Air taxi flight performance modeling and application

Abstract

Urban air mobility encompasses the idea of extending urban transportation to the airspace. For this purpose, several aircraft manufacturers and start-up companies have developed aircraft concepts for flying completely electrical. Electric aircraft have different behavior concerning flight performance, which mostly depends on battery characteristics. Due to this, electric vertical takeoff and landing aircraft (eVTOL) are more limited in their flight performance concerning range and endurance than conventional aircraft. Nowadays data on that topic are mostly published by eVTOL manufacturers and seem to be quite ambitious concerning the current state of battery technology. This paper aims at determining flight performance by considering state-of-the-art battery characteristics. Each flight segment has a different influence on battery discharge, due to different power requirements. Based on an application case, the range capabilities of three eVTOLs are estimated. Therefore, the results reveal a range of around 115 km for vectored thrust eVTOL, around 70 km for lift & cruise eVTOL, and around 50 km for multicopter eVTOL.

Full text

Fourteenth USA/Europe Air Traffic Management Research and Development Seminar (ATM2021)
Air taxi flight performance modeling and
application
Robert Br¨
uhl, Hartmut Fricke, Michael Schultz
Chair of Air Transport Technology and Logistics
Technische Universit¨
at Dresden
Dresden, Germany
robert.bruehl@tu-dresden.de
Abstract—Urban air mobility encompasses the idea of extend-
ing urban transportation to the airspace. For this purpose, several
aircraft manufacturers and start-up companies have developed
aircraft concepts for flying completely electrical. Electric aircraft
have different behavior concerning flight performance, which
mostly depends on battery characteristics. Due to this, electric
vertical take-off and landing aircraft (eVTOL) are more limited
in their flight performance concerning range and endurance
than conventional aircraft. Nowadays data on that topic are
mostly published by eVTOL manufacturers and seem to be quite
ambitious concerning the current state of battery technology. This
paper aims at determining flight performance by considering
state-of-the-art battery characteristics. Each flight segment has a
different influence on battery discharge, due to different power
requirements. Based on an application case, the range capabilities
of three eVTOLs are estimated. Therefore, the results reveal a
range of around 115 km for vectored thrust eVTOL, around 70
km for lift & cruise eVTOL, and around 50 km for multicopter
eVTOL.
Keywords—eVTOL, flight performance, battery characteris-
tics, energy consumption, range estimation
I. INTRODUCTION
A. State of the Art
The development of electric vertical take-off and landing
aircraft (eVTOL) innovates the whole aviation sector by
challenging it at the same time in terms of safe and secure
integration. Lots of different applications are considered to
be useful in the future. This consideration also includes the
passenger transport performed by eVTOLs, which are bigger
than today’s small electric unmanned aircraft systems (UAS).
The eVTOLs considered in this paper are intended to provide
passenger air taxi services from an origin to a destination
instead of transporting freight. Therefore, lots of manufac-
turers have created eVTOLs for passenger transport, which
have reached different stages of maturity. The operational
parameters range, flight speed, and passenger capacity (incl.
hand luggage) are the most relevant ones [1]. Since there
are only prototypes, there is a lack of detailed information
about network operation capabilities of these new passenger
aircraft. This paper delivers a framework to estimate the power
requirements for three different eVTOL types in each of the
mission flight segments. For each type (vectored thrust, lift
& cruise, and multicopter), the total energy consumption is
derived from the power requirements per flight segment and
transferred into an estimated range. Based on this, specific
flight routes in an urban area can be designed in the future for
recharging requirements to be considered in network planning
exercises.
B. Focus and Structure of the document
As stated before, there is a need to get an overview of
the power requirement to create a realistic picture of UAM
passenger operation in an urban environment. Therefore, sec-
tion II introduces a general flight mission profile for eVTOLs
before giving a short overview of existing eVTOL types.
This section closes with state-of-the-art on characteristics of
batteries, which are used for electric propulsion of eVTOLs.
Within section III, the methodology of performance modeling
is presented. Therefore, this section is divided into the before-
mentioned flight segments, which deliver the equations to de-
termine the required power to perform each of them. In section
IV, the methodology is applied to the different eVTOLs to
show first results on required power per flight segment. At
the end of this section, the required power per segment and
eVTOL is transferred into energy consumption to compare
with predefined values for today’s battery characteristics and
corresponding flight range of each eVTOL type. Within section
V, findings of our power modeling are presented before we
give a short outlook on the usage of our results in future
research within section VI.
II. OP ER ATIONA L BAC KG ROUND
A. General UAM flight mission
In the literature, there are different approaches to sketch
a general UAM mission profile. According to [2], the flight
mission is divided into five segments, namely: take-off, climb,
cruise, descent, and landing. As mentioned by the authors,
this mission profile is simplified because it does not consider
any forward flight during climb and descent, such that there
is potential for further investigation in the future. Within [3]
and [4], the UAM flight mission is extended by taxi segments
before take-off and after landing, as well as transition segments

in order to change eVTOL configuration from vertical (take-
off and landing) to horizontal flight (cruise flight) and vice
versa (see section II-B). The general flight mission is shown
in figure 1, which is adapted from [3] and [4]. In the following,
the segments are explained in more detail:
Fig. 1: General UAM mission profile
The way from point A to B describes the taxiing from the
eVTOL aircraft stand to the touchdown and lift-off (TLOF)
at the departure vertiport. There are different ways how
eVTOLs can perform this segment: hovering flight, rolling on
installed wheels at its landing gear, or via special ground-based
infrastructure that can move the eVTOL across the taxiways
on a skid undercarriage [4].
After the eVTOL reaches the TLOF, the take-off begins
and the eVTOL climbs vertically to a predefined altitude (B
to C), where a first transition/conversion is performed (C to
D). This segment is needed for a configuration change of the
eVTOL. At this point, the eVTOL changes from vertical to
horizontal flight configuration. It is important to note that only
the vectored thrust and lift & cruise eVTOLs do a transition
- multicopters do not (for more details, see section II-B) [4].
From point D to E, the climb segment follows until the
desired cruise altitude is achieved. The cruise flight (E to F)
within an UAM mission is comparable to the cruise segment of
conventional aircraft. In this segment, the altitude should not
change, except potential airspace characteristics or clearances
by local air traffic control (ATC) require such a change [4].
The segment from F to G describes the descent. In [2], [4]
it is assumed that this is done vertically. However, in [3] the
descent is not shown as a vertical descent. The descent stops
at a certain altitude to perform again a transition (G to H) back
from horizontal to vertical flight configuration (if it is assumed
like shown in figure 1). Possibly, a short hover holding could
be necessary next to get final clearances for landing [4] before
a vertical landing (H to I) is performed. After that, again a
taxi segment is assumed to get from the TLOF pad at arrival
vertiport (I) and/or to the corresponding eVTOL aircraft stand
(J).
B. eVTOL aircraft concepts
There are more than 400 aircraft concepts that intend to
take-off and land vertically with pure electric propulsion, but
not every eVTOL listed in [5] is considered as an air taxi (e.g.,
hover bikes). The basic assumption is that taxi services should
consider at least a capacity of two passengers (two seats), well
knowing that one of them is occupied by a pilot on board
at the beginning of operation due to VFR. The classification
of eVTOLs by [5] is focused on the propulsion system and
specifies the one made in [1], which is based on lift production
especially during cruise flight. According to both of them, the
following eVTOL categories can be summarized (see table I).
Propulsion system [5] Cruise lift production [1]
vectored thrust fixed-wing
lift & cruise fixed-wing
multicoper rotary-wing
TABLE I: eVTOL aircraft classification
The used electric propulsion system for eVTOL is called
distributed electric propulsion (DEP) technology, where mul-
tiple electrical units are distributed along the eVTOL and
powered by several electric motors directly, which get their
power from one or more battery packs [6].
eVTOLs with vectored thrust propulsion use any of their
electric engines for both take-off and cruise. Such eVTOLs
have tilting elements (wings or only propulsion units) to adjust
the propulsion vector to the desired direction (vertical for
VTOL and horizontal for cruise). The difference between the
two configurations is shown in figures 2 (vertical configura-
tion) and 3 (cruise configuration).
Fig. 2: Vectored thrust vertical configuration [7]
Fig. 3: Vectored thrust cruise configuration [8]
In comparison to vectored thrust configurations, lift and
cruise eVTOLs have independent propulsion units (one each
for VTOL and cruise) without any vectoring. An example is
given by figure 4:

•the first propulsion unit for the fixed propellers along the
wings, which are responsible for lift generation during
vertical segments, and
•a second one for the pusher propeller in the rear of the
eVTOL, which is for cruise flight.
Due to that, the vertical behavior is expected to be more
efficient in comparison to the vectored thrust concepts. In
the end, both concepts behave like fixed-wing aircraft during
cruise and rely on aerodynamic lift.
Fig. 4: Lift and cruise air taxi [9]
The last eVTOL class mentioned in table I is the mul-
ticopter. This eVTOL class is comparable to conventional
helicopters in terms of flight behavior, except for the missing
tail rotor and multiple horizontally mounted rotors hampering
lower aerodynamic efficiency for the sake of safety and
maneuverability (see figure 5). This is resulting in a high drag
such as flight efficiency during vertical segments, but in a
consequently very limited range when cruise.
Fig. 5: Multicopter air taxi [10]
C. Battery characteristics
Battery technology has already been implemented in other
transport segments. The car industry has presented various
electric cars over the last years which are limited in their
range between 120 km and 500 km (depending on the type of
car) due to lower specific energy (amount of energy per unit
weight) compared to fossil fuels [11]. For electric aviation
and especially for UAM, the operational parameter range is
one of the most relevant ones [1], relying on current battery
technology. Especially energy density is a crucial factor;
lithium-ion batteries reach a value of up to 260 Wh/kg [12].
III. POWE R REQUIREMENTS
Within this section, the methodology for the power mod-
eling of eVTOLs is presented. The focus of our work con-
centrates on unducted lift propellers as it is the case for the
previous presented eVTOLs in section II-B. Therefore, the
equations are delivered per flight segment.
A. Taxi
As mentioned in section II-A, there are several possibilities
to perform taxiing with eVTOLs. In this section, the equations
to perform a ground taxi (Pgt) segment on own wheels and
as a hovering flight (Pht) are formulated. According to [4],
the ground taxi on own wheels requires around 10% of cruise
flight power Pcruise (1).
Pgt = 0.1·Pcruise (1)
The requested power to hover taxi Pht is assumed to be
equal to the power to hover Ph, well knowing that this is a
simplification since there is no forward flight in a nominal
hovering flight. Phis the product of thrust Tand the velocity
vhat the rotor disc according to [13]. In hovering flight, the
thrust Tis equal to the eVTOL’s weight W. Besides, the power
for hovering flight also depends on the disc loading (DL (2)),
which is an important parameter for comparing eVTOLs. It is
defined as the ratio between eVTOL weight and its total disc
area (A). nrotor describes the number of rotors and rrotor is
the radius of every rotor.
DL =W
A=m·g
nrotor ·2πr2
rotor
(2)
With the DL, the air density ρ, and the eVTOL’s weight
Wthe equation for a hovering flight can be written as (3):
Pht =Ph=T·vh=T·sT
2ρA =W·sDL
2ρ(3)
(3) does not consider the loss of power due to profile drag
of the rotor blades. Therefore, a hover efficiency term ηhis
introduced and the required power Pht finally becomes:
Pht =W
ηhover
·sDL
2ρ(4)
The air density ρis considered at mean sea level (MSL).
B. Vertical climb (take-off)
After reaching the TLOF, the following take-off is per-
formed as a vertical climb to the transition altitude. The
required power Pto for this segment is estimated from he-
licopters theory [13] (5).
Pto =Ph·RoCto
vh
+vi
vh(5)

The required power for take-off depends on the power to
hover Ph, the RoC for the vertical climb, the hover velocity
vh, and the induced velocity viin the climb at the rotor disk
plane. During hovering flight, the velocity terms are equal [14].
According to [13], it is possible to define a ratio between them
during the vertical climb (6).
vi
vh
=−RoCto
2vh+sRoCto
2vh2
+ 1 (6)
Substituting (6) into (5) the required power for vertical take-
off Pto is finally delivered in (7).
Pto =Ph·

RoCto
2vh
+sRoCto
2vh2
+ 1
(7)
C. Transition
The next segment is the transition, which is only performed
by vectored thrust and lift & cruise eVTOLs due to their
configuration change from vertical to horizontal flight. Within
this segment, stability has to be preserved while avoiding any
loss of altitude [15]. Generally, the power required for the
transition segment is the sum of several power terms, which
are defined in (8).
Ptrans =Pinduced +Pdrag, rotor +Pdrag, aircraft (8)
The first power term is the induced power Pinduced during
the transition, which considers the tilt configuration by its tilt
angle (Θtilt), propulsive efficiency (ηtrans, and the induced
velocity at rotor disc plane ((9) according to [15]).
Pinduced =W
ηtrans ·sin(Θtilt)
·v
u
u
t−V2
∞
2+sV2
∞
22
+W
sin(Θtilt)·2ρA 2(9)
The second power term Pdrag, rotor describes the power
required to overcome the rotor profile drag, which depends on
rotor geometry (solidity σ), rotor blade drag (Cd) and blade
tip speed (Vtip). The solidity parameter σis defined as ratio
between blade area and rotor disc area (10), with chord c,N
number of blades per rotor and rrotor radius of a single rotor. σ
is the value for one rotor. To get the total value (necessary for
calculating Pdrag, rotor), it has to be multiplied by the number
of rotors nof the eVTOL, which are used for vertical lift
production.
σ=blade area
rotor disc area =N·c·rrotor
π·r2
rotor
·n=N·c
π·rrotor
·n(10)
The parameter µis the non-dimensional velocity at rotor
disc plane and defined by equation 11, where V∞corresponds
to the velocity the eVTOL is expected to gain after transition
(Vclimb, climb out speed; see section III-D). The angle used
in equation 11 describes the angle between the free stream
velocity and the velocity at the rotor disc Vtip. Because of the
tilt mechanism of the rotors at the vectored thrust eVTOL, the
angle is corresponds to the tilt angle Θtilt.
µ=V∞·cos(Θtilt)
Vtip
(11)
Finally, the power required to overcome the rotor profile
drag is delivered in (12) according to [15].
Pdrag, rotor =ρAV 3
tip ·σCd
8·(1 + 4.6µ2)(12)
The last power term of (8) is the power to overcome the
aircraft drag (Pdrag, aircraft) as it gains speed during the transition
phase. It is defined in (13) by multiplication of aerodynamic
drag and the expected velocity after transition V∞(which also
corresponds to later climb out speed Vclimb).
Pdrag,aircr aft = 0.5ρV 3
∞CDS(13)
For lift & cruise eVTOL, no tilt angle can be defined due
to two different propulsion systems - one for vertical and
one for horizontal flight segments (no tilting mechanism).
Following this, Θtilt is not considered in (9) and the ratio
between free stream velocity V∞and velocity at rotor disc Vtip
(µ, (11)) cannot be computed because the propulsion system
for the horizontal flight starts to push the eVTOL during the
transition while the vertical lift propulsion system reduces its
contribution. However, for simplification reason and to use
(12) also for required transition power of lift & cruise eVTOL,
µis set to zero.
The multicopter does not have this flight segment, such that
an instant passage between both flight segments (take-off to
climb) is assumed, similar to helicopter operations.
D. Climb to cruise altitude
The transition is followed by the climb segment, which ends
after reaching the cruise altitude. We assume that the eVTOLs
perform this segment with a constant RoC. It is the product of
climb angle γclimb and the climb out speed Vclimb (horizontal
climb speed), shown in (14).
RoCcl =Vclimb ·sin(γclimb)(14)
The required power within this segment can be simplified
by (15).
Pclimb =T·Vclimb
ηclimb
=Vclimb
ηclimb
·(m·g·sin(γ) + D)
=W
ηclimb RoCcl +Vclimb
L
Dclimb !(15)
In general, it is the product of thrust produced by the
eVTOL and the climb out speed, divided by the propulsive
efficiency (ηclimb). Thrust is approximately resolved into op-
posing drag force and eVTOL weight, dependent on the climb
angle γclimb. By assuming a small climb angle, the weight is
considered to be approximately equal to lift. Then, drag force
can be found by dividing weight by (L/D)climb.

E. Cruise and descent
After reaching the cruise altitude, the cruise segment begins.
It is expected to be the longest segment in terms of time
spent and achieved range/ distance. The required power in this
segment Pcruise is estimated by using a force balance between
lift and eVTOL weight, where the drag is considered equal to
thrust provided by the propulsion system (16).
Pcruise =T·Vcruise
ηcruise
=W·Vcruise
L
Dcruise ·ηcruise
(16)
Within this segment, the aerodynamic efficiency of fixed-
wing eVTOLs is higher than for multicopter. This leads to
minor power consumption.
For simplification reasons, we consider that the cruise seg-
ment also includes the descent phase until the second transition
starts. This is for reasons that there are no precise data
available about the descent segment. Therefore, following [15],
the cruise segment is extended and the cruise performance is
assumed for the whole duration.
F. Second Transition and Holding
For the second transition, the same approach is used as in
section III-C. We assume that the eVTOL reduces its speed to
the end of the cruise segment, starting the descent segment
with the same characteristics as the climb. Therefore, the
deceleration phase is neglected and this segment is performed
as the previous one (8), with v∞equal to descent velocity Vd.
This results in the equation to estimate the required power for
the second transition (Ptrans,2):
Ptrans,2 =W
ηtrans ·sin(Θtilt)
·v
u
u
t−V2
d
2+sV2
d
22
+W
sin(Θtilt)·2ρA 2
+ρAV 3
tip ·σCd
8·(1 + 4.6µ2)
+0.5ρV 3
dCDS
(17)
For lift & cruise, the same assumption is used as in
section III-C while multicopters do not have to perform this
second transition. As mentioned in subsection II-A, the second
transition could be followed by a holding phase, which is
performed by hovering flight (4).
G. Vertical Descent and landing
After the eVTOL is cleared for landing, the vertical descent
can start. Therefore, the eVTOLs use their lift propulsion
system, where the estimated power for vertical descent (Pvd)
has the same definition as the one for the vertical climb (see
equation 18), where instead of the RoC the rate of descent
(RoD) is used.
Pvd =Ph·RoDld
vh
+vi
vh(18)
The only numerical difference is that RoD is negative
because of the downward moving of the eVTOL while thrust
is orientated upwards. Another difference is the definition of
the ratio between induced and hover velocity (19) [16].
vi
vh
=−RoDld
2vh−sRoDld
2vh2
−1(19)
It is noted that the argument under the square root must not
be negative. Following this, (19) only is valid when:
|RoDld| ≥ 2vh(20)
The flight region of −2≤RoD ≤0describes the
vortex ring state, where the flow is turbulent having upward
and downward velocities [16]. To overcome this issue, it is
used an experimental approach by [17]. The corresponding
approximation of the velocity is shown in (21):
vi
vh
=k+
4
X
i=1
kiRoD
vhi
(21)
with k= 0.974, k1=−1.125, k2=−1.372, k3=−1.718,
and k4=−0.655.
H. Energy consumption and range estimation
After defining the power demand for each flight segment, it
is possible to obtain the demand for energy from the battery
pack in each flight segment. Therefore, it is necessary to know
how much time the eVTOLs spend in these segments because
the energy demand of each segment Eiis defined as the
product of corresponding power Piand time ti(22).
Ei=Pi·ti(22)
If nis the number of segments, the total energy consumed
Etot is the sum of all energy terms (shown in (23)). Finally,
it must be checked that the total energy consumed is less than
the total battery energy (see section IV-A).
Etot =
n
X
i=1
Ei=
n
X
i=1
Pi·ti(23)
When the energy demand for each segment is calculated, it
is possible to estimate a corresponding flight range according
to [18]. In general, the range Rcan be defined as the product
of horizontal flight speed v∞and flight time t(24):
R=v∞·t(24)
For electric aircraft, the flight time is equal to the time
to drain the battery, which depends on energy density E∗,
the mass of the battery mbattery, and the power supplied by it
Pbattery (25).
t=mbattery ·E∗
Pbattery
(25)
Substituting (25) into (24) yields:

R=v∞·mbattery ·E∗
Pbattery
.(26)
The released power of the battery depends on the required
propulsive power of the eVTOL Paircraft in cruise flight (for-
ward flight):
Pbattery =Paircraft
ηtot
,(27)
where the Paircraft is linked to its weight, lift over drag ratio
and horizontal flight speed:
Paircraft =Daircraft ·v∞=m·g
L
D·v∞(28)
By substituting (28) into (27), Pbattery becomes:
Pbattery =m·g
L
D·ηtot
·v∞(29)
and can be inserted into (26):
R=v∞·mbattery ·E∗
m·g
(L
D)·ηtot ·v∞
.(30)
The simplification of (30) delivers the range equation for
electric flight of battery powered aircraft (31):
R=E∗·ηtot ·1
g·L
D·mbattery
maircraft
.(31)
IV. MODEL APPLICATION
In this section, the previously presented equations are used
to obtain appropriate results for the required power per flight
mission segment. Therefore, parameters and values are as-
sumed for the presented eVTOL types. For vectored thrust
eVTOL Joby S4 (see figures 2 and 3) is considered, for lift &
cruise the Wisk Cora (former Kitty Hawk, see figure 4), and,
finally, the VoloCity for multicopters (see figure 5). Besides,
appropriate data about battery characteristics are chosen in
accordance to section II-C. The corresponding values are
summarised in table II based on scientific literature or made
by assumptions (see section IV-A).
A. Initial assumptions
The maximum take-off mass (MT O M) of the presented
eVTOLs is adopted from manufacturers data [7] [10] [19]. The
corresponding battery mass is measured in accordance with
[20], where a battery mass ratio of 0.33 is suggested. This
value is confirmed by [21]. The payload corresponds to the
passenger capacity (number of seats). Therefore, it assumed
by 100 kg per seat (passenger incl. hand luggage).
Finding suitable values for both specific energy and specific
power is quite challenging due to various lithium batteries
for different applications. The battery characteristics should
consider the expected higher peak power demand during
vertical segments of vectored thrust eVTOLs, whereas lift &
cruise and multicopter are expected to require more power
during horizontal segments. Following this, the corresponding
values of specific energy (E∗) and specific power (P∗) are
chosen according to [2] and [22] by considering state-of-the-
art battery characteristics (mentioned in section II-C). The
total values for energy and power are found by multiplying
corresponding specific values with battery mass. It should be
noted that the usable power (Puse) and energy (Euse) are lower
compared to total values (Pand E) because of the battery
efficiency ηbattery (due to heating losses; estimated by 0.95)
and the depth of discharge (DoD), necessary to preserve a
certain lifetime of the battery [23]. Especially for longevity,
the DoD represents a key factor, namely the part of the battery
capacity which has been removed from the fully charged
battery. To preserve a certain lifetime, the DoD for current
Li-ion batteries is suggested by 80% [24], so that there is a
remaining battery capacity (state of charge, SoC) of 20%. Due
to safety reasons, UBER [3] defines the minimum reserve by
a remaining SoC of 30%, as it is shown in figure 6 (line 3).
In nominal operating conditions, this minimum reserve SoC
should not drop below this level, whereas it is only allowed
to operate in this condition during a contingency mission.
However, also in contingency missions, the SoC of the battery
has to remain above the battery floor (line 4 in figure 6) as it is
a very unsafe battery condition due to suddenly occurring loss
of battery capacity [3]. To complete figure 6, Line 2 describes
a minimum SoC for an additional take-off/flight and line 1 is
the maximum SoC of the battery, which is decreasing during
operation.
Fig. 6: State of charge overview
For our application, we choose the DoD according to [24]
by 80%. To conclude, the Puse and Euse is then computed by
using (32) and (33).
Puse =P∗·mbattery ·ηbattery ·DoD (32)
Euse =E∗·mbattery ·ηbattery ·DoD (33)
As already shown in section III, there are several efficiency
values per flight segment. These values represent additional
power requirements due to losses of the propulsion system of
the eVTOLs compared to ideal conditions. During hovering
flight, the multicopter has the best efficiency (ηhover) due to its
helicopter-like configuration (assumed at 0.80) [2]. Contrary to
this, the efficiency during the cruise (ηcruise) is the lowest one
compared to the other eVTOLs (assumed at 0.60). The reason
for this is the lift production during the cruise segment (see
table I) and therefore the associated higher performance effort
for multicopters. ηhover for lift & cruise eVTOL is assumed

higher (0.75) than for vectored thrust eVTOL (0.70) because of
its independent propulsion system for vertical segments (DEP,
see section II-B). It is the same reason for a better transition
efficiency (ηtrans) value of the lift & cruise eVTOL (0.70) in
comparison to vectored thrust (0.65). During the cruise, the
vectored thrust eVTOL is assumed to be most efficient with
ηcruise at 0.80. The last one describes the efficiency during the
climb (ηclimb) and is considered to be the mean value between
ηhover and ηcruise.
Concerning the aerodynamic parameters, the values for
lift-drag-ratios during cruise and climb ((L/D)climb and
(L/D)cruise) are taken from [2] and [24], in which calculations
based on geometric characteristics of eVTOLs were performed
in order to estimate the drag coefficient CDof the eVTOLs.
The blade drag coefficient Cdis considered equal for all
eVTOLs and a typical one for helicopters according to [13].
The blade tip speed Mtip has an influence on the acoustic
footprint of the eVTOLs induced by the rotors. In [25], a
maximum value of 0.60 is mentioned, such that we assume
a slightly smaller one. The cruise speed vcruise is based on
manufacturers data [7] [10] [19]. Therefore, it is chosen at
80% of the proposed maximum cruise speed as a kind of econ
reference speed.
The parameters linked to the vertical segments are chosen
as follows: the rate of climb during climb segment (RoCcl)
corresponds to typical values in general aviation [25] and are
also expected for the rate of descent in the descent segment
(RoDdesc), only with a negative sign. The vertical RoC and
RoD during take-off and landing (ROCto and RoDld) are
chosen according to user comfort [4]. The tilt angle Θtilt is
defined as the rotation of lift propellers to pass from vertical
to climb configuration. It is only considered for those eVTOLs
which have to perform the transition segment.
Finally, there are reported parameters related to rotor ge-
ometry and corresponding lift area [24]. From the DL, it is
observable which eVTOL is more efficient in hovering flight
due to low values. For higher DL values, it is required more
power for hovering and vertical segments.
Within the next subsections, the previously described ap-
proach (see section III) to define the power required from the
batteries in each flight segment is presented. The results are
shown in table III and V. It is noted that the presented equation
concerning power consumption is only valid for unducted
rotors, as it is the case for the previously described eVTOL in
section II-B.
B. Power calculation
As described in subsection III-A, the taxiing could be
performed differently by each eVTOL. To make it more
comparable, we assume that the first taxi segment is performed
by a hovering flight (4) and the second one on a potential
installed landing gear (1). Due to the high DL of the vectored
thrust and lift & cruise eVTOLs, the required power for a
hovering taxi flight is much higher than for multicopters.
The required power for the vertical take-off is computed
by using (7). It is depending on the previous calculated Pht
Parameter Vect. Thrust Lift & Cruise Multicopter
M T OM [kg] 2,200 1,200 900
P ayload [kg] 400 200 200
mbattery [kg] 730 400 300
mbattery
MT O M [-] 0.33 0.33 0.33
E∗[Wh/kg] 150 180 180
E[kWh] 109 72 54
P∗[W/kg] 2,100 1,600 1,100
P[kW] 1,533 640 330
ηbattery [-] 0.95 0.95 0.95
DoD [-] 0.8 0.8 0.8
Euse [kWh] 83 55 41
Puse [kW] 1,165 486 251
ηhover [-] 0.70 0.75 0.80
ηcruise [-] 0.80 0.70 0.60
ηtrans [-] 0.65 0.70 -
ηclimb [-] 0.75 0.73 0.70
(L
D)climb [-] 15 12 3
(L
D)cruise [-] 16 13 4
CD[-] 0.039 0.061 0.098
Cd[-] 0.015 0.015 0.015
Mtip [-] 0.55 0.55 0.55
vcruise [m/s] 72 40 24
γclimb [°] 8 8 8
α[°] 8 8 8
RoCto [m/s] 0.5 0.5 0.5
RoCcl [m/s] 4.5 4.5 4.5
RoDld [m/s] -0.5 -0.5 -0.5
RoDdesc [m/s] -4.5 -4.5 -4.5
θtilt [°] 82 - -
n[-] 6 12 18
drotor [m] 1.3 1.0 2.3
A[m²] 8.0 9.4 74.8
S[m²] 11 11 -
N[-] 5 2 2
c[m] 0.3 0.2 0.1
TABLE II: Listed parameters for calculation
(which is assumed equal to the power for hovering flight Ph),
the RoC, and the corresponding vh.vhis taken out of (3).
The results for the first transition are based on (8). It is noted
that only vectored thrust and lift & cruise eVTOLs have to
perform the transition before the climb to cruise altitude may
start. As mentioned in section III-F, the same approach is used
for the second transition. Therefore, the values are equal and
we do not consider an additional holding.
The power required to perform the climb to cruise altitude
is determined by using (15).
As stated in subsection III-E, we assume that the descent
segment is included until the second transition begins. There-
fore, the values are obtained by using (16).
The results of vertical descent and landing are based on (18)
and (21), because RoDld is assumed at −0.5and therefore in
between the region of vortex ring state (−2≤RoD ≤0).
C. Calculation of energy consumption
To compute the energy consumption per flight segment,
it is necessary to define the period each eVTOL spends in
each segment (22). These times tiare assumed and listed in
table IV. Altogether, the whole flight mission is assumed by
1,800 seconds. This results in an energy consumption per flight
segment and total energy for the whole mission as presented
in table V.

Segment Vect. Thrust Lift & Cruise Multicopter
1st taxi 725.07 250.60 54.17
Take-off 732.82 254.55 57.00
1st transition 1,431.09 688.71 -
Climb 191.51 116.01 192.68
Cruise & descent 121.40 51.75 88.29
2nd transition 1,431.09 688.71 -
Landing 708.43 248.48 52.78
2nd taxi 12.14 5.18 8.83
TABLE III: Calculated required power per flight segment [kW]
Segment time ti
1st taxi 30
Take-off 45
1st transition 45
Climb 60
Cruise & descent 1500
2nd transition 45
Landing 45
2nd taxi 30
P1,800
TABLE IV: Time spent in each flight segment [s]
Considering that multicopters do not perform the transition
segment, the following assumptions are made:
•The time for the first transition is included in the climb
segment. Therefore, the climb segment for the multicopter
has a duration of 105 seconds.
•The time for the second transition is included in the cruise
and descent segment, which results in a duration of 1,545
seconds.
Segment Vect. Thrust Lift & Cruise Multicopter
1st taxi 6.02 2.08 0.45
Take-off 9.16 3.18 0.71
1st transition 17.89 8.61 -
Climb 3.20 1.94 5.63
Cruise & descent 50.59 21.56 37.89
2nd transition 17.89 8.61 -
Landing 8.86 3.11 0.66
2nd taxi 0.10 0.04 0.07
P113.71 49.13 45.41
TABLE V: Energy consumption per flight segment [kWh]
D. Range estimation
In this subsection, (31) is used to estimate the range
Rof each eVTOL. According to [18], the total efficiency
ηtotal is expressed as the product of several efficiency terms
(batteries, electric motors, electronic controllers, gearbox, and
propellers). In nominal conditions, ηtotal could reach a value
of about 0.7 [18]. To make it more realistic, in our application
ηtotal is considered by 0.65.
To estimate the range dependent on the calculated energy
consumption, it is necessary to get a corresponding energy
density value for the cruise and descent segment (E∗
cruise). This
is done by modifying (33) with Euse taken from table V for
cruise and descent energy consumption, mbattery listed in table
II, ηbattery = 0.95, and DoD = 0.8. The results for energy
density based on the results of the energy consumption (see
section IV-C) are shown in table VI.
Vect. Thrust Lift & Cruise Multicopter
E∗
cruise 91.19 70.92 166.18
R114.85 72.57 52.32
TABLE VI: Energy densities corresponding to computed
cruise and descent energy consumption [Wh/kg] and corre-
sponding range [km]
V. FINDINGS
A. Power calculation
Compared to vectored thrust and lift & cruise eVTOLs, it
is noted that the multicopter has the lowest power requirement
for a hovering taxi flight due to its helicopter-like configura-
tion. For the following take-off, the required power increases
of about one to 1.5% (vectored thrust and lift & cruise),
whereas the multicopters required take-off power Pto has an
increase of around 5.2%. Within the transition segment, the
required power for vectored thrust and lift & cruise eVTOLs
is higher than the assumed usable power value Puse provided
by the battery. For lift & cruise eVTOL, the required transition
power Ptrans is also higher than the corresponding maximum
power value P, whereas at least this value would fit for
vectored thrust eVTOL resulting in a higher DoD (more than
80%) by falling below the SoC for reserve (see table VII).
These results show that assumed specific power P∗for
vectored thrust and lift & cruise eVTOLs is chosen too low.
Therefore, both eVTOLs would not be able to perform the
transition (peak power demanding segment) with Euse in our
application. The required power for vectored thrust eVTOL
in transition is 22.8% higher than the usable power from the
battery. For lift & cruise eVTOL, it is even 41.7% higher in
this segment. At least this expresses the assumption that this
segment is the most power-consuming one for eVTOLs, which
have to perform this. Contrary to that, the assumed specific
power for the multicopter has a remaining power potential in
the climb segment (peak power demanding for multicopter) of
about 23% (see table VII).
For the climb, the calculation results show that the vectored
thrust eVTOL requires the lowest power from its battery. In
cruise and descent, the multicopter requires about one-third of
its usable power, whereas the other two eVTOLs only need
10%. This is due to their fixed wings and the corresponding
behavior like a normal passenger aircraft (resulting in a much
better lift to drag ratio compared to multicopter). The required
power for vertical landing is quite similar to those of vertical
take-off.
The last segments are the taxi segments. In our application
case, there are two different possibilities to perform these. The
first taxi segment is modeled by hovering flight, which is close
to the values of vertical take-off as already mentioned at the
beginning of this subsection. Then, the second taxi segment
is assumed to be performed on the eVTOLs own landing gear
(wheels), which requires significantly less power.
At this point, it has to be noted that normally, the influence
of the altitude is given by the air density ρwithin the presented
equations in section III. For our application, the influence of

Segment Vect. Thrust Lift & Cruise Multicopter
1st taxi 62.2 51.6 21.6
Take-off 62.9 52.4 22.7
1st transition 122.8 141.7 -
Climb 16.4 23.9 76.8
Cruise & descent 10.4 10.6 35.2
2nd transition 122.8 141.7 -
Landing 60.8 51.1 21.1
2nd taxi 1.0 1.1 3.5
TABLE VII: Required power per segment compared to Puse
[%]
the altitude is fully neglected by calculating with ρequal to
ISA conditions on MSL. Determining the altitude for UAM
passenger operations is challenging due to other existing air
traffic (e.g. arrivals and departures from conventional aircraft,
general aviation, helicopters, gliders) and also depending on
the prospected topography concerning obstacles.
B. Energy consumption
From table V, the results of the energy consumption for
our assumed mission can be obtained. These values have to
be compared to the usable energy Euse (see table II). From
an energetic point of view, the lift & cruise eVTOL is the
only one that could perform the assumed mission. It is noted
that there is a remaining energy capacity of 11% (see table
VIII). Both other eVTOLs would not be able to perform
this mission: the vectored thrust eVTOL requires 37% more
energy in comparison to its Euse and even 4.3% more when
compared to its maximum energy Eprovided by the battery.
The multicopter also requires 11% more energy for the whole
mission by comparing to Euse. However, at least it would be
able to perform the assumed flight mission with maximum
energy Eprovided by its battery. For this case, the multicopter
would have a remaining energy capacity of around 16%.
Vect. Thrust Lift & Cruise Multicopter
Euse [kWh] 83 55 41
Emission [kWh] 113.71 49.13 45.41
Perc. difference +37% -11% +11%
TABLE VIII: Required energy for flight mission compared to
Euse
C. Range estimation
The calculated range Rto the assumed flight mission is
based on the corresponding energy density E∗
cruise. It has to be
noted that this corresponds only to a theoretical range since
there are issues concerning the assumed values for specific
power and energy density of each eVTOL. That is the reason
why none of the presented eVTOLs would be able to reach
this range. Besides, the results in table VI also include the
descent phase in our application. When the range is only to be
considered for the cruise phase, the range would be decreasing.
Based on (31), it can be observed that the range is almost
independent of horizontal flight speed v∞(affects the range
only indirectly via lift to drag ratio). For reaching a higher
range, the following parameters should be maximized:
•battery mass ratio (corresponds to an increasing battery
mass while not increasing the MTOM of the eVTOL),
•energy density (also depending on battery mass),
•lift over drag ratio (for better aerodynamic resulting in
less power/energy consumption), and
•total system efficiency (from the battery to propulsive
power).
Besides, it has to be mentioned that the influence of the
temperature on the range is not considered within our appli-
cation, but we assume that there should be an influence on it
by temperature because it is affecting the battery.
VI. CONCLUSION
Within this paper, we presented a simplified approach to
determine the flight performance of three different eVTOLs,
which are considered to be suitable for air taxi operations
in urban areas. Based on this, we used a set of parameters
to demonstrate the methodology using state-of-the-art battery
parameters. The application shows that these battery parame-
ters (specific power and energy density) are not sufficient in
any case due to the limited battery mass. That is the reason
why there is a need of higher energy densities especially
for aviation application by keeping the mass of the battery
constant. In [26] it is predicted that rechargeable Lithium
batteries with an energy density up to 450 Wh/kg will be
produced by around 2025 (shown in figure 7).
Fig. 7: Battery Development [26]
When these values can be used for aviation applications,
usable energy values will be more than doubled (by assuming
a constant battery mass; see table IX). The predicted range
capabilities are calculated based on Euse, 2025 values in 2025.
The required energy demand is estimated by the ratio of
today’s energy consumption in cruise flight and the total
energy consumption of the whole flight mission for each eV-
TOL (see table V). The resulting values have been converted
into energy densities by using (33) and finally inserted into
(31) for delivering the predicted range capabilities in 2025
(by assuming constant battery masses and efficiency values).
Therefore, higher ranges or/and increased flight frequencies
(more flights on a single battery charge) are assumed in the
future. Based on our values concerning battery technology, it
can be stated that the value of specific power affects and limits
the vertical segments performing capability because these are

Vect. Thrust Lift & Cruise Multicopter
Euse, today [kWh] 83 55 41
Rtoday [km] 115 73 52
Euse,2025 [kWh] 250 137 103
R2025 [km] 261 194 118
TABLE IX: Usable energy today and in the future and
corresponding ranges
the peak power demanding phases (see table III), while energy
density will influence the achievable range (31).
For today, the obtained results will be used in further
research concerning network design for UAM operation. The
results of the range estimation for vectored thrust eVTOL seem
to be more realistic than the corresponding manufacturer’s data
(see [7]). The lift & cruise eVTOL and the multicopter have
higher ranges in our application than the corresponding value
published by manufacturer (see [10] and [19]). Nevertheless,
from an operational point of view, the results can contribute to
an improved image of passenger air taxi services in urban areas
within the framework of UAM due to the shown dependency
on battery characteristics.
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