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Performance and Design Optimization of the F-Helix
eVTOL Concept
Umberto Saetti
Graduate Assistant
Jacob Enciu
Assistant Research Professor
Department of Aerospace Engineering
The Pennsylvania State University
University Park, PA 16802
Joseph F. Horn
Professor
Abstract—The objective of the paper is to study the F-Helix
eVTOL concept. This concept modifies the SH-4 Silvercraft light
helicopter to use electric propulsion and a tip driven rotor. It
is intended to compete with rotorcraft in the light-weight class
and address future urban air mobility needs. The elimination of
shaft driven propulsion is intended to reduce weight and drag in
order to accommodate the added weight of batteries for energy
storage. Once the configuration of the rotorcraft is established,
the design is optimized to produce the least power required
while still meeting the structural and physical constraints of
its components. Next, a simulation model is developed to assess
the rotorcraft performance in hover and forward flight. The
payload/range performance is then evaluated for a typical aerial
urban transportation mission. Finally, the performance of the
eVTOL configuration is compared to the SH-4.
I. INTRODUCTION
A. Background
The increasing capabilities of batteries will soon justify
the transition of light helicopters from fossil fuel to electric
power. Numerous concepts of eVTOL rotorcraft were born
in recent years with the aim to revolutionize urban air mo-
bility. However, most of these concepts are intended to be
fully autonomous, require the development of entirely new
platforms, and will have to wait for the development of ad-
hoc regulations to become operational. Further, the majority
of concepts are based on small distributed propellers with
low inertia, which raises questions about their autorotation
capabilities. This paper focuses on the study of an eVTOL
concept that is intended to compete with existing rotorcraft of
the light weight class, and to address the problem of urban air
mobility. Some distinguishing features of the concept presented
are: it is a piloted rotorcraft, it is based on an existing platform,
and it is capable of performing an autorotation.
B. The Initial F-Helix eVTOL Concept
F-Helix is intended to be a 1-6 seats fly-by-wire electric he-
licopter that aims to compete with rotorcraft of the same weight
class [1]. The concept, as shown in Fig. 1 is based on the idea
of reducing initial cost, simplifying maintenance, and being
environmentally friendly. The F-Helix concept is powered by
two electric ducted fans (eFans) mounted on a “power-mast”
connected to the rotor hub. Lift is entirely generated by its two-
bladed rotor. The absence of torque exchanged between the
fuselage and the main rotor greatly reduces the yaw moment
required to trim and control the aircraft, such that small fans
can replace the tail rotor and no tail boom is required. The
removal of the tail boom reduces weight and drag, and allows
the rotor mast height to be reduced. The main transmission
is eliminated leading to lower air frame weight and reduced
maintenance costs. The weight saved this way is allocated
to the battery pack powering the eFans, thus justifying the
all-electric approach. Unlike other current eVTOL concepts,
F-Helix has a low disk loading and a relatively high rotor
inertia, which makes it capable of autorotation. Lastly, F-Helix
is based on an existing platform: the Silvercraft SH-4. Table I
shows the general characteristics of the SH-4.
TABLE I: Silvercraft SH-4 characteristics and performance.
Description Value
Main rotor radius 14.815 ft
Main rotor angular speed 410 RPM
Capacity 1 pilot + 2 passengers
Empty weight 1142 lbs
Maximum takeoff weight 1900 lbs
Power installed 235 shp (derated to 170 shp)
Maximum speed 87 kts
Cruise speed 63 kts
Range 200 mi
Endurance 3 hr
Service ceiling 15090 ft
Rate of climb 1180 ft/min
C. Motivation
It is necessary to understand whether the eFan configu-
ration is advantageous with respect to a standard helicopter
configuration with an electric motor in place of an internal
combustion engine, which will be referred to as an “electric
SH-4”. The F-Helix configuration retains the frame and main
rotor of the SH-4 (456 lbs) but eliminates the internal com-
bustion engine (Franklin SA-350, 307 lbs), transmission, tail
boom, and tail rotor (480 lbs); however it adds a power mast
and eFans (estimated weight of 200 lbs), and either a liquid or
(a)
(b)
Fig. 1: (a) Silvercraft SH-4, (b) F-Helix eVTOL initial
concept.
solid-state Li-Ion battery pack are added (1062 lbs, and 665
lbs, respectively). The electric SH-4 eliminates the combustion
engine but retains the transmission, tail boom, and tail rotor,
and adds an electric engine similar to a Siemens SP55D (100
lbs) used on the Siemens eAircraft [2], and either a liquid or
solid state battery pack. Comparing the configurations that use
the liquid battery pack, the ratio between the weight of an
electric SH-4 and the weight of the F-Helix concept is 1.23.
Since the power required (P) to hover is proportional to the
weight (W) of the rotorcraft in the following way: P α W 3/2,
the ratio of the power required by the two configurations is
1.233/2= 1.37. This means that the F-Helix concept using
a liquid battery pack is competitive with the electric SH-4
if the power losses associated with using the eFans are less
than 37%. Comparing the configurations that use the solid-
state battery pack, the ratio between the weight of an electric
SH-4 and the weight of the F-Helix concept is 1.31. This leads
to a ratio of the power required by the two configurations of
1.313/2= 1.5. This means that the F-Helix concept using a
solid-state pack is competitive with the electric SH-4 if the
power losses associated with using the eFans are less than
50%. The first part of this study assesses the power required
by the eFans and thus whether the F-Helix concept is justified.
D. Objectives
The objective of the paper is to validate the configuration
of the F-Helix eVTOL concept. Once the configuration of
the aircraft is established, the design is optimized to produce
the least power required while still meeting the structural
and physical constraints of the various components. Next, the
performance in hover and forward flight and the payload/range
performance for typical missions are assessed and compared
to the existing rotorcraft.
II. DESIGN OPTIMIZATION
A. Problems with the Initial Design
One concern about the initial design is that the eFans would
have to operate under very high centrifugal loads. The eFan
centrifugal acceleration is given by:
ac=reFanΩ2(1)
where reFan is the eFan radial location and Ωis the main rotor
angular speed. For an eFan located at a radial distance equiva-
lent to the main rotor radius, the centrifugal acceleration would
be in the order of thousands of g’s. Under these conditions
the loads on the bearings of fan and motors could possibly
create excessive friction and therefore lead to substantial power
losses. This effect can be reduced by lowering the main rotor
angular speed and moving the eFans inboard. Lowering the
main rotor RPM has the added benefit of reducing noise and
improving performance. The added inertia of the eFans will
offset the autorotation performance (i.e. can have the same
energy index with lower RPM).
The structural integrity of the eFan nacelles is also a matter
of concern with the eFans operating under high centrifugal
loads. Although ducted fans require less power compared to
unducted rotors of the same area to produce the same static
thrust, these power benefits tend to decrease with increasing
axial flow. Since the eFans are effectively operating in axial
flow, the benefits of using ducted fans may not be justified.
Further, the eFan nacelles would contribute to the profile drag
of the rotor and to the overall frontal drag of the aircraft. It is
thus decided to abandon the ducted fans in favour of unducted
rotors.
Since the eFans spin in a rotating frame (main rotor), they
would produce a large gyroscopic moment in the direction of
the power-mast:
Mgyro =IpropΩeFan Ω(2)
where Iprop is the propeller moment of inertia, and ΩeFan is the
eFan angular speed. To counteract the gyroscopic moment, it
is decided to mount two counter-rotating coaxial propellers so
that the overall gyroscopic moment is zero.
Since there is no torque exchanged between the main rotor
and the fuselage, the tail rotor is only used for maneuvering
purposes and for providing stability in the yaw axis. Given
that the aircraft is symmetric, in trimmed flight the tail rotor
has to provide a lower amount of thrust. Since the tail rotor
would have to provide thrust in both directions, when the
thrust direction changes, the wake rotor inflow has to reverse
directions. This would lead to an undesired delay in the control
action. For this reason, it is chosen to use two counter-rotating
fixed-pitch ducted fans that provide thrust in each direction.
These ducted fans will be referred to as “yaw fans”. The
amount of thrust in each direction is controlled by the angular
speed of the yaw fans. To eliminate time delays due to rotor
inflow development, so that the yaw fans are able to produce
instantaneous thrust, the yaw fans are chosen to rotate at an
idle speed that overall creates zero yaw moment.
Once the configuration of the aircraft is established, the
design is optimized to produce the least power required in
hover while still meeting the structural and physical constraints
of the various components.
B. Power Required by eFans in Hover
The first step towards the optimization is the theoretical
development of the power required by the eFans in hover. The
main rotor power required to hover is calculated by means of
momentum theory:
PMR =ρAΩ3R3 kC3/2
T
√2+1
8σCD0!(3)
where:
ρis the air density, Ais the rotor disk area,
Ωis the rotor angular speed, Ris the rotor radius,
kis the induced power correction factor,
CTthrust coefficient based on the weight of the rotorcraft,
σis the rotor solidity, and
CD0is the section profile drag coefficient.
In addition to the power required by the main rotor, the
eFans are required to provide enough power to overcome the
aerodynamic drag arising from the power mast. The power
dissipated by the aerodynamic drag of the power mast, assum-
ing the same profile power coefficient and chord of main rotor
blades, is calculated in a similar fashion to the profile power
of a rotor [3]:
Pmast =1
4ρΩ3cCD0r4
eFan (4)
The total power required by each eFan for the rotorcraft to
hover is:
PeFan =PMR +Pmast
2(5)
The thrust required by each eFan is:
TeFan =PeFan
ΩreFan
(6)
C. Coaxial Propeller in Axial Flow: Momentum Theory
To understand the power required by the eFans electric
motors in hover, the equations that describe a ducted fan in
an axial flow are derived, thus expanding the theory in [3].
The eFans can be idealized as coaxial propellers operating in
a constant axial flow, as shown in Fig. 2. The far upstream
velocity relative to the eFan upper rotor, or axial flow velocity,
in hover is:
Vc= ΩreFan (7)
To understand the power required by the electric motors
spinning the eFans, the equations that describe a coaxial rotor
in an axial flow have to be derived, thus expanding the theory
in [3]. Assuming that the thrust produced by each eFan is
equally split between the upper and lower rotor, the induced
velocity on the upper rotor is:
vu=−Vc
2+sVc
22
+TeFan
4ρAeFan
(8)
Fig. 2: Flow model assumed for coaxial propellers in axial
flow using momentum theory. Illustration modified from
Leishman [3].
where AeFan is the area of each propeller. The upper and lower
propellers are assumed to be equal in size and shape. The total
power required by the upper rotor is:
Pu=kTeFan
2(Vc+vu) + 1
8ρNBeFan Ω3
eFanceFanCD0eFanR4
eFan (9)
where:
NBeFan is the number of blades of each eFan propeller,
ceFan is the eFan blade chord, and
CD0eFan is the profile drag coefficient of the eFan blades.
The average far upstream velocity of the lower eFan rotor is
Vc+vu, which leads an induced velocity on the lower rotor
of:
vl=−1
2(3vu+Vc) + 1
2q(3vu+Vc)2+ 8v2
u+Vcvu(10)
The total power required by the lower rotor is:
Pl=kTeFan
2(Vc+vl) + 1
8ρNBeFan Ω3
eFanceFanCD0eFanR4
eFan (11)
The total power required by each eFan electric motor is:
Pmotor =Pu+Pl;(12)
The propulsive efficiency of each eFan is given by:
η=TeFanVc
Pmotor
(13)
D. Coaxial Propeller in Axial Flow: Blade Element Momen-
tum Theory (BEMT)
Momentum theory is useful for estimates of the power
required but for more detailed information such as the dis-
tribution of lift or angle of attack on the rotor blades it is not
sufficient. Thus, Blade Element Momentum Theory (BEMT)
is developed for the case of coaxial propellers in axial flow.
BEMT is a hybrid method that combines basic principles from
blade element and momentum theory approahes [3]. Consider
the application of the conservation laws to an annulus of a rotor
disk. The incremental thrust on the annulus in nondimensional
quantities is:
dCT= 2awλ(λ−λc)rdr (14)
where:
awis a wake contraction parameter,
λis the total inflow ratio of the eFan, and
λcis ratio between axial velocity and eFan blade tip speed.
By means of the equivalence between the circulation theory of
lift and the momentum theory of lift:
dCT=σCLα
2(θr2−λr)dr (15)
where θis the blade element pitch angle and CLαis the lift
curve slope on the blade profile. Equating the incremental
thrust coefficients from the momentum and blade element
theories one finds that:
λ(r, λc) = λc
2−awσeFanCLα
8+
sλc
2−awσeFanCLα
82
+awσeFanCLαθ(r)r
4(16)
Equation 16 allows for a solution of the inflow as a function of
radius and climb velocity for any given blade pitch, blade twist
distribution, planform (chord distribution), and airfoil section.
Once the inflow is obtained, rotor thrust is found by integration
across the rotor disk using:
CT=Zr=1
r=r0
dCT(17)
The power coefficient is:
CP=Zr=1
r=r0
λdCT+σeFan
2Zr=1
r=r0CD0+d1θ−λ
r+
d2θ−λ
r2r3dr (18)
as for most airfoils the sectional drag coefficient below stall
can be approximated by:
CD=CD0+d1α+d2α2(19)
where αis the angle on attack of each blade element. In
this particular appliccation the equations of BEMT are solved
numerically. This allows flexibility to incorporate arbitrary
variations in twist. The two variations considered are ideal
twist:
θ(r) = θ0
r(20)
and linear twist:
θ(r) = θ0+θtw(1 −r)(21)
Blade pitch, θ0, is obtained iteratively via bisection method to
obtain the required value of thrust coefficient. BEMT is applied
separately to the upper and lower eFan rotors with climb ratios
of respectively:
λcu=Vc
ΩeFanReFan
(22a)
λcL=Vc
ΩeFanReFan
+λu(22b)
The wake contraction parameter awis taken as 0.5 since the
eFan propellers are unducted [3].
E. Yaw Fans Design
Since the yaw rate response can be idealized as a first order
system, the required yaw acceleration is given by the ratio of
the desired yaw rate and the time constant of the system:
˙r=rmax
τ(23)
Values of the desired yaw rate are reported in the large-
amplitude heading changes guidelines from ADS-33E-PRF
specifications [4]. Assuming that the furthest yaw fan from
the CG has negligible thrust at idle angular speed, the yaw
acceleration can be related to the yaw fan distance from the
CG and to its thrust by the following equation:
˙r=TyFanlyFan
Izz
(24)
where Izz is the moment of inertia of the aircraft around the
vertical (z) axis. Since the thrust is proportional to the radius of
the yaw fan, an optimization can be carried on to determine the
optimal radius and distance from the CG that minimize the yaw
fans power while providing the necessary yaw acceleration.
F. Optimization Results
This section illustrates the results from the optimization of
the eFan radial location, radius, and angular speed to minimize
the power required from the electric motors spinning the eFans
in hovering condition. The variables to be optimized relative
to the eFans are the radial location, radius, number of blades
and angular speed. For each combination of radial location
and radius, the eFan angular speed is chosen to minimize the
power required by the eFan while guaranteeing that the angle
of attack along the blade span does not exceed 10 deg. This
prevents the blade to operate in stall conditions, with some
margin. Figure 3(a) shows how the power required changes
with varying eFan radial location and radius. Most notably,
the initial configuration with the eFans at a nondimensional
radial location of reFan = 1 would require approximately 105
shp to hover at maximum gross weight. It is suggested that the
initial configuration is modified such that eFans are located
at reFan = 0.54Rand have a radius of ReFan = 1.4ft. This
also has the positive side benefit of lowering the centrifugal
loads acting on the eFan. For this configuration, the ratio of
total power required by eFans electric motors and the power
required to spin the main rotor only is 1.23. This indicates that
for a constant weight, the F-Helix concept using eFans requires
(a)
(b)
Fig. 3: eFan optimization results: (a) power required and (b)
optimal angular speed with varying radial location and radius.
1.23 times the power that the main rotor only would need to
hover (less than a value of 1.37 derived in the Motivation
section). Figure 3(b) shows the optimal eFan angular speed
with varying eFan radial location and radius. The optimization
results are reported in Table II. The corresponding performance
in hover at maximum takeoff weight (1900 lbs) and sea level
standard day conditions are reported in Table III. Minimum
power is approximately 80 shp per eFan, for a total of 160
shp. The required thrust for each eFan 106 lbs. It is concluded
that the F-Helix concept using eFans is advantageous, from a
power required standpoint, with respect to a standard helicopter
configuration that uses an electric engine in place of an internal
combustion engine.
The variables to be optimized relative the yaw fans are
their radius and location along the aircraft longitudinal axis.
The assumed rotor solidity, number of blades, and maximum
angular speed are respectively 0.3, 8, and 10000 RPM (ap-
proximately 1050 rad/s). Since the yaw fans are ducted, the
TABLE II: eFan optimization results.
Parameter Description Value
reFan eFan radial location 8 ft
ReFan eFan radius 1.4 ft
NBeFan eFan number of blades 4 per propeller
ceFan eFan blade chord 0.174 ft
ΩeFan eFan angular speed 2510 RPM
TABLE III: F-Helix performance in hover.
Parameter Description Value
PeFan eFan power required 80 shp
Preq total power required 160 shp
TeFan eFan thrust 106 lbs
ηeFan propulsive efficiency 83 %
wake contraction factor awis assumed to be 1.25 [3]. For this
particular application, the maximum desired yaw rate is chosen
to be rmax =±9.5 deg/s. A common value for the time constant
for civil rotorcraft is τ=0.4 s. The study is approached with
BEMT and is effectively a trade-off between distance from
the CG (assumed to be located on the main rotor vertical axis)
and the yaw fan center. Figure 4 shows the minimum radius
to provide the necessary yaw acceleration while guaranteeing
that the angle of attack along the blade span does not exceed
10 deg. Although the power required to have the necessary
control authority decreases with increasing distance from the
CG, increasing distance from the CG leads to a longer and
heavier fuselage. For this reason, the distance from the CG of
the closest yaw fan is chosen to be 6 ft. The corresponding
minimum radius is 0.9 ft. Since the yaw fans amount of thrust
is obtained by solely varying the angular speed, the yaw fans
operate at constant thrust and power coefficient. The yaw fan
thrust and power coefficients are respectively 2.2e-2 and 3e-
3. Peak power required by the yaw fans is about 20 shp. This
would be at maximum yaw moment at the start of the yaw rate
step. For an assumed idle speed of 500 RPM (approximately
52 rad/s), the power required by each yaw fan is 0.013 shp,
which is negligible when compared to the power required by
the eFans.
Considering the results from the design optimization, a
rendering of the updated F-Helix concept is obtained and
showed in Fig. 5.
III. ROTOR CR AF T SIMULATION MOD EL
A simulation model of the helicopter is required to provide
a rigid body six degree of freedom simulation for evaluation
of the trim conditions and the basic stability and control
characteristics as well as the future design of an automatic
flight control system (AFCS) for the eVTOL configuration.
The helicopter is modeled as a six degree of freedom rigid
body. The model is first developed for a conventional single
main rotor helicopter and then modified to account for the
specifics of the eVTOL configuration. The simulation model
is broken down into modules representing the main and tail
rotors, the fuselage, the horizontal stabilizer and the vertical
tail. The main and tail rotor models were formulated using
Fig. 4: Yaw fans optimization results.
Fig. 5: F-Helix final concept.
a quasi-steady tip path plane model that is developed using
analytical integrations of the blade element equations. The Pitt-
Peters model [5] is used for the prediction of the dynamic
inflow components of the main and tail rotors. The rotor
model neglected the lead-lag dynamics as its effect on the
rotorcraft trim and primary stability and control characteristics
are secondary. The resulting closed form model allowed an
efficient calculation of the quasi-steady flapping angles of
both rotors and the forces and moments produced by them.
Static aerodynamic models were developed for the prediction
of the aerodynamic loads produced by the fuselage, horizontal
stabilizer, and vertical tail. Simplified wake models were
incorporated to simulate the effect of the main and tail rotor
wakes on the empennage components. The resulting equations
of motion of the rotorcraft can be represented as a nonlinear
dynamical system:
˙
x=F(x,u)(25)
where xis the state vector comprised by the rigid body states
(inertial velocity and angular rates in body fixed axis, and Euler
angles) and the main and tail rotor inflow components:
xT= [u v w p q r φ θ ψ (λ0λ1cλ1s)MR (λ0λ1cλ1s)TR]
(26)
and uis the control vector including the lateral and longitu-
dinal pitch command, the collective pitch, and the tail rotor
pitch:
uT= [A1cB1cθ0θTR](27)
A. Conventional Helicopter Model
As production of the Silvercraft SH-4 has ceased in the
late 1970s, only very basic engineering data could be tracked
down and used. Therefore, the bulk of the data required
for the assembly of the rotorcraft aeromechanical database
is collected from two publicly available sources: the specific
airworthiness specification for the SH-4 [6] and 1976-1977
edition of “Janes all the Worlds Aircraft” [7]. The fuselage
aerodynamic coefficients were approximated by using the
aerodynamic model of the UH60 Black Hawk fuselage of
Ref. [8] as a representative conventional fuselage shape. The
aerodynamic data is adapted to the SH-4 by using the main
rotor radius and disk area as the reference length and area,
respectively, for the nondimensional aerodynamic coefficients.
The horizontal stabilizer and vertical tail drag, lift and pitch
moments were estimated using simple finite wing models. The
performance data given in Ref. [7] for the SH-4 were for a
Franklin 6A-350-D1B engine derated to 170 shp (127 kW). To
allow prediction of the power available and fuel flow data of
the SH-4 for performance calculations, the data of an internal
combustion engine with a similar available power is used.
Therefore the data for a Lycoming HIO-360-B engine with
a normal rated maximum power available of 168 shp (125
kW) were utilized for building the power available and fuel
flow database. The data is retrieved online from the O, HO,
IO, AIO, HIO, TIO-360 Series Operators Manual [9].
B. eVTOL Rotorcraft Model
The simulation model for the F-Helix eVTOL configuration
is created by modifying the conventional SH-4 model. The tail
boom, horizontal stabilizer and vertical tail components were
removed from the model and the tail rotor model is replaced
by a pair of yaw fans to provide yaw control to the rotorcraft.
As described earlier, the idle speed of the yaw fans is assumed
to be 500 RPM. However, in order to maintain a net zero yaw
moment contribution by the fans at idle speed, the rear fan idle
speed is set to 484 RPM to account for its longer arm about the
rotorcraft center of gravity. The aerodynamic model of the F-
Helix fuselage is modified by reducing the drag, side, and and
lift forces by 19% to account for the removal of the tail boom
and for the smoother aerodynamic shape of the new fuselage in
comparison to that of the original SH-4. The reduction factor is
determined based on estimates of the expected drag reduction
due to the removal of the tail boom was confirmed by the data
in Table 6.1 of Ref. [3]. The aerodynamic pitch moment of
the new ellipsoid shaped fuselage was evaluated using slender
body theory:
M=1
2q∞kV sin 2α(28)
where:
Vis the fuselage volume,
kis the form factor,
q∞is the dynamic pressure, and
αis the fuselage angle of attack.
This new model replaces the aerodynamic pitch moment
coefficient that was used for the SH4. The lateral-directional
force and moment coefficients of the SH-4 were not modified
for the eVTOL configuration.
The electric power available for performance calculations
of the F-Helix is assumed to be independent of ambient
conditions. The power available to the eVTOL configuration
is assumed to be limited to 200 kW (268 shp). The amount
of electric energy available to the rotorcraft is determined by
the number and specific energy of the batteries carried by the
rotorcraft.
C. eFan Dynamic Inflow Model
Each eFan is constituted of two counter-rotating coaxial
propellers attached to a mast spinning with the main rotor.
In case of forward flight, the incident and parallel velocity
to each propeller change with rotor azimuth ψMR. Consider
now a reference eFan. The upper rotor propeller is subject to
both axial and tangential flow. The resulting climb and advance
ratios for the upper rotor are given by:
λcu=ΩreFan +V∞sin ψ
ΩeFanReFan
(29a)
µu=V∞cos ψ
ΩeFanReFan
(29b)
where V∞is the absolute speed of the aircraft and ψis the
azimuth angle of the reference eFan. Assuming that the lower
rotor acts in a region where the wake of the upper rotor is fully
developed, the incident velocity to the lower rotor is taken as
the average between the upper rotor wake velocity, acting on
the inner part of the rotor, and the incident velocity to the
eFan, acting on the outer part of the rotor. The resulting climb
and advance ratios for the lower rotor are:
λcL=λu+ΩreFan +V∞sin ψ
ΩeFanReFan
(30a)
µl=µu(30b)
where λuis the inflow of the upper rotor. Each propeller
is modelled with a 1-state inflow model similar to the one
described in [5]. The general form of the inflow model is:
˙
λ=−3
4πV λ +3
8πΩCT(31)
where:
λis the rotor inflow,
Ωis the rotor speed,
CTis the thrust coefficient, and
Vis a function of climb ratio, advance ratio, and inflow.
Vis given by the following equation:
V=µ2+ (λc+λ)(λc+ 2λ)
pµ2+ (λc+λ)2(32)
Since the eFans are collocated opposite to each other, the
second eFan will operate at an azimuth angle (ψ+π). This
leads to a 4-state nonlinear system describing the inflow of
the upper and lower propellers on each eFan. The thrust
coefficients are calculated by means of BEMT.
IV. PERFORMANCE
The current section presents the results of the trim, point
performance and mission performance analyses performed.
Trim results were obtained using the dynamic simulation mod-
els of the SH-4 and F-Helix. Databases of the power required
for hover and cruise were then compiled for point and mission
performance calculations. The Lycoming HIO-360-B engine
power available and fuel flow database is used for the SH-
4. For the F-Helix eVTOL configuration, the maximum power
available is assumed constant for all ambient atmospheric con-
ditions as described earlier. The following subsections present
the analysis results. Unless specified otherwise all the results
presented correspond to sea level standard day conditions (0
ft, 15◦C).
A. Trim Analysis
The trim analysis results are presented for the maximum
takeoff weight of 1900 lbs. For the SH-4, the longitudinal
center of gravity (CG) is assumed to be positioned halfway
between the forward and the aft CG limits. This puts the CG
0.33 ft forward of the main rotor mast. For the F-Helix the
longitudinal CG is assumed to be located below the main rotor
mast. It is assumed that the rotorcraft could be balanced to
this CG position during the detailed design process through
proper arrangement of the rotorcraft subsystems and payload
distribution.
Figures 6(a)-(f) present the rotorcraft trim attitude angles
and control commands as a function of airspeed for straight
and level flight. Figure 6(a) shows the fuselage trim pitch angle
as a function of airspeed. The results for the SH-4 conventional
configuration show that the pitch angle in hover is negative, a
result of the CG position being forward of the main rotor mast.
Moving from hover into forward flight the pitch angle first
increases with airspeed and then decreases. The initial positive
gradient of the slope is due to the pitch up moment produced
by the horizontal stabilizer. At higher airspeeds the main rotor
disk is tilted forward to overcome the fuselage drag and the
resulting nose down pitching moment produced by the main
rotor counters the nose-up pitch moment of the horizontal sta-
bilizer. In comparison, the hover pitch attitude of the F-Helix
is close to zero due to the location of the CG below the main
rotor mast. As the F-Helix configuration does not include a
horizontal stabilizer, the fuselage pitch angle is monotonically
decreasing with airspeed due to the need to tilt the main rotor
disk forward to overcome the increasing fuselage drag. The
comparison between the two rotorcraft configurations shows
that the F-Helix configuration should be more convenient for
the passengers due to the lower absolute values of the fuselage
trim pitch angles during hover and forward flight. Figure 6(b)
compares the fuselage roll trim angle of the two configurations.
Unlike the conventional configuration that shows a negative
trim angle at all airspeeds the eVTOL configuration has a trim
roll angle that is always close to zero. The difference in roll
angle between the two configurations is due to the elimination
of the tail rotor from the eVTOL configuration. Since the net
yaw fan thrust in trimmed flight is essentially zero, the aircraft
trims symmetrically, with no lateral tilt of the main rotor
required to balance the side force from the tail rotor. Figures
6(c)-(f) present the trim control commands: collective (θ0),
lateral cyclic (A1c), longitudinal cyclic (B1c) and tail rotor
pitch (θTR), respectively. To allow comparison of yaw control
commands between the two configurations the eVTOL yaw
fan RPM commands were converted to equivalent tail rotor
pitch commands using a conversion factor of 1124 RPM/deg.
This value is derived by assuming that 50% of the tail rotor
pitch travel (8.9 deg) corresponds to a maximum yaw fan RPM
of 10,000. The collective command for both configurations
shown in Fig. 6(c) follows the expected “bell shape” of a
conventional rotorcraft. The eVTOL configuration requires a
smaller collective pitch than the conventional configuration
due to the reduced fuselage drag following the removal of
the tail boom, horizontal stabilizer, vertical tail and tail rotor.
The lateral cyclic pitch command in Fig. 6(d) (positive to the
right) reflects the increasing right tilt of the main rotor disk
with airspeed that has to be countered by a left cyclic pitch
command. The longitudinal cyclic pitch command (Fig. 6(e)),
follows the trend explained earlier for the fuselage trim pitch
angle. The negative apparent longitudinal stability of the SH-
4 at airspeeds between 30 KTAS and 39 KTAS is a result
of the main rotor wake effect on the horizontal stabilizer. In
comparison, the F-Helix shows apparent positive stick stability
throughout the flight speed envelope. Finally, figure 6(f) that
shows the tail rotor pitch command as a function of airspeed
demonstrates the advantage of eliminating the tail rotor in the
eVTOL configuration. As the power to drive the main rotor
shaft is transmitted directly through the eFans, no torque is
transmitted to the fuselage. Therefore, the power required to
turn the tail rotor in a conventional rotorcraft is saved and
only a small amount of yaw control is required to balance
the contribution of the fuselage aerodynamic loads to the yaw
moment about the rotorcraft CG.
B. Point Performance
Hover out of ground effect (OGE) and forward flight
performance were calculated for both configurations and are
compared in the current subsection. The objective of the
comparison is to point out the key differences in point per-
formance between the conventional rotorcraft and the eVTOL
configuration. The torques required for hover and forward
flight were first calculated using the simulation models for
both configurations. The simulation model for the SH-4 is then
tuned to match the performance data of Ref. [7]. Specifically,
the maximum hover weight is matched by tuning the rotor
blades profile drag coefficient (CD0) and induced power factor
(k) and the “economic cruise speed” (speed for maximum
range) is matched by adjusting the horizontal equivalent flat
plate area (EFPA) of the fuselage. For the calculation of the F-
Helix performance the same values for main rotor parameters
were used, and the fuselage drag is reduced as explained earlier
to account for the removal of the tail boom. The following
figures present the point performance results for the light gross
weight of 1300 lbs and the maximum takeoff gross weight of
1900 lbs. Torques are presented in torque gage units assuming
that 100% torque corresponds to 170 shp at the nominal rotor
rpm of 418 RPM.
Figure 7 presents the torque required to hover OGE at sea
level standard atmospheric conditions. The results show that
while for low weights the F-Helix requires less power to hover
than the SH-4, in most gross weights the eVTOL configura-
tion is less efficient in hover compared to the conventional
rotorcraft. The gain in torque required due to the elimination
of the tail rotor is the reason for the better performance of
the F-Helix at very low gross weights. However, as weight is
increased this gain is quickly overcome by the increased power
demand of the eFans in comparison to the power required to
turn the main rotor when using an internal combustion engine.
At the maximum takeoff weight of 1900 lbs, the weight to
power gradient of the F-Helix is 4 lbs/shp compared to the 10.7
lbs/shp of the SH-4. Figure 8 shows the power available for
both configurations in various atmospheric conditions. While
the performance of the internal combustion engine decreases
with increasing pressure altitudes and ambient temperatures,
the power output of the batteries of the eVTOL rotorcraft
is approximately independent of ambient conditions, thereby
largely reducing the strong dependence of hover performance
on ambient conditions that is “traditional” in conventional
rotorcraft. As explained earlier, for the current research it is
assumed that the batteries could provide at least a maximum
power output of 200 kW (158% torque gage units) and that this
amount of power could be absorbed by the main rotor shaft.
Figure 9 combines the information presented in Figs. 7 and 8
to present the maximum weight for hover OGE in international
standard day (ISA) and international hot day (ISA+20◦C)
atmospheric conditions. It can be seen that the use of an
electric power source weakens the effect of ambient conditions
on the maximum takeoff weight. While in standard conditions
the conventional rotorcraft can takeoff at the maximum al-
lowed weight of 1900 lbs only near sea level, the eVTOL
configuration extends this capability to a pressure altitude of
4000 ft. The advantage of the eVTOL configuration in terms
of the maximum hover weight is even more apparent in hot
day conditions where the conventional rotorcraft is limited
to a maximum takeoff weight of 1780 lbs. In comparison,
the eVTOL configuration maintains the capability to take
of at the maximum allowed gross weight up to a pressure
altitude of 1700 ft. An increase of the maximum power output
limit of the batteries (which is artificially set) would increase
this capability further. It can be concluded that while the
aerodynamic hover performance of the eVTOL configuration is
inferior to that of the conventional rotorcraft, this disadvantage
is overcome by the significantly higher power output that can
be obtained by using an electric power source and by the
fact that this power output has practically no lapse rate with
ambient atmospheric conditions. As the vehicle is intended
mainly for urban air mobility in which the hover segments of
the typical mission are relatively short it seems that the higher
power required for hover of the eVTOL configuration is not a
concern.
Figures 10 and 11 summarize the results of the forward
flight performance of the F-Helix versus the SH-4. In Fig. 10
the torque required for straight and level flight are presented for
both configurations for the light gross weight and maximum
takeoff gross weight of 1300 lbs and 1900 lbs, respectively.
It can be observed that the torque required for cruise of the
eVTOL configuration is lower in significant portions of the
flight envelope. The improved cruise performance of the F-
Helix in these speeds is attributed mainly to the reduction in
the fuselage parasite drag due to the removal of the tail boom,
tail rotor and aerodynamic surfaces and the smaller pitch down
trim angle. At the lower and higher airspeeds the eVTOL
torque required increases above that of the SH-4 due to the
reduced propulsive efficiency of the eFans in comparison to
(a) (b)
(c) (d)
(e) (f)
Fig. 6: Trim attitude and control commands for standard day atmospheric conditions, 1900 lbs.
Fig. 7: Torque required for hover OGE in standard
atmospheric conditions.
Fig. 8: Torque available for various atmospheric conditions.
Fig. 9: Maximum hover weight OGE for standard day and
hot day atmospheric conditions.
that of the internal combustion engine overcoming the benefit
of the reduced parasite drag of the F-Helix. The dotted lines
in Fig. 10 show the optimal airspeeds for best endurance and
best range for the two rotorcraft configurations. The best range
speeds were determined assuming specific range values that
are 99% of the maxima as this allows the increase of the
best range flight speed with a minor reduction of the range
performance. It can be observed that the best endurance speed
of the two configurations is relatively close with the F-Helix
configuration providing the best endurance at an airspeed of
42 KTAS, slightly higher than the 40 KTAS for the SH-4
configuration for the maximum takeoff weight of 1900 lbs.
A much larger difference is observed for the maximum range
speeds that drop by 10 KTAS from 69 KTAS for the SH-
4 to 59 KTAS for the F-Helix. This is an important result
as it implies an increase of 17% in the time required by the
eVTOL configuration to reach a set distance relative to the
conventional rotorcraft. Figure 11 presents the specific range
performance for standard day conditions and a takeoff gross
weight of 1900 lbs. For this analysis, two different battery
types were considered for the eVTOL configuration. The first
battery type assumed is a liquid Li-ion battery with a specific
energy of 250 W-h/kg, which is the current state of the art for
Li-ion batteries. The second battery type assumed is a solid
state Li-ion battery with a specific energy of the future 625
W-h/kg. This battery type is assumed to represent the electric
energy storage capabilities projected for the next decade. The
results in Fig. 11 are important as they provide an estimate for
the distance provided by each one pound of fuel (for the SH-
4) or battery (for the F-Helix). For the conventional rotorcraft,
the specific range attained at the maximum range speed is 0.91
NM/lbs. In comparison, for the eVTOL configuration with
liquid Li-ion batteries at the corresponding maximum range
speed this values reduces by a factor of 9 to 0.10 NM/lbs. The
use of solid state batteries will provide a specific range that is
2.5 higher (0.25 NM/lbs) assuming the projected capabilities
of solid state batteries materialize. However, even in this case
the range performance of the eVTOL configuration will be 3.6
times lower than that of a conventional rotorcraft at the same
operating weight. It follows that although the torque required
for cruise by the eVTOL configuration is significantly lower
than that of the conventional rotorcraft, the range obtained for
each pound of battery is much lower compared to that obtained
per each pound of fuel for the conventional rotorcraft. This
result, a reflection of the inherently smaller energy density of
electric batteries in comparison to fossil fuels is not expected
to change in the near future. Therefore, in order for an
eVTOL configuration to offer similar performance to that of a
comparable conventional rotorcraft it should combine a more
efficient cruise power with a lighter empty weight.
C. Mission Performance
To allow the evaluation and comparison of mission per-
formance of both configurations a typical aerial urban trans-
portation mission is defined. The mission that is basically a
one leg transport of passengers or payload is defined in a
similar fashion to the preliminary mission requirements in the
UBER Elevate “eVTOL Vehicle Requirements and Missions”
document [10]. The segments of the urban transportation
mission used for the current analysis are presented in Table
IV and a graphic representation of the mission is brought in
Fig. 10: Torque required for cruise in standard atmospheric
conditions.
Fig. 11: Specific range in standard atmospheric conditions,
1900 lbs.
Fig. 12. The rotorcraft takes off vertically from a heliport at
sea level, hovers OGE 40 feet above ground level (AGL),
climbs to an altitude of 1000 ft and performs a maximum
range straight and level cruise to the destination heliport. The
cruise segment includes a reserve leg of 20 minutes that is
not counted in the total mission time and range. The rotorcraft
then descends to the destination heliport utilizing partial power,
hovers 5 minutes OGE to simulate a situation where the
heliport is busy, and lands vertically. Mission performance
is calculated assuming an empty weight of 1142 lbs for
the SH-4 and 650 lbs for the F-Helix for various payload
weights. Since the rotorcraft is primarily intended for urban
air transportation missions it is assumed that the pilot is one
of the passengers and therefore is counted as “payload” in the
rotorcraft configuration breakdown.
Mission performance is calculated for various payload
weights. For each payload case calculated, fuel/batteries were
TABLE IV: Mission Segments for Payload/Range
Calculation.
Segment Description
A Ground Idle - 5 min
B Vertical climb to 40 ft AGL
C Hover OGE - 0.5 min
D Horizontal acceleration to speed for best climb
E Climb to 1000 ft
F Maximum range cruise (+20 min reserve leg)
G Descent to 40 ft AGL
H Deceleration to hover OGE
I Hover OGE - 5 min
J Vertical descent to ground
K Ground idle - 1 min
“topped off” up to the maximum takeoff gross weight of 1900
lbs (for the SH-4 the maximum fuel quantity is limited not to
exceed the fuel tank capacity of 33.5 gallons). For simplicity
it is assumed that the weight of the batteries is continuous
so that for each payload case the maximum weight margin
available for battery carriage is used. Battery specific energy
is then multiplied by the battery weight for the calculation of
the amount of electric energy available for flight.
Figure 13 presents the results of the payload/range analysis
for the typical aerial urban transportation mission defined.
Results are shown for the conventional rotorcraft and for the
eVTOL configuration when utilizing liquid Li-Ion batteries
and solid state Li-Ion batteries. As noted above, the pilot is
counted as a passenger so that the minimal payload weight
in any configuration is 200 lbs, the weight of a pilot/single
passenger (including baggage).
Figure 14 presents the corresponding mission times from
engine startup to shutdown excluding the 20 minutes reserve
leg. These figures show that the maximum range that can
be attained by the SH-4 with a single passenger (pilot) is
183 NM with a corresponding mission time of 3 hours (180
min). As more passengers/payload are added the range (and
corresponding flight time) is reduced. The break-point in
the payload/range curve corresponds to the payload weight
above which fuel has be unloaded from the aircraft to keep
the maximum takeoff gross weight limit of 1900 lbs. The
conventional rotorcraft can seat one pilot and two passengers.
The mission range attained in this configuration is 123 NM
with a flight time of 124 min. The mission performance
is significantly degraded when the conventional rotorcraft
configuration is replaced by the eVTOL configuration with
the liquid Li-Ion batteries. The results show that despite the
reduced lower empty weight of the eVTOL rotorcraft and the
lower power required for forward flight the maximum range
attained with a single pilot is only 67 NM with a flight time
of 81 min. Also, as shown earlier, the average flight speed
is reduced from 69 KTAS with the SH-4 to 59 NM with
the F-Helix so that the eVTOL rotorcraft covers less distance
than the conventional rotorcraft and that the flight speed is
significantly slower. The inferior mission performance of the
eVTOL configuration with liquid batteries is primarily the
result of the high weight of the batteries. In addition, unlike
for the conventional configuration where fuel is burned during
the mission thus making the rotorcraft lighter, the eVTOL
Fig. 12: Typical mission definition for payload/range performance calculation.
configuration maintains a constant gross weight from mission
start to mission end.
With the current state of the art of liquid batteries, mission
performance is in line with NASA’s concept vehicles for VTOL
sir taxi operations [11]. However, with current state of the art
liquid batteries, F-Helix performance is inferior to that of the
SH-4. Future solid state batteries with higher specific energy
levels can provide mission performance levels that surpass
those of the conventional SH-4 rotorcraft. The use of solid
state batteries in place of liquid batteries with the eVTOL
configuration restores the performance levels to be similar and
even better than those of the conventional rotorcraft. With a
single passenger (pilot), the mission range increases from 183
NM for the SH-4 to 225 with the F-Helix with solid state
batteries. The corresponding flight times are 180 min and 242
min, respectively. The superior performance of the eVTOL
configuration in these conditions is due to the lower empty
weight of the F-Helix that allows more batteries to be added
to the rotorcraft. Compared to the maximal fuel capacity of
201 lbs for the SH-4 in these conditions, the F-Helix takes
off with a total battery weight of 1050 lbs. As the eVTOL
gross weight remains constant at 1900 lbs throughout the
mission, the range to payload gradient is constant. The lower
specific range of the eVTOL configuration in comparison to
the conventional configuration leads to the solid state eVTOL
configuration having better mission performance than the con-
ventional configuration, unless for payload weights between
400 lbs and 600 lbs. This effectively means that the SH-4
has better payload/range performance only when flying with
two passengers and additional payload of no more than 200
lbs. When three passengers are flown the two configurations
provide the same performance with a range of 123 NM and
flight times of 124 min and 139 min for the SH-4 and F-
Helix configurations, respectively. With four passengers on
board, the solid state F-Helix configuration will be able to
fly a distance of 74 NM with a mission time of 88 min. An
increase of the maximum takeoff gross weight to 2210 lbs or
future batteries enabling a specific energy of more than 741 W-
h/kg will make the solid state eVTOL configuration superior
in terms of mission performance in any payload weight.
V. CONCLUSION
First, the validity of the initial concept was assessed.
Once the configuration of the rotorcraft was established, the
design was optimized to produce the least power required
while still meeting the structural and physical constraints of
its components. Next, a simulation model was developed to
assess the performances in hover and forward flight. The
Fig. 13: Payload/range analysis results for the typical mission
in standard atmospheric conditions.
Fig. 14: Payload/mission-time results for the typical mission
in standard atmospheric conditions.
payload/range performance was then evaluated for a typical
aerial urban transportation mission. Finally, the performance
of the eVTOL configuration was compared to the SH-4. based
on this work, the following conclusions are drawn.
1) Because of the high centrifugal loads the eFans are
subjects to, they are moved inboard with respect to
the initial configuration. Since the structural integrity
of the nacelles of possibly ducted eFans is a matter
of concern under high centrifugal loads, unducted
propellers chosen in favor of ducted fans.
2) Since the eFans spin in a rotating frame, they are
subject to high gyroscopic moments. It is decided
to mount two counter-rotating coaxial propellers per
eFan, so that the overall gyroscopic moment is zero.
3) To control the yaw axis, it is chosen to use two
counter-rotating fixed-pitch ducted fans that provide
thrust in each directions. This is eliminates possible
delays in control action that a single tail rotor would
give if it had to reverse the direction of its thrust
vector.
4) The F-Helix eVTOL configuration allows trimmed
flight with near-zero fuselage roll angles and im-
proves the apparent longitudinal stability of the ro-
torcraft.
5) F-Helix power required to hover at maximum takeoff
weight (1900 lbs) is higher than that of the conven-
tional SH-4 rotorcraft due to the reduced propulsive
efficiency of the eFans in comparison to that of an
internal combustion engine. However, hover perfor-
mance of the F-Helix is superior due to the higher
power available by the batteries and the independence
of this power output on ambient atmospheric condi-
tions.
6) The elimination of the need for an anti-torque system
for the eVTOL configuration and the resulting exclu-
sion of the tail rotor, tail boom, and aerodynamic
surfaces reduces the power required for cruise in
comparison to the conventional rotorcraft for large
parts of the flight envelope. Best-endurance speeds for
the eVTOL configurations are similar to those of the
original SH-4 but best-range speeds are reduced by
10 KTAS. The F-Helix is thus expected to be slower
in maximum range cruise missions.
7) The specific range of the eVTOL configuration is
significantly lower than that of the conventional con-
figuration due to the inherent lower energy density
of electric batteries in comparison to fossil fuels.
Therefore, in order for an eVTOL configuration to
offer similar performance to that of a comparable
conventional rotorcraft, it should combine a more
efficient cruise power with a lighter empty weight.
8) With the current state of the art of liquid batteries,
mission performance is in line with, if not superior
to, NASA’s concept vehicles for VTOL sir taxi oper-
ations. However, with current state of the art liquid
batteries, F-Helix performance is inferior to that of
the SH-4. Future solid state batteries with higher spe-
cific energy levels can provide mission performance
levels that surpass those of the conventional SH-4
rotorcraft.
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