# Preliminary Design of a Small Unmanned Battery Powered Tailsitter

Authors: Bo Wang; Zhongxi Hou; Zhaowei Liu; Qingyang Chen; Xiongfeng Zhu
Journal: International Journal of Aerospace Engineering
 (2016)

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## Abstract

This paper presents a preliminary design methodology for small unmanned battery powered tailsitters. Subsystem models, including takeoff weight, power and energy consumption models, and battery discharge model, were investigated, respectively. Feasible design space was given by simulation with mission and weight constraints, while the influences of wing loading and battery ratio were analyzed. Case study was carried out according to the design process, and the results were validated by previous designs. The design methodology can be used to determine key parameters and make necessary preparations for detailed design and vehicle realization of small battery powered tailsitters.


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## Body

## 1. Introduction

Application Prospects of Battery Powered Tailsitters. A tailsitter has the capabilities of vertical takeoff and landing (VTOL), hover like a helicopter, transition between vertical flight and level flight, and efficient wing-borne flight as a fixed wing aircraft. Designed for reconnaissance, surveillance, delivering, and rescuing, tailsitters could vertically take off from confined environments, such as woodland, small islands, streets, disaster scene, and even mobile platforms on vehicles and ships. The Project Wing [1] of Google X intends to develop tailsitters for rapid package delivery in a wide range of situations, such as delivering defibrillators to heart attack victims in the countryside; the Small Business Innovation Research (SBIR) plan (2012) of the US Air Force aims for a ducted fan powered tailsitter with long endurance.Powered by batteries and brushless direct current (BLDC) motors, small unmanned tailsitters take the advantages of light weight, low cost, ease of use and maintenance, and low level of vibration and noise. What is more, battery powered tailsitters could take off from the surfaces of Mars and Titan without the help of any runways or launch equipment and then carry out long range exploration, hover on target points, or land directly for detailed detecting. The Surrey Space Centre [2] and the NASA Ames Research Center [3, 4] have studied on such explorer for better mobility and mission performance in Martian exploration.Design Methodology Review. There are many existing configurations of battery powered tailsitters, such as the Martian tailsitter [2] developed by the University of Surrey, the T-wing [5] and Bidule [6] developed by the University of Sydney, the ITU-Tailsitter [7] developed by Istanbul Technical University, the Japanese SkyEyeV [8], the ATOMS [9] developed by Delft University of Technology, and the Quadshot [10] developed by Transition Robotics. Within these vehicles, only the design methods and processes of T-wing, Surrey Martian tailsitter, and ITU-Tailsitter could be found by open literatures.Both electrical motor and reciprocating engine had ever been adopted in the development of T-wing unmanned aerial vehicle (UAV), while the battery powered propulsion system was utilized in the early validation phase [5]. The T-wing configuration with a canard and dual propellers was investigated by multidisciplinary optimization based on detailed subsystems, including aerodynamics-propulsion integrated model, weight and structure model, and control model. Such method was efficient for the design of battery powered tailsitter with different missions and constraints when there was little statistical guidance [11]. However, too many parameters and constraints, at least 13 equality constraints, 36 actual design variables, and 75 fixed design parameters, should be taken into consideration. Meanwhile, the feasible design space and the influence of key parameters, such as the ratio of battery weight to takeoff weight (battery ratio), on aircraft performance have not been discussed. A more general tailsitter configuration with twin rotors needs to be studied.The Surrey Martian tailsitter was an adaption version of QinetiQ’s terrestrial Eye-On, which was a “helicopter assembly” twin rotor design [2]. For this tailsitter, twelve disparate critical subsystems were detailedly designed according to the mission architecture and system requirements. High-level balance of mass and power demonstrates the feasibility of the tailsitter. This design method was well illustrated and more likely to be realized by engineers, while the tailsitter’s range and endurance performance could be improved if an integrated optimization was implemented.The ITU-Tailsitter utilized a hybrid-dual propulsion system [7], which was driven by a large diameter folding propeller located on the nose of the aircraft and a small diameter ducted fan system located on the tail of the aircraft. The former was used in the phase of hover, vertical takeoff, vertical landing, and low speed transition, while the latter was used in the phase of level and high speed flight. This is a novel attempt to deal with the efficiency problem of tailsitters, though some dead weight was introduced for each phase. Variables, such as maximum takeoff weight, wing loading, and battery weight, were optimized for maximum payload and cruise duration. Such method could be suitable for the circumstance that the propulsion propeller and ducted fan have been selected. Generally, for preliminary design, neither the propeller diameter nor the thrust function about propeller speed n and airspeed v as T=T(n,v) has been determined. So the optimization design could not go on successfully.About the Tailsitter. The simplified aerodynamic configuration of battery powered tailsitter consists of four main parts, as shown in Figure 1, fuselage, straight rectangular wing, twin contrarotation propellers, and twin elevons located on the trailing edge. Batteries, payloads, avionics, and other necessary instruments could be contained in the fuselage and the wing.Figure 1
Schematic of a small unmanned battery powered tailsitter.In order to utilize the propellers’ slipstream sufficiently for adequate control moment while attentions should be paid to propellers’ low speed vertical flight performance, a propeller radius ofRP≈bwing/4 was recommended. And variable pitch propellers are proposed for different flight modes, including low speed but high thrust vertical flight mode and high speed but low thrust level flight mode.The same as Bidule [6], twin elevons were utilized to provide roll-attitude and pitch-attitude control, while rotation speeds and collective pitches of such twin propellers were utilized to provide altitude and yaw-attitude control, respectively. The stability and controllability of such configuration have been validated by Bidule’s flight experiments, which will not be discussed here anymore. This paper will focus on weight, power, energy consumption, and endurance performance.The mission profile of a tailsitter was depicted by dashed lines in Figure2. The tailsitter climbs vertically from the takeoff point until reaching the mission height and then transits to horizontal flight (V2H); having accomplished the flight mission, the tailsitter will move to the target landing area and transit to vertical descent (H2V) until landing on the ground.Figure 2
Mission profile comparison between CTOL aircraft and tailsitters.Compared with conventional takeoff and landing (CTOL) aircraft’s mission profile, as real lines portrayed in Figure2, there is no horizontal speedup or slowdown for tailsitters. Each transition on the flight path of the tailsitter was simplified to be along with a right angle for preliminary design. However, an optimized curve transition path should be introduced for actual flight in further study.Aims and Paper Structure. This paper aims for a feasible solution for the preliminary design of small battery powered tailsitters, which could provide effective guidance about weight, geometry, power, and energy consumption for further detailed design and vehicle realization.A small battery powered tailsitter will be designed with current technology to accomplish the flight mission at the height of 1000 m as shown in Figure2. The allowable mass of the tailsitter is 10 kg, and the mass of the payload is 1.0 kg. The maximum level flight duration will be estimated and the corresponding optimum wing loading and battery ratio will be recommended by optimization.In Section2, three subsystems will be modeled, including takeoff weight, power level and energy consumption, and battery discharge. In Section 3, influences of wing loading and battery ratio will be analyzed, and the feasible design space for small battery powered tailsitters will be given. Section 4 will illustrate the preliminary design method and carry out a design case study for validation.


## 2. Subsystem Models

### 2.1. Takeoff Weight

Referring to electrically powered rotary-wing platform [12], takeoff weight of an unmanned battery powered tailsitter WTO is composed of four main components: airframe, BEMP propulsion system, avionics, and payloads. The BEMP system consists of batteries, electronic speed controllers (ESCs), motors, and propellers: (1)WTO=Wairframe+WBEMP+Wavionics+WPL=Wfu-str+Wwing_+WB+WEMP_+Wavionics+WPL,where Wfu-str represents the integrated weights of fuselage, joint structure, and tailsitter’s other structures except wing, WEMP represents the integrated weight of ESC, motor, and propeller, and WPL represents the weight of payloads. The wing weight Wwing and battery weight WB are listed to be discussed individually as they are more significant for aircraft’s endurance performance and share a main proportion of the takeoff weight.Serial weight ratios could be defined:kF=Wfu-str/WTO, kA=Wavionics/WTO, and battery ratio kB=WB/WTO. The wing weight could be expressed as Wwing=kWS, where S is the wing area and kW is the wing weight coefficient representing the weight per unit area of the wing in N/m2. The wing weight could also be expressed by WTO:(2)Wwing=kWWTO/SWTO=kWkWSWTO,where kWS=WTO/S represents the tailsitter’s wing loading in N/m2. And then (1) could be simplified as(3)WTO=WEMP+kWkWS+kB+kF+kAWTO+WPL.Solving (3) yields the takeoff weight as (4)WTO=WEMP+WPL1-kB-kA-kF-kW/kWS,where the weight of payloads WPL will be given by mission; WEMP should be determined by the maximum operation power of vertical climb phase. As can be seen from (4), the takeoff weight will increase as kWS decreases or kB increases for given payloads, when kB+kW/kWS<1-kA-kF is still satisfied.


### 2.2. Power and Energy

In order to realize vertical takeoff and landing, for tailsitters, the ratio of thrust to weightKT needs to be greater than one. The maximum design thrust of the tailsitter can be written as(5)Tmax=KTWTO.Stone [11] suggests that the maximum thrust needs to be 1.15 or higher times greater than takeoff weight, for dealing with nonideal conditions and transition maneuvers. Then a value of KT=1.2 is proposed for small battery powered tailsitters in this paper.The required power of a propeller supplied a thrustT for the aircraft which can be calculated by the momentum theory as [13] (6)PT,V=κTV21+1+2TρAV2,where A=πRP2 is the area of propeller disk; V is the axial forward velocity of the propeller; the induced power factor κ has a typical value in the range of [1.15,1.25] and a conservative value κ=1.2 was suggested. Although the momentum analysis can not give a precise result for power calculation, it takes the propeller’s efficiency about the thrust and the airspeed into consideration and provides an efficient solution for preliminary design without the need of propeller’s detailed parameters.


#### 2.2.1. Accelerating Climb

For vertical takeoff, the climb velocity will gradually increase from zero under the force of propeller thrustT (0<T<Tmax). Having gained the expected climb velocity VC (0<VC<Vmax), the tailsitter will climb to the mission height with the constant velocity.Supposing that the accelerating was performed by the allowable maximum thrustTmax, the tailsitter reaches height H(t) and the climb velocity is V(t) at time t. Ignoring wing-propeller interaction, forces acting on the aircraft include gravity, propeller thrust, and aerodynamic drag of the wing. It can be deduced by Newton’s second law that (7)∑Fj=T-WTO-ρSCD02V2=md2Hdt2,where m=WTO/g is the mass of the tailsitter, ρ is the air density, and CD0 is the wing’s zero-lift drag coefficient. According to the relationship between displacement and velocity, (7) can be converted into(8)dVdt=d2Hdt2=kT-1g-ρSCD02mV2.Combined with the initial climb velocity, (8) can be written as(9)dVa/b2-V2=b2dt,a=gkT-1,Vt=0=0,b=ρSCD02m.Simultaneous integral on both sides of the differential equation in (9) yields(10)t=12abln⁡a/b+Va/b-V=12abln⁡1+2a/bV-1.Referring to the actual situation, the feasible solution of climb velocity about time is (11)Vt=abexp⁡2abt-1exp⁡2abt+1,t∈0,tAC,where the duration of accelerating climb tAC depends on the expected constant climb velocity VC. Because the speed is the first derivative of the displacement(12)V=dHdt,Ht=0=0.The reached height about time in the phase of accelerating climb can be given by (13)Ht=∫Vtdt=1b2ln⁡exp⁡2abt+1-abt,t∈0,tAC.At the end of accelerating climb, the tailsitter reaches the height of HAC=H(tAC), which also depends on the expected constant climb velocity VC.


#### 2.2.2. Constant Velocity Climb

In the phase of constant velocity climb, ignoring wing-propeller interaction, the required thrust can be expressed as(14)TC=WTO+ρ2VC2SCD0.As can be seen from (14), the higher the rate of climb VC, the greater the thrust TC needed. In view of the maximum thrust T≤Tmax, the maximum allowable rate of climb is (15)Vmax=2ρCD0·KT-1·WTOS.Given the aerodynamic and propulsion characteristics of a tailsitter, Vmax would only depend on wing loading.Because the tailsitter was driven by twin contrarotation propellers, as shown in Figure1, each propeller needs to provide a half of the required thrust. The maximum operation power of each motor Preqmax was determined by Tmax and Vmax through (6) as Preqmax=PkTWTO/2,Vmax. So the necessary mass of each motor-propeller system, including the propeller, the motor, and the ESC, could be expressed as (16)mEMP=KEMPPreqmax,where KEMP is the mass-power coefficient of the motor-propeller system in unit of kg/W.


#### 2.2.3. Energy Consumption in Climb

The actual required power for each propeller in the phase of constant velocity climb is still calculated by the momentum theory asPC=PTC/2,VC by (6). The total energy consumption in the phase of constant climb for the tailsitter is (17)EC=2·PCηBηEηMHm-HACVC.For accelerating climb, the required power for each propeller at any timet∈0,tAC is calculated similarly by (6) as PACt=PTmax/2,Vt, where climb velocity V(t) can be yielded by (11). So the energy consumption in the phase of accelerating climb could be given by integration:(18)EAC=2∫0tACPACtdtηBηEηM,where the upper limit of the integration tAC can be yielded by (10) with the constant climb velocity VC. Then the total energy consumption for climb can be given by(19)Etot=EAC+EC.Equation (19) is a high order nonlinear function about expected velocity VC, which needs to be optimized within the feasible range [0,Vmax] to minimize the energy consumption. The optimization problem can be written as follows:(20)findVCminEtotsubjectto0<VC<Vmax.


#### 2.2.4. Power of Level Flight

For different flight missions, different level flight velocitiesVLF could be adopted by a tailsitter for better performance. And then, different required thrusts TLF and propeller efficiency result in the required power PLF for level flight various. Considering two typical flight conditions, maximum range and endurance, the level flight performance of a battery powered tailsitter will be analyzed.The steady level flight performance of a propeller-driven tailsitter could be estimated according to the literature [14]. When L/D and CL3/2/CD gain the maximum values at the flight conditions of KCL2=CD0 and KCL2=3CD0, respectively, the maximum level flight range and endurance can be yielded, where K=1/πeAR and e is Oswald’s efficiency which is set to 0.85 in this study because the wing configuration is nontapered and nonswept. The corresponding level flight velocities VR and VE can be deduced from the equality of the tailsitter’s lift L and weight WTO as(21)VR=2WTOρSwingKCD0,VE=2WTOρSwingK3CD0.Required thrustsTR and TE can be yielded by the equality of the thrust and the drag acting on the tailsitter:(22)TR=DR=ρ2VR2Swing·2CD0,TE=DE=ρ2VE2Swing·4CD0.For such two steady level flight conditions, power consumption of each propeller can be given by the momentum theory asPE=PDE/2,VE and PR=PDR/2,VR.


#### 2.2.5. Energy Consumption in Landing

Being subjected to structural constraints and landing quality requirements, the landing velocity of a tailsitter should be strictly restricted. The allowable landing loads for T-wing were a drop from 4.0-foot height [5], which meant a maximum allowable landing velocity of 4.88 m/s. Considering the stability of a descending tailsitter, the crucial elevons required a high dynamic pressure which was determined by the propellers’ slip velocity and the descent velocity. So high propeller disk loading and a low descending velocity were recommended.The induced velocityVH at the propeller disk in hover is an important reference for the analysis of tailsitter descent, which could be expressed as(23)VH=Thover2ρA=WTO4ρA.As propeller radius RP=0.25bwing=0.25S·AR, substituting propeller disk area A=πRP2 into (23) then we yield a more specific version of the reference velocity as(24)VH=4kWSρπAR.A descent velocity ofVDes=4 m/s was suggested in this paper, and then the propellers are working on a condition of low speed axial descent VDes<2VH. Assuming the variable x=-VDes/VH, the actual induced velocity Vi at the propeller disk can be given by the quartic approximation [13]: (25)Vi=κ-1.125x-1.372x2-1.718x3-0.655x4VH.And then, ignoring the aerodynamic forces on the wing, the required power of each propeller at such low rate of descent can be expressed as(26)PDes=κTreqVdisk=κWTOVi-VDes.Therefore, the total energy consumption EDes for vertical landing is(27)EDes=2κWTOVi-VDesHmηBηEηMVDes.


### 2.3. Battery Discharge

For current rechargeable batteries, such as lithium-polymer battery, the effective capacity has a relationship with actual current draw as Peukert effect [15, 16]. The operation powers of the tailsitter for vertical climb, level flight, and vertical descent are different from each other, and there is PC>PDes>PLF. With the same battery voltage level, the higher flight power leads to a higher current draw for each motor-propeller system, IC>IDes>ILF, and a consequential less effective capacity CC<CDes<CLF. Considering batteries’ voltage drop actually, the discharge processes for climb, level flight, and descent are sketched in Figure 3, where CC, CDes, and CLF represent the effective capacities corresponding to such three different current draws, respectively, and UB is the nominal terminal voltage. As residual capacity could be utilized for further discharge [17], the actual flight discharge process is illustrated by dash lines, where C1 represents the consumed capacity in climb, C2 represents the total capacity that has discharged before descent, and Cact represents the total capacity of a full discharge process.Figure 3
Illustration of the battery discharge process with variable current draw.Theoretical calculation based on the assumption of constant battery voltage was carried out to estimate the possible level flight endurance as(28)tLF=C2-C12ILF=Cact2ILF-CD′+CC′+CAC′2ILF,where CD′, CC′, CAC′ represent the consumed capacity in descent, constant velocity climb, and accelerating climb and multiplication by two in the denominator represents the fact that such two motor-propeller systems are powered by the same battery pack. It can be deduced from the experiments [17] that Cact≈CDes, so there is(29)tLF=CDesIDes·IDesUB2ILFUB-CD′+CC′+CAC′UB2ILFUB=CDesIDes·PDes2PLF-EDes+Etot2PLF.Peukert equation tells that CBIBn-1=CDesIDesn-1, and tB=1 hour for small battery gives(30)CDesIDes=CBIBn-1IDesn=tB1-nCBnUBnIDesnUBn=EBPDesn,where EB is the electric energy stored in battery; n is the Peukert coefficient; PLF represents the maximum range power PR or the maximum endurance power PE. Considering the efficiency of energy transformation, the level flight endurance is(31)tLF=mBKBEmηBηEηMPDesnPDes2PLF-EDes+Etot2PLF,where mB=kBWTO/g is the mass of battery and KBEm is the specific energy of battery.


## 2.1. Takeoff Weight

Referring to electrically powered rotary-wing platform [12], takeoff weight of an unmanned battery powered tailsitter WTO is composed of four main components: airframe, BEMP propulsion system, avionics, and payloads. The BEMP system consists of batteries, electronic speed controllers (ESCs), motors, and propellers: (1)WTO=Wairframe+WBEMP+Wavionics+WPL=Wfu-str+Wwing_+WB+WEMP_+Wavionics+WPL,where Wfu-str represents the integrated weights of fuselage, joint structure, and tailsitter’s other structures except wing, WEMP represents the integrated weight of ESC, motor, and propeller, and WPL represents the weight of payloads. The wing weight Wwing and battery weight WB are listed to be discussed individually as they are more significant for aircraft’s endurance performance and share a main proportion of the takeoff weight.Serial weight ratios could be defined:kF=Wfu-str/WTO, kA=Wavionics/WTO, and battery ratio kB=WB/WTO. The wing weight could be expressed as Wwing=kWS, where S is the wing area and kW is the wing weight coefficient representing the weight per unit area of the wing in N/m2. The wing weight could also be expressed by WTO:(2)Wwing=kWWTO/SWTO=kWkWSWTO,where kWS=WTO/S represents the tailsitter’s wing loading in N/m2. And then (1) could be simplified as(3)WTO=WEMP+kWkWS+kB+kF+kAWTO+WPL.Solving (3) yields the takeoff weight as (4)WTO=WEMP+WPL1-kB-kA-kF-kW/kWS,where the weight of payloads WPL will be given by mission; WEMP should be determined by the maximum operation power of vertical climb phase. As can be seen from (4), the takeoff weight will increase as kWS decreases or kB increases for given payloads, when kB+kW/kWS<1-kA-kF is still satisfied.


## 2.2. Power and Energy

In order to realize vertical takeoff and landing, for tailsitters, the ratio of thrust to weightKT needs to be greater than one. The maximum design thrust of the tailsitter can be written as(5)Tmax=KTWTO.Stone [11] suggests that the maximum thrust needs to be 1.15 or higher times greater than takeoff weight, for dealing with nonideal conditions and transition maneuvers. Then a value of KT=1.2 is proposed for small battery powered tailsitters in this paper.The required power of a propeller supplied a thrustT for the aircraft which can be calculated by the momentum theory as [13] (6)PT,V=κTV21+1+2TρAV2,where A=πRP2 is the area of propeller disk; V is the axial forward velocity of the propeller; the induced power factor κ has a typical value in the range of [1.15,1.25] and a conservative value κ=1.2 was suggested. Although the momentum analysis can not give a precise result for power calculation, it takes the propeller’s efficiency about the thrust and the airspeed into consideration and provides an efficient solution for preliminary design without the need of propeller’s detailed parameters.


### 2.2.1. Accelerating Climb

For vertical takeoff, the climb velocity will gradually increase from zero under the force of propeller thrustT (0<T<Tmax). Having gained the expected climb velocity VC (0<VC<Vmax), the tailsitter will climb to the mission height with the constant velocity.Supposing that the accelerating was performed by the allowable maximum thrustTmax, the tailsitter reaches height H(t) and the climb velocity is V(t) at time t. Ignoring wing-propeller interaction, forces acting on the aircraft include gravity, propeller thrust, and aerodynamic drag of the wing. It can be deduced by Newton’s second law that (7)∑Fj=T-WTO-ρSCD02V2=md2Hdt2,where m=WTO/g is the mass of the tailsitter, ρ is the air density, and CD0 is the wing’s zero-lift drag coefficient. According to the relationship between displacement and velocity, (7) can be converted into(8)dVdt=d2Hdt2=kT-1g-ρSCD02mV2.Combined with the initial climb velocity, (8) can be written as(9)dVa/b2-V2=b2dt,a=gkT-1,Vt=0=0,b=ρSCD02m.Simultaneous integral on both sides of the differential equation in (9) yields(10)t=12abln⁡a/b+Va/b-V=12abln⁡1+2a/bV-1.Referring to the actual situation, the feasible solution of climb velocity about time is (11)Vt=abexp⁡2abt-1exp⁡2abt+1,t∈0,tAC,where the duration of accelerating climb tAC depends on the expected constant climb velocity VC. Because the speed is the first derivative of the displacement(12)V=dHdt,Ht=0=0.The reached height about time in the phase of accelerating climb can be given by (13)Ht=∫Vtdt=1b2ln⁡exp⁡2abt+1-abt,t∈0,tAC.At the end of accelerating climb, the tailsitter reaches the height of HAC=H(tAC), which also depends on the expected constant climb velocity VC.


### 2.2.2. Constant Velocity Climb

In the phase of constant velocity climb, ignoring wing-propeller interaction, the required thrust can be expressed as(14)TC=WTO+ρ2VC2SCD0.As can be seen from (14), the higher the rate of climb VC, the greater the thrust TC needed. In view of the maximum thrust T≤Tmax, the maximum allowable rate of climb is (15)Vmax=2ρCD0·KT-1·WTOS.Given the aerodynamic and propulsion characteristics of a tailsitter, Vmax would only depend on wing loading.Because the tailsitter was driven by twin contrarotation propellers, as shown in Figure1, each propeller needs to provide a half of the required thrust. The maximum operation power of each motor Preqmax was determined by Tmax and Vmax through (6) as Preqmax=PkTWTO/2,Vmax. So the necessary mass of each motor-propeller system, including the propeller, the motor, and the ESC, could be expressed as (16)mEMP=KEMPPreqmax,where KEMP is the mass-power coefficient of the motor-propeller system in unit of kg/W.


### 2.2.3. Energy Consumption in Climb

The actual required power for each propeller in the phase of constant velocity climb is still calculated by the momentum theory asPC=PTC/2,VC by (6). The total energy consumption in the phase of constant climb for the tailsitter is (17)EC=2·PCηBηEηMHm-HACVC.For accelerating climb, the required power for each propeller at any timet∈0,tAC is calculated similarly by (6) as PACt=PTmax/2,Vt, where climb velocity V(t) can be yielded by (11). So the energy consumption in the phase of accelerating climb could be given by integration:(18)EAC=2∫0tACPACtdtηBηEηM,where the upper limit of the integration tAC can be yielded by (10) with the constant climb velocity VC. Then the total energy consumption for climb can be given by(19)Etot=EAC+EC.Equation (19) is a high order nonlinear function about expected velocity VC, which needs to be optimized within the feasible range [0,Vmax] to minimize the energy consumption. The optimization problem can be written as follows:(20)findVCminEtotsubjectto0<VC<Vmax.


### 2.2.4. Power of Level Flight

For different flight missions, different level flight velocitiesVLF could be adopted by a tailsitter for better performance. And then, different required thrusts TLF and propeller efficiency result in the required power PLF for level flight various. Considering two typical flight conditions, maximum range and endurance, the level flight performance of a battery powered tailsitter will be analyzed.The steady level flight performance of a propeller-driven tailsitter could be estimated according to the literature [14]. When L/D and CL3/2/CD gain the maximum values at the flight conditions of KCL2=CD0 and KCL2=3CD0, respectively, the maximum level flight range and endurance can be yielded, where K=1/πeAR and e is Oswald’s efficiency which is set to 0.85 in this study because the wing configuration is nontapered and nonswept. The corresponding level flight velocities VR and VE can be deduced from the equality of the tailsitter’s lift L and weight WTO as(21)VR=2WTOρSwingKCD0,VE=2WTOρSwingK3CD0.Required thrustsTR and TE can be yielded by the equality of the thrust and the drag acting on the tailsitter:(22)TR=DR=ρ2VR2Swing·2CD0,TE=DE=ρ2VE2Swing·4CD0.For such two steady level flight conditions, power consumption of each propeller can be given by the momentum theory asPE=PDE/2,VE and PR=PDR/2,VR.


### 2.2.5. Energy Consumption in Landing

Being subjected to structural constraints and landing quality requirements, the landing velocity of a tailsitter should be strictly restricted. The allowable landing loads for T-wing were a drop from 4.0-foot height [5], which meant a maximum allowable landing velocity of 4.88 m/s. Considering the stability of a descending tailsitter, the crucial elevons required a high dynamic pressure which was determined by the propellers’ slip velocity and the descent velocity. So high propeller disk loading and a low descending velocity were recommended.The induced velocityVH at the propeller disk in hover is an important reference for the analysis of tailsitter descent, which could be expressed as(23)VH=Thover2ρA=WTO4ρA.As propeller radius RP=0.25bwing=0.25S·AR, substituting propeller disk area A=πRP2 into (23) then we yield a more specific version of the reference velocity as(24)VH=4kWSρπAR.A descent velocity ofVDes=4 m/s was suggested in this paper, and then the propellers are working on a condition of low speed axial descent VDes<2VH. Assuming the variable x=-VDes/VH, the actual induced velocity Vi at the propeller disk can be given by the quartic approximation [13]: (25)Vi=κ-1.125x-1.372x2-1.718x3-0.655x4VH.And then, ignoring the aerodynamic forces on the wing, the required power of each propeller at such low rate of descent can be expressed as(26)PDes=κTreqVdisk=κWTOVi-VDes.Therefore, the total energy consumption EDes for vertical landing is(27)EDes=2κWTOVi-VDesHmηBηEηMVDes.


## 2.2.1. Accelerating Climb

For vertical takeoff, the climb velocity will gradually increase from zero under the force of propeller thrustT (0<T<Tmax). Having gained the expected climb velocity VC (0<VC<Vmax), the tailsitter will climb to the mission height with the constant velocity.Supposing that the accelerating was performed by the allowable maximum thrustTmax, the tailsitter reaches height H(t) and the climb velocity is V(t) at time t. Ignoring wing-propeller interaction, forces acting on the aircraft include gravity, propeller thrust, and aerodynamic drag of the wing. It can be deduced by Newton’s second law that (7)∑Fj=T-WTO-ρSCD02V2=md2Hdt2,where m=WTO/g is the mass of the tailsitter, ρ is the air density, and CD0 is the wing’s zero-lift drag coefficient. According to the relationship between displacement and velocity, (7) can be converted into(8)dVdt=d2Hdt2=kT-1g-ρSCD02mV2.Combined with the initial climb velocity, (8) can be written as(9)dVa/b2-V2=b2dt,a=gkT-1,Vt=0=0,b=ρSCD02m.Simultaneous integral on both sides of the differential equation in (9) yields(10)t=12abln⁡a/b+Va/b-V=12abln⁡1+2a/bV-1.Referring to the actual situation, the feasible solution of climb velocity about time is (11)Vt=abexp⁡2abt-1exp⁡2abt+1,t∈0,tAC,where the duration of accelerating climb tAC depends on the expected constant climb velocity VC. Because the speed is the first derivative of the displacement(12)V=dHdt,Ht=0=0.The reached height about time in the phase of accelerating climb can be given by (13)Ht=∫Vtdt=1b2ln⁡exp⁡2abt+1-abt,t∈0,tAC.At the end of accelerating climb, the tailsitter reaches the height of HAC=H(tAC), which also depends on the expected constant climb velocity VC.


## 2.2.2. Constant Velocity Climb

In the phase of constant velocity climb, ignoring wing-propeller interaction, the required thrust can be expressed as(14)TC=WTO+ρ2VC2SCD0.As can be seen from (14), the higher the rate of climb VC, the greater the thrust TC needed. In view of the maximum thrust T≤Tmax, the maximum allowable rate of climb is (15)Vmax=2ρCD0·KT-1·WTOS.Given the aerodynamic and propulsion characteristics of a tailsitter, Vmax would only depend on wing loading.Because the tailsitter was driven by twin contrarotation propellers, as shown in Figure1, each propeller needs to provide a half of the required thrust. The maximum operation power of each motor Preqmax was determined by Tmax and Vmax through (6) as Preqmax=PkTWTO/2,Vmax. So the necessary mass of each motor-propeller system, including the propeller, the motor, and the ESC, could be expressed as (16)mEMP=KEMPPreqmax,where KEMP is the mass-power coefficient of the motor-propeller system in unit of kg/W.


## 2.2.3. Energy Consumption in Climb

The actual required power for each propeller in the phase of constant velocity climb is still calculated by the momentum theory asPC=PTC/2,VC by (6). The total energy consumption in the phase of constant climb for the tailsitter is (17)EC=2·PCηBηEηMHm-HACVC.For accelerating climb, the required power for each propeller at any timet∈0,tAC is calculated similarly by (6) as PACt=PTmax/2,Vt, where climb velocity V(t) can be yielded by (11). So the energy consumption in the phase of accelerating climb could be given by integration:(18)EAC=2∫0tACPACtdtηBηEηM,where the upper limit of the integration tAC can be yielded by (10) with the constant climb velocity VC. Then the total energy consumption for climb can be given by(19)Etot=EAC+EC.Equation (19) is a high order nonlinear function about expected velocity VC, which needs to be optimized within the feasible range [0,Vmax] to minimize the energy consumption. The optimization problem can be written as follows:(20)findVCminEtotsubjectto0<VC<Vmax.


## 2.2.4. Power of Level Flight

For different flight missions, different level flight velocitiesVLF could be adopted by a tailsitter for better performance. And then, different required thrusts TLF and propeller efficiency result in the required power PLF for level flight various. Considering two typical flight conditions, maximum range and endurance, the level flight performance of a battery powered tailsitter will be analyzed.The steady level flight performance of a propeller-driven tailsitter could be estimated according to the literature [14]. When L/D and CL3/2/CD gain the maximum values at the flight conditions of KCL2=CD0 and KCL2=3CD0, respectively, the maximum level flight range and endurance can be yielded, where K=1/πeAR and e is Oswald’s efficiency which is set to 0.85 in this study because the wing configuration is nontapered and nonswept. The corresponding level flight velocities VR and VE can be deduced from the equality of the tailsitter’s lift L and weight WTO as(21)VR=2WTOρSwingKCD0,VE=2WTOρSwingK3CD0.Required thrustsTR and TE can be yielded by the equality of the thrust and the drag acting on the tailsitter:(22)TR=DR=ρ2VR2Swing·2CD0,TE=DE=ρ2VE2Swing·4CD0.For such two steady level flight conditions, power consumption of each propeller can be given by the momentum theory asPE=PDE/2,VE and PR=PDR/2,VR.


## 2.2.5. Energy Consumption in Landing

Being subjected to structural constraints and landing quality requirements, the landing velocity of a tailsitter should be strictly restricted. The allowable landing loads for T-wing were a drop from 4.0-foot height [5], which meant a maximum allowable landing velocity of 4.88 m/s. Considering the stability of a descending tailsitter, the crucial elevons required a high dynamic pressure which was determined by the propellers’ slip velocity and the descent velocity. So high propeller disk loading and a low descending velocity were recommended.The induced velocityVH at the propeller disk in hover is an important reference for the analysis of tailsitter descent, which could be expressed as(23)VH=Thover2ρA=WTO4ρA.As propeller radius RP=0.25bwing=0.25S·AR, substituting propeller disk area A=πRP2 into (23) then we yield a more specific version of the reference velocity as(24)VH=4kWSρπAR.A descent velocity ofVDes=4 m/s was suggested in this paper, and then the propellers are working on a condition of low speed axial descent VDes<2VH. Assuming the variable x=-VDes/VH, the actual induced velocity Vi at the propeller disk can be given by the quartic approximation [13]: (25)Vi=κ-1.125x-1.372x2-1.718x3-0.655x4VH.And then, ignoring the aerodynamic forces on the wing, the required power of each propeller at such low rate of descent can be expressed as(26)PDes=κTreqVdisk=κWTOVi-VDes.Therefore, the total energy consumption EDes for vertical landing is(27)EDes=2κWTOVi-VDesHmηBηEηMVDes.


## 2.3. Battery Discharge

For current rechargeable batteries, such as lithium-polymer battery, the effective capacity has a relationship with actual current draw as Peukert effect [15, 16]. The operation powers of the tailsitter for vertical climb, level flight, and vertical descent are different from each other, and there is PC>PDes>PLF. With the same battery voltage level, the higher flight power leads to a higher current draw for each motor-propeller system, IC>IDes>ILF, and a consequential less effective capacity CC<CDes<CLF. Considering batteries’ voltage drop actually, the discharge processes for climb, level flight, and descent are sketched in Figure 3, where CC, CDes, and CLF represent the effective capacities corresponding to such three different current draws, respectively, and UB is the nominal terminal voltage. As residual capacity could be utilized for further discharge [17], the actual flight discharge process is illustrated by dash lines, where C1 represents the consumed capacity in climb, C2 represents the total capacity that has discharged before descent, and Cact represents the total capacity of a full discharge process.Figure 3
Illustration of the battery discharge process with variable current draw.Theoretical calculation based on the assumption of constant battery voltage was carried out to estimate the possible level flight endurance as(28)tLF=C2-C12ILF=Cact2ILF-CD′+CC′+CAC′2ILF,where CD′, CC′, CAC′ represent the consumed capacity in descent, constant velocity climb, and accelerating climb and multiplication by two in the denominator represents the fact that such two motor-propeller systems are powered by the same battery pack. It can be deduced from the experiments [17] that Cact≈CDes, so there is(29)tLF=CDesIDes·IDesUB2ILFUB-CD′+CC′+CAC′UB2ILFUB=CDesIDes·PDes2PLF-EDes+Etot2PLF.Peukert equation tells that CBIBn-1=CDesIDesn-1, and tB=1 hour for small battery gives(30)CDesIDes=CBIBn-1IDesn=tB1-nCBnUBnIDesnUBn=EBPDesn,where EB is the electric energy stored in battery; n is the Peukert coefficient; PLF represents the maximum range power PR or the maximum endurance power PE. Considering the efficiency of energy transformation, the level flight endurance is(31)tLF=mBKBEmηBηEηMPDesnPDes2PLF-EDes+Etot2PLF,where mB=kBWTO/g is the mass of battery and KBEm is the specific energy of battery.


## 3. Parameter Influence Study

For conventional battery powered airplane, the required power for level flight is(32)PLF¯=CDCL3/22ρWTO3S.Generally, the propeller’s efficiency was regarded as constant ηP that was independent of flight conditions; a total efficiency of BEMP propulsion system ηtot=ηBηEηMηP could be used to evaluate the influence of wing loading and battery ratio on endurance performance as (33)tLF¯≈EBηtotPLF¯n=ρ2CL3/2CDkBKBEmηtotgkWSn∝kBkWSn.As can be seen from (33), there is a positive correlation between the endurance and battery ratio and a negative correlation between the endurance and wing loading.Simulations were carried out to examine the influence of wing loading and battery ratio on battery powered tailsitters’ range and endurance performance.


### 3.1. Parameters

At the beginning of numerical analysis, it is necessary to distinguish former parameters and constraints between three different classes: constant or assumed constant parameters, design variables, and intermediate variables.(1)
Parameters that are constant or assumed to be constant are listed in Table 1, which are linked to the design experience of tailsitters [2], general level of current technology about wing structure [18], lithium-polymer (Li-Po) batteries, ESCs and BLDC motors [19], typical mission performance of small battery powered UAVs [20, 21], and so forth.(2)
Design variables are wing loading kWS and ratio of battery weight kB. It is known from (4) that kWS>kW/1-kA-kF=kWS0 and kB<1-kA-kF-kW/kWS=kB0. Analysis will focus on small tailsitters of WTO<20 kg; therefore numerical approximations of kWS≥2kWS0 and kB≤0.9kB0 will be applied.(3)
Intermediate variables include the climb velocity VC and the mass of motor-propeller system mEMP, which need to be optimized, and powers and energy consumption of climb and descent, PC, EC, PDes, and EDes, which need to be evaluated.Table 1
Parameters that are constant or assumed to be constant.
Parameter
Value
Unit
Description
k
A
0.1
—
Avionics weight ratio
k
F
0.2
—
Fuselage and strength structure weight ratio
k
W
20
N/m2
Wing weight coefficient
AR
5.0
—
Wing aspect ratio
C
D
0
0.03
—
Wing zero-lift drag coefficient
K
B
E
m
150
Wh/kg
Battery specific energy
K
E
M
P
5 × 10−4
kg/W
Mass-power coefficient of motor-propeller system
η
B
0.95
—
Efficiency of battery discharge
η
E
0.95
—
Efficiency of ESC
η
M
0.9
—
Efficiency of BLDC motor
n
1.3
Peukert coefficient for Li-Po battery
H
m
1000
m
Mission height
m
P
L
1.0
kg
Mass of mission payloads


### 3.2. Simulation Results

(
1) Feasible Design Space. As can be seen from Figure 4, there are consistent left and right margins for Figures 4(a) and 4(b), between which the feasible design space for battery powered tailsitters about wing loading and battery ratio is demonstrated. The left margin represents the minimum kB for different kWS, which means that carried battery could only support the tailsitter to vertically climb to the mission height and land back on the ground. There are tLF=0 and range=0 on the left margin. The theoretic right margin is determined by wing loading’s lower limit kWS0 and battery ratio’s upper limit kB0. Because numerical calculation could not reach such limits directly, Figure 4 shows a dynamic approximation of the theoretic right margin.Figure 4
Feasible design space about wing loading and battery ratio.
(a)
t
L
F
>
0
(b)
R
a
n
g
e
>
0In feasible design space, the level flight range and endurance performance vary withkB and kWS. Both the optimum wing loading and battery ratio for maximum range, kWSR and kBR, are higher than the optimum values of kWSE and kBE for maximum endurance, respectively. Meanwhile, it can be deduced from Figure 4 that too small wing loading will not be proposed for better level flight performance. The reason is that a smaller kWS leads to a smaller upper limit of battery ratio, while kB plays a more important role in level flight performance improvement as (33) shows.(
2) Weight and Power Level. Takeoff weights for all possible designs based on possible wing loading and battery ratios are shown in Figure 5(a), and partly designs are unfeasible as battery energy could not support any level flight at the mission height. As kWS→kWS0 and kB→kB0, WTO will increase quickly, and level flight endurance and range increase correspondingly as shown in Figure 4.Figure 5
(a) Takeoff weight for all possible designs; (b) optimum constant climb velocity and motor-propeller system weight for different wing loading.
(a)
(b)Optimization results indicate that the optimum constant climb velocityVCopti and the necessary weight ratio of motor-propeller system kEMP=WEMP/WTO are only related to tailsitter’s wing loading, as shown in Figure 5(b). Motor-propeller system weight increases gradually from less than 10 percent of WTO to nearly 20 percent, while VCopti firstly increases and then decreases slightly as kWS>300 N/m2.Given the values ofkB and kWS, for a determinate design of battery powered tailsitter in other words, the power of constant velocity climb PC is approximately 10 times PE, as the comparison shown in Figure 6. That is the significant distinction between the tailsitter and the CTOL UAVs. Optimizations on climb path and transition maneuver will be significant for tailsitter’s performance improvement.Figure 6
Power levels comparison between climb and maximum endurance level flight.
(a)
(b)In summary, the wing loading and battery ratio of battery powered tailsitters should be optimized based on mission parameters for better level flight performance.


## 3.1. Parameters

At the beginning of numerical analysis, it is necessary to distinguish former parameters and constraints between three different classes: constant or assumed constant parameters, design variables, and intermediate variables.(1)
Parameters that are constant or assumed to be constant are listed in Table 1, which are linked to the design experience of tailsitters [2], general level of current technology about wing structure [18], lithium-polymer (Li-Po) batteries, ESCs and BLDC motors [19], typical mission performance of small battery powered UAVs [20, 21], and so forth.(2)
Design variables are wing loading kWS and ratio of battery weight kB. It is known from (4) that kWS>kW/1-kA-kF=kWS0 and kB<1-kA-kF-kW/kWS=kB0. Analysis will focus on small tailsitters of WTO<20 kg; therefore numerical approximations of kWS≥2kWS0 and kB≤0.9kB0 will be applied.(3)
Intermediate variables include the climb velocity VC and the mass of motor-propeller system mEMP, which need to be optimized, and powers and energy consumption of climb and descent, PC, EC, PDes, and EDes, which need to be evaluated.Table 1
Parameters that are constant or assumed to be constant.
Parameter
Value
Unit
Description
k
A
0.1
—
Avionics weight ratio
k
F
0.2
—
Fuselage and strength structure weight ratio
k
W
20
N/m2
Wing weight coefficient
AR
5.0
—
Wing aspect ratio
C
D
0
0.03
—
Wing zero-lift drag coefficient
K
B
E
m
150
Wh/kg
Battery specific energy
K
E
M
P
5 × 10−4
kg/W
Mass-power coefficient of motor-propeller system
η
B
0.95
—
Efficiency of battery discharge
η
E
0.95
—
Efficiency of ESC
η
M
0.9
—
Efficiency of BLDC motor
n
1.3
Peukert coefficient for Li-Po battery
H
m
1000
m
Mission height
m
P
L
1.0
kg
Mass of mission payloads


## 3.2. Simulation Results

(
1) Feasible Design Space. As can be seen from Figure 4, there are consistent left and right margins for Figures 4(a) and 4(b), between which the feasible design space for battery powered tailsitters about wing loading and battery ratio is demonstrated. The left margin represents the minimum kB for different kWS, which means that carried battery could only support the tailsitter to vertically climb to the mission height and land back on the ground. There are tLF=0 and range=0 on the left margin. The theoretic right margin is determined by wing loading’s lower limit kWS0 and battery ratio’s upper limit kB0. Because numerical calculation could not reach such limits directly, Figure 4 shows a dynamic approximation of the theoretic right margin.Figure 4
Feasible design space about wing loading and battery ratio.
(a)
t
L
F
>
0
(b)
R
a
n
g
e
>
0In feasible design space, the level flight range and endurance performance vary withkB and kWS. Both the optimum wing loading and battery ratio for maximum range, kWSR and kBR, are higher than the optimum values of kWSE and kBE for maximum endurance, respectively. Meanwhile, it can be deduced from Figure 4 that too small wing loading will not be proposed for better level flight performance. The reason is that a smaller kWS leads to a smaller upper limit of battery ratio, while kB plays a more important role in level flight performance improvement as (33) shows.(
2) Weight and Power Level. Takeoff weights for all possible designs based on possible wing loading and battery ratios are shown in Figure 5(a), and partly designs are unfeasible as battery energy could not support any level flight at the mission height. As kWS→kWS0 and kB→kB0, WTO will increase quickly, and level flight endurance and range increase correspondingly as shown in Figure 4.Figure 5
(a) Takeoff weight for all possible designs; (b) optimum constant climb velocity and motor-propeller system weight for different wing loading.
(a)
(b)Optimization results indicate that the optimum constant climb velocityVCopti and the necessary weight ratio of motor-propeller system kEMP=WEMP/WTO are only related to tailsitter’s wing loading, as shown in Figure 5(b). Motor-propeller system weight increases gradually from less than 10 percent of WTO to nearly 20 percent, while VCopti firstly increases and then decreases slightly as kWS>300 N/m2.Given the values ofkB and kWS, for a determinate design of battery powered tailsitter in other words, the power of constant velocity climb PC is approximately 10 times PE, as the comparison shown in Figure 6. That is the significant distinction between the tailsitter and the CTOL UAVs. Optimizations on climb path and transition maneuver will be significant for tailsitter’s performance improvement.Figure 6
Power levels comparison between climb and maximum endurance level flight.
(a)
(b)In summary, the wing loading and battery ratio of battery powered tailsitters should be optimized based on mission parameters for better level flight performance.


## 4. Preliminary Design Case

### 4.1. Design Method and Process

Being subjected to the constraints of allowable takeoff weight and maximum climb velocity, the optimum wing loading and battery ratio need to be determined, and the constant climb velocity should be optimized for maximum level flight endurance for given mission height and payloads. The design method for a small unmanned battery powered tailsitter could be summarized to an optimization problem, expressed as follows:(34)maxendurancekB,kWSsubjecttoWTO≤Wallow,0<VC<Vmax.The weight of the motor-propeller systemWEMP is determined by the maximum takeoff power Preqmax=PkTWTO/2,Vmax. Iterations are carried out with (4), (15), and (16) for an appropriate solution. The flowchart of the preliminary design process for battery powered tailsitters is shown in Figure 7.Figure 7
Flowchart of preliminary design for battery powered tailsitters.


### 4.2. Results and Discussion

In order to examine the influences of mission parameters and design constraints, four mission heights, 250 m, 500 m, 750 m, and 1000 m, were introduced; allowable mass of the tailsitter was set to3≤mTO≤20 kg. Other parameters were consistent with former simulation listed in Table 1. Maximum level flight endurance for different mission heights and allowable takeoff weights is shown in Figure 8. For the same mission height, level flight endurance increases when greater takeoff weight was allowed. But such increasing will slow down especially as mTO>10 kg. The maximum level flight endurance for a 10 kg battery powered tailsitter is about 2.792 hours while the mission height is 250 m. Lower mission height contributes to longer level flight endurance for an expected takeoff weight. When the mission height drops from 1000 m to 250 m, there is about 0.7 hours’ extension with the allowable mass more than 10 kg. That is less obvious for small battery powered tailsitters lighter than 5 kg.Figure 8
Maximum endurance for different mission heights and takeoff weights.Correspondingly, Figures9 and 10 show that the optimum values of wing loading and battery ratio decrease with mission height falling, while that is not very clear for small tailsitters as mTO<5 kg. For the same mission height, Figures 9 and 10 show that, with the greater allowable takeoff weight, the higher battery ratio and the smaller wing loading are necessary for optimum level flight endurance. It is not difficult to deduce from (4) that kB+kW/kWS=1-kA-kF-WM+WPL/WTO, so greater WTO means the feasible ranges of kB and kWS extend. A higher battery ratio and smaller wing loading are help for flight performance improvement, as demonstrated by Figure 4 and (33).Figure 9
Optimum wing loading for different mission heights and takeoff weights.Figure 10
Optimum battery ratios for different mission heights and takeoff weights.In order to validate the reasonability of the design result, design parameters and performance characteristics of four battery powered terrestrial UAVs were collected, as listed in Table2, where electrical T-wing [22] (E-T-wing for short) and ITU-Tailsitter [7] are tailsitter configuration; TURAC [21] has a configuration of separate propulsion systems used for vertical flight and level flight, respectively; ITU-Tailless [20] is a CTOL UAV with flying wing configuration.Table 2
Parameters and performances of four battery powered UAVs.
Items
E-T-wing
ITU-Tailsitter
TURAC
ITU-Tailless
Takeoff
VTOL
VTOL
VTOL
CTOL
W
T
O (kg)
22.72
10.0
47.0
7.74
W
P
L (kg)
1.8
1.0
8.0
1.3
H
m (m)
1 min†
1000
1000
250
AR
6.47
5.78
5.25
8.89
C
D
0
0.048
—#
0.0266
0.033
k
W
S (N/m2)
304.3
196.0
137.1
99.8
k
B
0.4004
—#
0.468
0.3876
t
L
F (h)
≤0.1
≈2.0
≈1.5
≈3.0
†Mission height is not known, while 1 minute vertical flight has been mentioned [5].
#Data could not be obtained by open literatures.The E-T-wing demonstrator vehicle was powered by 9.1 kg Ni-Cd batteries, the specific energy of which is 110 J/g, approximately 396 Wh/kg. Except for the problems with motor speed controllers induced unreliability [5], there might be other problems leading to the electrical powered scheme cancelled. These problems might involve heavy takeoff weight causing too heavy wing loading and small diameter (less than 0.6 m) propellers causing inefficient propulsion. High power operations, 3.138 kW for hover and 1.021 kW for level flight, not only cause batteries’ discharge duration reduced, but also lead to effective battery capacity reduced caused by high current draw [15].Both ITU-Tailsitter and TURAC employed separate-dual propulsion system, independent propulsion for vertical takeoff and landing in other words, which introduced dead weight for level flight inevitably. As (33) presented, heavy wing loading listed in Table 2 was not help for endurance performance improvement. CTOL ITU-Tailless was listed for comparison. Hand-launch could reduce takeoff energy consumption and large aspect ratio wing leads to better aerodynamic performance, so the level flight duration is much longer.Carrying 1.0 kg payloads, the optimization designed 10 kg unmanned battery powered tailsitter has level flight endurance of 2.18 hours at the mission height of 1000 m, a comparative performance of ITU-Tailsitter. Meanwhile, Figures9 and 10 show that the corresponding optimum wing loading and battery ratio are kWS=108.2 N/m2 and kB=0.4152, respectively. The energy consumption of avionics and other instruments needs to be counted in further study for more precise endurance estimation.


## 4.1. Design Method and Process

Being subjected to the constraints of allowable takeoff weight and maximum climb velocity, the optimum wing loading and battery ratio need to be determined, and the constant climb velocity should be optimized for maximum level flight endurance for given mission height and payloads. The design method for a small unmanned battery powered tailsitter could be summarized to an optimization problem, expressed as follows:(34)maxendurancekB,kWSsubjecttoWTO≤Wallow,0<VC<Vmax.The weight of the motor-propeller systemWEMP is determined by the maximum takeoff power Preqmax=PkTWTO/2,Vmax. Iterations are carried out with (4), (15), and (16) for an appropriate solution. The flowchart of the preliminary design process for battery powered tailsitters is shown in Figure 7.Figure 7
Flowchart of preliminary design for battery powered tailsitters.


## 4.2. Results and Discussion

In order to examine the influences of mission parameters and design constraints, four mission heights, 250 m, 500 m, 750 m, and 1000 m, were introduced; allowable mass of the tailsitter was set to3≤mTO≤20 kg. Other parameters were consistent with former simulation listed in Table 1. Maximum level flight endurance for different mission heights and allowable takeoff weights is shown in Figure 8. For the same mission height, level flight endurance increases when greater takeoff weight was allowed. But such increasing will slow down especially as mTO>10 kg. The maximum level flight endurance for a 10 kg battery powered tailsitter is about 2.792 hours while the mission height is 250 m. Lower mission height contributes to longer level flight endurance for an expected takeoff weight. When the mission height drops from 1000 m to 250 m, there is about 0.7 hours’ extension with the allowable mass more than 10 kg. That is less obvious for small battery powered tailsitters lighter than 5 kg.Figure 8
Maximum endurance for different mission heights and takeoff weights.Correspondingly, Figures9 and 10 show that the optimum values of wing loading and battery ratio decrease with mission height falling, while that is not very clear for small tailsitters as mTO<5 kg. For the same mission height, Figures 9 and 10 show that, with the greater allowable takeoff weight, the higher battery ratio and the smaller wing loading are necessary for optimum level flight endurance. It is not difficult to deduce from (4) that kB+kW/kWS=1-kA-kF-WM+WPL/WTO, so greater WTO means the feasible ranges of kB and kWS extend. A higher battery ratio and smaller wing loading are help for flight performance improvement, as demonstrated by Figure 4 and (33).Figure 9
Optimum wing loading for different mission heights and takeoff weights.Figure 10
Optimum battery ratios for different mission heights and takeoff weights.In order to validate the reasonability of the design result, design parameters and performance characteristics of four battery powered terrestrial UAVs were collected, as listed in Table2, where electrical T-wing [22] (E-T-wing for short) and ITU-Tailsitter [7] are tailsitter configuration; TURAC [21] has a configuration of separate propulsion systems used for vertical flight and level flight, respectively; ITU-Tailless [20] is a CTOL UAV with flying wing configuration.Table 2
Parameters and performances of four battery powered UAVs.
Items
E-T-wing
ITU-Tailsitter
TURAC
ITU-Tailless
Takeoff
VTOL
VTOL
VTOL
CTOL
W
T
O (kg)
22.72
10.0
47.0
7.74
W
P
L (kg)
1.8
1.0
8.0
1.3
H
m (m)
1 min†
1000
1000
250
AR
6.47
5.78
5.25
8.89
C
D
0
0.048
—#
0.0266
0.033
k
W
S (N/m2)
304.3
196.0
137.1
99.8
k
B
0.4004
—#
0.468
0.3876
t
L
F (h)
≤0.1
≈2.0
≈1.5
≈3.0
†Mission height is not known, while 1 minute vertical flight has been mentioned [5].
#Data could not be obtained by open literatures.The E-T-wing demonstrator vehicle was powered by 9.1 kg Ni-Cd batteries, the specific energy of which is 110 J/g, approximately 396 Wh/kg. Except for the problems with motor speed controllers induced unreliability [5], there might be other problems leading to the electrical powered scheme cancelled. These problems might involve heavy takeoff weight causing too heavy wing loading and small diameter (less than 0.6 m) propellers causing inefficient propulsion. High power operations, 3.138 kW for hover and 1.021 kW for level flight, not only cause batteries’ discharge duration reduced, but also lead to effective battery capacity reduced caused by high current draw [15].Both ITU-Tailsitter and TURAC employed separate-dual propulsion system, independent propulsion for vertical takeoff and landing in other words, which introduced dead weight for level flight inevitably. As (33) presented, heavy wing loading listed in Table 2 was not help for endurance performance improvement. CTOL ITU-Tailless was listed for comparison. Hand-launch could reduce takeoff energy consumption and large aspect ratio wing leads to better aerodynamic performance, so the level flight duration is much longer.Carrying 1.0 kg payloads, the optimization designed 10 kg unmanned battery powered tailsitter has level flight endurance of 2.18 hours at the mission height of 1000 m, a comparative performance of ITU-Tailsitter. Meanwhile, Figures9 and 10 show that the corresponding optimum wing loading and battery ratio are kWS=108.2 N/m2 and kB=0.4152, respectively. The energy consumption of avionics and other instruments needs to be counted in further study for more precise endurance estimation.


## 5. Summary and Conclusion

Focusing on the level flight performance, this paper simplified the design process of battery powered tailsitters. A complete flight profile for small unmanned tailsitters has been established and detailedly discussed phase by phase, which set a basic reference for tailsitter’s flight path optimization. The feasible design space and illustrated design method, as well as the power level and energy consumption of each flight phase, can be used to provide guidance for the tailsitter’s detailed design. Although the design methodology was initially intended for terrestrial UAVs, that can be also adapted for Martian tailsitters with the considering of environment parameters and flight missions.



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*Source: 3570581-2016-05-23.xml*