45 demonstrates that the cruise and climb phase dominate energy consumption at the 1200 nmi range, but the divert and reserve requirements also consume a sizable fraction of the available energy. The total mission block time for the 1200 nmi mission is about 5 hours. Figure 45: Energy budget – 1200 nmi mission and 100 nmi reserve Land at alt 1%
Loiter 5%
Divert climb 8% Divert Descent 2% to Loiter 4% Descent alternate divert 0% Desc to Land 2%
Loiter at alt 5%
TO 0% Climb 20%
Cruise 53%
For the 400 nmi mission, Figure 46 illustrates that a much larger portion of the energy budget is devoted to reserve components, and climb dominates the planned mission phase compared to cruise. The block time for the economic mission is about 2 hours.
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Figure 46: Energy budget - 400 nmi mission Loiter at alt 9%
Land at alt 4%
TO 0%
Climb 31%
Loiter 9% Divert climb 16%
Divert 2%
Cruise 20%
Descent to Loiter Desc to Land 4% 5%
Descent alternate divert 0%
Figure 47: Block time components - 400 nmi mission (minutes) TO, 1
Climb, 20 Loiter, 30
Descent to Loiter, 15
Cruise, 40
Desc to Land, 13
11 Design Refinement and Optimization 11.1 Preliminary Refinement and Trade Studies Prior to conducting a true multidisciplinary design optimization (MDO) study of the aircraft, the initial design point was first optimized sequentially using 3-D contour response plots with respect to several important flight parameters. An example of the type of trade plot used during the preliminary study is the power-wing area constrained DOC plot shown as Figure 48. For more trade plots, see Appendix 16.5.
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Figure 48: Power-wing area constrained optimization
Following the 2-D optimization sequence, the design’s economic mission DOC was about $0.099 / AS nmi. 11.2 Multivariate Optimization Strategy In order to systematically optimize for operating cost, a multidisciplinary design optimization (MDO) code was constructed. The first strategic choice was whether to explore the design space using gradientbased optimization and how many variables would be feasible for optimization. In the end, the team identified ten variables to explore design tradeoffs. For consideration, inputs either were required to possess reliable weight estimations or be negligible in weight, and improve aerodynamic performance or ease a constraint. Table 18: Optimizer variables and constraints Optimizer variables
Constraints
Swing
Landing field length
Wing aspect ratio
Takeoff BFL power
Taper ratio
Takeoff T/W
Wing incidence angle
Takeoff climb power
Twist (linear, root to tip)
Clean, optimum climb power
Wing axial position
Cruise power
Power
Cruise maximum CL
Propeller diameter
Battery compartment volume
Cruise altitude (max range) Wingspan gate constraint Cruise Mach (max range) Static margin > 5%
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Research suggests that gradient based optimizers require around 100 evaluations for convergence of ten variables, while non-gradient based methods require between 1000 and 10,000 evaluations [23]. We therefore chose to pursue gradient based optimization in the interest of computational run time. Table 18 lists the optimizer-controlled variables and the non-linear constraints obeyed by the optimization function. Figure 49: Planform comparision - D8 and Vision Vision-DOC
Vision-L/D
A unique challenge of this optimization was numerical precision of the L/D estimating panel code. AVL software is written to display only four decimal places of precision, whereas the step for the finite difference gradient solver in fmincon is on the order of 1*10-6. An imperfect solution is to increase the step size of the gradient optimizer to 0.02 and capture the miniscule aerodynamic impacts of design changes. In order to validate that the optimizer was producing reasonable results, three objectives were chosen to compare to previous MDO studies: DOC (primary objective), WTOG, and L/Dcruise. Three separate optimizations were conducted and the results are presented below. Only the DOC-optimized version represents a design recommendation; the L/D and WTOG optimizations are for validation of the code and research interest. Figure 50: DOC optimized planform 11.3 Direct Operating Cost Optimization The objective function, DOC, was optimized until convergence using fmincon. The following plots track DOC performance during the optimization, as well as the values of all ten process inputs during the optimization. The result was a 5% decrease in operating cost. Aspect ratio dropped to 11, but traded off with 2000 lb in empty weight reduction. The long-range cruise Mach number converged to the AIAA competition limit of 0.45. Figure 50 is a planform view of the final optimized DOC configuration.
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Figure 51: DOC optimization – Objective function history
Figure 52: DOC optimization - Variable histories
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Aspect ratio
Incidence
Twist
Taper
Wing position
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Cruise altitude
Cruise Mach number
Total power
To explore the DOC optimization in more detail, a Pareto front was constructed between takeoff weight and DOC (Figure 53). The results indicated that while it is initially advantageous to increase weight to take advantage of aerodynamic efficiencies, once sufficiently low DOC is attained, DOC scales with takeoff weight reductions. Figure 53: Pareto front between DOC and MTOW
11.4 Aerodynamic Optimization An alternative objective function, L/D, was identified as a means of testing the ability of the MDO code to account for aerodynamic improvements. A new objective function was written to call L/D, calculated by AVL, after each function evaluation and optimize the result using fmincon and the variables listed in Table 18. The optimizer ultimately achieved over a point of L/D improvement compared to the optimizer starting point. The aircraft “gained” over 2000 lbs to reach almost 71,000 lb gross takeoff weight. DOC increased compared to the baseline, but only by $0.0010 or about 1%. The optimization performance is displayed in Figure 54.
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Figure 54: L/D optimization history Figure 55: Optimized L/D planform
11.5 Takeoff Weight Optimization Another alternative objective function, WTOG, was identified as a means of testing the structural optimization capability of the code. Using fmincon and the variables listed in Table 18 produced major changes in takeoff weight through 70 iterations. Most notably, MTOW decreased by almost 4,000 lbs. The change is due in part to reduced battery weight at maximum takeoff through efficiency improvements. The wing boasts an aspect ratio of more than 16, in contrast with the aspect ratio of 10.8 of the DOC-optimized design. However, the wing area also decreased by almost 200 ft2 overall, trading off with an increase in takeoff power available to meet the field length requirement. DOC is only about $0.0010 higher for the MTOW optimized configuration compared to the DOC-optimized Vision Figure 56: MTOW optimization history
Figure 57: Optimized MTOW planform
12 Structures and Loads Considering the array of new and innovative technologies implemented in the design of the Vision, the aircraft’s structural layout is comparatively simple and traditional. Despite the oblong fuselage cross section, it is fundamentally a tube and wing construction with a semi-monocoque fuselage and a wing with a continuous wing box. The wing box of the Vision continues through a fairing underneath the ACCELERA CRITICAL DESIGN REVIEW 42
fuselage, supporting it from below (Figure 58). Additionally, the aircraft is constructed almost exclusively with composites, which, in part, enable the Vision to have a low empty weight in comparison to other aircraft in its class, despite the increased width of the fuselage. 12.1 Fuselage and Wing Box Figure 58: Wingbox carrythrough
The fuselage of the Vision consists of a semi-monocoque made up of frame and stringers that provide stiffness for the outer skin panels. As the aerodynamic load continues through the wing box and into the fuselage, the composite frames accept the load and disperse it around the passenger cabin (Figure 59). These composite frames differ from the traditional in that they feature the same double bubble shape as the fuselage cross section. Because of this irregular shape, the frames (as well as the stringers) on the flattened top and bottom sections of the fuselage are stiffened to accept the increased cabin pressure loads and aerodynamic loads produced by the lifting fuselage. Figure 59: Fuselage load diagram
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12.2 Design of Battery Compartment The primary configuration change to be made during the final stages of the design process involved moving the battery compartments from the rear of the aircraft to the midpoint of the fuselage (Figure 60). This decision was primarily motivated by tip-over issues during loading and unloading. However, placing the batteries has a number of other structural advantages. Figure 60: Battery compartment structural design
Initially there was some concern that the floor of the battery compartment would have to be strengthened in order to support the high local pressure on the floor panels caused by the high density battery stacks. However, now that the battery compartment is located directly over top of the wing box, the wing box itself provides the extra stiffening. Additionally, locating the batteries near the center of pressure longitudinally greatly decreases the fuselage bending stress compared to that which would have been present by placing the batteries farther away from the wing. 12.3 Structural Design of Tail The need to have the propeller disk located directly behind the fuselage in order to ingest the boundary layer during flight led to the adoption of a novel tail design. The H-tail allows the nacelle containing the electric motors to be placed on the underside of the middle segment of the horizontal stabilizer, placing the propeller disk in an ideal position to ingest the boundary layer coming off of the upper surface of the lifting fuselage. Figure 61: Tail structural configuration
In order to accommodate the weight of the motors and the large propeller disk, the horizontal stabilizer features a 15% t/c airfoil to allow more internal volume for a tail box which spans the distance between ACCELERA CRITICAL DESIGN REVIEW 44
the two vertical tail sections. This horizontal box attaches to the vertical structural boxes inside each of the vertical tail sections. 12.4 Loads Analysis Figure 62: V-n diagram Table 19: Design speed definitions
Maneuver condition
Speed (kts)
VA
191.5
VB
195.9
VC
206.0
VMO
218.4
VD
233.7
Gust lines
Maneuver lines
The Vn diagram (Figure 62) displays the load factors applied on aircraft structures as a function of the equivalent airspeed. This analysis defines the maneuvers and conditions that the aircraft is designed to withstand structurally; the lines are calculated using formulas from Raymer (Equation 11 - Equation 12) [6]. Stall / maneuver line
Gust line
Equation 11 ⁄ Equation 12 ⁄
Take note that the black lines on the plot describe the boundaries of the maneuver envelope while the six red lines describe the gust loads applied to the aircraft. The outermost gust lines which correspond to the worst case “rough air” gust condition are active on both the positive and negative load factor limits. The relatively low CLmax and altitude of the Vision during cruise cause the aircraft to face higher assumed gust loads and lengthen the stall lines of the Vn Diagram. These effects combine to cause gust loads to be critical. Due to the stall properties of the BLAM-7 laminar airfoil, the Vision has a low value of CLmin. This prevents the load factors from reaching the maximum factor of -1 in a negative lift situation. However, the airfoil’s stall is docile due to its laminar design which mitigates the detrimental effect of a low CLmin on aircraft stability.
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13 Computational Procedure 13.1 Methods of Analysis Our computational architecture builds up aircraft performance from geometry and estimates of weight. Figure 63 illustrates the top-level steps and sub-tasks. The algorithm can be run over a range of input scenarios to generate optimization plots or iteratively to allow for automated optimization and manual design refinement. Figure 63: Computational flow
Geometric Analysis
Weight and Balance Analysis
Aerodynamic Analysis
Constraint Evaluation
•Calculate surface geometry based on taper, aspect ratio, twist, incidence, and planform area •Calculate Cg locations of weight line items
•Estimate empty weight of components based on historical data •Generate initial estimate of takeoff weight based on "design weight" guess or previous weight iteration •Calculate Cg position of aircraft configuration •Calculate moments of inertia
•Estimate friction drag based on airfoili geometry and Reynolds number •Calculate lift-to-drag ratio at cruise condition based on total weight estimate and geometry using AVL •Calculate neutral point and static margin using AVL •Calculate trim elevator deflection using AVL •Calculate loiter and climb drag polars based on friction drag increment and Oswald efficiency
•Estimate takeoff and landing distance based on power, converged weight, and geometric parameters •Calculate required climb power •Calculate volume required for battery stowage •Calculate cruise CL
•Calculate flyaway cost based on historical data •Calculate direct operating cost based on historical data and current financial data
Cost Estimation
13.2 Software Design We sought to assemble an aircraft- and mission-based approach to structuring the code, which is written in MATLAB. ACCELERA
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Figure 64: Initialization routine and data structure Labor burden rate Energy prices User chooses any combination of mission, airplane, and cost structure. Running the script brings a struct into the workspace
Rate Struct
InitRateAirplane.m
Financing and depreciation rates Geometry data
Aerodynamic data
InitAirplane.m Airplane Struct
InitMission.m Mission profile
Mission Struct
Structs
Propulsion sizing and performance
Weight data
Layout data
Payload requirements
Atmospheric conditions
Data points
Data is stored almost entirely in structs. A struct is generated to represent an aircraft design, a mission profile, and a set of cost assumptions. Figure 64 illustrates the relationships between the structs, describes the initialization routine, and gives examples of the types of information the structs might hold. A unique feature of our code is our extensive deployment of open-source toolboxes to reduce routine errors – a unit conversion toolbox and a standard atmosphere code. The unit conversion toolbox creates a new class called “unit” which contains both a value and a unit. When values are cast into units, they are converted to the equivalent SI values and can be operated on like any other number. Conversions (for example, when using Imperial unit regression models) are integrated into the toolbox [21]. We also modified a MATLAB implementation of a 1976 US Standard Atmosphere to function with the unit class [22]. The analysis code overall was restructured to function with fmincon, which involved passing only a vector of the design variables into the function. To ensure that all the necessary (but static) data points were passed into the function and avoid re-initializing huge structs on every iteration, a global struct was created for each airplane, mission, and cost assumption. The iterative procedure first finds a converged takeoff weight at the maximum range mission, checks all climb, takeoff, and landing constraints, then re-calculates the actual takeoff weight and energy consumption for the economic mission (Figure 65).
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Figure 65: Objective function code structure Vec of optimizer vars
Global airplane, cost, and mission structs
Objective.m [Objective function]
AeroGeoCalc.m [Calculates implied geometry from design vars]
Long range mission data
WeightBalance.m [Calculates AC weight and CG]
Global “C” vector passed back to fmincon
EnergyElectric [Estimates energy consumption]
No AVL routine [Passes back L/D at cruise]
WTO within 200 kg of guess? Yes CheckConstraints [Verifies that NL constraints met at MTOW]
Economic mission data
DOC returned to function as a scalar
WeightBalance.m [Calculates AC weight and CG based on actual MTOW]
EnergyElectric [Estimates energy consumption]
CostFunc.m [Calculates DOC]
AVL routine [Passes back L/D at cruise]
13.3 AVL Implementation To bring Athena Vortex Lattice (AVL) into the loop, we needed to figure out how to make MATLAB and AVL interact. Rather than wrapping the AVL binary directly, we chose to use data input and batch files to allow the two programs to communicate indirectly. Individual functions in MATLAB write .avl, .mass, and .run text files, and a final calling function in MATLAB runs AVL at the command line (Figure 66). The arrangement evaluates our paneling layout in about 2 seconds per iteration, which was sufficiently fast for our implementation.
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Figure 66: AVL implementation Airplane geometry and weight data
AVL_Output.m
Airplane.avl
AVLmassfile.m
Airplane.mass
runAVL.m
Airplane.run
Flight condition and atmosphere data
AVL.exe [Calculates L/D and neutral point]
L/D, Neutral point location
Airplane.sb
Parseruncasefile.m
14 Conclusions Accelera has designed the Vision in order to achieve a low direct operating cost (DOC), operational feasibility, and marketability. A multidisciplinary design optimization (MDO) strategy was utilized to achieve the greatest aircraft performance with the given design resources. Through the adjustment of 10 parameters using Accelera’s optimizer, the Vision was able to achieve 25% lower operating cost than a Q400 regional aircraft, at 9.58 cents per available seat mile. Key performance advantages of the design include:
Superior L/D performance due to lifting fuselage, boundary layer ingestion, and aerostructural optimization Reduced trim drag due to fuselage lift moment and MDO placement of wing Increased passenger safety due to redundant, stacked Halbach Array motor discs Increased propulsive efficiency due to boundary layer ingestion and counter-rotating propellers Reduced weight and complexity by avoiding turbines and fuel systems Increased efficiency due to the use of smart leading and trailing edges Lower DOC as a result of greatly reduced energy cost Potential for reduced maintenance cost due to electric propulsion system Reduced airline exposure to unpredictable fuel prices or carbon taxation Quieter cabin due to aft-mounted electric propulsion Great appeal to passengers as a result of “green” technology and futuristic look
The Vision, with its many advancements may seem like an exotic aircraft today, but upon detailed analysis, is only a mere decade and a half from being a viable and accepted step forward in aircraft design and technology. ACCELERA
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15 Citations [1] Bombardier, "Q400," June 2003. [Online]. Available: http://www2.bombardier.com/en/3_0/3_8/BCAU/pdf/RU_Jun03_1.pdf. [Accessed October 2012]. [2] N. Meier, "Civil Turboshaft/Turboprop Specifications," 2005. [Online]. Available: http://www.jetengine.net/civtsspec.html. [Accessed October 2012]. [3] American Institute of Aeronautics and Astronautics, "Design of a 2030 Regional Airliner Considering Hybrid Electric Propulsion," 2012. [Online]. Available: https://www.aiaa.org/uploadedFiles/Events/Other/Student_Competitions/20122013%20Ugrad%20Team%20Aircraft.pdf. [Accessed 25 10 2012]. [4] H. P. Monner and J. Riemenschneider, "Morphing high lift structures," 30 March 2011. [Online]. Available: http://www.cdti.es/recursos/doc/eventosCDTI/Aerodays2011/2E3.pdf. [Accessed October 2012]. [5] L. R. Jenkinson, Civil Jet Aircraft Design, Reston, VA: American Institute of Aeronautics and Astronautics, 1999. [6] D. P. Raymer, Aircraft Design: A Conceptual Approach, Reston, VA: American Institute of Aeronautics and Astronautics, 2012. [7] E. Torenbeek, Synthesis of subsonic airplane design, Netherlands: Delft University Press, 2008. [8] M. Drela and H. Youngren, XFOIL 6.9, Cambridge, MA: Massachusetts Institute of Technology, 2001. [9] A. Girard and N. H. McClamroch, "Notes for AE 345 Flight Dynamics and Control," 2012. [Online]. Available: ctools.umich.edu. [Accessed 6 December 2012]. [10] H.-G. Jung, J. Hassoun, J.-B. Park, Y.-K. Sun and B. Scrosati, "An improved high-performance lithiumair battery," Nature Chemistry, July 2012. [11] G. Girishkumar, B. McCloskey, A. Luntz and S. Swanson, "Lithium-Air Battery: Promise and Challenges," J. Phys. Chem. Lett., vol. 1, no. 14, pp. 2193-2203, 2010. [12] M. Ricci, "High Efficiency, High Power Density Electric Motors," 2010. [Online]. Available: http://www.launchpnt.com/Default.aspx?app=LeadgenDownload&shortpath=docs%2flaunchpointhalbach-motor-presentation-2010.ppt. [Accessed October 2012]. [13] Z. Spakovsky, "Unified Thermodynamics and Propulsion," 2007. [Online]. Available: http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node82.html. [Accessed October 2012]. [14] M. Drela, "Development of the D8 Transport Configuration," 2011. [Online]. Available: http://web.mit.edu/drela/Public/papers/Hawaii_11/Drela_AIAA2011_3970.pdf. [Accessed October 2012]. [15] P. Schimming, "Counter rotating fans - An aircraft propulsion for the future," Journal of Thermal Science, vol. 12, no. 2, pp. 97-103, 2003. [16] J. Roskam, "Airplane Design," in Part IV: Layout of Landing Gear and Systems, Lawrence, KS, Design, ACCELERA
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Analysis, and Research Corporation, 2007. [17] R. Liebeck, "Advanced Subsonic Airplane Design and Economic Studies," April 1995. [Online]. Available: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950017884_1995117884.pdf. [Accessed October 2012]. [18] Bureau of Labor Statistics, "Employer Costs for Employee Compensation," June 2012. [Online]. Available: http://www.bls.gov/news.release/ecec.nr0.htm. [Accessed October 2012]. [19] Air Line Pilots Association, "Cleared to Dream: A Pilot's Life," 2008. [Online]. Available: http://education.alpa.org/APilotsLife/tabid/322/Default.aspx. [Accessed October 2012]. [20] Bureau of Labor Statistics, "Occupational Outlook Handbook," 2012. [Online]. Available: http://www.bls.gov/ooh/transportation-and-material-moving/flight-attendants.htm#tab-5. [Accessed October 2012]. [21] J. R. Martins, "Class Notes," October 2012. [Online]. [Accessed 25 October 2012]. [22] I. Kroo, "Aircraft Design: Synthesis and Analysis," [Online]. Available: http://adg.stanford.edu/aa241/AircraftDesign.html. [Accessed October 2012]. [23] J. R. R. A. Martins, "High-Fidelity Multidisciplinary Design Optimizatin of Aircraft Configurations," University of Michigan, Ann Arbor, 2012. [24] J. McDermid, "MATLAB Unit Conversion Toolbox," 2010. [Online]. Available: http://www.mathworks.com/matlabcentral/fileexchange/29621. [Accessed September 2012]. [25] B. Lewis, "Complete 1976 Standard Atmosphere," 11 January 2007. [Online]. Available: http://www.mathworks.com/matlabcentral/fileexchange/13635-complete-1976-standardatmosphere. [Accessed September 2012]. [26] International Air Transport Association, "Aircraft Financing: Risk and Reward," August 2010. [Online]. Available: http://www.iata.org/pressroom/airlines-international/august2010/pages/07.aspx. [27] Bloomberg, "Corporate Bond Rates," 2012. [Online]. Ava [23]ilable: http://www.bloomberg.com/markets/rates-bonds/corporate-bonds/. [Accessed 25 October 2012]. [28] Forecast International, "The Market for Aviation Turboprop Engines," 2010. [Online]. Available: http://www.forecastinternational.com/samples/F641_CompleteSample.pdf. [Accessed October 2012]. [29] Massachusetts Institute of Technology, "NASA N+3 MIT Team Final Review," 23 April 2010. [Online]. Available: http://aviationweek.typepad.com/files/mit_n3_final_presentation.pdf. [Accessed October 2012]. [30] P. Rudolph, "High-Lift Systems on Commercial Subsonic Airliners," September 1996. [Online]. Available: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19960052267_1996080955.pdf. [Accessed October 2012]. [31] I. Kroo, "Nonplanar Wing Concepts for Increased Aircraft Efficiency," 6 June 2005. [Online]. Available: http://aero.stanford.edu/reports/VKI_nonplanar_Kroo.pdf. [Accessed October 2012]. ACCELERA
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[32] M. Bradley and C. K. Droney, "Subsonic Ultra Green Aircraft Research: Phase I Final Report," April 2011. [Online]. Available: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110011321_2011011863.pdf. [Accessed October 2012]. [33] E. Greitzer and H. Slater, "N+3 Aircraft Concept Designs and Trade Studies," 2010. [Online]. Available: http://web.mit.edu/drela/Public/N+3/Final_Report.pdf. [Accessed October 2012]. [34] J. Roskam, Airplane Design, Aviation and Engineering Corporation, 1989. [35] L. Ranson, "GE cites strong interest in CPX38 turboprop engine," Flightglobal, 17 May 2011. [36] M. Drela, Athena Vortex Lattice, Massachusetts Institute of Technology, Cambridge, MA [Accessed 11/2012]
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16 Appendices 16.1 List of symbols Variable AR A b c C Caircraft Ccrew Ccrew,annual Cdepreciation Cd0 CEF Cenergy Cf CFCe CFHe Cfinancing Cinsurance CL CLα Cmaintenance D Dmission DOC e Esegment E/W Etotal,Emission f fbenefits fl hcombustion I IRa Kg KFCe KFHe L ACCELERA
Definition Aspect Ratio Propeller Disk Area Wingspan or base (depending on equation) Chord Total cost (2012 US dollars) Aircraft cost Crew Cost Yearly Salary Depreciation Cost Drag Coefficient Cost Escalation Factor Energy Cost Coefficent of Friction Engine Material Cost per Cycle Engine Material Cost per Hour of Use Finacing Cost Insurance Cost 3D Lift Coefficient Lift Curve Slope Maintenance Cost Drag Mission Length Direct Operating Cost Oswald Efficiency Energy Used During Mission Segment Energy to Weight Ratio Total Energy Used on Mission Parasite Area fraction Crew Benefits Pay Factor Fraction of Lift due to Fuselage Heat of Combustion of Gasoline Moment of Inertia Insurance Rate (% of Caircraft) Gust Alleviation Factor Engine Maintence Cost per Cycle Engine Maintence Cost per Hour of Use Lift or Length (depending on equation) CRITICAL DESIGN REVIEW
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Lfus M MAC MPG Nz n P P/W PAX pf PSFC q qf Rcrew Re Rmechanic S Scsw Swet Swing tsegment tutil T/W tb tf Tstatic Uannual Ue VA VB VC VD VEAS Vfuel VMO W WmaxTO Wpropulsion W/S Wbatt Wdg We ACCELERA
Fuselage Lift Moment Mean Aerodynamic Chord Fuel Miles Per Gallon Z-Direction Load Factor Aircraft Useful Life (years) Power Power to Weight Ratio Number of Passengers Corporate Bond Yield Power Specific Fuel Consumption Dynamic Pressure Yearly Interest Crew Pay Rate Reynolds Number Mechanic Pay Rate Wing Area Control Surface Area Wetted Area Wing Planform (reference) Area Total Time Duration of Mission Segment Utilization Time per Month Thrust to Weight Ratio Block Time Flight Time Static Thrust Annual Utilization Equivalent Gust Velocity Design Maneuver Airspeed Maximum Gust Intensity Airspeed Design Cruise Speed for Loads Design Dive Speed Equivalent Airspeed Total Fuel Volume Used Maximum Operating Airspeed Weight Maximum Takeoff Weight Weight of the Propulsion System Wing Loading Battery Weight Design Gross Weight Empty Weight CRITICAL DESIGN REVIEW
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Wenergy Wf Wmzf Wpay Wto Xcg Λ γ η ηgen ηp ρ ρe ρP ρSL ω λ
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Weight of Energy (Fuel or Battery) Fuel Weight Zero Fuel Weight Payload Weight Takeoff Weight Center of Gravity Position Wing Sweep Angle Glide Slope Efficiency Generational Efficiency Improvement Propulsive Efficiency Air Density Energy Density Power Density Sea Level Air Density Frequency BLI factor
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16.2 Supplementary Engineering Drawings and Visuals Figure 67: Halbach Array Motors
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Figure 68: Takeoff field length requirement
Since our aircraft was designed to just meet the takeoff field length requirement at sea level, we wanted to explore what kind of high-and-hot performance the airplane could achieve. As demonstrated by Figure 68, to take off from 7,000 ft pressure altitude requires 4,350 balanced field length at maximum takeoff weight, or a 5,000 lb reduction in takeoff weight in order to meet the 4,000 field length requirement at that altitude.
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16.3 Details of Analysis Stall Speed The stall speed for our aircraft designs was calculated using the equations provided in section 5.3.2 of Raymer. Using the lift equals weight relationship, a simple equation for stall speed can be derived that includes only the wing loading and the maximum lift coefficient as inputs. A form of this equation is given as equation 5.6 in Raymer. Wing Geometry Many of the critical values relative to wing geometry were determined using the advice and equations in the Raymer text. Of particular use were the equations given as part of figures 4.15 and 4.17 that defined the root chord, tip chord, and MAC of the wing as a function of our previously chosen wing loading, aspect ratio and taper ratio. As suggested in the Raymer text, we assumed a taper ratio of 0.45 to provide an ideal lift distribution with a simple wing shape. Empennage Sizing The initial sizing of the empennage was done using the method of volume coefficients as detailed in section 6.5.3 of Raymer. Using the historical averages for both the vertical and horizontal tail volume coefficients given in Table 6.4 for the “twin turboprop” class of aircraft, we found an initial value for required tail area. However, these initial estimates were marginally reduced by several reduction factors given by Raymer to account for the aerodynamic benefits of a T-tail, in the case of the Red and White designs, and for an H-tail in the case of the Vision design. Drag Polars To estimate the drag polars for our aircraft design, we used the drag build-up method in section 12.5 of Raymer along with an induced and trim drag supplied by AVL. Friction coefficients for the drag build-up method were calculated from average friction coefficients for various conditions, as calculated with Xfoil. This higher fidelity method allowed us to capture laminar flow benefits more accurately. The average friction coefficient for the fuselage and wing were averaged at 7 Reynolds numbers spanning the full flight regime and correlated with Reynolds number. These correlations are shown below: Cf,BLAM-7 = 6.769610-18Re2 - 2.108710-10Re + 3.249910-3 Cf,DB-38 = 1.126610-20Re2 – 6.196310-12Re + 2.932910-3 High-Lift Calculations High-lift performance, including lift and drag, was adapted to 3D using Raymer’s methods, outlined in section 12.1 and 12.6. CLmax values were confirmed with Trefftz plane analysis in AVL to confirm that local stall conditions were satisfied. Component Weight Method/Weight Buildup To determine a more accurate value for the total weight of each aircraft, the weight buildup method was used as discussed in Raymer sections 15.3.2 and the wing equation from Torenbeek. One modification performed on our weight buildup was the adjustment of the weight factors to account for composite construction, as employed on our White and Blue designs. This effect is covered in Raymer section 15.4 in which a range of percentage factors are given to account for this weight ACCELERA
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reduction. Given recent advances in composite construction and assuming some generational improvement, we selected the more optimistic values from these ranges. These percentages selected are provided in Table 20 below. Table 20: Composite Weight Adjustments [5] Composite Part Wing Tails Fuselage Landing Gear
Weight Benefit 85% 83% 90% 95%
Several modifications had to be made to the Raymer methods for weight estimation to account for the presence of electric batteries. To estimate battery weight, a simple calculation was done involving the total energy required for the aircraft to fly the design mission, the efficiency of the electric motors, and the assumed energy density of the batteries. This calculation is given in Equation 13 below. To find the takeoff weight of the aircraft, Equation 14 was used given the calculated empty weight from the weight buildup method, the payload required, and the overall energy (whether fuel or battery) weight to takeoff weight ratio as calculated by the code. Equation 13
(
)
Equation 14
Center of Gravity The calculation of the center of gravity of the aircraft was performed as a part of the weight buildup method. Each of the component weights was assigned a longitudinal position and these were used to find the longitudinal location of the center of gravity. Section 15.1.3 of Raymer was referenced during this process. Direct Operating Cost Reference Section 10 of this report for discussion on the following equations involved in calculating the direct operating cost. Equation 15
(
) )√
(
[ ][
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Equation 16
Equation 17
59
(
)
(
Equation 18
)
(
Equation 19
) Equation 20
[
[
(
(
]
) (
) (
)
(
] )
Equation 21 Equation 22
)
Equation 23
(
)
Equation 24
(
)
Equation 25
Table 21: Cost-of-ownership constants Constant Kdepreciation n pf qf IRa
Value 0.15 20 0.04 1.04 0.02
Source IATA [23] Notes [19] Bloomberg [24] Calculated from pf Notes
Equivalent Passenger Miles per Gallon Calculation To provide a telling metric for energy usage comparison, the energy usage of each of the Red, White, and Blue designs was calculated as an equivalent passenger miles per gallon of fuel. Baseline (formerly Red) Calculation To determine the equivalent passenger fuel miles per gallon of the Red design is a fairly simple process, starting with the total fuel usage in the design mission as output by our DOC code. The calculation is given below Equation 26
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Finding the equivalent fuel miles per gallon for a fully electrical aircraft involves another step of analysis. Instead of beginning with the fuel volume, the DOC code outputs the total energy usage during the design mission. This energy value can be modeled as an equivalent volume of fuel using the standard heat of combustion of gasoline. The remaining parts of the calculation proceed as in the fuel burning MPG equation given above.
Equation 27
Static Thrust Model and Takeoff Takeoff static thrust was a critical input into our takeoff field length calculation. We used the detailed takeoff length calculation presented in Raymer, p. 692. This resulted in a takeoff thrust estimate of over 12,000 lbs. For the analysis we treated the Halbach array as two independent motors of half-power each, but in reality this is a worst-case scenario because the Halbach disks are unlikely to fail together, resulting in a much more incremental power loss. Vn Diagram To calculate the Vn Diagram for our aircraft, equations 12.2, 12.4, and 12.5 mentioned and explained in section 12.3.4 of the class notes were used to calculate the necessary lines in the Diagram, including the maneuver curves and gust lines. Additionally, the required equivalent gust velocities for the gust line equations were taken from figure 12.5 in the same section. Additionally, Vmo and VD were calculated as percentages of the VC as suggested in section 12.3.2. 16.4 Motor Price Regression Model Model No.
Weight (kg)
Weight (lb)
Power (W)
Power (HP)
Cost
GPMGPMG4560
0.054
0.1188
220 0.295302013
49.99
GPMGPMG4595
0.071
0.1562
390 0.523489933
54.99
SUPSUPG8050
0.069
0.1518
370 0.496644295
29.99
GPMGPMG4700
0.198
0.4356
1480 1.986577181
89.99
0.19
0.418
1387.5 1.862416107
79.98
GPMGPMG4725
0.268
0.5896
1850 2.483221477
99.99
OSM51014004
0.405
0.891
2664 3.575838926
119.98
GPMGPMG4805
1.48
3.256
8400 11.27516779
279.99
GPMGPMG4800
1.25
2.75
6500 8.724832215
249.99
GPMGPMG4795
0.634
1.3948
3200 4.295302013
179.99
OSM51012004
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Source: http://www.hobbylinc.com/rc_brushless_airplane_motors
Figure 69: Motor pricing regression model
Large, hobby-grade electric DC motors were the best point of comparison on cost we could find for aerospace motors. For the cost model, we applied a 3x multiplier to account for the cost of designing and certified motors approved for powering commercial flight. The cost performance of DC motors is very impressive relative to turbines (and they possess nearly identical power density).
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16.5 Optimization Auxiliary Plots L/D Optimization Variable History Figure 70: L/D optimization history Figure 71: Optimized L/D planform
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Takeoff Weight Optimization Variable History Figure 72: MTOW optimization history
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Figure 73: Optimized MTOW planform
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Preliminary 2-D Trade Study Plots
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[23]
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