Model Development for a Comparison of Vtol and Stol Electric Aircraft Using Geometric Programming

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MODEL DEVELOPMENT FOR A COMPARISON OF VTOL AND STOL ELECTRIC AIRCRAFT USING GEOMETRIC PROGRAMMING

Christopher B. Courtin and R. John Hansman

This report presents research published under the same title at the 2019 American Institute of Aeronautics and Astronautics (AIAA) Aviation forum. Citations should be made to the original work

Report No. ICAT-2019-09 June 2019

MIT International Center for Air Transportation (ICAT) Department of Aeronautics & Astronautics Massachusetts Institute of Technology Cambridge, MA 02139 USA

1 of 1 Model Development for a Comparison of VTOL and STOL Electric Aircraft Using Geometric Programming

Christopher Courtin, R. John Hansman† Massachusetts Institute of Technology, Cambridge, 02139, USA

There is widespread interest in the use of electric aircraft for short missions in and around urban areas. Most of the vehicle configurations proposed for these missions are electric Vertical Takeoand Landing (VTOL) configurations, due to perceived limitations on the available infrastructure. Several recent studies have proposed electric Short Takeoand Landing (STOL) aircraft with externally blown flaps as viable alternatives for urban operations. One of the claimed benefits of STOL aircraft is increased mission performance (in terms of range, payload, or speed) compared to an VTOL aircraft of the same weight. This study discusses the development of the models necessary to investigates this claim for a variety of possible missions, available infrastructure sizes, and levels of technology. Preliminary mission spaces where STOL or VTOL aircraft are the most weight-ecient choice are identified. The analysis is done using geometric programming, a convex optimization framework that enables rapid design re-optimization over a broad mission space.

I. Nomenclature

bmax Max. wing span CL Vehicle lift coecient b Wing span CX Vehicle streamwise force coecient, = CD CT c Wing chord Dfuse Fuselage center diameter cJ Section jet momentum-excess coecient Dboom Boom diameter c` Section lift coecient `fuse Fuselage length ct Section thrust coecient `max Vehicle max. length cd Section drag coecient Rclimb Climb range cx Section streamwise force coecient Rcruise Cruise range h0 Takeoand landing altitude Rtotal Total mission range hcruise Cruise altitude Sref wing reference area hd 2D actuator disk height VJ Jet velocity hJ section eective jet height Vs0 Stall speed in landing conﬁguration hmin Min. transition altitude V Freestream velocity 1 hobs Obstacle height ↵ Angle of attack sarrive Arrival procedure distance ↵in Tretz plane induced angle of attack 1 sobs Obstacle distance ↵in Wing induced angle of attack srnwy Runway length F Flap deﬂection sTO Takeodistance Wake circulation strans Transition distance µ Wheel friction coecient treserve Reserve segment time ' Velocity potential w Downwash velocity Horseshoe vortex circulation Adisk Propeller disk area CJ Vehicle jet momentum-excess coecient

II. Introduction the aviation industry there is currently substantial interest in the development of electric aircraft for a variety Wof potential applications, especially for Urban Air Mobility (UAM) missions. UAM broadly refers to the concept of using ﬂeets of relatively small aircraft to conduct short-hop missions in and around major urban areas[1]. Due to

Graduate Student, Aeronautics and Astronautics Engineering, MIT, 77 Mass Ave, Cambridge MA, 02139, AIAA Student. †T. Wilson Professor, Aeronautics and Astronautics Engineering, MIT, 77 Mass Ave, Cambridge MA, 02139, AIAA Fellow.

1 limited space for ground infrastructure within cities, there is a widely perceived need for UAM aircraft to have vertical takeoand land (VTOL) capability[2]. However, recent studies have shown that short takeoand landing (STOL) aircraft may be feasible for UAM missions if they can operate oof runways smaller than 300ft[3][4]. This short field performance is enabled by distributed electric propulsion, which allows externally blown flaps across almost the entire span of the wing. This high lift arrangement, commonly referred to as blown lift or blown flaps, can generate wing lift coecents much greater than a conventional high-lift system [5]. There are several advantages STOL aircraft may have for UAM markets, including a potentially easier pathway towards certification[6], a lower noise footprint, and improved performance/eciency for a given mission[4]. To date, there has been relatively little work looking at the direct comparison between electric STOL and VTOL aircraft across the range of possible missions profiles. While many dierent UAM VTOL designs have been evaluated and discussed in literature, the design missions (range, passengers, and speed) as well as critical technology parameters (such as battery specific energy) vary widely. This makes direct comparison between the dierent studies dicult, and hence it is dicult to quantitatively assess the performance dierence between STOL and VTOL configurations. The goal of this paper is to discuss the development of the models needed to rigorously assess this dierence across a variety of possible missions. The bulk of the model development eort is focused on developing suitable blown wing models, as the methods for sizing VTOL configurations are becoming well-established. Preliminary results derived from both STOL and VTOL models will be discussed. As part of this paper, existing literature on STOL aircraft[3][5][7][8], VTOL aircraft[9][10][11], and vehicle design optimization[12] is considered.

III. Approach For the passenger transport market, vehicle direct operating cost (DOC) per passenger over some design mission is a typical figure of merit for assessing aircraft configurations. DOC is dicult to model directly at the conceptual design stage, but it is highly correlated with vehicle maximum takeoweight. In this study, maximum takeoweight is used as the basis of comparison between the a STOL and VTOL configuration sized to carry the same payload on the same design mission. The design mission used as the reference is shown in Figure 1. The high level parameters that define this mission, such as total range, are changed parametrically to assess the dierence between the configuration options across the mission space of interest. The individual mission segments are described in more detail in Section V. STOL VTOL Both Takeoff Climb Cruise Arrival Land Reserve hcruise

hobs

Rclimb Rcruise Sarrive treserve

Rtotal

Fig. 1 Design mission overview for comparing STOL and VTOL conﬁgurations. The primary dierences are in the takeoand landing segments.

. All else being equal, any weight dierence between a STOL and VTOL configuration will be dictated primarily by the dierences in flight mechanics during the takeoand landing phases; the weight of the VTOL must be supported by direct lift from its motors, with the associated high power requirement and propulsion system weight. The weight of the STOL vehicle, conversely, is supported by power-augmented lift from the wing. The amount of lift augmentation, and therefore power required, depends on the speed at which the wing must support the weight of the vehicle. This relates directly to the amount of runway available for the ground roll. The imposed requirements that define the takeoand landing area (TOLA) - the available space for the takeoand landing roll, as well as the height and location of any obstacles - are clearly critical to the whether the STOL or VTOL configuration is advantageous. Figure 2 shows the two types of TOLAs that will be considered for this study. In the first case, the size of the TOLA is dictated only by the size of the runway available, without any obstacles beyond the runway threshold. This is relevant to several proposed TOLA

2 locations near urban areas, such as a on top of a building, elevated over the surrounding terrain, or on a barge. In the second case, the size is deﬁned by the height and location of some obstacle, as well as the size of the runway.

No ObstacleSTOL VTOL Obstacle

hcruise

hobs

hmin h0 srnwy srnwy sobs strans strans sTO sclimb sTO sclimb

Fig. 2 The two types of takeoproﬁles considered, with and one without an obstacle

The presence or absence of an obstacle clearly will have a significant eect on the STOL vehicle, but will also eect the VTOL takeoprofile. Due to the high power requirements of the vertical flight phase, it is advantageous for a VTOL vehicle to transition to horizontal flight as soon as possible. If there is no obstacle, in principle that transition could occur only a few feet above the ground. This is analogous to current helicopter operations, where the transition to forward flight occurs almost immediately if the operating environment permits. However, if the VTOL takeoarea is obstructed then the vehicle must climb above the obstacle before transitioning, requiring more high-power flight time and therefore a heavier vehicle. Like the other parameters that define the design mission, the required TOLA size will also be varied parametrically. As the available TOLA ground area decreases and/or the obstacles increase in height, the VTOL configuration becomes more attractive. Identifying the TOLA size where VTOL capability "buys its way on" is a key goal of this study. The VTOL design space is large, with many potential configurations. This study will compare a nominal STOL configuration with a representative VTOL configuration. The STOL configuration features a blown flap high lift system, similar to that being developed for the X-57 Maxwell. The VTOL configuration is based on the Kitty Hawk Cora. The Cora is an example of a hybrid-lift configuration, with a powered-lift system for vertical takeoand a wing for high-ecient cruising flight. Thrust for the cruise portions of the mission comes from a separate motor. One emerging consensus in the VTOL design space is that, for battery-powered vehicles especially, wings are required for long-range or high-speed missions. Figure 3 shows images of these aircraft, as well as the abstracted geometry used for this study. Key imposed constraints are highlighted in blue; these will be discussed further in subsequent sections.

Blown Lift Hybrid Lift

NASA X-57 KittyHawk Cora

Fig. 3 A blown lift conﬁguration, based on the NASA X-57, will be compared to a hybrid lift VTOL conﬁguration based on the Kitty Hawk Cora

The modeling approach for this study is dictated by the need to rapidly assess the performance of many dierent aircraft with varying design missions. Robust optimization of critical aircraft parameters like wing loading or disk

3 loading is important as arbitrary selection of these parameters may bias one vehicle over the other if the selection is poorly made. Therefore, the optimal choice needs to be made for each design parameter, for each vehicle configuration, in each mission of interest. This would be excessively time-consuming to do manually and so the aircraft design problem will be formulated as a convex optimization problem, using geometric programming. This approach, described in more detail by [12], has been shown to be very powerful for large conceptual design space explorations due to it’s fast solution times (on the order of a few seconds) and robust optimization capability. Geometric programming has been used to model both electric STOL[3] and VTOL[9] aircraft. Geometric programming does impose limitations on the mathematical structure of the underlying models and hence in some cases the fidelity that can be achieved. Identical models will be used between the two configurations for common components such as propellers, batteries, and structural elements to limit biasing one configuration or the other due to dierences in modeling fidelity. Also used in this work is signomial programming, a useful extension of geometric programming described in [13]. This extension makes the model sensitive to initial conditions and removes the formal guarantee of global optimality, but in practice is useful to include constraints that cannot otherwise be formulated as a GP. Figure 4 shows the high-level structure of the model. The key inputs are a set of underlying technology parameters as well as the details of the required design mission. The technology parameters feed into a set of models of the various vehicle components, which are used in both the VTOL and STOL models. The two vehicle models and a design mission model are combined to create the optimization model for each vehicle, which outputs the vehicle weight as well as details of the geometry and various subsystems.

Design Mission Parameters Configuration Comparison

Takeoff and Landing Area: Max. Takeoff Weight Runway size Obstacle height Hover time Obstacle location Mission: VTOL Model VTOL Results Range Min. climb rate Components Weights Speed Altitude Geometry Payload Approach procedure Mission Subsystem Sizes Reserves Config Footprint: Max Span STOL Model STOL Results Max Length Components Weights Geometry Mission Blown Wing Subsystem Sizes Config Shared Components Battery Fuselage Tech. Parameters Motor Boom Wiring Horz. Tail Battery Specific Energy Controllers Vert. Tail Powertrain Specific Powers Propeller Aux. Weight Material Properties Wing Component Efficiencies

Fig. 4 The model compares the optimal vehicle size for common design missions and underlying technology parameters.

The structure of a GP model is essentially a list of constraints that define the optimization problem to be solved, and the values of any fixed parameters. As a consequence, this approach lends itself well to modular subsystem model development; the constraints describing the performance of a motor are the same whether that motor is powering a VTOL lift fan or a STOL blowing motor. The majority of the models can be reused for both configurations, and there are well-developed methods for modeling most major subsystems as GPs, such as those described in [9] for various VTOL configurations. For this particular study, there is a need to develop a more accurate GP-compatible model of the performance of a blown wing aircraft, especially in order to realistically predict the relationship between wing lift and motor power.

4 Section IV.A describes the development of the blown lift model. The remainder of Section IV describes the shared vehicle components. For simplicity in assessing initial results, this current work only models fully-electric configurations, where all vehicle power is stored in batteries. Hybrid-electric powertrains oer substantial range benefits over all-electric configurations [14], at the cost of increased complexity, local emissions, and noise. This range benefit would be expected to apply to both STOL and VTOL configurations; propulsion system architecture is another part of the design space over which the configurations should be compared. Simple models for some important subsystems, such as the motors, propellers, and batteries, are also used. Higher-fidelity models that more accurately account for thermal eects, the link between torque/RPM requirements and motor weight/eciency, changing propeller eciency with flight condition, and the eect of discharge rate on battery specific energy will enable the comparison to be made more accurately. [15] and [16] have shown that models which capture these eects can be formulated as geometric or signomial programs. Since these are not included in the present work, the results discussed in Section VI should be considered preliminary.

IV. Vehicle & Component Models

A. Blown Wing In a blown-lift configuration, high lift is generated in large part through the interaction between the trailing edge flap and propeller wake [5]. To assess the performance of a blown-wing aircraft, it is critical to be able to estimate the relationship between wing lift coecient CL, flap deflection F , and the power to the propellers. There are theoretical models based on potential flow theory [17] that oer some insight, but since the performance of blown-lift systems is highly dependent on viscous phenomena there are significant limitations to the use of these methods. This study will take advantage of recent wind tunnel testing of a blown-wing section, detailed in [18]. That testing approximated the 2D section performance of a blown wing with a single-slotted trailing edge flap over a range of angles of attack, flap deflections, and blowing power settings. The two key parameters of interest for this study are c` ↵,F, cJ and cx ↵,F, cJ , where cx is the net streamwise force coecient cx = ct cd. cJ is a dimensionless ( ) ( ) parameter that quantifies the momentum excess in the jet. It can be estimated from the measured jet total pressure excess and a downstream jet height hJ estimated from the actuator disk relation 2hJVJ = hd V + VJ . ( 1 ) 2 2 hJ VJ hd VJ V cJ = 2 1 = 1 1 + 1 (1) c V2 ! c V2 ! VJ 1 1 ✓ ◆

The net streamwise force coecient cx is treated since this can be measured directly, and avoids the ambiguities between drag and thrust inherent in blown wing systems. To incorporate this data into the modeling framework, in must ﬁrst be corrected for 3D eects. This is done using a nonlinear Weissenger method, which yields overall vehicle CL and CX values. In its current implementation it is not directly compatible with the GP optimization framework. Therefore, a GP-compatible surrogate model was created across the parameter ranges of interest using the method described in [19].

1. 2D Section Data The 2D section data used in this model is a fit to the wind tunnel test data, across the range of flap deflection, angles of attack, and cJ tested. The details of this fitting are described in [18]; it shows reasonably agreement with the experimental data across the range of test data. Figure 5 shows a comparison between this wind tunnel data fit (solid red line) and a theoretical thin airfoil theory model (dashed blue line) for one representative high lift case with 40 flaps and cJ = 3. The theoretical model, derived in detail in [20], assumes a linear relationship between lift, angle of attack, and flap deflection and is shown in Eqn. 2- 4.

@c` @c` c` = ↵ + F (2) @↵ @F

@c` = 2⇡ 1 + 0.151pcJ + 0.219cJ (3) @↵ ( ) @c` 1 = 2p⇡cJ 1 + 0.151pcJ + 0.139cJ 2 (4) @F 5 The jet momentum coecient cJ is closely related to cJ by

2 ⇢JV hJ hJ c = J = c + J 2 J 2 (5) 1 2⇢ V c c / 1 1 Because the case of interest is low-speed ﬂight, ⇢J = ⇢ is assumed throughout. 1 2D Section Lift Curve: C = 3.00, =40 J F 12 Wind Tunnel Data Fit 11 Theoretical Estimate

3 0 5 10 15 20 25 30 Angle of attack (deg)

Fig. 5 The lift polar of the blown wing at F = 40 deg and cJ = 3 is shown as calculated based on ﬁtted wind tunnel data (solid red) and thin airfoil theory (dashed blue).

It can be seen that the measured lift slope agrees fairly well with theory at low angles of attack, and that c`0 measured in the experiment is substantially less than the theoretical value. While perfect agreement is unlikely, this gap suggests there is further possible refinement of the design details of the blown wing. These details, such airfoil geometry, flap gap geometry, and motor number, size, location, and inclination relative to the wing, were initial estimates of the correct values. The STOL vehicle performance predicted by the wind tunnel test and consequently this analysis will therefore reflect the specific choices made for the wind tunnel test article. Future work is required to assess to what extent improved performance is possible through dierent design choices.

2. 3D Corrections The vorticity shed from the tips of the finite vehicle wing, as well as the edges of the flaps, induces significant downwash on the wing which changes the eective CL and CX . Non-uniform blowing of the aircraft wing, for example at the fuselage attachment point, will also eect the downwash on the rest of the wing and add additional drag. To account for these eects,a non-linear version of the standard Weissenger method [21] is used. The wing is modeled as a line of horseshoe vortices, with the bound leg of the vortex located at the wing c/4 point, as show in Figure 6. At each control point, the 3D wing LE location, chord length, flap and power settings, and twist are defined. A cosine spacing is imposed on the trailing vortices and control points. The objective of this calculation is to determine the circulation and downwash angle at each control point; since circulation (lift) is a function of downwash and vice versa the system is described by set of simultaneous non-linear equations. Commonly in vortex lattice methods a linear approximation to these equations is used, which can be solved rapidly and for airfoils far from stall yields quite good results. This approach is the standard Weissenger method as described by [22] and [23]. However, because of the strong non-linear behavior of a blown wing and the large induced angles that are possible, linear approximations may introduce unacceptable uncertainty in some areas of interest. The iterative approach described here is used instead to solve for the circulation distribution across the wing. From this, the relevant force coecients can be directly calculated. At each control point, the strength of the bound vortex per unit velocity is represented by

i 1 ¯i = cicl (6) ⌘ V 2 i 1

6 wvl_dia.png

Fig. 6 The blown wing is modeled as a single line of horseshoe vortices, each with a bound leg lying along wing c/4 line. The strength of each vortex is shown by the red i, while the blue j denotes the net vorticity shed into the Tretz plane.

From the knowledge of the circulation distribution across the wing (all values of ¯i) the downwash at each control point can be calculated by summing the inﬂuence of all other bound and trailing vortex legs at that point. This is done xa via a Tretz plane analysis as described by [23]. For each control point i, the trailing leg locations rai = ya and 2 3 6za 7 6 7 6 7 xb 6 7 6 7 rbi = yb are known from the geometry deﬁnition and imposed control point cosine spacing. 4 5 2 3 6zb 7 6 7 6 7 6 7 6 7 4 5 7 At each trailing leg, the net vorticity shed into the wake per unit velocity ¯j is the dierence between between the circulation per velocity of the panels on either side. If there are N control points, then there are N + 1 trailing legs. This is shown in Figure 6.

¯j = ¯i 1 ¯i, i 2...N, j 2...N (7) 2 2 At the wingtips, the circulation must go to zero. Therefore,

¯1 = ¯1 (8)

and ¯N+1 = ¯ N (9)

The velocity at each panel midpoint is given by the gradient of the velocity potential at that point 'i.

N+1 'i 1 xˆ ri rj r = ¯j ⇥( ) (10) V 2⇡ 2 1 j=1 ri rj ’ The induced angle of attack in the Tretz plane ↵in ,i is therefore 1 'i zˆ w w ↵in ,i = arctan r · = arctan 1 1 (11) 1 V V ⇡ V 1 1 1 which can also be expressed in terms of the downwash velocity w. The downwash at each wing control point win,i is half the corresponding Tretz plane downwash.

w ,i = 2wi (12) 1 This downwash is assumed to be constant across the chord of each section. Because at least one surface of the wing is within the jet, the eective streamwise velocity is approximately

V + VJ V = 1 (13) e 2 which, combined with the downwash, deﬁnes the local induced angle at the wing.

wi ↵in,i (14) ⇡ Ve The eective angle of attack that each control point sees is the sum of the induced, geometric, and twist angles of attack.

↵ei = ↵ + ↵in,i + ↵ti (15)

Based on the speciﬁed F,i and CJ,i, the forces on that control point can be interpolated from the wind tunnel data.

c˜` = c` ↵ ,F,i, cJ,i (16) i ( ei ) c˜x = cx ↵ ,F,i, cJ,i (17) i ( ei ) The forces calculated here are relative to the eective velocity at the wing, which diers from the freestream velocity as shown in Figure 7. c˜` represents the lift coecient in the frame aligned the relative wind, while c` represents the lift coecient in the frame aligned with the freestream. The two are related by a rotation around the induced angle ↵in.

c` = c˜` cos ↵ c˜x sin ↵ (18) in in

cx = c˜` sin ↵in + c˜x cos ↵in (19)

For a typical aircraft where cx = cd0 has a negligible dependence on ↵ and ↵in is small, the c˜` sin ↵in term can be 2 c` rewritten as the more familiar expression for induced drag ⇡eAR . However, these assumptions are not appropriate for the heavily blown wing, and the more general form will be maintained. This analysis does not currently include corrections for Reynolds or Mach number eects.

8 c ` cf` αi cx V1 α in α cfx αeﬀ Veﬀ

δF

Fig. 7 The force coecients c˜` and c˜x calculated based on the apparent velocity must be rotated to the reference frame aligned with the freestream, which is more appropriate for force calculations on the vehicle as a whole.

The total force coecients for the entire aircraft can be calculated via spanwise integration.

b 2 1 / CL = c` y c y dy (20) Sref b 2 ( ) ( ) π / b 2 1 / CXwing = cx y c y dy (21) Sref b 2 ( ) ( ) π / For convenience with the surrogate model ﬁtting and motor sizing calculations, the 3D CJ is deﬁned by integrating only over the blown span of the wing bblown.

b 2 1 blown/ CJwing = cJ y c y dy (22) Sref b 2 ( ) ( ) π blown/ This chain of calculation is straightforward if the initial distribution for ¯ is known; in general that is not the case. The system of equations can be solved for ¯ by deﬁning the residual 1 Ri = ¯i cic` (23) 2 i at each spanwise station, and converging R to zero using Newton’s method. In reality, there are additional factors that eect the induced angle at the wing beyond what is modeled here. One key assumption of this method is that all the lift measured in the wind tunnel is caused by the circulation of the wing, which is enhanced by the jet. In reality, there is there is also vorticity in the wake, which will induce an upwash at the wing. This will reduce the induced angle at the wing beyond what is modeled here. Additionally, the eective velocity will vary along the chord and span. While this calculation gives reasonable estimates of the induced drag for a given CL the angle of attack required is likely overestimated. In this model a nominal 20 deg. maximum angle of attack at takeo rotation is used. This maximum allowable angle will change with blowing, and in reality will be dierent from what this calculation predicts. More work to is required to assess the accuracy of this method vs. experimental data and to better account for the wake vorticity.

3. Surrogate modeling The calculation described above requires detailed knowledge of the aircraft ﬂight condition, control settings, and geometry. The correct choice of these parameters are not known a priori and will ultimately need to be chosen in the context of the overall optimization and sizing model. As currently formulated, the model is not directly compatible with the GP framework.

9 However, with a reasonable initial choice of some key parameters, a GP-compatible surrogate model can be fit to the results of the above calculation to get a preliminary sense of the design space. This surrogate model assumes a wing aspect ratio of 9.2, with 70% of the span blown with a uniform blowing, while the center 10% of the wing and outer 10% of each wingtip is unblown. The blown section has a constant chord, while the outer unblown wingtips have a .6 taper ratio. Fixing these parameters is a restriction of this method,as the choices may not be optimal and will likely change with the design mission of the vehicle. However these choices are reasonable for a feasible-to-build aircraft, and account several real-world eects such additional drag from non-uniform blowing and the eective reduction in lift from a partially blown wing. All motors on the vehicle are assumed to operate together oa single commanded throttle. cJ is therefore constant across the span of the blown wing, and zero at the unblown sections. In reality dierential control of motors may be desirable for yaw authority, glide path management, cruise eciency, and engine-out response. Additional work is needed to assess the best balance of these dierent requirements. The surrogate model was created by solving for the total wing CL and CX across a range of angle of attack, flap deflection, and jet momentum coecients using the Weissenger method for the specified geometry. These parameters were separately fit with GP-compatible functions as described in [24]. Table 1 shows the fitted range of each parameter.

The resulting fits are given by Table 1 Fitted range of 0.943 0.462 0.053 0.032 each parameter in the sur- C 0.343↵ C L  J F rogate model. 0.841 0.921 0.010 + 0.038↵ CJ F (24) 0.063 0.778 1.033 + 0.015↵ CJ F Min Max 4 4.6 10 1 ⇥ 7 0.166 0.039 1.677 2.515 10 ↵ C ↵ 1 20 C ⇥ J F ✓ Xwing ◆ 5 4 5 1 50 9.432 10 5.142 10 2.113 10 F + ↵ ⇥ CJ ⇥ F ⇥ (25) 6 0.883 3.203 0.469 CJ .1 10 + 6.081 10 ↵ C ⇥ J F 12 5.121 0.987 1.281 + 2.719 10 ↵ C ⇥ J F 1 where ↵ and F are both given in degrees. The fit is in terms of C because that parameter is convex and Xwing non-negative across the parameter range of interest. In this case, the CXwing term includes the net streamwise force of the wing blowing motors, the induced drag due to lift, and the profile drag of the wing.

Xwing CXwing = = CX blowing + CDi + CDp,wing (26) qSref ( ) This surrogate model agrees well with the underlying data; the comparison between the surrogate model (dashed lines) 1 and computation results (solid lines) is shown in Figure 8. The RMS error is 1% for the C fit and 4% for the fit. L CX The blue line in Figure 8 corresponds to the same flap and power condition shown for the 2D results in Figure 5. As expected, the total vehicle CL at a given angle of attack is reduced relative to section test data.

B. Propulsion System Models The propulsion system components (propellers, motors, motor controllers, wiring and batteries) were sized based on the maximum power that they were required to supply. For this analysis, an all-electric propulsion system is assumed. Actuator disk theory was used to determine the relationships between propeller shaft power and thrust or wake velocity VJ . For the blown wing propellers and the thrust propeller of the VTOL vehicle, the overall propeller eciency ⌘prop is given by the constraint ⌘prop = ⌘v⌘i (27)

where ⌘v represents viscous loss of the propeller blades (nominally a constant 0.85), and ⌘i is the ideal eciency of the propeller at a given thrust and inlet velocity. ⌘i is constrained by motor jet velocity VJ 2 ⌘i (28) VJ 1 + V 1

10 F : 40 F : 40

CJ :3.0 CJ :3.0 9 CJ :6.0 CJ :6.0 C :9.5 2.0 C :9.5 8 J J 3D Correction Calculation 3D Correction Calculation GP-compatible ﬁt GP-compatible ﬁt 7 1.5 L 1 X C C 6 1.0 5

4 0.5 3

6 8 10 12 14 16 18 6 8 10 12 14 16 18 Angle of attack (deg) Angle of attack (deg)

Fig. 8 Comparison between the CL and CX values as calculated by the 3D correction calculation (solid lines) and surrogate model(dashed lines) across a range of ↵ and CJ , shown at 40 deg. ﬂap deﬂection.

and the shaft power of the propeller and motor is therefore TV Pshaft = 1 (29) ⌘prop Thrust relates to jet velocity by V 2 2T J + 2 1 (30) V  AdiskV ⇢ ✓ 1 ◆ 1 which is an inequality constraint that requires the use of signomial programming. VJ is then related to the jet momentum excess-coecient CJ , and hence wing CL/CX , as described above. The propeller radius is limited by a speciﬁed tip mach number and RPM ⌦.

2 2 2 Mtipa <= ⌦R + V (31) ( ) 1 In hover, the propeller power is given by

T PshaftKFM = T (32) s2Adisk ⇢

with a nominal figure of merit FM = 0.75, which is typically of a well-design rotor[5]. K is a correction factor to account for the additional power due to increased inflow velocity during a vertical climb. As discussed by [25], this factor can be estimated from the ratio of vertical climb speed Vc to hover inflow velocity uh,

2 1 Vc 1 Vc K = + 1 (33) s 2 uh 2 uh ✓ ◆ where T uh = (34) s2Adisk ⇢ and K = 1 when the vehicle is in stationary hover. The weight of each of the propulsion system components is determined by an input specific power and its maximum power requirement. The battery is determined by a fixed specific energy. The total battery energy required in each mission segment is the sum of the total power used in that segment (accounting for all intermediate component eciencies and auxiliary power requirements) multiplied by the duration of the segment. The total battery energy is then the sum of all the mission segments. An 80% discharge limit is also included.

11 C. Wing and Tails The wing structural model used for the STOL and VTOL wing, and the wing aerodynamic model used for the VTOL case, has been described in [16] and [3]. The profile drag estimate is from a GP-compatible fir to a GAW-1 airfoil drag polar created in XFOIL. The wing primary structural weight is estimated from simple beam bending theory, with weight fractions to account for other components. The wing is assumed to be of composite construction. For the STOL aircraft, additional weight is accounted for to represent the weight of the flap system. This is taken to be 12% of the wing total weight, which is an estimate from larger commercial aircraft [26]. The sizing case for the wing primary structure is a 5g pull up. The same wing model is used to calculate the drag and weight of the vertical and horizontal tails. The sizing load for both tails is set by the maximum lift coecient at cruise speed.

D. Fuselage The fuselage is modeled as an elliptical body, with a weight specified by a minimum gauge of carbon fiber layup and drag based on fineness ratio and wetted area. The details of this fuselage model are described in [27]. In both cases, fuselage primary structure to transfer load from the landing gear to the wing is not accounted for.

E. Drag Buildup

The landing gear was taken to be fixed throughout the flight, with a drag increment CDLG = 0.025, which is estimated from [28]. A 10% excresence drag factor fexcr = 1.1was applied to the fuselage and booms on both configurations. The drag coecients of the vertical and horizontal tails, booms, and fuselage was based on wetted area and form factor estimates. As mentioned, the wing drag was accounted for separately for convenience with the blown lift analysis. Interaction eects are not accounted for.

CD CD f + CD + CD f + CD + CD (35) rem fuse excr LG booms excr v h

F. Additional Weights To estimate the ﬁxed weights associated with items like landing gear, passenger furnishings, climate control, and ﬂight control, weight fractions were used based on a modern GA aircraft, the Cirrus SR-22. The the estimates in Table 2 are used, based on the published equipment weights from [29]. The landing gear weight includes both nose and main

Table 2 Weight fractions and ﬁxed weights based on the Cirrus SR-22

Weight Group Weight (Fraction) Based on

Landing Gear 5.1% WMTO

Furnishings 12% Wpay

Paint 1% WMTO Fixed 90 lbs Seats 25.5 lbs per passenger

gear. Furnishings accounts for items like air conditioning and internal power distribution, and is assumed to scale with passenger weight. Fixed weights account for pilot controls,communications, instrumentation, emergency beacons, lighting, and ﬁre protection. The weight of the seats is assumed to scale with the number of passengers. No weight is currently included for a ballistic recovery system.

W >= f + f + f W addl ( LG equip paint) MTO + ffurnishWpay (36)

+ WseatsNpax + Wcontrol

12 G. Geometry Constraints In each case, the same key geometric parameters such as fuselage size and maximum length and wingspan are applied to both configurations. The fuselage size is fixed, and volume constraints to fit the passengers and required batteries are not modeled. The number of motors is fixed in each case, which also fixes the number of support pylons for the VTOL and motor mount pylons for the STOL. All pylons are have a specified diameter. The vertical and horizontal tails are sized by tail volume coecients, and the wing c/4 point is nominally aligned with the fuselage center. Weight and balance constraints are not explicitly considered.

1. STOL For the STOL aircraft, the propeller diameter is constrained that the blown section of the wing (70% of the total span) is lined with propellers, with a 10% diameter spacing between each rotor.

0.7b 1.05N D (37) max props prop The vertical and horizontal tail volumes are sized for the high blowing cases as described by [30]. The vertical and horizontal tails are taken to have the same moment arm `t , which is limited by the speciﬁc `mathrmmax. 3 ` >= ` 2 + `t + c , (38) max fuse/ 4 root h The motors are attached to the wing via booms mounted at the wing c/4 point, and are nominally located a distance of c/4 in front of the leading edge. The attachment booms are modeled with the same weight and drag models as fuselage, with the same boom radius as speciﬁed for the VTOL case. The length of the boom is taken to be half the wing chord.

2. VTOL In the VTOL conﬁguration, the propeller radius is limited by the need to arrange one row of propellers along the leading edge of the wing. 10% rotor diameter is also used as the minimum required spacing between rotor blades.

Nprops b >= D 1.05 + D (39) max 2 prop fuse The vertical and horizontal tail volumes are speciﬁed as .05 and .6, which are typical for GA aircraft. The constraints on the tail moment arm are the same as those described for the STOL aircraft. The number of propeller mounting booms are half the number of propellers, and the length of the boom is the wing chord plus the rotor diameter, with a 10% clearance around it.

`boom >= 1.05Dprop + c¯w (40) The nominal boom diameter is 6in. The same drag and weight model is used for the booms and fuselage, with correspondingly dierent ﬁneness ratios. That, and the other component models shared between both vehicle conﬁgurations are discussed below. Interaction eects between the vertical lift motors and the aircraft are not accounted for.

V. Mission Modeling Figure 1 shows the design mission profiles for the VTOL and STOL vehicles. The design mission for each consists of a takeosegment, followed by a climb to altitude and a cruise portion of the flight. Key parameters that define the design mission are total range (the sum of the distance covered during the climb and cruise portions of the flight), minimum cruise speed, cruise altitude, and during the climb portion the minimum vertical speed or maximum time to cruise altitude. No descent phase is modeled; it is assumed to be included in the cruise distance. Before the landing maneuver there is a two mile arrival procedure phase, followed by a landing maneuver. Reserves, specified by a fixed duration wing-borne flight segment at cruise altitude, are also included. The key modeling details for each segment are given below.

13 A. Takeo The STOL ground roll is calculated from the equations of motion W dV X µ W L = MTO (41) ( MTO GR) g dt

dV dV ds dV With the convenient substitution dt = ds dt = ds V (where s is the distance along the runway) and the simplifying assumption that lift during the ground roll is negligible, the ground roll equation becomes W dV X µ W = MTO V (42) ( MTO) g ds For GP compatibility, it is useful to deﬁne the net thrust T X. If the assumption is made of constant T = T , net ⌘ net TO calculated at a value corresponding to 0.7Vlo, then this equation can be integrated and rearranged as the GP-compatible expression

1 WMTO 2 TTO Vlo + µWMTO (43) 2 sgrg

Uniquely for a blown-wing aircraft, both TTO and Vlo are functions of motor maximum power; Vlo = 1.1Vstall [31], where 2WMTO Vstall = (44) ⇢S CL ↵ ,F, CJ s ref max ( max ) and 1 2 T = ⇢ 0.7V S CX (45) TO 2 ( lo) ref The maximum angle of attack ↵max and ground roll angle of attack ↵GR are specified to be 20 and 3 degrees, respectively. The flap deflection and motor power, which is reflected in the dimensionless CJ parameter, are free variables. In the obstructed takeocase, the runway distance is the sum of the ground roll distance plus the distance required to clear a 50ft. obstacle. The STOL ground roll models are unchanged in the obstacle case, and there is an additional specified sobs which dictates the climb gradient from the end of the ground roll to clear the obstacle. The total required takeodistance is the sum of both of these. In the VTOL case, the required ground area is likely set by regulation and vehicle footprint. The VTOL takeoprofile consists of a takeohover/climb which must exceed the minimum hover time (nominally 5 sec) and minimum hover altitude (nominally 20 ft). It also must not exceed the aircraft cruising altitude, although in practice this constraint is not active. After the vertical climb segment, the vehicle transitions to wing-borne flight, and climbs to cruising altitude, with a specified minimum climb rate. This minimum climb rate is also applied to the STOL vehicle. The transition power and distance for the VTOL is calculated using Eqn 43, with the µWMTO term dropped since there is no rolling resistance. At the beginning of transition, the entire weight of the vehicle is supported by the lifting motors, while at the end of transition the entire weight is supported by the wing. The average lifting thrust during transition is therefore assumed to be half the takeoweight. Limitations on average acceleration can also be applied, as passenger comfort requirements may be important considerations for this class of aircraft. These may be applied to both STOL and VTOL aircraft.

B. Landing The landing constraints are very similar to the takeoconstraints. In the case of the STOL vehicle, only aerodynamic drag and braking forces are considered to act on the aircraft during the landing ground roll. Other sources of deceleration, such as thrust reversal or additional drag devices, are not included.

1 WMTO 2 µbrkWMTO + Daero Vtd (46) 2 sgrg

The touchdown speed Vtd = 1.15Vs0 [31]. When there is an obstacle to be considered for the landing case, the ﬂare distance between the top of the obstacle and the touchdown point is strongly dependent on the vehicle L D in / the landing conﬁguration, and what the lower limits of that number might be. Due to the strong power eects, this is

14 dicult to estimate accurately. Currently, it is assumed that drag can be added such that the landing obstacle clearance distance is the same as that on takeo. More study in this area is required to assess the limits of approach angle. The VTOL landing transition is assumed to end at the same minimum hover altitude as on the takeocase. The minimum hover time during landing is taken to be the same as during takeo. In the case where there is an obstacle, the vehicle is assumed to descend at 100fpm, with the power requirement equal to that at hover.

C. Cruise, Climb, and Reserve The cruise, climb, and reserve models are similar for both types of aircraft. In all cases the vehicles are assumed to be in wing-borne ﬂight, in a steady ﬂight condition. The force balance expressions

1 2 W = ⇢V S CL (47) MTO 2 ref and 1 2 T >= ⇢V S CD + W (48) net 2 ref rem MTO are enforced through all three phases, where T = X as defined above. In the unblown case, T = T net wing net qS CD CD . CD accounts for the remaining sources of drag on the vehicle; from the fuselage, empennage, ref( p,wing i ) rem landing gear, and other sources. The details of this drag buildup are discussed in Section IV.E The cruise lift coecient is a free parameter in the vehicle optimization, and during the cruise phase a minimum required flight speed is enforced. Level flight = 0 is assumed during the cruise and reserve phases. The flight speed in the reserve case must be greater than the landing approach speed.

D. Runway Arrival Studies of trac management strategies for UAM operations suggest that some form of arrival and departure procedures will be necessary for ecient high-volume operations [32]. The exact design of these procedures in unclear but a 2 nmi precision arrival approach is one reasonable possibility[33], and is included in the mission model. This arrival segment does not contribute towards the total range of the vehicle, as the best landing procedure may not be a straight-in approach. There is a slight dierence between how the arrival section is modeled for the STOL and VTOL vehicles. In the case of the VTOL vehicle this is modeled as a level flight segment at the standard approach speed Vapp = 1.3Vstall [31]. No flaps or other high-lift devices are accounted for on the VTOL aircraft. At the end of this arrival phase the vehicle begins its transition and landing maneuver. In the case of the STOL aircraft, the stall and hence approach speed is a function of both the flap setting and the approach power. In high-blowing cases the stall approach speeds can be quite low, and a flight of two miles could take upwards of four minutes. This may not be desirable from a trac management standpoint, as high throughput is a feature of many UAM mission concepts, or necessary from a piloting perspective. In this model, the STOL arrival is broken up into two segments, long- and short-final. The short-final segment represents a stabilized approach immediately

preceding touchdown, and has a nominal duration of 30 seconds. It is modeled as level flight at Vapp = 1.3VS0 , where VS0 is the stall speed in the landing configuration (maximum flaps and blowing). The long-final segment is the remainder of

the two miles, and is modeled as level flight at VLF = 1.3VS1 , where VS1 is the stall speed corresponding to half the landing flaps and no blowing power. The required amount of time for the short- and long-final segments likely depends on the specific details of the aircraft performance characteristics and control scheme; further study is required to identify conclusively the required characteristics of this flight phase.

VI. Results and Discussion Figure 9 shows a preliminary comparison between the STOL and VTOL configurations, with the mission and technology parameters inputs specified in Table 3. The missions will be defined by the required high-level parameters such as range, passengers carried, and minimum cruise speed, as well as the details of the takeoarea. The level of technology assumed will have a significant eect on the vehicle sizing, especially is it relates to motor and battery weights and structural materials. Values for various component eciency’s were taken from [34], roughly corresponding with the current commercially available state of the art. Figure 9 a) shows the comparison between maximum takeoweight of the STOL aircraft (blue) and VTOL aircraft (red) as the required takeoand landing distance is decreased, for the same nominal design mission. The solid lines

15 Table 3 Design Mission & Technology parameters used for initial comparison

t 10 min Battery Speciﬁc Energy 200 Whr kg reserve / t , 5 sec Motor Speciﬁc Power 6 kW kg hover min / hcruise 2000 ft Motor Eciency 95%

N 4 Controller Speciﬁc Power 20 kW kg pax / Wpax 185lbs / pax Controller Eciency 98%

Wbags 20lbs / pax Min. ROC 1000 fpm

`fuse 12 ft Dfuse 5 ft

`max 40 ft bmax 40 ft N Motors, STOL 10 N Lift Motors, VTOL 12 N Thrust Motors, VTOL 1 Aux. Power 1 kW

Rcruise: 50nmi Vcruise: 120 kts Contours of 2500lb MTOW

STOL - 100ft Runway, No Obstacle VTOL - No Obstacle

a) b)

Fig. 9 STOL and VTOL aircraft can be compared across a range of takeoand landing location parameters (left) or design missions parameters (right)

correspond to the case without an obstacle, where for the STOL aircraft the takeo/landing distance is equal to the required runway size (takeo/landing ground roll). No restriction was placed on the transition distance of the VTOL. The dashed lines represent the case where takeoand landing distance is defined by the requirement to clear a 50ft. obstacle. For the STOL aircraft, the required runway distance is half the required takeoand landing distance, and the other half is the obstacle clearance distance. The VTOL aircraft is required to climb clear of the obstacle before transitioning. No margin is added to the required takeoand landing distance. In reality, there will be some landing dispersion due to weather, pilot technique, and the handling characteristics of the vehicle. The correct margin for these vehicles will depend strongly on many parameters, including the level of autonomy and the use of landing guidance systems, and additional work is required to determine what the correct margin should be. This comparison suggests that, if there are no obstacles, the STOL configuration has a weight benefit over the VTOL configuration down to ground rolls of 1-2 vehicle lengths. The presence of a 50 ft. obstacle has a significant eect on the STOL while having a relatively minor eect on the VTOL, which is the lighter-weight configuration in for very

16 small, confined TOLAs. However, even with the obstacle the runway lengths for which STOL vehicles are short enough to feasibly place in urban settings. In the case where an obstacle is placed very close to a short runway, achievable descent gradient may become the limiting factor. Improved modeling in this area is also necessary to determine the vehicle performance in the case where obstacle clearance or other factors (such as population noise exposure) favor very steep approaches. Figure 9 b) shows a comparison of range/speed capability for a constant vehicle weight of 2500 lbs, which roughly correlates to vehicle capability for a given cost. The specified runway for the STOL aircraft was 100ft; no takeo obstacle was included. This plot suggests that, with runways small enough to fit within major urban areas, there may be significant capability benefits from the STOL configuration, as compared to a VTOL vehicle of the same size.

VII. Conclusion The primary takeaway of this work is that the method outlined to compare STOL and VTOL aircraft is able to capture the key trades that drive the aircraft sizing, especially those that relate to the realistic performance of a blown wing aircraft. The results of that comparison shown here are preliminary, and higher-fidelity subsystem models are required to improve the confidence in these results before solid conclusions can be drawn. These results do suggest that there is a relatively broad class of missions for which STOL aircraft are potentially advantageous, even with takeoand landing areas (TOLAs) suciently small to fit within an urban area. The actual constraints of the TOLA are significant, especially the size and location of any obstacles. Due to the reliance on the wind tunnel test data and approach to 3D corrections, the performance predictions of the STOL aircraft represent many discrete design choices. Depending on the desired vehicle capability, dierent choices may yield better performance. While further work is required to increase the confidence in STOL vehicle concept viability and modeling accuracy, the potential benefits of the configuration warrant further consideration for UAM and other applications.

Acknowledgments The authors would like to thank Aurora Flight Sciences: A Boeing Company for sponsoring this research, and Prof. Mark Drela for guidance in the blown wing modeling.

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