Modeling and Simulation of Heavy-Lift Tethered Multicopter Considering Mechanical Properties of Electric Power Cable

aerospace
Article
Modeling and Simulation of Heavy-Lift Tethered Multicopter
Considering Mechanical Properties of Electric Power Cable
Hyeok-Min Kwon and Dong-Kyu Lee *

 Department of Aeronautical and Mechanical Design Engineering, Korea National University of Transportation,
 50 Daehak-ro, Chungju-si 27469, Korea; ghm8260@naver.com
 * Correspondence: dklee@ut.ac.kr

 Abstract: In case of a fire at a high-rise building which is densely populated, an extension ladder is
 used to rescue people who have yet to evacuate to a safe place away from the fire, whereas those
 who are stranded at a height that is unreachable with the ladder should be promptly saved with
 different rescue methods. In this case, an application of the tethered flight system capable of receiving
 power over a power cable from the ground to a multicopter may guarantee effective execution of
 the rescue plan at the scene where fire is raging without any restrictions of the flight time. This
 article identified restrictions that should be considered in the design of a multicopter capable of
 tethered flight aimed to rescue stranded people at an inaccessible location with an extension ladder
 at a fire-ravaged high-rise building and assessed its feasibility. A power cable capable of providing
 dozens of kilowatts of electricity should be installed to enable the implementation of the rescue
 mission using the tethered multicopter. A flexible multi-body dynamics modeling and simulation
 with viscoelastic characteristics and heavy weight of power cable were carried out to evaluate the
 


 effects of such cable of the tethered flight system on the dynamic characteristics of the multicopter.
 

 The results indicate that as for a heavy-lift tethered multicopter designed to be utilized for rescue
Citation: Kwon, H.-M.; Lee, D.-K.
 operations, the properties of the power cable, such as weight, rigidity and length, have a major
Modeling and Simulation of
 impact on the position and attitude control performance.
Heavy-Lift Tethered Multicopter
Considering Mechanical Properties of
 Keywords: multicopter; heavy lift; tethered flight; flexible multi-body dynamics
Electric Power Cable. Aerospace 2021,
8, 208. https://doi.org/10.3390/
aerospace8080208

Academic Editor: Hyun-Ung Oh 1. Introduction
 In contrast with the past when unmanned air vehicles (UAVs) were originally used for
Received: 21 June 2021 military operations, such as reconnaissance or surveillance, they are now being proactively
Accepted: 28 July 2021 employed for civilian purposes. You can easily find in reality a variety of cases where they
Published: 1 August 2021 are put in use, ranging from drones for Amazon Prime Air delivery services in the US
 which are capable of carrying an item less than 2.26 kgf, through unmanned aerial vehicles
Publisher’s Note: MDPI stays neutral from AeroVironment offering observation services and communication support at a fire
with regard to jurisdictional claims in scene and Google’s SkyBender engaging in 5G wireless communication testing, to flying
published maps and institutional affil- autonomous robots developed by Tevel Aerobotics Technologies to grow fruits without any
iations.
 wastes of human resources by selecting fruits of optimum quality based on their size and
 conditions [1–4]. eVTOL (electric Vertical Takeoff and Landing) vehicles, including multi-
 copters as most representative, are at the center of the situations where unmanned aerial
 vehicles are being more widely used in the civil application. In particular, multicopters,
Copyright: © 2021 by the authors. which are capable of hovering, have been utilized in more diverse areas. Existing heli-
Licensee MDPI, Basel, Switzerland. copters can also hover and have the advantage of being superior to multicopters in terms
This article is an open access article of payload capacity and endurance. However, they are mechanically complex because
distributed under the terms and they require mechanisms such as a transmission system to transmit the rotational motion
conditions of the Creative Commons
 produced by turbine or piston engine to the rotor blades, and a swashplate for cyclic and
Attribution (CC BY) license (https://
 collective control. Most multicopters do not need additional transmission system because
creativecommons.org/licenses/by/
 each propeller is directly connected to the out-runner type BLDC motor. In addition, since
4.0/).

Aerospace 2021, 8, 208. https://doi.org/10.3390/aerospace8080208 https://www.mdpi.com/journal/aerospace

transmission system because each propeller is directly connected to the out-runner type
 BLDC motor. In addition, since every propeller has pair to rotate at the same speed in 2 of 18
Aerospace 2021, 8, 208
 opposite directions, gyroscopic precession caused by the spinning rotor can be neglected
 in many cases, and cyclic control is not required as it has symmetrical aerodynamic char-
 acteristics. The forces for propeller
 every attitudehas control
 pair toare generated
 rotate by changing
 at the same the rotational
 speed in opposite directions,speed
 gyroscopic
 of the motor. For those reasons, multicopters do not have to use a swashplate
 precession caused by the spinning rotor can be neglected in many cases, and cyclic and can control
 is not required
 carry out control commands more as itfrequently.
 has symmetrical
 It is aerodynamic
 also possible characteristics.
 to guide a The forces for
 relatively attitude
 safe
 landing even if one control
 of theirarepropellers
 generated by changing the rotational speed of the motor. For those reasons,
 fails since most of multicopters has more than four
 multicopters do not have to use a swashplate and can carry out control commands more
 propellers. Based onfrequently.
 these advantages, a research
 It is also possible to guide aon spacesafe
 relatively application
 landing even ofifmulticopter is
 one of their propellers
 also in progress. NASA Jet Propulsion
 fails since Laboratory
 most of multicopters (JPL),
 has more thaninfour
 collaboration withon
 propellers. Based AeroViron-
 these advantages,
 ment Inc., NASA Ames Research Center and NASA Langley Research Center, hasJetdevel-
 a research on space application of multicopter is also in progress. NASA Propulsion
 Laboratory
 oped a vehicle capable (JPL),take-off
 of vertical in collaboration with AeroVironment
 and landing on Mars [5,6] Inc.,asNASA
 shown Ames Research1,Center
 in Figure
 and NASA Langley Research Center, has developed a vehicle capable of vertical take-off
 and the vehicle has succeeded in several flight tests on Mars. The Mars Helicopter, named
 and landing on Mars [5,6] as shown in Figure 1, and the vehicle has succeeded in several
 Ingenuity, is an eVTOL
 flight vehicle equipped
 tests on Mars. The Marswith a coaxial
 Helicopter, rotor
 named which isisancomposed
 Ingenuity, eVTOL vehicleof two
 equipped
 propellers rotating in
 with opposite
 a coaxial directions.
 rotor which isIncomposed
 order toofreflect the difference
 two propellers rotating in inopposite
 gravitydirections.
 be-
 tween Earth and Mars during the flight test of the demonstration model of Ingenuity, an test
 In order to reflect the difference in gravity between Earth and Mars during the flight
 electrical tether wasofused
 the demonstration model of Ingenuity, an electrical tether was used to supply power
 to supply power from the ground while removing the battery
 from the ground while removing the battery [7,8]. The technological advancements of the
 [7,8]. The technological advancements
 electrical of the such
 propulsion system, electrical propulsion
 as propellers, electricsystem,
 motors such as propel-
 and batteries, have led
 lers, electric motorstoand batteries, have led to the recent development
 the recent development of large manned multicopters aimed to be integrated of large manned into the
 multicopters aimed Urban
 to be integrated
 Air Mobility into (UAM) theecosystem
 Urban Air Mobility (UAM) ecosystem [9–11].
 [9–11].

 Figure 1. Example of space application of multicopter: (a) illustration of Mars Helicopter Ingenuity [6]; (b) demonstration
 Figure 1. Example of space application of multicopter: (a) illustration of Mars Helicopter Ingenuity
 model of Mars Helicopter powered through an electrical tether hanging below the vehicle during controlled-flight test [8].
 [6]; (b) demonstration model of Mars Helicopter powered through an electrical tether hanging be-
 low the vehicle during controlled-flight test [8].
 Meanwhile, eVTOL sufficiently large enough to carry passengers is expected to be
 effective in rescue operations in case of a fire or disaster. In the process of industrial
 development,
 Meanwhile, eVTOL the urban
 sufficiently concentration
 large enough tophenomenon,
 carry passengersin whichismany people to
 expected flock
 beto the
 city, has resulted in high-rise buildings being built in large cities. As skyscrapers built
 effective in rescue operations in case of a fire or disaster. In the process of industrial de-
 mostly to accommodate residential places or office spaces are more densely populated than
 velopment, the urban concentration
 low-rise counterparts,phenomenon,
 they are likelyintowhich many people
 have relatively flockdamages
 more severe to the city,when an
 has resulted in high-rise buildings
 accident beingout,
 or a fire breaks built
 thusinhaving
 largevarious
 cities. evacuation
 As skyscrapers built mostly
 and preventive measures in
 place, including
 to accommodate residential places emergency
 or officestaircase,
 spaces emergency
 are more shelter
 densely or emergency
 populatedlift. However,
 than low- such
 evacuation and prevention measures may not cover all unexpected situations which leave
 rise counterparts, they are likely to have relatively more severe damages when an accident
 some people stranded as they fail to promptly evacuate to a safe place, and generally a fire
 or a fire breaks out,truck
 thusladder
 having various
 directly evacuation
 accessible andwall
 to the external preventive
 of a high-risemeasures
 building is inused
 place,
 to rescue
 including emergency staircase,
 them. During theemergency shelter
 rescue operation of or
 theemergency
 people stranded lift.atHowever, such
 a high altitude evac-
 using the aerial
 uation and prevention measures
 ladder, may notare
 various restrictions cover all [12].
 entailed unexpected
 A fire trucksituations which
 ladder consists leave to
 of outriggers
 some people stranded as they fail to promptly evacuate to a safe place, and generally a and a
 hold the weight, a lift to carry people, an electric control system for the lift operation
 safety system to respond to an emergency. Table 1 shows the safe operational conditions of
 fire truck ladder directly accessible to the external wall of a high-rise building is used to
 the constituents of the fire truck ladder. As the ideal climbing angle of the aerial ladder for
 rescue them. Duringsafetheoperation
 rescue operation
 ranges fromof 30 the
 to 70people
 degrees,stranded at a to
 it can be used high
 carryaltitude using
 out a rescue mission
 the aerial ladder, various
 within anrestrictions
 altitude lower arethan
 entailed [12].
 the actual A fire
 length truck
 of the ladder.ladder consists
 In addition, of out-should
 a clearance
 be secured
 riggers to hold the weight, fromtothe
 a lift building
 carry where
 people, anfire occurs control
 electric depending on thefor
 system climbing
 the liftangle
 op-of the
 eration and a safety system to respond to an emergency. Table 1 shows the safe opera-
 tional conditions of the constituents of the fire truck ladder. As the ideal climbing angle
 of the aerial ladder for safe operation ranges from 30 to 70 degrees, it can be used to carry
 out a rescue mission within an altitude lower than the actual length of the ladder. In ad-

the climbing angle of the ladder, which determines its reachable height. Generally, a clear-
 ance of approx. 13.7 m away from the external wall of the building is required to install
 an extension ladder as long as 50 m, whereas a 70-m-long ladder, used only in some cases
Aerospace 2021, 8, 208 3 of 18
 to reach a high altitude, can have access to the height of up to approx. 64 m, which is about
 24 story high given the average floor height (approx. 2.6~2.8 m) of an apartment building.
 In a situation where more skyscrapers with more than 30 stories are being built due to the
 ladder, which determines its reachable height. Generally, a clearance of approx. 13.7 m
 above mentioned growth in the urban population, it becomes inevitable in some cases for
 away from the external wall of the building is required to install an extension ladder as
 some people to become trapped in a location
 long as 50 m, whereas higher
 a 70-m-long than
 ladder, usedthe
 onlyheight
 in somethat
 casesthe ladder
 to reach can
 a high altitude,
 reach or impossible can
 to secure a clearance
 have access to of
 to the height install the ladder.
 up to approx. 64 m, eVTOL vehicle
 which is about capable
 24 story of the
 high given
 average
 transporting passengers floor height
 is deemed as (approx. 2.6~2.8 m)
 an alternative of an apartment
 solution building.
 to promptly In a people.
 rescue situation where
 more skyscrapers with more than 30 stories are being built due to the above mentioned
 growth in the urban population, it becomes inevitable in some cases for some people to
 Table 1. Safe operational conditions for elevated ladder of fire truck.
 become trapped in a location higher than the height that the ladder can reach or impossible
 to secure a clearance to install the ladder. eVTOL vehicle capable of transporting passengers
 Components Operational Constraints
 is deemed as an alternative solution to promptly rescue people.
 Road slope < 5°
 Loading vehicle
 Ground
 Table 1. Safe operational conditions rigidityladder
 for elevated should
 of firebe ensured
 truck.

 Components Maximum allowable load:Constraints
 Operational 80 T
 Outrigger Deployment radius: Road5.2 m< 5◦
 slope
 Loading vehicle
 Deployment angle: −7° ~ 70° be ensured
 Ground rigidity should

 Working Maximum
 speed: 1allowable
 m/s load: 80 T
 Outrigger Deployment radius: 5.2 m
 Lift Ladder deployment angle: 30°
 Deployment angle:~ −
 −70°
 7◦ ~70◦
 Ladder deployment length: 23 ~ 53.2
 Working speed: 1 m/sm
 Lift Ladder deployment angle: 30◦ ~−70◦
 Ladder deployment length: 23~53.2 m
 Regular eVTOL vehicles are not capable of executing a long-duration mission due to
 limited battery capacity, but there were cases where a tethered flight system was devel-
 Regular eVTOL vehicles are not capable of executing a long-duration mission due to
 oped to overcome such limitation
 limited of flight
 battery capacity, time.were
 but there UCON Systems
 cases where developed
 a tethered T-Rotor
 flight system for
 was developed
 military operations, toand Israel Aerospace Industries (IAI) came up with Hover Mast
 overcome such limitation of flight time. UCON Systems developed T-Rotor for military in a
 joint partnership with Sky Sapience.
 operations, There
 and Israel are several
 Aerospace products
 Industries capable
 (IAI) came of tethered
 up with flight,
 Hover Mast in a joint
 such as Elistair’s safe-T and Power Line of Network Time Protocole, which replace the flight,
 partnership with Sky Sapience. There are several products capable of tethered
 such as Elistair’s safe-T and Power Line of Network Time Protocole, which replace the
 existing multicopters’ power system [13–15] which are shown in Figure 2. However, as
 existing multicopters’ power system [13–15] which are shown in Figure 2. However, as
 these tethered flight systems are used
 these tethered flightto provide
 systems are electricity to and
 used to provide communicate
 electricity with mul- with
 to and communicate
 ticopters of small sizemulticopters
 designed mostly for observation
 of small size designed mostly and forcommunication relay, the pres-
 observation and communication relay, the
 ence of power cable presence
 does notofgreatly
 power cable does
 affect thenotdynamic
 greatly affect the dynamic characteristics
 characteristics of multicopters.
 of multicopters.

 Figure
 Figure 2. Tethered
 2. Tethered multicopters
 multicopters andflight
 and tethered tethered
 systemflight system for
 for multicopters: multicopters:
 T-Rotor T-Rotor
 [13], Hover Mast [13], Hover
 [14], Power Line [15].
 Mast [14], Power Line [15].
 Weight and flexural rigidity of the power cable greatly changes depending on the
 operating voltage and current. As tethered multicopters for rescue purposes should be
 Weight and flexural
 able to rigidity of the power
 perform hovering cable
 flight with greatly
 at least changes depending
 one passenger onshould
 on board, there the be a
 operating voltage and current. As tethered multicopters for rescue purposes should
 heavy-duty power cable installed to ensure stable power supply from the ground, be which
 generates
 able to perform hovering a relatively
 flight with atlarge
 leasteffect
 oneonpassenger
 flight dynamics brought
 on board, by changes
 there should in be
 theaweight
 and flexural rigidity of the cable. In order to analyze the
 heavy-duty power cable installed to ensure stable power supply from the ground, whichflight dynamic characteristics
 of a tethered multicopter, dynamics for each of the multicopter and the electric power
 generates a relatively large
 cable effect
 should on flightGiernacki
 be modeled. dynamics brought
 et al. by changes
 [16] obtained in the
 information suchweight
 as geometric
 and flexural rigidity of the cable. In order to analyze the flight dynamic characteristics of
 a tethered multicopter, dynamics for each of the multicopter and the electric power cable
 should be modeled. Giernacki et al. [16] obtained information such as geometric dimen-

Aerospace 2021, 8, 208 4 of 18

 dimensions, masses and moment of inertial, which are major parameters of the equation
 of motion, from the technical documentation provided by the multicopter manufacturer.
 Ivler et al. [17] built a multicopter flight dynamics model close to reality by performing
 system identification using actual flight test data. In relation to the dynamic character-
 istics of the tethered system, various studies have been carried out especially for space
 applications. Aslanov et al. [18] conducted a study to identify the dynamic characteristics
 based on mathematical modeling of the space tethered system, which collectively refers to
 applications such as space escalator, space elevator, lifting and descent of a payload into
 an orbit and placing a spacecraft into orbit. Misra et al. [19] studied the transverse and
 longitudinal vibration of sub-satellite tethered to the space shuttle. Based on the modeling
 of the tether elevator system installed on both sides of the space station, Lorenzini et al. [20]
 investigated the dynamics of the space elevator to maintain the center of mass of the entire
 system within the space station by controlling the length change of a tether while the
 elevator is operated on the other tether. Williams et al. examined the influence of thermal
 induced flexibility change of tether on tethered aerocapture missions [21]. They constructed
 two temperature-dependent dynamics models of the tether based on Lagrange’s equation
 and Kane’s equation, respectively. Through numerical simulations, it was confirmed that
 the longitudinal stiffness of the tether has a significant effect on the maneuver of the en-
 tire system. There have been several studies on helicopters or multicopters with slung
 load [22–24], of which configurations are similar to tethered multicopters, but most studies
 were conducted on applications where the effects of mass and flexural rigidity of cables
 could be neglected.
 This study analyzed restrictions integrated in the design of tethered multicopters for
 rescue mission, which require a heavy and thick power cable, to identify the requirements
 of the tethered flight system and the power cable. Based on the mechanical properties of
 the power cable obtained from bending tests, a flexible multi-body dynamics modeling
 was conducted on tethered multicopter with a power cable. Later, a simulation for position
 and attitude control was carried out, based on a model where the power cable of differ-
 ent lengths depending on the flight altitude was integrated, to observe change in flight
 dynamics of the multicopter.

 2. Design of Heavy-Lift Tethered Multicopter
 2.1. Mission Profile
 Multicopters can be used to perform lifesaving missions in areas inaccessible to fire-
 fighting ladders or where there are restrictions on the deployment of elevated ladders.
 However, the battery-equipped multicopter has a relatively short endurance due to limited
 battery capacity, so it cannot reliably perform rescue missions for a long time. The size
 of multicopter should be suitable for lifesaving operations without causing an accident
 and interfering with the performance of other workers’ missions after arriving at the
 site regardless of the method of transport to the fire or disaster site. In addition, it is
 required to guarantee good flight performance in various conditions such as ascending
 flight for approach, hovering while on board and descending flight for landing during
 rescue missions. Figure 3 shows the operational process of a tethered multicopter for rescue
 purposes. Once an emergency is reported, fire trucks and multicopters are immediately
 dispatched to the emergency site. After arriving at the fire site, a safety space of a certain
 size necessary for multicopter take-off and landing must be secured. Once the safety space
 is secured, the conditions and location of stranded people should be identified in detail.
 When the detailed information is obtained, the heavy-lift tethered multicopter should start
 its flight for rescue mission. It has to hold not only its position to hover around the contact
 point, but also its attitude angles even when there exists weight shift while rescued person
 is boarding. After the multicopter safely lands on the truck and unloading the rescued
 person, it continues the rescue operation repeatedly until there are no people left in the
 building. After the execution of such a mission, the power supply system and the entire
 multicopter as well as its equipment should be checked, and in case repairs are required,

PEER REVIEW 5 of 18

 Aerospace 2021, 8, 208 5 of 18

 and the entire multicopter as well as its equipment should be checked, and in case repairs
 are required, they should be carried out in line with the proper procedures with mainte-
 they should be carried out in line with the proper procedures with maintenance being
 nance being conducted on a on
 conducted regular basis
 a regular basis [25,26].
 [25,26].

 Figure 3. Mission profile
 Figure of heavy-lift
 3. Mission tethered
 profile of heavy-lift multicopter
 tethered forforlifesaving
 multicopter mission.
 lifesaving mission.

 2.2. Analysis on Design Constraints
 2.2. Analysis on Design Constraints
 2.2.1. Size Constraints
 2.2.1. Size Constraints A tethered multicopter is required to rapidly move to a site where fire or disaster
 occurs to execute a rescue operation. There are two ways for them to move to the scene:
 A tethered multicopter
 first, they flyisto required
 the site directlyto and
 rapidly
 connectmove
 to on-siteto infrastructure,
 a site where such fire
 as aor firedisaster
 hydrant
 occurs to execute a rescue operation. There are two ways for them to move to theSecond,
 or streetlamp, to be supplied electric power from ground for tethered flight. scene:
 they are loaded onto an existing automotive vehicle, retrofitted for this purpose, to be
 first, they fly to the site directly and connect to on-site infrastructure, such as a fire hydrant
 transported to the site. As multicopters have autonomous flight capability, they are able to
 or streetlamp, to be movesupplied
 quicklyelectric
 to the scenepower frombyground
 unaffected the trafficfor tethered
 conditions flight.
 without Second, ofthey
 any assistance an
 are loaded onto an additional
 existing loading
 automotive vehicle,this
 vehicle. However, retrofitted
 requires thefor this purpose,
 establishment to be trans-
 of infrastructure, as a
 precondition, that includes a power supply system near high-rise building, a traffic control
 ported to the site. As multicopters have autonomous flight capability, they are able to
 system and spatial information of downtown areas required for flights of large eVTOL in
 move quickly to thethescene urbanunaffected
 area. The second by way
 the of traffic
 moving conditions
 the tethered without
 multicopter any
 to theassistance
 scene which of
 an additional loading vehicle.
 involves However,
 a loading vehicle has this
 itsrequires the
 limitation as it isestablishment
 affected by trafficof infrastructure,
 conditions and may
 result in belated arrival, but there is an upside as well in that the loading vehicle can carry
 as a precondition, that includes a power supply system near high-rise building, a traffic
 the power supply system and equipment for the mission as well as additional devices,
 control system and guaranteeing
 spatial information
 stable execution ofofdowntown
 the operation. areas required
 As a result, for flights
 it is concluded of large
 that transporting
 eVTOL in the urbanthe area. The second
 multicopter tethered way
 to theofloading
 moving theistethered
 vehicle more effectivemulticopter
 than direct to thetoscene
 flight a fire
 which involves a loading vehicle has its limitation as it is affected by traffic conditionswith
 or disaster site, and if it is designed in a size enough to be loaded onto a fire truck and
 water pump dispatched to a fire scene, it will be easily transported on the road. Table 2
 may result in belated arrival,
 shows but
 a list of there
 overall is anwidth
 length, upside as well
 and height in that
 of each size the loading
 of generally used vehicle can
 fire trucks
 carry the power supply system
 with water pump. and equipment
 Considering for thesize
 the expected mission as well
 of a multicopter ascan
 that additional
 lift at least one de-
 person and the applicability in cramped urban areas,
 vices, guaranteeing stable execution of the operation. As a result, it is concluded that trans- the frame width and length of the
 multicopter are decided as 1800 mm and 2400 mm, respectively. This size of multicopter
 porting the multicopter allowstethered
 the small fireto pump
 the loading
 car can bevehicle istomore
 retrofitted effective
 load the than direct flight
 tethered multicopter.
 to a fire or disaster site, and if it is designed in a size enough to be loaded onto a fire truck
 2.2.2. Weight Constraints
 with water pump dispatched to a fire scene, it will be easily transported on the road. Table
 As multicopters for rescue purposes should be able to take off and land vertically with
 2 shows a list of overall length,
 passengers widththey
 on board, and height
 should ofsimilar
 share eachcapabilities
 size of generally
 with eVTOL used firethat
 vehicles trucks
 are
 with water pump. Considering
 being developedthe
 to beexpected sizeUAM
 integrated into of aecosystem.
 multicopter
 eVTOL that can tolift
 vehicles be at least one
 incorporated
 into the UAM
 person and the applicability inecosystem
 crampedis urbanclassifiedareas,
 as the following
 the framethree categories:
 width and vectored
 length thrust,
 of the
 multicopter are decided as 1800 mm and 2400 mm, respectively. This size of multicopter
 allows the small fire pump car can be retrofitted to load the tethered multicopter.

Aerospace 2021, 8, 208 6 of 18

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 2021, x8,FOR
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 66of
 of18
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 lift-cruise and multicopter. In case of the vectored thrust and lift-cruise types, which are
 capable of vertical take-off/landing and long-range cruise flight, they need an additional
 fixed wing structure as well as additional mechanisms for propulsion system. As for
 2.2.2.
 2.2.2.Weight
 2.2.2.
 rescueWeight
 Weight Constraints
 Constraints
 missionsConstraints
 at a fire site which require repeated vertical take-offs and landings while
 receiving
 AsAs
 As electricity
 multicopters
 multicopters
 multicopters from
 forfor
 for the power
 rescue
 rescue
 rescue purposes cableshould
 purposes
 purposes within
 should
 should abe
 be limited
 beable
 able
 able range,
 tototake
 to take
 take without
 off
 offand
 off and
 and cruise
 land
 land
 land flight, the
 vertically
 vertically
 vertically
 withmulticopter
 with
 withpassengers
 passengers
 passengers type
 onon
 onisboard,
 most
 board,
 board, suitable.
 they
 they
 theyshould
 should
 should Table
 share 3similar
 share
 share shows
 similar
 similar the specifications
 capabilities
 capabilities
 capabilities with eVTOL
 with
 with of UAM
 eVTOL
 eVTOL vehicles
 vehicles
 vehicles
 vehicles that
 thatof
 that
 are multicopter
 arebeing
 are being
 being type that
 developed
 developed
 developed totobeare
 to be
 be currentlyinto
 integrated
 integrated
 integrated being
 intoUAM
 into developed.
 UAM
 UAM ecosystem.
 ecosystem.
 ecosystem.Among
 eVTOL
 eVTOL
 eVTOLthem, Ehang
 vehicles
 vehicles
 vehicles toto184,
 be
 tobe
 be aincorpo-
 vehicle
 incorpo-
 incorpo-
 whose
 rated
 rated
 rated into performance
 into
 into the
 theUAM
 the UAM
 UAM was
 ecosystemverified
 ecosystem
 ecosystem inclassified
 isisis numerous
 classified
 classifiedasasflight
 the
 as the
 the tests
 following andthree
 following
 following which
 three is of relatively
 categories:
 three categories:
 categories: vectoredsimple
 vectored
 vectored
 structure,
 thrust,
 thrust,
 thrust, was
 lift-cruise
 lift-cruisechosen
 lift-cruiseand
 and
 and as a
 multicopter.reference
 multicopter.
 multicopter. InInto
 case
 In analyze
 caseofof
 case the
 of the
 the
 the weight-related
 vectored
 vectored
 vectored thrust
 thrust
 thrust constraints
 and
 and
 and lift-cruise of
 lift-cruise
 lift-cruise tethered
 types,
 types,
 types,
 multicopters
 which
 which
 which areare
 arecapablefor of
 capable
 capablerescue
 of
 of missions.
 vertical
 vertical
 vertical take-off/landing
 take-off/landing
 take-off/landing and
 and
 and long-range
 long-range
 long-range cruise
 cruise flight,
 cruise flight,
 flight, they
 they
 theyneed
 need
 needananan
 additional
 additional
 additional fixed
 fixedwing
 fixed wing
 wingstructure
 structure
 structure asaswell
 as well
 wellasas
 additional
 as additional
 additional mechanisms
 mechanisms
 mechanisms forforpropulsion
 for propulsion
 propulsion system.
 system.
 system.
 Table 2. Size of various types of fire pump car.
 AsAs
 Asfor rescue
 for
 for rescue
 rescuemissions
 missions
 missionsatat a fire
 at aafiresite
 fire sitewhich
 site which
 whichrequire
 require
 requirerepeated
 repeated
 repeated vertical
 vertical
 verticaltake-offs
 take-offs
 take-offsand and
 and landings
 landings
 landings
 while
 while
 while receiving
 Type electricity
 receiving
 receiving electricity
 electricity from
 from
 from the
 Length the
 thepower
 power
 power
 (mm) cable
 cable
 cablewithin
 Widtha (mm)
 within
 within alimited
 a limited
 limited range,
 range,
 range,without
 without
 without
 Height cruise
 (mm) cruise
 cruise
 flight,
 flight,the
 flight, the
 themulticopter
 multicopter
 multicopter type
 type
 typeisisis
 most
 most
 most suitable.
 suitable.
 suitable.Table
 Table
 Table3 3shows
 3shows
 shows the
 thespecifications
 the specifications
 specifications ofof UAM
 of UAM
 UAM ve-
 ve-
 ve-
 Large 8500 2500 3400
 hicles
 hicles
 hiclesofofmulticopter
 of multicopter
 multicopter
 Medium type
 type
 type that
 thatare
 that arecurrently
 are
 8000currently
 currently being
 being
 beingdeveloped.
 developed.
 developed.
 2500 Among
 Among
 Among them,
 them,
 them,Ehang
 Ehang
 Ehang
 3200 184,
 184,a
 184, aa
 vehicle
 vehicle
 vehiclewhose
 whose
 whose performance
 Smallperformance
 performance waswas
 wasverified
 verified
 verified
 6800 in numerous
 in
 in numerous
 numerous flight
 flight
 flight
 1900 tests and
 tests
 tests and
 and which
 which
 whichis of
 is
 is relatively
 of
 of
 2800relatively
 relatively
 simple
 simple
 simple structure,
 Light was
 structure,
 structure, was
 was chosen
 chosen
 chosen asasa5200
 as areference
 a reference
 reference totoanalyze
 to analyze
 analyze thethe
 the
 1200 weight-related
 weight-related
 weight-related constraints
 constraints
 constraints
 2800 ofof
 of
 tethered
 tethered
 tethered multicopters
 multicopters
 multicoptersforforrescue
 for rescue
 rescue missions.
 missions.
 missions.

 Table
 Table
 Table
 Table 3. Specifications
 3.Specifications
 3. 3.
 Specifications
 Specifications ofmulticopter
 ofof
 of multicopter
 multicopter
 multicopter type
 type heavy-lift
 heavy-lift
 type
 type eVTOL.
 eVTOL.
 heavy-lift
 heavy-lifteVTOL.
 eVTOL.
 Manufacturer
 Manufacturer
 Manufacturer
 Manufacturer Ehang
 Ehang
 Ehang
 Ehang Airbus
 Airbus
 Airbus
 Airbus Volocopter
 Volocopter
 Volocopter
 Volocopter
 Ehang
 Ehang184
 Ehang
 Ehang 184
 184184 City
 CityAirbus
 City Airbus
 Airbus
 Airbus 2X2X
 2X
 2X
 Model

 Model
 Model
 Model

 Size
 Size(m)
 Size
 Size(m)
 (m)
 (m) 444×
 4×××3.9 ××1.4
 3.93.9
 3.9 ××1.4
 1.4
 1.4 8 888××××8888 3.2 × ××9.15
 3.2
 3.2
 3.2 9.15××
 ×9.15
 9.15 ××2.15
 2.15
 2.15
 2.15
 MTOW (kgf) 360 2200 450
 MTOW
 MTOW
 MTOW (kgf)
 (kgf)
 (kgf) 360360
 360 22002200
 2200 450
 450
 450
 Payload (kgf) 100 250 150
 Payload
 Payload(kgf)
 Payload (kgf)
 (kgf) 100100
 100 250 250
 250 150
 150
 150

 AsAsAs
 Asthe the
 the
 the tethered
 tethered
 tethered
 tethered multicopters
 multicopters
 multicopters
 multicopters receive
 receive
 receive
 receive power
 power
 power
 power from from
 from
 from the
 thethe
 the ground
 ground
 ground
 ground via via
 via
 via power
 power
 power
 power cable,
 cable,
 cable, battery
 battery
 cable, battery
 battery
 can can
 can
 canbebebe
 be removed
 removed
 removed
 removed from from
 from
 from the the
 the
 the vehicle
 vehicle
 vehicle
 vehicleand and
 and
 and the the
 the
 the tethered
 tethered
 tethered
 tethered flight
 flight
 flight
 flight system
 system
 system
 system can can
 can
 can be
 bebe
 be loaded
 loaded
 loaded
 loaded as
 asas much
 much
 as much
 much asasas
 as
 the the
 the
 the weight
 weight
 weight
 weight ofofof
 the
 of the
 the
 the battery.
 battery.
 battery.
 battery. Ehang
 Ehang
 Ehang
 Ehang 184 184
 184
 184 is
 isisis
 knownknown
 known
 known toto
 toto
 use use
 use
 use a lithium-based
 a alithium-based
 a lithium-based
 lithium-based secondary
 secondary
 secondary
 secondary battery,
 battery,
 battery,
 battery,
 which
 which widely
 widely powers
 powers various
 various electric
 electric mobilities
 mobilities because
 because it
 it ithashas relatively
 relatively highhigh energy
 energy andand
 which
 which widely
 widely powers
 powers various
 various electric
 electric mobilities
 mobilities because
 because ithas
 has relatively
 relatively high
 high energy
 energy and
 and
 power density, long life expectancy and excellent temperature stability. The capacity of the
 power
 power
 power density,
 density,
 density, long
 long
 long life
 lifeexpectancy
 life expectancy
 expectancy andand
 and excellent
 excellent
 excellent temperature
 temperature
 temperature stability.
 stability.
 stability.TheThe
 Thecapacity
 capacity
 capacity ofof
 of
 battery loaded in Ehang 184 is known to be 14.4 kWh, and when the weight energy density
 the
 the
 thebattery
 battery
 battery loaded
 loaded
 loaded ininEhang
 in Ehang
 Ehang 184
 184
 184isisis
 known
 known
 known toto bebe
 to be14.4
 14.4
 14.4kWh,
 kWh,
 kWh, andand
 and when
 when
 when the
 the
 theweight
 weight
 weight energy
 energy
 energy
 of a small lithium-ion battery of about 117 wh/kgf is applied, the weight of the battery
 density
 density
 density ofof a asmall
 of a small
 small lithium-ion
 lithium-ion
 lithium-ion battery
 battery
 battery ofofofabout
 about
 about 117117
 117wh/kgf
 wh/kgf
 wh/kgf isisis
 applied,
 applied,
 applied, thetheweight
 the weight
 weightofofthe
 of the
 the
 can be estimated to be about 123 kgf [27–29]. Accordingly, the total weight of the mooring
 battery
 battery cancan bebeestimated
 estimated to be
 to beabout
 about 123
 123 kgfkgf [27–29].
 [27–29]. Accordingly,
 Accordingly,
 battery can be estimated to be about 123 kgf [27–29]. Accordingly, the total weight of the the
 thetotal
 totalweight
 weight of the
 of the
 flight system including the weight of the power cable that changes in proportion to the
 mooring
 mooring
 mooring flight
 flight
 flightsystem
 system
 system including
 including
 including thethe
 theweight
 weight
 weight ofofthe
 of the
 thepower
 power
 power cable
 cable
 cable that
 that
 thatchanges
 changes
 changes inin
 proportion
 inproportion
 proportion
 flight altitude should not exceed 123 kgf at the maximum flight altitude.
 toto
 the
 to theflight
 the flight
 flightaltitude
 altitude
 altitude should
 should
 should not
 not
 notexceed
 exceed
 exceed 123123
 123kgfkgf
 kgfatatthe
 at themaximum
 the maximum
 maximum flight
 flightaltitude.
 flight altitude.
 altitude.
 2.2.3. Initial Design of Tethered Flight System
 2.2.3.
 2.2.3.
 2.2.3. Initial
 Initial
 Initial Design
 Design
 Design ofofTethered
 of Tethered
 Tethered Flight
 Flight
 Flight System
 System
 System
 For the flight of a tethered multicopter for rescue purposes, electrical power should
 beFor Forthe
 For
 supplied the
 theflight
 flight
 flight
 to the ofofa atethered
 of a tethered
 tethered
 electric multicopter
 multicopter
 multicopter
 propulsion system forforrescue
 for rescue
 viarescue
 powerpurposes,
 purposes,
 purposes,
 cable, and electrical
 electrical
 electrical
 the size power
 power
 power
 of the should
 should
 should
 current
 bebe
 besupplied
 supplied
 supplied to tothe
 to the
 theelectric
 electric
 electric propulsion
 propulsion
 propulsion system
 system
 system via power
 via
 via
 flowing through the power cable varies depending on the size of the supplied voltage. power
 power cable,
 cable,
 cable, and
 and
 and the the
 thesize
 sizeof
 size the
 of
 of the
 thecurrent
 current
 current
 flowing
 flowing
 flowing
 Assuming through
 throughthat the
 through the
 thethepower
 power
 power
 power cable
 cable
 cablevaries
 consumption varies
 varies depending
 depending
 depending
 during onon
 hovering onthe
 the
 thesize
 size
 size
 flight of
 isofthe
 of the
 the
 about supplied kW,voltage.
 supplied
 supplied
 57.8 voltage.
 voltage.
 the same
 Assuming
 amount that
 Assuming
 Assuming tothat
 that the
 that the
 thepower
 of power
 power
 Ehang consumption
 consumption
 consumption
 184, a current during
 during
 during
 of abouthovering480 Aflight
 hovering
 hovering flight
 flight
 must isbeabout
 is
 isabout
 about 57.8
 57.8
 transmitted kW,
 57.8 kW,
 kW, thethesame
 the
 through same
 samethe
 amount
 powertocable
 amount
 amount tothat
 to that
 that ofof
 from Ehang
 of Ehang
 Ehang 184,
 the ground 184,
 184,a acurrent
 current
 awith
 current
 DC ofof about
 of
 powerabout
 about 480
 of 480
 480
 120 AA must
 A
 V. must
 must
 The bebe
 betransmitted
 weight per unitthrough
 transmitted
 transmitted through
 through
 length the
 ofthe
 the
 the
 power
 power
 power cable
 cable
 cable from
 from
 from the
 the
 theground
 ground
 ground with
 with
 withDC DC
 DC power
 power
 power of 120
 of
 of 120
 120
 power cable, in this case, is estimated to be about 1.5 kgf/m to meet IEC 60,227 standard.V.V.The
 V. The
 The weight
 weight
 weight perper
 perunit
 unitlength
 unit length
 length of the
 of
 of the
 the
 power
 power
 power
 While cable,
 cable,
 acable,
 coupleinin this
 in thiscase,
 this
 of case,
 case,
 power isisestimated
 is estimated
 estimated
 cables totobebe
 to
 are required beabout for 1.5
 about
 about DC 1.5kgf/m
 1.5 kgf/m
 kgf/m
 powe to tomeet
 to
 supply,meet
 meet IEC
 the IEC
 IEC60,227
 60,227
 60,227
 maximum standard.
 standard.
 standard.
 length of
 While
 While
 While a
 the cablecouple
 a couple
 a couple of
 is about power
 of power
 of power cables
 cables
 40 m ifcables are
 arerequired
 required
 are required
 the weight forfor
 of the existing DCDC powepowe
 for DCbattery supply,
 supply,
 powe supply, thethe maximum
 maximum
 the maximum
 is all converted length
 into the length
 length ofof
 weight of
 the ofcable
 the
 the cable
 cable
 the isis
 power about
 isabout
 about 4040
 cable. mm
 40 mif if
 This the
 ifthe weight
 the weight
 weight
 concludes ofthat
 the
 of
 of the
 the existing
 it existing
 existing
 is battery
 impossiblebattery
 battery isis
 to all
 isallconverted
 all
 perform converted
 converted into
 the rescueinto
 intothetheweight
 the
 mission weight
 weightat a
 ofofthe
 of the
 the
 higher power
 power
 power cable.
 altitude cable.
 cable. This
 This
 This
 compared concludes
 concludes
 concludes that
 that
 that
 to the existing it itis
 itisimpossible
 isimpossible
 fire impossible
 truck ladder.totoperform
 to perform
 perform thethe
 therescue
 rescue
 rescue mission
 mission
 mission atata aa
 at
 higher
 higher
 higher altitude
 altitude
 altitude compared
 compared
 compared totothe
 to theexisting
 the existing
 existing firefire
 firetruck
 truck
 truckladder.
 ladder.
 ladder.
 Since
 Since
 Since thethe
 theweight
 weight
 weight ofof the
 of the
 thepower
 power
 power cables
 cables
 cables per per
 per unit
 unitlength
 unit length
 length depends
 depends
 depends onon the
 on the
 thecurrent
 current
 current that
 that
 thatruns
 runs
 runs
 through
 through them,
 throughthem, them,the the supplied
 thesupplied voltage
 suppliedvoltage should
 voltageshouldshouldbe be increased
 beincreased
 increasedto to deliver
 todeliver same
 deliversame amount
 sameamount
 amountof of electric
 ofelectric
 electric

Aerospace 2021, 8, 208 7 of 18

 Aerospace 2021, 8, x FOR PEER REVIEW 7 of 18

 Since the weight of the power cables per unit length depends on the current that runs
 through them, the supplied voltage should be increased to deliver same amount of electric
 power.For
 power. Formany
 manypower
 powertransmission
 transmissionapplications,
 applications,three-phase
 three-phasefour-wire
 four-wireAC ACscheme
 schemeisis
 adoptedto
 adopted tominimize
 minimizeelectric
 electriccurrent
 currentandandincrease
 increasetransmission
 transmissionefficiency.
 efficiency.TheTheweight
 weightof of
 the power
 the power cable per per unit
 unitlength
 lengthcancanalso
 alsobebereduced
 reduced with this
 with scheme.
 this scheme.Meanwhile,
 Meanwhile, as they
 as
 should
 they be flame-retardant
 should be flame-retardant because they they
 because are used at a fire
 are used at asite, HF-CO,
 fire site, TFR-CV
 HF-CO, TFR-CVand TFR-
 and
 8 cables,
 TFR-8 which
 cables, whichareare
 widely
 widelyused
 usedforfor
 high
 highsupply
 supplyvoltage
 voltageand and temperature applications,
 temperature applications,
 canbe
 can beused
 used for
 for this
 this purpose.
 purpose. The weights per unit unit length
 length of of HF-CO,
 HF-CO, TFR-CV
 TFR-CV and andTFR-8
 TFR-
 8cables
 cableswere
 weremeasured
 measured asas
 0.78 kgf/m,
 0.78 kgf/m, 0.790.79
 kgf/m and 0.83
 kgf/m and kgf/m, respectively,
 0.83 kgf/m, and Figure
 respectively, and
 Figure 4 indicates
 4 indicates the maximum
 the maximum ceiling
 ceiling of of the tethered
 the tethered multicopter multicopter
 with those with those
 power power
 cables de-
 cables
 pendingdepending on theofweight
 on the weight of anconverter
 an AC/DC AC/DC converter
 to be loaded to be loaded
 onto onto the600
 the airframe. airframe.
 V was
 600 V was considered
 considered as the supply as the supply
 voltage forvoltage for the three-phase
 the three-phase and four-wire and four-wire
 system. When system.the
 When
 weighttheof weight
 the AC/DC of the AC/DC of
 converter converter of the
 the tethered tethered
 flight systemflight system
 is 50 is 50
 kgf [30], thekgf [30], the
 ceiling alti-
 ceiling altitude according
 tude according to the application
 to the application of HF-CO, of TFR-CV
 HF-CO, TFR-CV
 and TFR-CV and TFR-CV is calculated
 is calculated as 94 m,
 as
 9394
 mm,and 9388
 mm, and 88 m, respectively.
 respectively.

 Figure4.4. Maximum
 Figure Maximum flight
 flight altitude
 altitudeofofthe
 thetethered
 tetheredmulticopter
 multicopterfor
 forvarious
 varioustypes of of
 types power cable
 power ac-
 cable
 cording to the weight of AD/DC converter.
 according to the weight of AD/DC converter.

 The layout
 The layout ofofthe
 thetethered
 tetheredmulticopter
 multicopterforforrescue
 rescuepurposes
 purposesin inconsideration
 considerationof ofthe
 the
 above restrictions
 above restrictions relevant
 relevant to the size and and weight
 weight isis shown
 shownin inFigure
 Figure5.5.AtAtthe
 thebottom
 bottom of
 the loading space of the small fire pump car, there should be a power
 of the loading space of the small fire pump car, there should be a power supply systemsupply system with
 a capacity
 with of 100
 a capacity of kW
 100 kWas well as aas
 as well winch thatthat
 a winch adjusts
 adjuststhe the
 length of the
 length power
 of the powercables de-
 cables
 pending onon
 depending thethe
 flight altitude,
 flight altitude,and thethe
 and airframe
 airframeshould
 should include thethe
 include AC/DC
 AC/DC converter that
 converter
 properly
 that distributes
 properly electricity
 distributes fromfrom
 electricity the three-phase
 the three-phase four-wire AC power
 four-wire AC powersource to each
 source to
 BLDC
 each motor,
 BLDC and and
 motor, flight control
 flight systems.
 control systems.

8, x FOR PEER REVIEW 8 of 18
 Aerospace 2021, 8, 208 8 of 18
1, 8, x FOR PEER REVIEW 8 of 18

 Figure 5. Layout of heavy-lift tethered multicopter for lifesaving Mission.
 Figure 5. Layout of heavy-lift
 Figure 5. Layout tethered multicopter
 of heavy-lift for lifesaving
 tethered multicopter Mission.Mission.
 for lifesaving
 3. Flexible Multi-Body Dynamics Simulation of Heavy-Lift Tethered Multicopter
 3. Flexible
 3.1. Mechanical 3. Flexible
 Multi-Body
 Properties of Multi-Body
 Dynamics
 Power Dynamicsof
 Simulation
 Cable Simulation of Heavy-Lift
 Heavy-Lift Tethered Multicopter
 Tethered Multicopter
 3.1. Mechanical Properties of Power Cable
 3.1.The
 Mechanical
 weight Properties
 and flexural of Power
 rigidityCable
 of the power cable, one of the main components of
 The weight and flexural rigidity of the power cable, one of the main components of
 the tethered flight
 The weightthe system,
 and can
 flexural have
 rigidity a significant
 ofcan
 thehave
 power effect on the
 cable, one dynamic
 of on
 thethe characteristics
 main components ofof
 tethered flight system, a significant effect dynamic characteristics of the
 the
 theheavy-lift
 tethered tethered
 flight multicopter.
 system,
 heavy-lift can have
 tethered It isa required
 significant
 multicopter. torequired
 It is identify
 effect the
 ontothe weight
 dynamic
 identify and
 the flexural
 and rigid-
 characteristics
 weight of rigidity
 flexural
 ity
 theofheavy-lift
 the powertethered
 cables
 of the for dynamics
 multicopter.
 power cables formodeling
 It dynamics ofmodeling
 is required the
 to tethered
 identify multicopter,
 the
 of the and
 weightmulticopter,
 tethered and especially,
 flexural
 andrigid-
 especially, it
 itity
 is extremely
 of the powerdifficult
 cables
 is tofor
 extremely theoretically
 dynamics
 difficult to evaluate
 modeling the flexural
 of the
 theoretically rigidity
 tethered
 evaluate of the
 the multicopter,
 flexural cables made of made of
 andofespecially,
 rigidity the cables
 complex materials, including
 complex conductor,
 materials, including insulator,
 conductor, binder tape
 insulator, and
 binder sheath.
 it is extremely difficult to theoretically evaluate the flexural rigidity of the cables madeestimate
 tape and To estimate
 sheath. To of the
 the flexuralmaterials,
 complex rigidityflexuraltherigidity
 ofincluding ofinthe
 ancables
 cablesconductor, in an experiment,
 experiment,
 insulator, bindera tape
 a bending bending
 test on
 and test on cantilever
 cantilever
 sheath. structures built
 structures
 To estimate
 built with power with
 cables power
 were cables
 carriedwereout carried
 as out
 shown as
 inshown
 Figurein Figure
 6.
 the flexural rigidity of the cables in an experiment, a bending test on cantilever structures6.
 built with power cables were carried out as shown in Figure 6.

 Figure 6. Experimental setup for measurement
 Figure 6. Experimental of flexural
 setup for measurement rigidityrigidity
 of flexural of power cable.cable.
 of power
 Figure 6. Experimental setup for measurement of flexural rigidity of power cable.
 To calculate the equivalent flexural rigidity of the cables based on the test results, the
 cables To
 were assumed
 calculate the to be madeflexural
 equivalent of isotropic material,
 rigidity and the
 of the cables correlation
 based between
 on the test results,the
 the
 applied load and the free end displacement as shown in Equation (1) was used.
 cables were assumed to be made of isotropic material, and the correlation between the
 applied load and the free end displacement as shown in Equation (1) was used.

Aerospace 2021, 8, 208 9 of 18

 To calculate the equivalent flexural rigidity of the cables based on the test results, the
 cables were assumed to be made of isotropic material, and the correlation between the
 applied load and the free end displacement as shown in Equation (1) was used.

 FL3
 δ= (1)
 3( EI )eq

 δ referes to the free end displacement, F is the applied load on the free end, L is
 the length of the power cable and ( EI )eq means the equivalent flexural rigidity of the
 power cables. In order to reduce errors due to clearance, storage conditions and cutting
 methods while preparing the specimen, bending tests were carried out repeatedly with
 multiple specimens.

 3.1.1. Static Bending Test
 In order to proceed the bending tests, four specimens for each type of power wire of
 HF-CO, TFR-CV and TFR-8 were prepared, and the detailed specifications of each specimen
 are shown in Table 4. After clamping a power cable specimen as a cantilever, a laser sensor
 was located to measure the free end displacement. Balance weights were used to apply
 load at the free end of the specimen. The free end displacement for each applied load was
 measured after it converged to a certain value.

 Table 4. Dimensions of power cable specimen.

 Weight Per Unit
 Cable Type Length (mm) Diameter (mm)
 Length (kgf/m)
 HF-CO 400 17 0.78
 TFR-CV 400 17 0.79
 TFR-8 400 20 0.83

 Figures 7–9 show the relationship between the free end displacement and the applied
 load, and the calculated equivalent flexural rigidity for each type of power cable. The coef-
 ficients of determination of each bending test with HF-CO, TFR-CV and TFR-8 cables were
 calculated as 0.998, 0.996 and 0.996, respectively. It shows that structural characteristics of
 power cables are linear. Table 5 summarizes the equivalent flexural rigidity of each power
 cable calculated from the experimental results. Even though the dimensions and electrical
 characteristics of the power cables are similar, the equivalent flexural rigidity may vary
 depending on the cable type. It can be expected that the dynamic characteristics of the
 heavy-lift tethered multicopter, based on the above results, are significantly affected by the
 types of power cable applied for the electric power transmission.

 Table 5. Equivalent flexural rigidity for various types of electric power cable.

 Cable Type Equivalent Flexural Rigidity (Nm2 ) Standard Deviation (Nm2 )
 HF-CO 9.74 0.48
 TFR-CV 5.66 0.42
 TFR-8 2.53 0.13

were calculated as 0.998, 0.996 and 0.996, respectively. It shows that structural character-
 istics of power cables are linear. Table 5 summarizes the equivalent flexural rigidity of
 each power cable calculated from the experimental results. Even though the dimensions
 and electrical characteristics of the power cables are similar, the equivalent flexural rigid-
 Aerospace 2021, 8, 208 ity may vary depending on the cable type. It can be expected that the dynamic character- 10 of 18
 istics of the heavy-lift tethered multicopter, based on the above results, are significantly
 affected by the types of power cable applied for the electric power transmission.

Aerospace 2021,8,8,xxFOR
erospace 2021, FORPEER
 PEERREVIEW
 REVIEW 10 of 18
 10 of 18
 Figure 7. StaticFigure
 bending test results
 7. Static bendingfortest
 HF-CO:
 results(a)
 forFree end displacement
 HF-CO: versus applied
 (a) Free end displacement loadapplied
 versus (coefficient of determination:
 load (co-
 0.998); (b) Equivalent flexural rigidity.
 efficient of determination: 0.998); (b) Equivalent flexural rigidity.

 Figure 8. StaticFigure
 bending test
 Figure8.8.Staticresults
 Static
 bending fortest
 bending TFR-8:
 test (a)for
 results
 results Free end (a)
 forTFR-8:
 TFR-8:displacement
 (a)Free
 Freeend versus applied
 enddisplacement
 displacement load
 versus
 versus (coefficient
 applied
 applied of determination:
 load(coef-
 load (coef-
 ficientof
 0.996); (b) Equivalent
 ficient ofdetermination:
 determination:
 flexural 0.996);(b)
 rigidity. 0.996); (b)Equivalent
 Equivalentflexural
 flexuralrigidity.
 rigidity.

 Figure 9. StaticFigure
 bending test
 Figure9.9.Staticresults
 Static
 bendingfortest
 bending TFR-CV:
 testresults(a)
 results Free
 for
 for end displacement
 TFR-CV:
 TFR-CV: (a)Free
 (a) Freeend versus applied
 enddisplacement
 displacement loadapplied
 versus
 versus (coefficient
 applied of(co-
 load(co-
 load determination:
 0.996); (b) Equivalent flexural
 efficient
 efficient rigidity. 0.996);
 ofofdetermination:
 determination: 0.996);(b)
 (b)Equivalent
 Equivalentflexural
 flexuralrigidity.
 rigidity.

 Table5.5.Equivalent
 Table Equivalentflexural
 flexuralrigidity
 rigidityfor
 forvarious
 varioustypes
 typesofofelectric
 electricpower
 powercable.
 cable.

 CableType
 Cable Type EquivalentFlexural
 Equivalent FlexuralRigidity
 Rigidity(Nm
 (Nm2)2) StandardDeviation
 Standard Deviation(Nm
 (Nm2)2)
 HF-CO
 HF-CO 9.74
 9.74 0.48
 0.48

Aerospace 2021, 8, 208 11 of 18

 3.1.2. Consideration of Viscoelasticity
 As mentioned above, it takes several minutes for the level of displacement to converge
 to a certain value after a balance weight is applied on the free end of the power cable. It
 may be attributed to creep, which leads to an assumption that power cables are made
 of viscoelastic materials. Once a load is applied on a viscoelastic material, an elasticity-
 Aerospace 2021, 8, x FOR PEER REVIEW 11 of 18
 induced displacement is immediately observed and subsequently a displacement triggered
 by viscosity starts to be slowly created. To generate a model of such viscoelastic material,
 one of the following models is usually utilized: Maxwell model, Kelvin-Voigt model, Zener
 model, Zener
 model and model and
 Burgers Burgers
 model model
 [31,32]. [31,32].
 Maxwell Maxwell
 model, model,
 which whichofconsists
 consists of linear
 linear spring and
 spring
 linear viscous dashpot, is adopted in this study to estimate the flexural rigidity of rigidity
 and linear viscous dashpot, is adopted in this study to estimate the flexural the power
 of the power
 cables cables
 in a more in a more
 accurate accurate
 manner manner
 and the formulaand used
 the formula
 is shownused is shown
 below below (2)
 in Equation in
 Equation (2)
 dε
 = 11 dσ
 + σ
 dt E dt η (2)(2)
 
 where ε means
 where means strain, η refers refers to viscosity,
 viscosity, which
 whichcouldcouldchange
 changedepending
 depending onon
 various
 various
 factors,
 factors, such
 such as astemperatures
 temperaturesand andthetheconditions
 conditionsofofthe thepower
 power cable
 cablespecimen.
 specimen.
 Viscosity
 Viscositycan canbebeexpressed
 expressedasasaadamping
 dampingcoefficient
 coefficientofof a power
 a power cable
 cable byby expressing
 expressing
 Equation (2), which is a relational expression between stress and
 Equation (2), which is a relational expression between stress and strain, as a relation strain, as a relation be-
 tween force and displacement. In order to consider the viscoelasticity
 between force and displacement. In order to consider the viscoelasticity of the power of the power cable,
 the change
 cable, in the displacement
 the change accordingaccording
 in the displacement to the application of the free end
 to the application loadfree
 of the wasend
 meas-load
 ured in time domain.
 was measured in time Figure 10 shows
 domain. the change
 Figure 10 shows in the
 thedisplacement
 change in the of displacement
 a TFR-CV speci- of a
 men;
 TFR-CV balance weightbalance
 specimen; of 100 gfweight
 was applied
 of 100and removed
 gf was appliedat about 5 min, and
 and removed at 15 min,5re-
 about min,
 spectively,
 and 15 min,after the measurement
 respectively, after thewas started. was
 measurement is the displacement
 started. δk is themade by the linear
 displacement made
 spring, whereas
 by the linear means
 spring, whereasthe displacement
 δη means the triggered
 displacement by the linear viscous
 triggered by thedashpot. The
 linear viscous
 equivalent
 dashpot. The flexural rigidities
 equivalent obtained
 flexural through
 rigidities the previous
 obtained through static
 thebending
 previous tests were
 static the
 bending
 result of adding the displacement by the linear spring and the linear
 tests were the result of adding the displacement by the linear spring and the linear viscous viscous dashpot.
 Therefore, if the equivalent
 dashpot. Therefore, flexural rigidity
 if the equivalent flexuralofrigidity
 the power cable
 of the poweris more
 cableaccurately calcu-
 is more accurately
 lated by considering
 calculated by consideringonly the
 onlydisplacement causedcaused
 the displacement by theby linear springspring
 the linear excluding the lin-the
 excluding
 ear viscous
 linear viscousdashpot,
 dashpot,a larger value
 a larger will will
 value be obtained than the
 be obtained thanresult measured
 the result measuredthrough the
 through
 static bending
 the static bending test.test.
 According
 Accordingto the maxwell
 to the maxwell model,
 model,thethe
 section
 sectionin which
 in which displacement
 displacement
 due
 due to
 to the
 the viscous
 viscousdashpot
 dashpotisisobserved
 observedcan canbebeassumed
 assumed asasa first-order
 a first-order linear
 linearfunction
 functionas as
 shown
 shown in in Figure
 Figure11. 11.

 Figure 10.
 Figure Freeend
 10. Free enddisplacement
 displacementchanges
 changesinintime
 timedomain
 domain due
 due toto viscoelasticity.
 viscoelasticity.

 Table 6 summarizes the results of measuring the maximum displacement and perma-
 nent displacement for each TFR-CV specimen. By applying the linear Maxwell model to
 the results, the damping coefficient and the equivalent flexural rigidity of TFR-CV were
 calculated as 6.5 × 105 Ns/m and 7.14 Nm2 , respectively. Considering the creep effect, the