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 Takeoffand Landing (VTOL) configurations, due to perceived limitations on the available infrastructure. Several recent studies have proposed electric Short Takeoffand 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-efficient 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 coefficient b Wing span CX Vehicle streamwise force coefficient, = CD CT − c Wing chord Dfuse Fuselage center diameter ∆cJ Section jet momentum-excess coefficient Dboom Boom diameter c` Section lift coefficient `fuse Fuselage length ct Section thrust coefficient `max Vehicle max. length cd Section drag coefficient Rclimb Climb range cx Section streamwise force coefficient Rcruise Cruise range h0 Takeoffand landing altitude Rtotal Total mission range hcruise Cruise altitude Sref wing reference area hd 2D actuator disk height VJ Jet velocity hJ section effective 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 Trefftz plane induced angle of attack 1 sobs Obstacle distance ↵in Wing induced angle of attack srnwy Runway length δF Flap deflection sTO Takeoffdistance γ Wake circulation strans Transition distance µ Wheel friction coefficient treserve Reserve segment time ' Velocity potential w Downwash velocity Γ Horseshoe vortex circulation Adisk Propeller disk area ∆CJ Vehicle jet momentum-excess coefficient 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 takeoffand land (VTOL) capability[2]. However, recent studies have shown that short takeoffand landing (STOL) aircraft may be feasible for UAM missions if they can operate offof 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 coefficents 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/efficiency 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 different 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 different studies difficult, and hence it is difficult to quantitatively assess the performance difference between STOL and VTOL configurations. The goal of this paper is to discuss the development of the models needed to rigorously assess this difference across a variety of possible missions. The bulk of the model development effort 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 difficult to model directly at the conceptual design stage, but it is highly correlated with vehicle maximum takeoffweight. In this study, maximum takeoffweight 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 difference 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 h0 Rclimb Rcruise Sarrive treserve Rtotal Fig. 1 Design mission overview for comparing STOL and VTOL configurations. The primary differences are in the takeoffand landing segments. All else being equal, any weight difference between a STOL and VTOL configuration will be dictated primarily by the differences in flight mechanics during the takeoffand 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 takeoffand landing area (TOLA) - the available space for the takeoffand 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 takeoffprofiles considered, with and one without an obstacle The presence or absence of an obstacle clearly will have a significant effect on the STOL vehicle, but will also effect the VTOL takeoffprofile. 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 takeoffarea 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 takeoffand a wing for high-efficient 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.