Anna Occhipinti
email: anna.occhipinti@pace.de.

Aleksandar Joksimović

Mathias Emeneth
email: mathias.emeneth@pacelab.com

Urban Air Vehicle Mission Sizing and Performance Estimation Using Pacelab APD TM

Modern aviation has been focusing on hybrid-electric propulsion in

recent years, aiming for concepts with lower atmospheric and acoustic pollution to improve social acceptance of the sector. Development of such new enabling technologies results in emergence of whole new aircraft concepts like Electric Vertical Take-Off and Landing (eVTOL) for urban air mobility. The present work focuses on the preliminary design of a hybrid-electric Vertical Take-Off and Landing (VTOL) air vehicle with multiple ducted fans. A theoretical preliminary sizing model is proposed and then implemented in Pacelab APD TM , a commercial preliminary design tool developed by PACE Aerospace Engineering and Information Technology GmbH. The performance deck for electric ducted fans is developed in parallel using PROOSIS TM , a separate dedicated propulsive system simulation software, using flight conditions as input and providing appropriate performance characteristics as output. The targeted powertrain is completed with a turbogenerator, also modelled in PROOSIS as a generic turboshaft engine with an additional electric generator efficiency accounting. After having sized it at cruise condition, a specific fuel consumption map is retrieved. A typical urban air mobility operational framework is considered when building the design mission -composed of vertical take-off, hover, cruise and vertical landing -as well as a range of off-design use case scenarios. Power requirement in vertical flight segments is also estimated. An example of the developed model application in Pacelab APD is provided; it is inspired by existing concepts on the market. It presents a hybrid-electric powertrain with eight ducted fans and a fully composite airframe. The model is implemented in a customized version of APD, along with coding of the missing engineering objects and the propulsive system performance decks exported from PROOSIS. The design mission is then simulated and analysed, suggesting a feasible aircraft solution, which is later subject to sensitivity studies.

I. Nomenclature

II. Introduction

During the past few decades, various factors such as urban population growth worldwide, global passenger (air and ground alike) growth and the associated environmental impact thereof have resulted in increasingly more incentives to explore new means of short-distance mobility, and potentially create a whole new civil transport domain now commonly dubbed "Urban Air Mobility" (UAM). Arguments in favour of creating such new market niche are mainly based on it being a potential solution to congestion problems in big cities (see Cotton and Wing [START_REF] Cotton | Airborne Trajectory Management for Urban Air Mobility[END_REF] for an estimation on the numbers of vehicles necessary to respond to this need) as well as to need for flexible local multi-modal transport linked to the greater long-distance transport network. [START_REF] Bennaceur | Passenger-centric Urban Air Mobility: Fairness trade-offs and operational efficiency[END_REF] The appeal of the emergent sector is best seen in the variety of companies that come up with various air vehicle concepts which seem to target operating envelopes of small payload and range at moderate speeds and operating altitudes.

Aside from technological feasibility of problems such as vertical take-off, propulsion and control, energy densities and performance levels that could be achieved, given the potential tight integration of these vehicles into urban environments the questions of noise, safety and regulation are of utter importance. This is all the more true because there is no precedent, i.e. no experience to gauge the regulatory and certification framework for these applications. All of these will play into likelihood for this sort of technology to succeed commercially, to do what it does in environmentally responsible way, and be accepted by the society. [START_REF] Afonso | On the design of environmentally sustainable aircraft for urban air mobility[END_REF] For the above reasons, a need is identified for adapted preliminary design tools and methods which could tackle urban air mobility vehicle preliminary sizing and design and integrated mission performance calculation. The work presented in this paper employs Pacelab APD TM as the platform of interest for development of a vehicle-level sizing and mission performance estimation model of a UAM aircraft.

A. State of the Art

Urban Air Mobility (UAM) is a concept that is steadily shifting from futuristic to realistic in the near future. It was already the 20th century when the first concept of flying car was engineered, with the first successful vertical and landing take off flight [4]. The technology and general state of the art back in 1924 permitted only to achieve less than 2 minutes endurance but, one century later, the concept has gained feasibility and real interest from industry and also society.

Latest studies estimate a boost of UAM market reaching USD 15.5 billion in 2030, experiencing a further growth to 90 billion by 2050 [START_REF] Tuncer | Urban Air Mobility Industry Outlook[END_REF][START_REF] Manfred | Urban Air Mobility | USD 90 billion of potential: How to capture a share of the passenger drone market[END_REF]. The advantages of this transport solution are well known: ability to land and take off from small infrastructures, called vertiports, travel time savings with respect to congested city roads exploiting the much larger capacity of urban air space and lower in-flight environmental impact thanks to a more electric propulsion. The development and investment on new transport solutions is also encouraged by the fact that by 2030 60% of the population will live in urbanized areas and e-commerce volumes is constantly increasing by 10 billion dollar per year, boosted in the post-COVID era [START_REF] Babetto | Recent Development of a Conceptual Design Methodology for Unmanned Aerial Vehicles[END_REF][START_REF]Unmanned aerial vehicles in logistics[END_REF]. The business models of (electric) Vertical Take-Off and Landing -(e)VTOL -air vehicles in an urban environment are very different, from personal commuting both on demand (air taxi) and fixed public routes (air metro), from package delivery to emergency situation as air ambulance and law enforcement. [START_REF] Graydon | Guidance for Designing Safety into Urban Air Mobility: Hazard Analysis Techniques[END_REF][START_REF] Salucci | Capturing the Demand for an Electric-Powered Short-Haul Air Transportation Network[END_REF] The development of urban air mobility brings advantages as well as challenges. For instance, it is true that urban air space has larger capacity than roads but it is not infinite, and to assure safety and efficiency a set of flying rules and procedures are required. By consequence, if companies are racing to design the best UAM prototype, there is pressure on cities and government agencies to create rules for using urban airspace even if there is still no clear agreement on the type of airspace design that should be implemented, e.g. whether separation standards or predefined paths are the best solution. Security and traffic management issues come along with social factors like noise, visual pollution and privacy concerns. [START_REF] Graydon | Guidance for Designing Safety into Urban Air Mobility: Hazard Analysis Techniques[END_REF][START_REF] Bauranov | Designing airspace for urban air mobility: A review of concepts and approaches[END_REF] All these considerations affect, directly or indirectly, the air vehicle design. While traditional aircraft configuration have consolidated preliminary sizing procedures adjusted over the years thanks to experience, when it comes to new solutions a great amount of uncertainty is still present. To fill this gap, research and experiments have been done and several approaches are proposed with different levels of accuracy and stability. The final aim is to arrive to a robust method as for traditional designs, even if it is a long road ahead. Several studies have already been proposed in the past, each trying to apply design constraint from market analysis with the current technology level, mainly coping with the limiting battery specific energy and power [START_REF] Afonso | On the design of environmentally sustainable aircraft for urban air mobility[END_REF][START_REF] Lee | Generic Design Methodology for Vertical Takeoff and Landing Aircraft with Hybrid-Electric Propulsion[END_REF][START_REF] Kadhiresan | Conceptual Design and Mission Analysis for eVTOL Urban Air Mobility Flight Vehicle Configurations[END_REF][START_REF] Donateo | A Methodology for the Comparative Analysis of Hybrid Electric and All-Electric Power Systems for Urban Air Mobility[END_REF][START_REF] Saias | Preliminary Design of Hybrid-Electric Propulsion Systems for Emerging Urban Air Mobility Rotorcraft Architectures[END_REF][START_REF] Trainelli | Methodologies for the initial design studies of an innovative community-friendly miniliner[END_REF][START_REF] Hendricks | Multidisciplinary Optimization of an Electric Quadrotor Urban Air Mobility Aircraft[END_REF]. All the suggested available methods are mainly analytical, since no insight from empirical data and corresponding regressions is yet available. However, there are some companies which already presented solutions to the markets, some are still in the conceptual stage, others are now approaching the flight test phase. Umut [START_REF] Tuncer | Urban Air Mobility Industry Outlook[END_REF] presented a non-exhaustive list of worldwide UAM public-and industry-led initiatives has been listed. In the framework of air taxi, the one of interest for the present paper, one can cite Joby Aviation [START_REF] Aviation | Joby Aviation website[END_REF], Lilium [START_REF] Air | Lilium website[END_REF], Uber [START_REF] Uber | UberAir Vehicle Requirements and Missions[END_REF] or Airbus Urban Mobility [START_REF] Airbus | Urban Air Mobility -Taking Urban Transport into the Sky[END_REF].

The UAM vehicle concept space is conventionally divided into 4 typical concept families [START_REF] Cakin | Initial Sizing of Hybrid Electric VTOL Aircraft for Intercity Urban Air Mobility[END_REF]: lift-cruise, multicopter, helicopter and vectored thrust configuration. The lift-cruise configuration has two different propulsion systems for cruise and vertical flight, which increases the design complexity and makes the propulsion group not used in a specific flight phase an unnecessary load and drag. The multicopter does not present a wing and its propulsion system is composed by multi engines used for cruise and vertical flight. This configuration maybe has the least complexity level in design but has least efficiency in cruise, not having a wing. Helicopter is somehow similar, but with just one main rotor that can be tilted to give flight direction. Last but not least, vectored thrust configuration have tilting mechanism to tilt the direction of thrust vector, and mostly present a distributed propulsion system with rotors located in the wing. The current case study is of type lift-cruise, since it will present a wing and some rotors dedicated for specific flight segments. However it also presents the possibility to tilt some propulsors that are dedicated for both horizontal and vertical flight.

To provide vectored thrust in horizontal and vertical flight, Electric Ducted Fans (EDF) can be employed. They present the following advantages [START_REF] Ohanian | Ducted fan aerodynamics and modeling, with applications of steady and synthetic jet flow control[END_REF][START_REF] Jin | Modeling of Ducted-Fan and Motor in an Electric Aircraft and a Preliminary Integrated Design[END_REF]:

• An increased flexibility of location and compactness: they can even be embedded in the aircraft structure, e.g. the wing trailing edge or the fuselage; • High aerodynamic efficiency at low speed, optimal for vertical take-off and hovering, due to lower blade tip losses thanks to the shroud; • Lower acoustic impact, thanks to the duct that shields the blade noise;

• Improved safety related to blade integrity and foreign object damage. Even if only low subsonic condition is discussed in the present work, EDF can also be applied in large commercial aircraft for high subsonic flight. Work by Wick et al. [START_REF] Wick | Integrated Aerodynamic Benefits of Distributed Propulsion[END_REF] presents an interesting study of the aerodynamic effects of distributed EDF's with respect to different possible configurations in high subsonic application and Sgueglia et al. [START_REF] Sgueglia | Exploration and Sizing of a Large Passenger Aircraft with Distributed Ducted Electric Fans[END_REF] applied a sizing procedure for a large passenger aircraft with distributed fans mounted on wing trailing edge.

B. Paper Objectives

In light of the elaborated context and the state of the art, the presented work aims to contribute to this research framework by providing a parametric preliminary design approach for hybrid electric VTOL air vehicles with multiple ducted fans. The following objectives are formulated for the work presented in this paper:

1) Development of a preliminary Urban Air Mobility vehicle sizing model; the baseline application case for the developed work was inspired by an existing aircraft concept -the ANN2 model from Manta Aircraft. 2) Implementing the model in the aircraft preliminary design software Pacelab APD in order to include capabilities for mission sizing and performance estimation. 3) To that end, development of a preliminary design modules for electric ducted fans, turbogenerator and vertical flight segments for integration into Pacelab APD. 4) Provide preliminary verification of the developed framework by performing relevant trade studies for the target vehicle model over an operating envelope of interest. To that end, the paper will be organised as follows: Chapter III presents the development and assumptions behind the necessary elementary modules used for UAM vehicle modelling in Pacelab APD; Chapter IV presents the baseline case study and the test matrix of interest to this first exploration of the design space; Chapter V presents the obtained results, and the key takeaways are discussed in Chapter VI. Finally, Chapter VII provides the overall summary of the work along with perspectives for possible further developments.

III. Model Development

A. Pacelab APD Overview

Pacelab APD TM [START_REF]Pacelab APD[END_REF] is the modelling platform chosen for the purpose of this study. The software, developed by PACE Aerospace & IT GmbH, supports aircraft modeling, sizing, analysis and optimization in the conceptual and preliminary design. It supports a fast and multi-level evaluation of a wide range of possible aircraft configurations. The software's extensive library of ready-to-use aircraft models and methods is expandable and customizable in order to include new and innovative case studies.

Pacelab APD is composed of two main applications:

• Knowledge Designer, where engineering knowledge components are built, combining methods and parameters and creating a local database of reusable items; a set of knowledge components is already implemented in the tool, such as individual segments of a mission (e.g. cruise, take-off) or propulsive units; • Engineering Workbench, where the assembly of knowledge components is made in order to launch the analysis and design optimization; in practical terms, this is the application where the aircraft model is built and its performance is studied. Version 8.1 of Pacelab APD is used for the presented work; the associated documentation can be found in [START_REF] Pace Gmbh -A Txt Company | Pacelab APD 8.1 Documentation[END_REF].

B. Whole Aircraft Model of the UAM Vehicle

Development of an UAM vehicle in Pacelab APD starts from the mathematical models already available on the tool, with subsequent addition of customisation where necessary in order to create a closed loop for aircraft preliminary design. Hereafter an overview of the different methodologies is presented, focusing on the single application of interest.

Aerodynamic methods

Conventional aircraft preliminary design methods from Torenbeek [START_REF] Torenbeek | Synthesis of Subsonic Airplane Design: An introduction to the preliminary design of subsonic general aviation and transport aircraft, with emphasis on layout, aerodynamic design, propulsion and performance[END_REF] and Raymer [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF] were implemented for estimation of aerodynamic behaviour. Whenever necessary, subsonic flight conditions were assumed for lift and drag computation. At the moment, no robust methods were found in the literature for estimation of vertical flight aerodynamics, so a simplified approach was chosen. Pacelab APD was customized in order to take into account the fuselage downwash effect, that is an additional force on the fuselage due to blowing, which needs to be taken into account for power requirement estimation. This effect can be modelled through a simple coefficient [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF] as explained in detail in Section III.D.1.

Mass methods

Mass methods considered in APD also come from aircraft preliminary design literature, mainly from Raymer [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF], Torenbeek [START_REF] Torenbeek | Synthesis of Subsonic Airplane Design: An introduction to the preliminary design of subsonic general aviation and transport aircraft, with emphasis on layout, aerodynamic design, propulsion and performance[END_REF] and Nicolai [START_REF] Nicolai | Fundamentals of aircraft and airship design. Volume I, Aircraft design[END_REF] books. Most estimations differ depending on the air vehicle category; robust methods exist for commercial aircraft, fighters and freighter founded on empirical data adjusted with experience. However, urban air mobility is still far from being mature in that sense, so no such methodologies are available in open literature. (An alternative approach based on versatile and rapid finite-element analytical structural weight calculation, not applicable in the scope of the Pacelab APD model development, was presented by Winter et al. [START_REF] Winter | Structural Weight Prediction for an Urban Air Mobility Concept[END_REF][START_REF] Winter | Conceptual Design Structural Sizing for Urban Air Mobility[END_REF]) In the current study, whenever necessary, the assumption of general aviation aircraft is applied for purpose of mass estimation using the conventional methods for creating this preliminary UAM model.

Concerning the turbogenerator mass in particular, it was modelled by means of a historical regression. Burguburu and Basset [START_REF] Burguburu | Turboshaft engine predesign and performance assessment[END_REF] presented a study done on 130 turboshaft engines, using the collected data to correlate the turboshaft shaft power and mass as in Eq.1.

𝑚 𝑇𝑆 = 0.625(𝑃 𝑇𝑆 + 200) 0.8 (1)

Madonna et al. [START_REF] Madonna | Electrical Power Generation in Aircraft: Review, Challenges, and Opportunities[END_REF] studied the aircraft onboard electrical power generation trends, setting 20 kW/kg as power density goal for electric generators by year 2035.

The targeted design is assumed to have a full composite structure, so a calibration of traditional methods is performed; more details are provided in Section III.E.3.

Propulsion and performance

Pacelab APD contains a set of ready-to-use engineering concepts for aircraft configuration and performance computation. The library delivered with the software includes the most common propulsion solutions, e.g. turbofan and turboprop, and a powertrain feature where single components can be linked to create new power supply chains, including hybrid-electric and fuel-cell-powered configurations. This increases the flexibility and enhances the variety of propulsive solutions to be explored. Each propulsive system type is modelled using parametric performance tablesdubbed "performance decks" in Pacelab APD -that contain thrust, fuel or electric consumption data for a range of flight conditions, along with reference values and dimensions often resulting from previous preliminary sizing experience. This information is normally sufficient to enable a full mission evaluation of the aircraft. New performance data needed for the propulsive solution implemented in the present model are generated in PROOSIS TM , a sizing and performance modelling software for engine architectures; more details on this modelling can be found in the following Section.

A reference mission needs to be defined in Pacelab APD for purposes of vehicle sizing; along with this design mission, multiple off-design mission profiles can be created to estimate the performance of the designed vehicle. The individual flight segments are defined as generic engineering objects coded in Pacelab Knowledge Designer, and they can be accessed and linked together to create a complete flight profile of interest for the specific project. Conventional flight segments (e.g. take-off, cruise, diversion) are available in the current version of APD, but no vertical flight segment description is present. In order to carry out an urban air mobility case study, vertical take-off, vertical landing and hover are coded in a customized version of APD. More details about the implementation can be found in Section III.E.1.

C. Propulsive System Performance Deck -Modelling Approach and Assumptions

Overview

The aircraft under investigation and the associated model will be presented in detail in Section IV.A. This section summarises the details behind the procedure employed to produce the generic UAM propulsive system performance decks to be used in the Pacelab APD model. The baseline case propulsive system envisioned for the model at hand is a series hybrid architecture, composed of an array of ducted fans powered by a gas-turbine generator and a battery; two types of ducted fan propulsors are envisioned to be employed in the chosen concept vehicle; in this preliminary study the two ducted fans are assumed to differ only in their size and delivered thrust level. The Pacelab APD model under development treats such hybrid propulsive systems as an assembly of the underlying objects-subsystems:

• Gas-turbine generator (performance deck generated in PROOSIS);

• Unit ducted fan/propulsor assembly (performance deck generated in PROOSIS);

• Battery (simple linear scaling model).

PROOSIS

PROOSIS TM [36] is object-oriented software dedicated to system architecture sizing and performance modelling, mainly dedicated to gas turbine engine architecture model creation. As explained previously, PROOSIS was employed in this study to create generic performance tables for two distinct subsystems contained in the UAM vehicle of interest: the turboshaft engine and a single ducted fan propulsor.

PROOSIS modelling structure comprises three distinct levels, which successively build upon each other to create a full system model. Firstly, a "Schematic" is constructed using the available component libraries or custom-written components. Conventionally, the components are modelled using standard zero-dimensional thermodynamics, enhanced by the tabulated turbo-machinery performance maps to enable meaningful off-design simulations as well as to capture operating constraints imposed by aerodynamics of the respective components. The Schematic therefore represents the system architecture of interest and contains all the governing equations, component data, and lookup tables. The Schematics representing the respective turbogenerator and ducted fan architectures are shown in Fig. 1.

Fig. 1 PROOSIS Schematics of the elementary ducted electric fan assembly (left) and the turboshaft engine (right).

The next step in PROOSIS model generation is creation of the mathematical model called "Partition", which enables the user to define the calculation case of interest, that is -choose between system sizing at design point or system performance (off-design) simulation; moreover, the input-output structure of the model is created by choosing the boundary conditions at this level. Finally, the user creates an "Experiment" on the top of the previously defined structure in order to set up simulations for the system architecture and the calculation case of interest: e.g. design at steady state or off-design studies such as single point or parametric steady state, transient, sensitivity, optimisation, etc.

PROOSIS was selected for this study due to its capability for coherent first-order design space exploration of systems that employ turbo-machinery enabled by use of component performance maps. Unless a real-life system is modelled of which all the component-and system-level knowledge is available -preliminary design of a system of interest requires that a sizing procedure be firstly carried out. The result typically of this sizing procedure are the mass flows through the system, as well as the component performance maps scalars that enable them to fit the objective operating envelope for the system. The scaling procedure is carried out by correlating the reference library component maps design point with the objective design point for the system; the tool uses these specifications to derive scaling factors for the performance maps. This procedure can be done using only one ("single-point") or more than one ("multi-point") design points as reference. Once the scaling procedure is carried out, the results are used to initialise the "off-design" studies, where the performance of system under consideration is evaluated at any operating scenario of interest.

Turbogenerator model

The turbogenerator subsystem is modelled as a standard turboshaft engine consisting of an inlet component, single-spool core, power turbine and exhaust nozzle. (Fig. 1, right) Since the employed component library ("TURBO" library, available in the standard PROOSIS package) does not contain any electrical machine components, the electrical generator has been accounted for in the Pacelab APD powertrain.

In accordance with the vehicle sizing scenarios defined in the previous sections, the first approach consisted of sizing the turboshaft thermodynamic cycle for a single design point. The cycle characteristics at design point are summarised in Table 1.

Once the cycle was sized at the selected design point, a parametric performance table is generated to be imported into Pacelab APD model to be used in whole vehicle sizing. The table is generated by varying flight conditions (altitude and Mach number) and power setting of the engine for the relevant flight phases -vertical take-off/landing, hover and cruise.

Ducted fan model

Despite there being two distinct ducted fan types on the modelled vehicle (see Section IV.A) the Pacelab APD model of the UAM vehicle is constructed such that a single reference performance deck is used for any instance of the ducted fan component; the deck would be scaled accordingly for each instance of the ducted fan to match any given size and thrust specifications. Therefore, only one such propulsor model was created in PROOSIS, based on a single set of specifications. The ducted fan subsystem architecture was modelled such that the propulsor assembly consists of an inlet (customised to exclude ram drag force of typical gas turbine engine inlets), an electrically-powered fan (taking power as input), and an exhaust nozzle. (Fig. 1, left)

The procedure for performance deck creation is equivalent to the one previously elaborated for the turboshaft model. As opposed to the latter, envisioned to operate in rather conventional manner despite being installed on an unconventional vehicle, the fan needs to operate in an envelope of altitudes, Mach numbers and power settings idiosyncratic of UAM mission profile, i.e. which differs from the envelopes commonly modelled in PROOSIS when designing conventional turbofan engine cycles. For this reason, successful fan map scaling within a ducted fan thermodynamic cycle design was a somewhat challenging task. To manage to fit the operating envelope consisting of the particular flight phases characterising a UAM vehicle, we resorted to the multi-point component map scaling [START_REF] Schutte | schutte_jeffrey_s_200905_phd.pdf[END_REF] feature available in PROOSIS.

To that end, two typical operating conditions were sampled from the identified operating envelope (cf. Section III.D): Cruise and Vertical Take-Off/Landing. The design conditions were result of numerous iterations starting from basic thermodynamic analysis, going through single-point cycle sizing trials, in order to better initialise the multi-point sizing process at hand. The design operating points and cycle conditions used are summarised in Table 2.

Parameter RC40 (cruise) RC55 (VTO/VLND)

Altitude 2 Operating points and design conditions for ducted fan multi-point sizing.

Once the cycle was sized, the results were employed to generate the performance decks by means of parametric off-design calculations. For the same underlying architecture, three distinct scenarios were defined, typical of each of the three previously outlined flight phases: vertical take-off/landing, hover and cruise. Each point was then parameterised around the respective reference flight conditions (altitude, Mach number) and input power values. Once poorly converged results, or the points placed outside of the performance map (e.g. inside the surge zone) were filtered out from the resulting dataset, the performance deck was assembled and exported to Pacelab APD.

While beyond the scope of the current work, it is instructive to mention that the full robustness of the above-described method for the current application is to be further investigated. This is mainly in order to ascertain how the difficulty of fitting the typical UAM vehicle operating envelope onto a conventional (turbofan) fan performance map by means of simple scaling process can be overcome. If the current approach is retained, that is a conventional turbofan component map is scaled for the current (not necessarily well-adapted) purpose, then an option of variable nozzle inclusion could be investigated in order to ensure that the operating line at different operating conditions stays inside the performance map, and in the zones of good efficiency and surge stability. In the broader scheme of things, if more detailed design endeavours are pursued for ducted-fan-powered small vehicles, it might be instructive to look into particularities of physics of shrouded propellers, which seems to lie somewhere in between open propellers and ducted fans. While some insight into the behaviour of such components exists (see work by Lagha [START_REF] Lagha | Étude architecturale et aérodynamique d'un effecteur propulsif à Mach de vol intermédiaire[END_REF]), no such modelling exists yet in tools like PROOSIS.

Battery model

Expected entry in service of the vehicle is assumed to be 2050, so the batteries are sized accordingly: specific energy and specific power are estimated at 1872 Wh/kg and 5619 W/kg respectively, assuming a Li-ion battery [START_REF] Salucci | Design of electric-powered aircraft for commercial transportation[END_REF]. Batteries are approximated in Pacelab APD using a linear discharge rate model, with state of charge always between 80% and 20% for optimal battery life considerations.

D. UAM Mission Model

The market analysis highlighted several use cases in urban air mobility (cf. Section II.A) for both intra-and intercity operational ranges, however the definition of a single sizing mission is necessary for the design process. After some investigation, the intercity context is selected to be the most designing one and intra-city use cases will be used as off-design. In Fig. 2 the chosen design mission is shown. The simple design mission is composed by vertical take-off, hover, cruise, a second hover and vertical landing; the possibility of an extension of cruise typically needs to be taken into account for safety reasons. Transition phases, instead, are not considered at this time for the sake of simplicity; nevertheless, such simplification need not impair an overall good estimation of power requirement for such vehicles, as suggested by Kadhiresan and Duffy [START_REF] Kadhiresan | Conceptual Design and Mission Analysis for eVTOL Urban Air Mobility Flight Vehicle Configurations[END_REF].

Several studies [START_REF] Donateo | A Methodology for the Comparative Analysis of Hybrid Electric and All-Electric Power Systems for Urban Air Mobility[END_REF][START_REF] Uber | UberAir Vehicle Requirements and Missions[END_REF][START_REF] Kadhiresan | Conceptual Design and Mission Analysis for eVTOL Urban Air Mobility Flight Vehicle Configurations[END_REF][START_REF] Datta | Commercial Intra-City On-Demand Electric-VTOL: Status of Technology[END_REF][START_REF] Fredericks | Performance Metrics Required of Next-Generation Batteries to Electrify Vertical Takeoff and Landing (VTOL) Aircraft[END_REF][START_REF] Aircraft | MANTA website[END_REF] have been done in recent years in order to establish typical requirements that will drive urban air mobility. Of each modelled segment, an indicative value for specifications are collected in Table 3. The presented requirements for diversion segment, which are mutually exclusive by definition, are very different in terms of conservativeness they enable. At the moment, no certification framework is present for electric nor hybrid-electric VTOL aircraft, which is why the reserve endurance requirement is taken from FAA for aircraft (30 min) or for helicopter (20 min) VFR operation rules. However, a proper regulatory class for VTOL aircraft is expected in the future, for which a 10 km distance diversion could be considered [START_REF] Uber | UberAir Vehicle Requirements and Missions[END_REF][START_REF] Kadhiresan | Conceptual Design and Mission Analysis for eVTOL Urban Air Mobility Flight Vehicle Configurations[END_REF]. This evident decrease in diversion requirement is probably related to the ability of eVTOL to land in small spaces, increasing versatility and security with respect to traditional aircraft. Hover and diversion are intended to be performed at the same altitude as cruise. Some studies [START_REF] Kadhiresan | Conceptual Design and Mission Analysis for eVTOL Urban Air Mobility Flight Vehicle Configurations[END_REF] presented a design mission considering VTO and hover together, with a total duration of 120-180 s, however here the two segments will be analysed separately. Firstly a VTO at target 500 fpm from 0 to hover altitude is completed, and then an hover is performed. In literature, no particular requirements are defined for vertical landing. For the purpose of this work, it will be performed with a target vertical rate of descent of 500 fpm.

The feasibility of the mission coming from these requirements is strictly depending on the state of the art of propulsion technology, batteries in the first place. As the object of this preliminary design aims at a hybrid-electric solution, it permits the possibility of having more demanding requirements with respect to an equivalent pure electric solution. The specific mission details used for the model application in APD will be presented in Section IV.A.

Concerning the payload, the urban air vehicle of interest is intended for passengers transportation. on the market there are several solutions with up to 4 passengers. For the purpose of this study only 2 passengers are considered, in order to keep up with high performance requirements and to stay coherent with the baseline that inspired the current model -Manta Aircraft 𝐴𝑁 𝑁2 [START_REF] Aircraft | MANTA website[END_REF].

Power requirement estimation

Power requirement in horizontal flight has been estimated through the thrust-drag balance in cruise flight (Eq.2), while for vertical flight a different estimation is needed.

𝑃 = 1 2 𝜌𝑉 3 𝑆𝑐 𝐷 (2)
Raymer [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF] proposes an estimation of power in vertical flight using the momentum theory as starting point for the proposed approach. Power is estimated without taking the ground effect into consideration, and the main assumption at the basis of the formula is that thrust disk loading (𝑇/𝐴) is equal to weight loading (𝑊/𝐴) with a calibrated increase by a small percentage -typically between 3% and 7% -to account for the downwash blowing force on the fuselage. (Eq.3)

𝑇 𝐴 = 𝑊 𝐴 𝑓 with 𝑓 ∈ [1.03 -1.07] (3)
𝑓 is the coefficient modelling the downwash effect and 𝐴 is the total propulsive area as sum of the single rotor areas (𝐴 𝑖 ) engaged in vertical flight, with 𝑁 the total number of propulsive units for vertical flight. (Eq.4)

𝐴 = 𝑁 ∑ 𝑖=1 𝐴 𝑖 (4)
Since hover is a steady state segment and vertical climb and descent are assumed to be performed as stationary, it is convenient to estimate thrust requirement as total weight increased by fuselage downwash factor 𝑓 . (Eq.5)

𝑇 = 𝑊 𝑓 (5)
Given all the above considerations, the final formula for power requirement in vertical flight is expressed in Eq.6.

𝑃 = 𝑓 𝑊 𝑐 𝐹𝑜𝑀 √ 𝑓 𝑊/𝐴 2𝜌 + 𝑊 𝑉 𝑉 𝑅𝑂𝐶 2 1 𝜂 𝑚𝑒𝑐 (6)
Power depends on aircraft weight (𝑊), vertical rate of climb (𝑉 𝑉 𝑅𝑂𝐶 ), fuselage downwash coefficient ( 𝑓 ), a figure of merit defined by Raymer (𝑐 𝐹𝑜𝑀 ) and the total propulsive area (𝐴). In particular, the employed rotor figure of merit is used to correct the momentum theory estimation of required power, in the same fashion as propeller thrust should be adjusted by an efficiency parameter. Its typical value is between 0.6 and 0.8; it is almost constant with rotational speed as demonstrated by experimental studies in [START_REF] Russell | Wind Tunnel and Hover Performance Test Results for Multicopter UAS Vehicles[END_REF]. Mechanical efficiency is fixed at 80% instead.

E. Customization of Pacelab APD

For the purpose of this work, certain items are created or customized in Pacelab APD since vertical flight solutions are not available in the library associated to the current release of the software.

Vertical Take-Off and Landing (VTOL) and Hover (HOV) mission segments are implemented to represent a typical target mission. In the meantime the propulsion module is customized with the installation of performance decks for electric ducted fan and turboshaft objects, both created with PROOSIS tool. An overview of the implementation strategy is presented for each item in the following subsections.

Vertical flight segments

The implementation of vertical flight on APD follows the same approach as other mission segments in the tool library. The users commonly build a mission in APD by assembling different ports and engineering objects that represent single segments such as cruise, take-off, etc. Each port comes with a set of parameters needed for the performance calculation. In order to build a history data table, which collects the time evolution of relevant mission parameters, a performance method is needed to compute point performance. One performance method is associated to a single segment type, and this association is created by means of a Smart Formula (Pacelab nomenclature). The latter is capable of collecting all the engineering objects in a single interface, and dealing with them all at once before calling the performance methods. More details on Smart Formulas can be found in the documentation [START_REF] Pace Gmbh -A Txt Company | Pacelab APD 8.1 Documentation[END_REF].

For the sake of clarity, this approach is schematized in Fig. 3 for the specific case of vertical flight. Three mission ports are created on APD Knowledge Designer: vertical take-off, vertical landing and hover. The user will be able to insert input parameters (i.e. duration, altitude, ...) and to connect them to the mission in APD Engineering Workbench. The ports are connected to an interface which is created to collect all vertical flight segments of the mission profile. A vertical flight Smart Formula is written, interfacing with those ports and collecting useful data. Its last task is to call the correct method for point performance computation. The mathematical model for each segment type (Section III.D.1) is implemented in a different performance method, computing history of thrust and power, resulting in battery discharge and fuel consumption estimation. A more detailed insight into each mission segment is provided in the following:

• Vertical take-off (VTO)
This segment is performed at maximum available thrust, given that it is greater than the required thrust (Eq. 5).

An initial vertical rate of climb (VROC) is asked to the user, as well as its minimum value. The actual VROC is then variable depending on the available power through the relation presented in Eq.6. The list of input parameters is the following:

vertical rate of climb (initial); minimum vertical rate of climb; target altitude; downwash coefficient;

figure of merit; mechanical efficiency. In order to complete the formula, propulsive area is computed by collecting and summing fan areas from each propulsive unit and aircraft weight is updated from the mission development. Minimum required thrust is estimated considering the fuselage downwash effect (Eq. 5) and in the event of insufficient thrust, no vertical climb is computed and a warning message is produced. The segment exit condition is the user-defined target altitude.

• Vertical landing (VLND)

It is implemented with the same approach of take-off, considering a vertical rate of descent instead of climb. A warning message is produced in case target altitude is higher than the instantaneous altitude.

• Hover (HOV)

There are two main differences with respect to vertical take-off and landing:

thrust is adjusted to the required one (Eq. 5) and segment is performed at the required part power; exit condition is time driven, depending on the user-defined segment endurance; The resulting design mission modeled in the Engineering Workbench is illustrated in Fig. 4, representing what is decided upon market and theory study (Fig. 2, Table 3). Each port is connected sequentially, hence each connection creates a temporal link giving the last condition of each port (e.g. weight, altitude, time) as the starting point of the subsequent segment.

Powertrain

Pacelab APD enables the creation and customization of different powertrain solutions: each component can be added and linked in a power supply chain creating a variety of solutions ranging from the fuel burning ones to the most innovative ones powered by hybrid-electric sources and/or fuel cells.

Pacelab APD evaluates propulsive system performance through the use of performance decks, meaning multidimensionaldata tables mapping available power and thrust in different flight conditions and engine settings. Those tables are then extrapolated and interpolated in the solving process to evaluate the full mission. Due to obvious different technology characteristic, each component is characterized by a different physical model, whose details are provided in the following.

• Gas turbine Gas turbine is mainly characterized by a reference shaft power, reference RPM and a mass, through which it will contribute to the overall mass and CG estimation of the aircraft. The mass estimation is adapted based on Eq.1, mainly dependent on reference shaft power which is a design parameter. The performance deck provides fuel consumption values as a function of flight conditions and torque. An estimation of shaft power and exhaust net thrust is also given. The resulting deck has the structure presented in Fig. 5, where white parameters are input and brown are output. A linear approximation strategy is chosen for interpolation and extrapolation purposes. The rating code is a code associated to a specific flight mission segment.

• Electric generator

The electric generator is a very simple component characterized by a reference power and a mass, estimated assuming the specific power as presented in Section III.B.2. Its performance in converting mechanical to electric power is mapped through a simple single efficiency, that will be assumed constant in the whole mission. Fig. 6 shows the structure of the performance deck.

• Battery

The battery pack is modelled with a linear discharge process. Specific power and energy are dictated by the technology at the assumed entry of service, which provide an estimation of mass.

• Electric motor

Each electric motor element is characterized by a reference power and a specific power to estimate the mass. The performance model is similar to the electric generator one: the conversion from electric power to mechanical is affected by an efficiency, that will be assumed constant in the whole mission.

• Gearbox

The same applies for the gearbox: reference power is the main parameter, linked to mass estimation thanks to the specific power. Performance decks presents only an efficiency of shaft power transmission.

• Propeller with nacelle

The propeller or in our case in particular the fan is placed inside a nacelle and is characterized by a reference power, influencing mass estimation. Performance decks maps the thrust, normalized by the reference thrust power, at different flight conditions and power setting. The structure of the multidimensional-data table is shown in Fig. 7.

Fig. 7 Propeller performance deck structure on APD.

Simulation output of turboshaft and electric ducted fan PROOSIS models is translated into performance decks for APD. In particular, turboshaft is simulated and normalized to be scaled later with respect to reference power. More comments are needed for the ducted fan: even though the PROOSIS simulation is meant to represent the entire electric ducted fan assembly, the electric motor and the gearbox efficiencies are not book-kept here, but in the respective APD power train components.

The ducted fan shape must be defined since it plays an important role in volume and wetted area computation. A very simple cylindrical shape is chosen for the duct. Fig. 8 presents an example of final EDF geometric design in APD.

Mass

The targeted case study is meant to have a fully composite structure. Raymer [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF] suggests an approach with calibration factors which approximate the reduction in mass with respect to traditional structures. Structural weight prediction for conventional aircraft is already implemented in APD, with the possibility to insert a mass factor for each component in order to modify their estimation as needed. Calibration factors recovered from Raymer [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF] are collected in Table 4.

Component

Mass factor

Wing group 0.85 Fin upper and canard 0.8 Fuselage 0.9 Landing gear 0.95 Table 4 Composite materials mass factors [START_REF] Raymer | Aircraft Design: A conceptual approach[END_REF].

IV. Case Study

A. Baseline Case

The inspiration for the baseline case (illustrated in Fig. 9) was 𝐴𝑁 𝑁2 concept by Manta Aircraft. It is a hybrid-electric VTOL vehicle targeting regional and inter-regional air mobility applications. It has a fully composite structure and a canard configuration with a twin tail. The configuration, geometry and propulsive system architecture are chosen to be as representative as possible of the reference design, using whatever public information was found. The overall dimensions of the vehicle are summarised in Table 5.

Length Wingspan Height

m

6.8 m 1.7 m Table 5 Overall dimensions of the modelled vehicle.

Powertrain

The most important and innovative subsystem is the propulsive system: it is composed of four electrical ducted fans mounted on the wing, and four more fans mounted inside the fuselage. The propulsive system architecture is series hybrid-electric: depending on the flight phase the ducted fans are driven by the batteries and/or the turbogenerator. The resulting configuration on Pacelab APD is presented in Fig. 10. As it can be seen, the electric ducted fans, each of them composed by an electric motor, gearbox and a propeller, are divided in two different groups:

• Wing group, comprehending the electric ducted fans installed on the wing leading edge, capable of tilting to provide power in both horizontal and vertical flight. • Fuselage group, comprehending the ones installed inside the fuselage, two in the rear and two in front of the cabin.

These EDFs are fixed vertically and will be shut down and shielded with sliders during horizontal flight segments, e.g. cruise. Each wing group EDF, at least initially, is designed as bigger with respect to the ones in the fuselage group for vertical flight only. This is lead mainly by space constraint of fuselage accommodation, due to the relation between produced power and fan propulsive area, and the functionality of those EDFs just as vertical flight "booster". As an initial assumption, the contribution to total power and thrust in vertical take-off, landing and hover will be divided as follows: 40% of contribution will come from fuselage EDFs and 60% from the wing EDFs. This will subject to sensitivity studies.

The powertrain is placed in the aircraft structure, paying attention at the center of gravity. Four electric ducted fans are placed inside the fuselage and four more on the leading edge. The turbogenerator is behind the cabin while the batteries are under the cabin floor. The resulting configuration is shown in Fig. 11, where the powertrain components are highlighted in red.

Fig. 11 Aircraft with the propulsion group highlighted.

Design mission

The design mission is the output of the market analysis (cf. Section III.D); segment requirements are proposed in Table 6. Cruise and cruise extension distances are kept as output of the design, as well as the MTOM. Pacelab APD permits the user full flexibility in defining the power management for each flight segment of a mission, starting from the definition of the power share between fuel burning and pure electric energy sources, to the split ratio and so the contribution of every single ducted fan to the total produced thrust. For environmental pollution reasons, both atmospheric and acoustic, it is chosen to perform vertical take-off and landing pure electric and to fly hybrid electric, turning on the gas turbine, in hover and cruise, so only when a certain altitude is reached. Other power management solutions have been explored in the purpose of off design analysis.

Segment

B. Off-Design Cases

Once the parametric design procedure is implemented in Pacelab APD TM and the baseline model is fully consolidated, it is possible to perform the final sizing and subsequent trade studies in order to explore the design space. In particular, after the baseline design is created from the design mission proposed in Section IV.A it is of interest the investigation of the effect of the following case studies:

• Different off-design use cases: how will the same air vehicle perform in a intra-city mission? i.e. a simple multicruise scenario of about 40 km each [START_REF] Uber | UberAir Vehicle Requirements and Missions[END_REF]. • Different power management on the same mission: what is the impact of using the gas turbine on the vertical take-off and landing segments? Some sensitivity analysis to design parameters are also carried out, to answer the following questions: • What would be the impact of different sizing mission requirements? (e.g. different target altitudes or different cruise mach speed); • What would be the impact of different propulsive system nominal (design) characteristics? (e.g. turbogenerator reference power or battery nominal power).

V. Results

This chapter presents the results obtained for the design mission and the respective off-design and sensitivity studies.

A. Baseline Case Results

Starting from the baseline case, a successful design is accomplished. This chapter is dedicated to the presentation of the results: starting from geometries and mass breakdown a more detailed performance analysis is also given.

Mass and geometries

Table 7 presents the mass breakdown, while the detailed geometric characteristics of the vehicle are summarised in Table 8.

Name

Performance

The baseline design is sized on the design mission as described in Section IV.A.2, assuring the battery state of charge never exceeding the 80-20% range. The time evolution of parameters of particular interest are here reported. Fig. 12a plots time evolution of altitude and distance. Note that distance is not credited during vertical segments. The design range, which was an output in Pacelab APD, is about 112 km (60.45 NM), which fully satisfies the requirements from market analysis (cf. Section III.D). True airspeed (TAS) and Mach number change in time as prescribed by the design mission (Fig. 12b). The thrust provided by a single EDF in the wing propulsion group and in the fuselage one are compared in 12d. As modeled, available thrust is proportional to fan area during vertical flight, whereas only the tilting ducted fans are driving cruise. From the same graph, it is evident how vertical segments are significantly more power-demanding in contrast to cruise. This explains the need of vertically fixed electric ducted fans boosting available power with respect to horizontal segments. Fuel and battery electricity consumption in Fig. 12c show that the state of charge does not go below 20% as recommended for optimal battery life and almost 78 kg of fuel is needed to complete the mission. The fuel consumption is null during vertical take off and landing, it starts in hover and it is almost linear during cruise. Battery instead are discharged with an almost constant rate in the vertical flight and are not used in cruise, as chosen previously.

The extended cruise is considered as a reserve segment and so it is not part of the design flight profile. It is executed with the same setting as the main cruise meaning that only the turbogenerator is operational and the batteries are not consumed. It is assumed to be performed at the same altitude (3000 ft) and same speed (0.2 Mach) as cruise too. As a result, it has a range of almost 16 km (8.62 miles) with an endurance of almost 4 minutes, for which only about 10 kg of fuel is needed. Also regarding the diversion, the guidelines from Section III.D are respected.

Exploring different use scenarios

Urban air mobility has many use cases, which at the end could be classified in two categories with respect to the flight range: intra-or intercity flight mission. The latter one is taken into consideration as the sizing mission, accomplishing a range of 110 km (60 NM) plus a diversion of 16 km (8.5 NM). It is of interest the exploration of the behaviour of the same design but on a mission composed of several consecutive cruises segments, imagining a function of air city taxi for commuting purposes, which could also be considered in both scenario: on demand or scheduled.

The multi-cruise mission is shown in Fig. 13: each sub-mission is composed by a vertical take-off, a hover and a cruise. Specifications of each segment are highlighted in Table 9. Each single cruise range has been set to input to 40 km (cf. Section III.D), constraining the fuel capacity to design point (88.11 kg, cf. Table 7) and the maximum take-off mass (1476.6 kg). Hover time has been reduced to 2 minutes each whereas target altitude is still 3000 ft. Vertical take-offs and landings are still performed fully electric as for the design condition. 9 Intra-city mission requirements.

Results are shown in Fig. 14 andhereafter described: • The mission has a total endurance of almost 41 minutes, for which 81.8 kg of fuel is burn, with a take off mass of 1469.4 kg,

• The whole mission can be performed without any battery recharge stop. State of charge is assumed to start at 80% and ends at 25.12%. • The fuel burning in cruise is not producing an tangible effect in power requirement reduction in cruise. Concluding, in this second scenario performances are in line with expectations, no further special considerations are needed. The second explored scenario is a different power management. Fixing the mass breakdown and the mission structure as in the sizing case (cf. Section IV.A.2), but this time the mission will be fully hybrid electric, i.e. turning on the gas turbine also in vertical take-off and landing and using the battery in cruise. As a result, some improvement in performances are gained: resulting cruise range is 133.7 km (72.2 NM). Just for the sake of completeness, some relevant graphs of this off design scenario are presented in Fig. 15. Velocities and power from EDF are not reported since they are equivalent to the sizing mission (see Fig. 12).

Sensitivity analysis

Sensitivity analysis gives a overview on the dependencies and the impact of changes in input parameters to the final design. In the framework of this research, sensitivity has been run in two main input categories in which there was space for doubts and change:

• Propulsion reference value: what will be the impact of decreasing the installed power on the mission performance? would an increase, instead, produce a more competitive range on the market, maintaining a reasonable take-off weight? • Mission segment requirements: the design mission could be modified changing the target altitude, the cruise Mach number and the hovering time and it is of interest to understand the impact on range and other performance parameters, keeping the installed power constant. In Table 10 the range of input for the explored parameters are reported, divided in the two domains. Please note that the fuselage EDF has been always considered with the same ratio of 4:6 with respect to the wing EDF, as by design. Constraints have been also applied, of main interest regarding minimum state of charge of batteries (>20%), the peak Results have been analysed and those of particular interest are reported graphically in Fig. 16 and Fig. 17. Constraints are always checked: the red area means that the area does not represent a feasible design space. When a converged solution is not attained, the point is not represented, which explains the void segments in some graphs. From the analysis it seems that the chosen design point has is optimal in terms of design range and take off weight. With respect to mission requirements, more distance could be gained giving up some hover time, and this is what is also experienced in the intracity mission.

C. Discussion

First of all, as already discussed in Section III.B.2, the mass breakdown has been approximated assuming a conventional commercial aircraft, calibrated just to take into account of the composite structure. For more accuracy there is the need of a tailored mass method for UAM category, which is difficult to create at this moment due to lack of empirical data.

For similar reasons, aerodynamic estimation can be improved. The peculiarity of the case study configuration would require a detailed aerodynamic simulation, also for a better estimation of the fuselage downwash effect in the vertical flight. The accuracy of the method could be improved, validating a tailored method for urban and personal air mobility configurations. Pacelab APD TM permits to insert data retrieved with external aerodynamic simulation software for the specific case study. Such effort is out of scope of this preliminary sizing approach so aerodynamic approximation is done with calibration factors and regression from traditional methods.

Overall, this project showed capability of Pacelab APD tool adapt to various configurations outside of the conventional design space, in this particular case -UAM vehicles. This is enabled by customising the tool with dedicated performance models, flight segments and introduction of flexible power train modelling capability complemented by detailed scalable performance maps obtained from dedicated tools.

VI. Conclusions

The paper presents development of a baseline model of an Urban Air Mobility vehicle for parametric mission sizing and performance estimation using aircraft preliminary design software Pacelab APD TM . A working model of a vehicle designed to carry two passengers over a 110 𝑘𝑚 design range has been assembled in APD; the model employs propulsive system performance decks generated independently using gas turbine system architecture modelling software PROOSIS TM . A preliminary UAM vehicle design capability is demonstrated in Pacelab APD, which includes both design mission study for a nominal, as well as off-design mission exploration, trade studies and sensitivity studies with respect to configuration details, mission profile and propulsive system architecture layout and performance characteristics.

A case study is presented for a nominal mission consisting of vertical take-off, hover, cruise, a second hover and vertical landing flight segments. The suggested preliminary solution results in a maximum take-off weight of 1477 kg, with 178 kg of batteries and 88 kg of fuel. The design power management strategy consists of the turbogenerator sized for cruise power and used only in hover and cruise. Batteries are meant to compensate the available power deficit in vertical flight instead, while operating in a 80%-20% state of charge range.

After determining a design point, off-design studies and sensitivity studies have been accomplished. Off-design studies mainly dealt with the exploration of different use cases for UAM:

• a mission composed by three repeated cruises of 40 km is performed to simulate an air taxi working in an urban context; • a mission like the sizing one but trying a different power management scenario i.e. gas turbine, throughout the entire mission. In parallel, Pacelab APD was also used to perform sensitivity study on a selection of input parameters related to propulsive systems and mission requirements. No evidence was found with respect to a better design point. Overall, a good idea of a performance envelope is obtained. Feasibility of UAM is still uncertain due to many factors (e.g. technological, operational, safety, etc.), of which the most important one in the scope of the presented work is the lack of experience and empirical data to modify and calibrate estimations in terms of mass break down and aerodynamic in vertical flight. For example, a better estimation of the fuselage downwash effect, maybe accounting for the specific vehicle configuration, would lead to more robust and reliable results. Overall, however, the growing interest of the industry and the society to new air transport solution is boosting the research field in this direction.

  thrust [𝑁] 𝑒𝑉𝑇𝑂 𝐿 = electric Vertical Take-Off and Landing 𝑚 = Mass [𝑘𝑔] 𝑀𝑇𝑂 𝑀 = Max Take-Off Mass [𝑘𝑔] 1 𝑀 𝑍 𝐹 𝑀 = Max Zero Fuel Mass [𝑘𝑔] 𝑂𝐸 𝑀 = Operational Empty Mass [𝑘𝑔] 𝑃 = Power [𝑊] 𝑅𝐶 = Rating Code 𝑆 = Surface [𝑚 2 ] 𝑆𝐹𝐶 = Specific Fuel Consumption [𝑔/𝑘 𝑁 𝑠] 𝑇 = Thrust [𝑁] 𝑇𝐺 = Turbogenerator 𝑇 𝑆 = Turboshaft 𝑈 𝐴𝑀 = Urban Air Mobility 𝑉 = Velocity [𝑚/𝑠] 𝑉 𝐹 𝑅 = Visual Flight Rules 𝑉 𝐿𝑁 𝐷 = Vertical Landing 𝑉 𝑅𝑂𝐶 = Vertical Rate of Climb 𝑉𝑇𝑂 𝐿 = Vertical Take-Off and Landing 𝑊 = Weight [𝑁] 𝜂 = Efficiency [-] 𝜌 = Density [𝑘𝑔/𝑚 3 ]

Fig. 2

 2 Fig. 2 Urban air mobility design mission.

Fig. 3

 3 Fig. 3 Vertical flight segments implementation approach.

Fig. 4

 4 Fig. 4 Schematic representation of the design mission in Pacelab APD.

Fig. 5 Fig. 6

 56 Fig. 5 Gas turbine performance deck structure on APD.

Fig. 8

 8 Fig. 8 Geometrical representation of the electric ducted fan in APD, with and without the duct.

Fig. 9

 9 Fig. 9 Baseline case study visualisation in Pacelab APD.

Fig. 10

 10 Fig. 10 Powertrain of the baseline case study in Pacelab APD.

  state of charge and fuel. (d) Power from wing EDF and fuselage EDF.

Fig. 12

 12 Fig. 12 Sizing mission.

Fig. 13

 13 Fig. 13 Multi-profile mission in an intra-city operational scenario.

  (a) Altitude and distance. (b) TAS and Mach. (c) Battery state of charge and fuel. (d) Power from wing EDF and fuselage EDF.

Fig. 14

 14 Fig. 14 Intracity off design mission.

  state of charge and fuel.

Fig. 15

 15 Fig. 15 Full hybrid-electric off design mission.

( a )

 a Mission distance and take off mass with respect to battery nominal power and wing and fuselage reference power; fixing turbogenerator power at design (680 kW). (b) Mission distance and take off mass with respect to turbogenerator nominal power and wing and fuselage reference power; fixing battery power at design (1000 kW). (c) Mission distance and take off mass with respect to turbogenerator and battery nominal power; fixing EDF power at design (170 and 120 kW).

Fig. 16

 16 Fig. 16 Sensitivity study result: propulsive system characteristics.

( a )

 a Minimum SOC and mission distance with respect to cruise Mach number and target altitude; fixing hover time at design endurance (5 min). (b) Minimum SOC and mission distance with respect to hover time and target altitude; fixing cruise mach number at design value (Mach 0.2). (c) Minimum SOC and mission distance with respect to hover time and Mach number in cruise; fixing target altitude of vertical climb (3000 ft).

Fig. 17

 17 Fig. 17 Sensitivity study result: mission requirements.

Table 1 Turboshaft design point cycle details.

 1

	Parameter	RC40 (cruise)
	Altitude [ft]	3000
	Mach number [-]	0.25
	ISA deviation [-]	0
	Input power [kW]	170
	Core (high-pressure compressor) pressure ratio [-]	12
	High-pressure compressor efficiency [-]	0.89
	High-pressure turbine efficiency [-]	0.9
	Power turbine efficiency [-]	0.9
	Power-specific fuel consumption [g/Wh]	0.23

Table 3 Urban air mobility mission segments: indicative requirements. VROC and VROD stand respectively for vertical rate of climb and descent.

 3 At the moment

	Segment	Altitude	Velocity	Distance	Endurance
	Vertical take-off	-	(VROC) 300-500 fpm	-	-
	Hover	1500-3000 ft	0	-	2-5 min
	Cruise	1500-3000 ft	80-300 km/h	about 100 km or 40 km repeated	up to 2 h
	Vertical landing	-	(VROD) 300-500 fpm	-	-
	Diversion	> 500 ft	-	about 10 km	20-30 min

Table 6 Urban air mobility sizing mission requirements.

 6

		Altitude	Velocity	Distance Endurance
	Vertical take-off	0 -3000 ft	(VROC) 500 fpm	-	-
	Hover	3000 ft	0	-	5 min
	Cruise	3000 ft	Mach 0.2	-	-
	Vertical landing	3000 -0 ft (VROD) -500 fpm	-	-
	Extension of cruise	3000 ft	Mach 0.2	-	-

Table 7 Mass breakdown of the baseline case.

 7

		Value	Name	Value
	MTOM	1476.6 kg MZFM	1209.7 kg
	OEM	1009.7 kg Propulsion group 418.1 kg
	Max Fuel 88.11 kg Max Payload	200 kg
	Component Parameter	Value
	Wing	Area		12.7 m 2
		Span		6.8 m
		Aspect ratio	3.642
		Taper ratio	0.373
		Mean aerodynamic chord	1.98
	Canard	Area		3.11 m 2
		Span		3.77 m
		Aspect ratio	4.57
		Taper ratio	0.398
		Mean aerodynamic chord 0.88 m
	Fin upper	Area		1.41 m 2
		Inclination	24 deg
	Fuselage	Length		8.15 m
		Height		1.34 m
		Width		0.88 m

Table 8 Geometrical characteristics of the baseline case.

 8

Table 10 Sensitivity analysis: range of the parameters.

 10

	Nominal powers	Mission requirement
	Component	Range	Component	Range
	Battery	900 -1300 kW VTO target altitude	1500 -1400 ft
	Turbogenerator 600 -720 kW Cruise Mach number 0.2 -0.3 Mach
	Wing EDF	145 -200 kW Hover endurance	2 -5 min
	Fuselage EDF	102 -141 kW

Acknowledgments

The authors would like to thank PACE Aerospace & IT preliminary design team for the precious help in the creation the presented model, in particular Carlos Castro. The contribution of professor Alberto Rolando from Politecnico di Milano university is also acknowledged.