Radimir Y. Yanev va Ingo Staack ishlab chiqqan tadqiqot elektr vertikal uchish va qo‘nish qobiliyatiga ega havo vositalarining (electric vertical take-off and landing, eVTOL) konseptual dizaynida ko‘plab turli konfiguratsiyalarni tez baholash uchun integratsiyalashgan o‘lchamlash va ishlash tahlili asosini taqdim etadi. Usul vehicle components geometrik sizingini, flight mission analysisni, battery sizingni power va energy requirement asosida va component-based mass estimationni bir xil iterativ loop ichida birlashtiradi. Verification resultsda rotor/propeller solidity uchun mean absolute percentage error %7,5, hover power uchun %8,0 bo‘lgan; battery discharge model experimental data bilan taqqoslanganda new cell discharge depthda taxminan %5, end-of-life conditionda esa %1 dan kam deviation ko‘rsatgan. NASA reference designs bilan vehicle-level comparisonda maximum take-off mass deviation Quadrotor uchun %0,6, Lift + Cruise uchun %3,2 darajada.

Tadqiqotning asosiy xabari low-fidelity, ammo fizik munosabatlarni saqlovchi modeling approach erta eVTOL design space ni tez toraytirish uchun ishlatilishi mumkinligidir. Biroq usul final aerodynamic design, detailed structural verification, certification yoki real flight performance uchun ishlab chiqilmagan. Propeller model tip losses, non-uniform flow, rotor–wing va rotor–rotor interactions kabi higher-order aerodynamic effectsni batafsil yechmaydi; battery model esa temperature, aging, cell balancing va degradation mechanismsni bevosita modellashtirmaydi.

Tadqiqotning eVTOL design nuqtayi nazaridan muhim tomonlaridan biri faqat total battery energyga qaramasligidir. Vertical take-off, transition flight va landing kabi high-power segments bilan cruise flight energy requirements bir mission profile ichida hisoblanadi. Ayniqsa landing phase da battery state of charge kamaygan paytda yana high power talab qilinishi battery sizing faqat Wh/kg bo‘yicha qilinishi yetarli bo‘lmasligi mumkinligini ko‘rsatadi.

eVTOL designning asosiy muammosi nima?

Distributed electric propulsion systems klassik helicopter yoki fixed-wing aircraftga nisbatan ancha keng configuration space yaratadi. eVTOL designida rotor soni, rotor diameter, wing geometry, vertical flight va cruise uchun alohida yoki umumiy propulsion elements ishlatilishi, battery size, motor power, mission range va landing area size bir-biridan mustaqil emas. Masalan, kichikroq rotorlar vehicle footprintni kamaytirishi mumkin; biroq disk loadingni oshirib hover powerni ko‘paytirishi mumkin. Higher hover power kattaroq motor va battery talab qilishi mumkin; ortgan battery mass esa yana total take-off massni oshirishi mumkin.

Tadqiqot ishlab chiqqan framework aynan shu feedback design problemni hal qiladi. Vehicle bir marta fixed parameters bilan hisoblanmaydi; maximum take-off mass (MTOM) va required battery capacity convergence qilguncha component sizing, mission analysis, battery sizing va mass estimation takrorlanadi.

Nega propeller sizing designning markazida?

Vertical flight qiladigan eVTOLda rotor yoki lift propellers disk loading hover paytida required powerga bevosita ta’sir qiluvchi asosiy variablesdan biridir. Tadqiqotda har VTOL propeller uchun design thrust maximum take-off mass, gravitational acceleration, propeller number va %10 maneuver margin yordamida belgilanadi:

\[ T_{\mathrm{prop,des}} = \frac{k_{\mathrm{maneuver}}\,m_{\mathrm{MTO}}\,g} {N_{\mathrm{prop,VTOL}}} \]

Bu yerda \(T_{\mathrm{prop,des}}\) bitta VTOL propellerning design thrusti; \(k_{\mathrm{maneuver}}\) maneuver marginni, \(m_{\mathrm{MTO}}\) maximum take-off massni, \(g\) gravitational accelerationni va \(N_{\mathrm{prop,VTOL}}\) vertical flightda ishlatiladigan propeller sonini bildiradi.

Propeller radius imkon qadar katta tanlanadi, ammo landing area geometric limits va propellerlar orasidagi required clearance bu o‘lchamni cheklaydi. Bu approachning maqsadi disk loading va shu orqali hover uchun required induced powerni kamaytirishdir.

Propeller power esa induced power va profile power yig‘indisi sifatida modellashtiriladi:

\[ P_{\mathrm{prop}} = \kappa T(v_i + V_z) + \rho A_d(\omega R)^3 C_{P0} \]

Bu equationda \(\kappa\) induced power correction coefficient, \(T\) thrust, \(v_i\) induced velocity, \(V_z\) disk axis yo‘nalishidagi flow velocity, \(\rho\) air density, \(A_d\) disk area, \(\omega\) angular speed, \(R\) propeller radius va \(C_{P0}\) profile power coefficient. Tadqiqot modeli conceptual designga qaratilgan; tip loss, rotor–rotor interaction, rotor–wing interaction, non-uniform inflow va transition flightdagi time-dependent aerodynamic effects bevosita yechilmaydi.

Wing va fuselage design systemga qanday bog‘lanadi?

Winged eVTOL configurationsda wing cruise flightga ko‘ra optimallashtiriladi. Tadqiqotda wingspan landing-area geometry bilan cheklanadi; wing area, aspect ratio va cruise lift coefficient esa aerodynamic drag bilan structural mass orasidagi balance asosida aniqlanadi. Kichikroq wing area va higher aspect ratio aerodynamic efficiency ni oshirishi mumkin, ammo structural massni ko‘paytirishi mumkinligi sabab faqat maximum aerodynamic efficiency maqsad qilinmaydi.

Aft fuselage va tail design ham alohida constrained optimization problem sifatida ko‘riladi. Maqsad aft fuselage total wetted areani kamaytirgan holda horizontal va vertical tail volume coefficients, tail position, geometric convergence va tail aspect ratio limitsni qondirishdir.

Battery faqat energy capacity bo‘yicha sizing qilinmaydi

Frameworkning farqlovchi jihatlaridan biri batteryni faqat ma’lum Wh/kg energy density bilan ifodalamasligidir. Mission davomida har control pointda required electrical power cellsga taqsimlanadi; cell open-circuit voltage, under-load voltage va internal resistance orqali current iteratively yechiladi:

\[ I = \frac{P_{\mathrm{demand,cell}}}{V_{\mathrm{UL}}}, \qquad V_{\mathrm{UL}} = V_{\mathrm{OC}} - R_{\mathrm{tot}} I \]

Bu yerda \(I\) cell current, \(P_{\mathrm{demand,cell}}\) power demand per cell, \(V_{\mathrm{UL}}\) under-load cell voltage, \(V_{\mathrm{OC}}\) open-circuit voltage va \(R_{\mathrm{tot}}\) cell total internal resistance.

State of charge mission davomida Coulomb counting bilan yangilanadi:

\[ SOC_{i+1} = SOC_i - \frac{I_i\Delta t_i}{C_{\mathrm{act}}} \]

\(SOC_i\) current state of charge, \(I_i\) current, \(\Delta t_i\) time step va \(C_{\mathrm{act}}\) effective usable cell capacityni bildiradi. Battery size mission oxiridagi required SOC va maximum C-rate bilan belgilanadigan power limitni qondirguncha iteratively oshiriladi yoki kamaytiriladi.

Nega mass calculation feedbacklidir?

Total vehicle mass bitta historical mass fraction bilan emas, components yig‘indisi sifatida tuziladi:

\[ m_{\mathrm{total}} = \sum_{i=1}^{N}m_i \]

Bu yig‘indi wing, fuselage, tail, pylon va landing gear kabi structural elements; propeller, electric motor va power electronics; flight control, avionics va environmental control systems; passenger va baggage payload; shuningdek battery cells va packaging additional massni o‘z ichiga oladi. Battery kattalashganda vehicle og‘irlashadi, og‘ir vehicle ko‘proq thrust va power talab qiladi va bu battery hamda motor sizeni yana o‘zgartirishi mumkin. Iterative solution shu bog‘liqlikni yopadi.

Tadqiqot Usuli va Natijalari

Verifikatsiya uch xil darajada bajarildi

Mualliflar frameworkni faqat bitta vehicle misolida verifikatsiya qilish o‘rniga uch alohida darajada sinaganlar. Birinchi bosqichda propeller sizing va hover performance model real helicopter rotors va NASA eVTOL reference propellers bilan taqqoslangan. Ikkinchi bosqichda battery discharge model eVTOL mission profiles ostida o‘lchangan experimental cell data bilan test qilingan. Nihoyat, butun vehicle sizing loop NASAning NDARC-based Urban Air Mobility reference vehicles bilan taqqoslangan.

Propeller validation data set

Rotor data setda MBB Bo 105, Eurocopter EC 135, Aérospatiale SA 365N Dauphin va Sikorsky UH-60A Black Hawk kabi conventional helicopters bilan birga NASAning turli rotorcraft va powered-lift eVTOL concepts mavjud. Data setdagi rotor diameters 2,23 m dan 16,36 m gacha, hover thrust 3,8 kN dan 73,6 kN gacha, hover power esa 54 kW dan 1569 kW gacha o‘zgaradi. Shu tariqa model faqat bitta scale uchun emas, sezilarli turli disk loading va rotor size ga ega vehiclesda sinovdan o‘tkazilgan.

Calculated rotor solidity valuesning referencesga nisbatan mean absolute percentage errori %7,5, blade loading uchun esa %7,14 deb bildirilgan. Hover power calculationda mean absolute percentage error %8,0. Model low disk loadingga ega ayrim helicopter rotorsda solidity va hover powerni past, high disk loadingga ega ayrim distributed propulsion systemsda esa yuqori baholashga moyillik ko‘rsatgan.

Battery model real cell experiments bilan qanday taqqoslandi?

Battery validationda Sony-Murata 18650 VTC-6 lithium-ion cells uchun published experimental data set ishlatilgan. Cell nominal capacity 3200 mAh, nominal voltage 3,6 V va tadqiqotda berilgan specific energy taxminan 230 Wh/kg. Tanlangan VAH02 mission profile 75 soniya davomida 54 W take-off load, 1000 soniya davomida 16 W cruise load va 105 soniya davomida yana 54 W landing loaddan iborat.

New-cell experimentda SOC taxminan %100 dan %36 gacha tushgan paytda model taxminan %38 final SOC bashorat qilgan va mualliflar bu farqni taxminan %5 deviation sifatida baholaganlar. End-of-life conditionda experiment taxminan %82 dan %13 SOCgacha tushgan, model result deviation esa %1 dan past qolgan.

Biroq real cell aging model ichida fizik ravishda simulyatsiya qilinmagan. Tadqiqotda end-of-life batteryni ifodalash uchun initial SOCni taxminan %80 gacha tushirish proxy approach sifatida ishlatilgan. Shuning uchun natija detailed battery-aging model verifikatsiya qilingan degani emas.

Eng katta instantaneous difference mission oxiridagi low SOC va high power talab qiluvchi landing phase da ko‘rilgan. Modelning instantaneous current/C-rate predictiondagi maximum deviation bu hududda taxminan %15 gacha chiqadi. Mualliflar bu farq qisqa muddatli ekanini va total discharged energyga ta’siri cheklanganini bildiradilar.

NASA reference vehicles bilan vehicle-level validation

Umumiy sizing validationda ikkita vehicle ko‘rib chiqilgan. Birinchisi to‘rtta katta lift rotorga ega qanotsiz Quadrotor, ikkinchisi sakkizta distributed lift-propeller va cruise uchun alohida pusher propeller ishlatadigan qanotli Lift + Cruise configuration.

Validation mission olti yo‘lovchini tashish uchun belgilangan. Design payload taxminan 540 kg. Mission ikki flight legdan iborat; tadqiqotda har bir leg 37,5 nautical mile, ya’ni taxminan 70 km deb belgilangan va qo‘shimcha 20 daqiqalik cruise-power reserve ishlatiladi. Battery uchun pack-level effective gravimetric energy density 400 Wh/kg va %80 usable discharge range qabul qilingan.

Quadrotor uchun calculated maximum take-off mass 2957 kg, NASA reference value 2939 kg; manba bu deviationni %0,6 deb beradi. Lift + Cruise uchun qiymatlar mos ravishda 3843 kg va 3724 kg, reported difference esa %3,2. Empty mass deviations Quadrotor uchun %1,1, Lift + Cruise uchun %4,0 deb bildirilgan.

Source-internal numerical inconsistency: Table 6 da Lift + Cruise MTOM values 3724 kg va 3843 kg deb berilgan bo‘lsa-da, undan keyingi explanation paragraph absolute difference ni “79 kg” deb yozadi. Ayni paragraph %3,2 value ni saqlaydi. Shu sabab absolute-difference statement source ichida o‘z table values bilan consistent emas.

Nega energy storage total massning eng katta qismi?

Model mass breakdownida energy storage Quadrotor MTOMning taxminan %31,9 ini, Lift + Cruise vehicle esa taxminan %29,4 ini tashkil qiladi. Structural mass har ikki vehicleda total massning taxminan chorak qismi. Lift + Cruise designida propulsion-system mass ulushi Quadrotorga nisbatan ancha yuqori.

Tadqiqot izohiga ko‘ra, bu farqning muhim sabablaridan biri Lift + Cruise vehicle higher disk loadingga ega bo‘lishidir. Quadrotorning katta rotorlari lower disk loading bilan ishlaydi, Lift + Cruise configurationning sakkizta kichik lift propelleri esa vertical flightda ancha higher power talab qiladi.

Lift + Cruise configurationning calculated hover poweri taxminan 932 kW, Quadrotor uchun esa taxminan 381 kW. Aksincha cruise flightda ikki vehicle calculated powers bir-biriga yaqinlashadi; Quadrotor taxminan 268 kW, Lift + Cruise esa taxminan 273 kW talab qiladi. Tadqiqot bu farqni winged vehicle cruiseda higher aerodynamic efficiencyga ega bo‘lishi bilan bog‘liq design trade-off sifatida izohlaydi.

Effective lift/drag indicator \(WV/P\) calculated vehicleda Quadrotor uchun 5,4, Lift + Cruise uchun 8,1. Demak winged configuration cruiseda afzalroq ko‘rinadi, ammo vertical flightda higher power requirementga ega.

Batteryga eng og‘ir load qaysi flight phasesda tushadi?

Mission davomida highest C-rate values hover va climb kabi high-power vertical-flight segmentsda yuzaga kelgan. Lift + Cruise vehicleda first take-off hover paytida taxminan %95 SOC da C-rate taxminan 1,9, ikkinchi flight leg oxiridagi landingda SOC taxminan %35 gacha tushganda ayni high power demand uchun C-rate taxminan 2,2 gacha oshgan. Highest value transition climbda taxminan 2,5 deb hisoblangan. Cruiseda esa C-rate asosan 0,6–0,7 oralig‘ida.

Quadrotor battery load mission davomida muvozanatliroq. Hoverda C-rate taxminan 1,0, climbda maximum taxminan 1,2 va cruiseda taxminan 0,6–0,7.

Battery efficiency Quadrotor uchun missionning ko‘p qismida taxminan %98–99 oralig‘ida qolgan. Lift + Cruise vehicleda high-power vertical-flight segmentsda taxminan %96 gacha tushib, cruiseda taxminan %98. Modelda SOC kamaygan sari internal-resistance lossesning relative effecti oshgani sabab ayni power demandda efficiency ham pasayadi.

Tadqiqot qo‘llab-quvvatlaydigan natijalar

• Low computational costli, component-based va iterative method early-stage eVTOL configuration comparisons uchun amaliy natijalar ishlab chiqishi mumkin.
• Propeller sizing model o‘rganilgan reference setda rotor solidity va hover powerning umumiy trendsini taxminan %8 darajasidagi mean absolute percentage error bilan ushlaydi.
• Simplified equivalent-circuit battery model ishlatilgan experimental VTC-6 data setda SOC evolutionni conceptual sizing uchun yaqin tarzda reproduce qiladi.
• Quadrotor va Lift + Cruise vehiclesning high-level MTOM va empty mass results NASA NDARC referencesga bir necha percentage point ichida yaqinlashadi.
• Lift + Cruise configuration cruiseda aerodynamic jihatdan samaraliroq bo‘lsa-da, high disk loading sabab vertical flightda Quadrotordan sezilarli ko‘proq power talab qiladi.
• eVTOL battery sizingda total energy bilan birga mission oxiridagi low-SOC conditionda qondirilishi kerak bo‘lgan high instantaneous power ham muhim.

Tadqiqot qo‘llab-quvvatlamagan yoki bevosita sinamagan natijalar

• Framework results production-ready yoki certification-ready final eVTOL design sifatida talqin qilinmaydi.
• Real prototype flight test yoki real urban eVTOL operation bajarilmagan.
• Propeller modelda tip losses, rotor–rotor interaction, rotor–wing interaction va transition flightning detailed time-dependent aerodynamicsi yechilmaydi.
• Battery temperature, real aging mechanisms, cell balancing va degradation bevosita modellashtirilmaydi.
• Noise, certification safety, detailed flight dynamics va control derivatives holistic tarzda verifikatsiya qilinmagan.
• Tadqiqot Turkiyaga xos airspace, vertiport, infrastructure, cost yoki operational data o‘z ichiga olmagani sabab Turkiya uchun commercial yoki operational suitability xulosasi bermaydi.

Manba va Usul Haqida Izoh

Manba turi va publication status: Ushbu ish peer-reviewed research/modeling article. Aerospace jurnalida 2026 yilda volume 13, issue 7, article 566 sifatida chop etilgan. Preprint emas.

Asl tadqiqot: Radimir Y. Yanev va Ingo Staack, “Framework for Rapid eVTOL Aircraft Configuration Design: Methodology and Verification”. DOI: 10.3390/aerospace13070566.

Corresponding author: Radimir Y. Yanev.

Muassasa: Institute of Aircraft Design and Lightweight Structures, Technische Universität Braunschweig, 38108 Braunschweig, Germaniya.

Method class: Tadqiqot low-fidelity, physics-based va semi-empirical submodelsni integratsiya qiladigan conceptual aircraft design and verification ishidir. Propeller model momentum theory va simplified blade-element approachni; battery model equivalent electrical circuitni; structure va system masses esa physics-based va semi-empirical mass-estimation methods kombinatsiyasini ishlatadi.

Verification: Propeller model conventional helicopter rotors va NASA eVTOL designs bilan; battery model experimental Sony-Murata VTC-6 cell data bilan; whole-vehicle sizing esa NASA UAM reference Quadrotor va Lift + Cruise vehiclesning NDARC results bilan taqqoslangan.

Asosiy limitation: Frameworkning maqsadi final vehicle certification yoki high-fidelity flight-physics analysis emas, conceptual design space ni tez scan qilishdir. Aerodynamic interactions, battery thermal and aging processes va ayrim system-level details soddalashtirilgan.

Source-internal inconsistency note: Source Table 6 da Lift + Cruise MTOM values 3724 kg va 3843 kg deb beriladi, ammo keyingi paragraph difference ni 79 kg deb ifodalaydi. Ayni text %3,2 deviation bildiradi. Bu numerical inconsistency source ichida mavjud bo‘lgani sabab jimlik bilan tuzatilmagan.

Moliyalashtirish: Tadqiqot Germaniya Federal Iqtisodiyot va Energetika Vazirligi doirasidagi German Aviation Research Program ichida PEANUT va AIRDRIVE projects tomonidan qo‘llab-quvvatlangan. Open-access publication fee Technische Universität Braunschweig open-access funds tomonidan qoplangan.

Data availability: Mualliflar tadqiqotda taqdim etilgan final data corresponding authordan request asosida olinishi mumkinligini bildiradilar.

Conflict of interest: Mualliflar conflict of interest bildirmagan.

AI-use declaration: Mualliflar maqolani tayyorlashda ChatGPT GPT-5.3 Instantdan language improvement va graph generation uchun ishlatilgan kodni ishlab chiqishda foydalanganlarini; outputsni o‘zlari review va edit qilganlarini va publication content uchun responsibility olganlarini bildirganlar. Bu declaration scientific validation method emas, mualliflarning publication process bo‘yicha transparency statementidir.

License: Maqola Creative Commons Attribution (CC BY) license ostida open access chop etilgan.

Rasmiy manba: https://doi.org/10.3390/aerospace13070566