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Energy Optimal Speed Profile for Arrival of Tandem Tilt-Wing Evtol

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Energy Optimal Speed Profile for Arrival of Tandem Tilt-Wing Evtol Energy Optimal Speed Profile for Arrival of Tandem Tilt-Wing eVTOL Aircraft with RTA Constraint Priyank Pradeep1 and Peng Wei2 Abstract— The electric vertical takeoff and landing (eVTOL) in vertiport capacity and battery endurance). To the best of aircraft can alleviate transportation congestion on the ground our knowledge, no significant research work has been carried by utilizing three-dimensional airspace efficiently. However, the out for the energy efficient arrival with the required time of endurance of Lithium-ion Polymer (Li-Po) batteries imposes severe constraints on the operational time span of an eVTOL arrival (RTA) for various types of eVTOL aircraft in the on urban air mobility (UAM) passenger transportation mission. UAM context [5], [6]. This paper aims to work towards This research focuses on the formulation of a fixed final time filling the research gap to enable safe and energy efficient multiphase optimal control problem with energy consumption arrival operations of a tandem tilt-wing eVTOL aircraft given as the performance index for a tandem tilt-wing eVTOL the limited vertiport capacity and endurance of Lithium-ion aircraft. The proposed multiphase optimal control problem formulation and the numerical solution enable the eVTOL polymer (Li-Po) batteries [5]. aircraft to meet the given required time of arrival (RTA) with Considerable efficiency improvements are possible utiliz- the optimal speed profile for the most energy efficient arrival. ing distributed electric propulsion (DEP) technology because The problem formulation is validated in a UAM passenger it enables fixed-wing VTOL aircraft to provide lift with far transport use case with Airbus Vahana eVTOL aircraft, and higher efficiency than rotors especially in cruise phase [4]. the Uber Elevate proposed vertiport concept in numerical simulations. Engine failure accounts for 18 % of general aviation acci- Index Terms— Concept of Operation (CONOP), Electric dents when combined with fuel management errors. The use Vertical Takeoff and Landing (eVTOL) aircraft, Required Time of DEP, controllers, and a redundant battery bus architecture of Arrival (RTA), Urban Air Mobility (UAM). avoids the problems of catastrophic engine failure by having full propulsion system redundancy [4], [7]. In addition to I. INTRODUCTION the improved cruise efficiency, a tandem tilt-wing has an In 2014, road-traffic congestion resulted in a wastage of advantage of lower power consumption in hover than a tilt- 6.9 billion person-hours and 3.1 billion gallons of excess fuel rotor as the impact of the rotor downwash on the wing is consumed in the USA alone [1]. Transportation as a whole substantially reduced [7], [8]. A tilt-wing has an additional accounted for approximately 33 % of CO2 emissions in the benefit as the induced airflow behind the rotors reduces the USA, of which 80 % are from cars and trucks traveling on angle-of-attack on the wing in hover and low-speed forward the roadway system [2]. A study in the American Journal of flight [7]. Preventative Medicine, for example, found that those who commute more than 10 miles were at increased odds of B. Motivation elevated blood pressure [3]. The electric vertical takeoff and Electric propulsion is the preferred propulsion choice for landing (eVTOL) aircraft can alleviate transportation conges- the urban VTOL aircraft because of the zero operational tion on the ground by utilizing three-dimensional airspace emissions [4]. However, the specific energy (the amount of efficiently, just as skyscrapers allowed cities to use limited energy per unit weight provided by the battery) of Lithium- land more efficiently [4]. Recently, technological advances ion polymer (Li-Po) batteries today is insufficient for long- have made it possible to build eVTOL aircraft. Over a range commutes [5], [12]. Also, from the certification point dozen companies, for example, Airbus, Aurora, Ehang, Jobby of view, eVTOL aircraft may require landing with reserve Aviation, Lilium, Volocopter, etc., with many different design battery charge/usage time (analogous to reserve fuel for con- approaches, are passionately working to make eVTOLs a ventional aircraft). This research paper focuses on optimal reality [4], [5]. (minimum battery usage) speed profile computation under arrival time-constraint for the operational success of tandem II. BACKGROUND AND MOTIVATION tilt-wing eVTOL aircraft [5]. A. Background III. MULTIPHASE OPTIMAL CONTROL PROBLEM The possibility of urban air mobility (UAM) has been FORMULATION explored by NASA, Uber, Airbus and university researchers A. Aircraft Model since 2016 [5]. Most of the UAM operations of the eVTOL aircraft are in a constrained environment (due to limitations In this paper, the aircraft dynamics are modeled based on the tandem tilt-wing eVTOL (Airbus Vahana) from Airbus 1Priyank Pradeep is a Ph.D. candidate in Aerospace Engineering Depart- A3 [7]. This eVTOL aircraft has two tandem tilt-wings with ment, Iowa State University, [email protected] 2Peng Wei is an Assistant Professor in Aerospace Engineering Depart- eight rotors. ment, Iowa State University, [email protected] • The transition phase, consists of the following sub- phases: i) deceleration to hover speed and ii) hover above the vertiport at the cruise altitude. • The descent phase includes vertical descent. Therefore, only the speed profile of the eVTOL aircraft is free for the optimization. However, since the arrival time constraint has been imposed on the eVTOL aircraft, the trajectory optimization problem involves computation of an energy efficient speed profile for the eVTOL aircraft with fixed final time [5]. C. Cruise Flight Dynamics Fig. 1. Airbus Vahana: Tandem tilt-wing configuration during the cruise phase [7] B. Trajectory Optimization In this research, the longitudinal flight dynamics for the tandem tilt-wing aircraft are decoupled from the lateral flight dynamics as the eVTOL has a symmetrical: i) wing structure and ii) placements of rotors about the longitudinal axis; like fixed-wing aircraft and quadrotors respectively. Hence, the decoupling logic used by researchers for fixed-wing aircraft [13], [14], [15], [16], [17], conventional rotorcraft [8], [9], [10], [11] and quadrotors [5], [12] are assumed to be applicable for the tandem tilt-wing eVTOL as well. Fig. 3. Free body diagram of the eVTOL [17] In this paper, the following assumptions have been made: • The lateral trajectory is a geodesic path. The decoupling of the longitudinal and lateral flight dy- • The vertical trajectory of arrival consists of a portion of namics allows us to solve the vertical trajectory generation the cruise, transition, and descent phases. problem as a two-dimensional flight dynamics problem in • Only, a part of the cruise phase is considered to study the vertical plane. Therefore, the equations of motion for energy efficient delay absorption while airborne. the tandem tilt-wing eVTOL aircraft (shown in Fig. 1) in • The transition phase involves tandem tilt of rotors and aerodynamic frame of reference are as follows [13], [14], wings for the transition from cruise speed to hover [15], [16], [17]: for the vertical descent per the concept of operation (CONOP) of Airbus Vahana [7]. dV T cos α − D − W sin γ = (1) • In the transition phase, the rotation of rotors and wings dt m from cruise to vertical descent configuration occurs in negligible time with ignorable mechanical energy dx = V cos γ (2) losses. dt dh = V sin γ (3) dt 8 X T = Ti (4) i=1 where [x; h] is the position vector (along track distance, altitude) of the center of mass relative to the initial position, α is the angle between the thrust vector and the aerodynamic velocity, γ is the aerodynamic flight path angle, T is the net thrust produced by DEP of the eVTOL, D is the net drag, th L is the net Lift, Ti is the thrust produced by the i rotor, m is the mass, V is the true airspeed, W is the weight of Fig. 2. Vertical trajectory of the eVTOL’s arrival [7] the eVTOL aircraft and g is the acceleration due to gravity. D. Path Constraints in Cruise Phase true air speed of the eVTOL aircraft. The path constraints for the tandem tilt-wing eVTOL Therefore, the total energy consumed (Ecruise) by DEP in aircraft in the cruise phase are as follows: cruise phase is as follows: i) Assuming the cruise phase consists of constant level cruise Z tf flight segments: Ecruise = P dt (15) 0 T sin α + L − W cos γ = 0 (5) dh G. Transition Flight Dynamics = 0 (6) dt In the transition phase, the eVTOL is assumed to de- γ = 0 (7) celerate from cruise speed to hover at a constant altitude [7]. Hence, transition phase consists of deceleration of the ii) Lower and upper bounds on the cruise speed: eVTOL followed by hover above the vertiport at the cruise 1:3Vstall ≤ V ≤ Vmax cruise (8) altitude. In this research, we have assumed the following: i) rotation of wings and rotors from cruise configuration E. Drag Model in Cruise (Fig. 1) to vertical descent configuration (Fig. 4) occurs in The cruise performance of the tandem tilt-wing eVTOL negligible duration of time and ii) deceleration of the eVTOL aircraft is based on a traditional quadratic drag polar with a aircraft occurs solely due to the aerodynamic drag. Hence, span efficiency factor (e) of 1.3 [7]. The drag model used the equations of motion in transition phase is given by: in this research is based on Airbus Vahana’s drag model as dV D follows [7]: = − (16) 2L dt m Sref = 2 (9) ρVstallCLmax dx where C = 1:1, V = 35 m/s, ρ is the density of air = V (17) Lmax stall dt at the cruising altitude and Sref is the reference area of the eVTOL (both wings combined). 8 2 X b T = Ti (18) AR = ref (10) i=1 Sref where AR is the equivalent aspect ratio of the eVTOL H.
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