Multirotor Sizing Methodology with Flight Time Estimation

is paper addresses the need for sizing of rotors for multirotor vehicle applications such as personal air transport, delivery, surveillance, and photography. A methodology for the propeller and motor selection is developed and augmented with ight time estimation capabilities. Being multirotor-specic it makes use of the platform’s simplicity to rapidly provide a set of o-the-shelf components ready to be used in the vehicle. Use of operating points makes the comparison process fast, precise, and tailored to specic application. e method is easily implemented in soware to provide an automated tool. Furthermore, clearly dened input and output parameters make it also usable as a module in other multicriteria optimisation algorithms. e new methodology is validated through comparison with a consumer-grade drone and the calculated results are compliant with manufacturer’s specication in terms of maximum hover time.


Introduction
In recent years, Unmanned Aerial Vehicles (UAVs) have become a popular solution for a variety of civil and military applications including surveillance, photo-and videography, and land surveying. e versatility of these systems has even found them in many nonstandard purposes such as automated package delivery or Personal Air Vehicles (PAVs). Multirotor UAV platforms have gained particular attention due to their Vertical Take O and Landing (VTOL) capabilities as well as their simple construction and control. Of paramount importance is safety and reliability, especially when it comes to autonomous solutions, and so the enterprise market o ers complete, closed drone solutions at di erent size/weight points. ese are simple-to-use systems with a high degree of user support and good performance for most applications. However, the mechanical simplicity of the platform means that customized and open solutions should be available for specialized applications. Furthermore, the main limitation of multirotor systems is their ight time, mostly due to battery weight and energy storage constraints. erefore, a set of tools needs to be created that can aid the design of customized solutions that can be speci cally tailored for a particular application. us there is a need for a methodology to automatically select the best consumer-grade components to build a custom solution at a given weight and performance level.
ere are some methodologies in the open literature for this purpose, but few lead directly to a "bill-of-materials" level solution. e most popular approach to obtaining a " yable" con guration seems to be to test various motor + propeller combinations and choose one that suits the application [1]. Although popular with hobbyists, the method has little value in the commercial or research environment due to high cost (purchase of components), time requirement, and the need for specialized equipment (thrust stand, dynamometer). is method provides the most accurate results, but the number of combinations needed to be tested increases geometrically with each added component. is process can be signi cantly sped up using calculators such as Drive Calculator [2] and eCalc [3], which incorporate some of the data in their databases, but still the selection needs to be performed manually. is lack of search automatization capability and weak interfacing with other so ware (e.g., MATLAB) renders it di cult when analysing more than one case. In addition, eCalc does not pay that much attention to the main li ing body -the propeller, and uses a mathematical model (diameter and pitch can be input manually) for the performance calculation, as opposed to a more accurate database of measured/simulated data. erefore, methodology is the ability to model the dynamic motor thrust response, which is a useful tool for dynamic performance analysis. However, for basic sizing applications the complexity (up to 3091 variables in the example problem) may be too overwhelming and a simpler solution may be preferred.
is paper presents a method for sizing of the multirotor propulsion system through the selection of propeller and motor. Furthermore, the method provides the necessary data for the selection of the Electronic Speed Controller (ESC) and battery. Additionally, it gives a way of comparing di erent con gurations through estimation of ight time by modelling battery discharge at constant power requirement. e key point of the methodology is the fact that it works on real components (propellers and motors) increasing the precision of the estimation. Another feature is the ability for the selection process to be automated making it an useful module for use in novel optimisation algorithms. Elements of optimisation are included in order to provide e cient and feasible solution. However, it should be noted that the resultant con guration is based on estimations, assumptions and inaccurate data, and therefore not optimal, so the methodology results should be treated only as a good rst guess. e paper is structured as follows; Section 2 details all the elements of the multirotor propulsion chain and their interaction; Section 3 describes the methodology based on the inverted model from the previous section; Section 4 presents example results for a small drone such as DJI Phantom 4 V2.0 and extends the ndings onto Personal Air Vehicles; nally, Section 5 concludes the paper and highlights the most important outcomes.

Multirotor Propulsion Chain
Multirotors as a category of ying vehicles cover a lot of variants di ering not only in the number of rotors, but also their placement. Currently, the most popular con guration seems to be quad with four parallel rotors placed diagonally from the center, as shown in Figure 1. One of the characteristic properties of most multirotors is their symmetry and the fact that every arm is the same, except for the rotor spinning direction. is makes it easy to analyse the propulsion system for the general case by analysing only one arm (one propulsion chain). e Flight Controller (FC) is responsible for control strategy for the whole platform and preparing a set point for each arm, but it does not participate in the propulsion chain as such.
In most cases, Brushless DC (BLDC) motors are used for multirotor propulsion, but sometimes, usually for toys under 100 g, DC motors are also used. is paper focuses only on BLDC; however, most concepts shown apply to both types. Brushless motors do not have physical brushes, so they require Electronic Speed Controllers (ESC) to achieve electronic commutation. erefore, the main components of the propulsion chain are identi ed to be: propeller, motor, ESC, and battery. A schematic of the propulsion model of a multirotor is shown in Figure 2. It can be seen that there is one input of a set point (given by FC) and one output, namely the thrust generated by the propeller. erefore, the propulsion chain can be identi ed as a open-loop Single Input Single Output (SISO) system, which makes it relatively easy to size components one at a time. In the next part of this section, each component will be described in detail.
2.1. Propeller. Aircra propellers are characterized by 3 main parameters: diameter, pitch, and the number of blades. Generally, the higher these are, the higher the thrust generated, but also higher torque is exerted on the motor. However, long, slowly spinning, 2-bladed propellers are known to be more aerodynamically e cient than small, fast-spinning, multibladed ones. Propeller characteristics are mainly a function of its rotational speed and the speed of incoming air. However, if we consider air density to be constant and the air to be static (at hover in still air), the thrust, torque, and power depend only on propeller speed. Additionally, there are secondary parameters such as mass and geometry template expressed as manufacturing series (e.g., Multirotor, Slow Flyer, Carbon, etc.).

Motor.
In a multirotor, the motor's main objective is to drive the propeller reliably and with high acceleration, so the speed can be changed quickly. e main limitations of a BLDC motor are in terms of speed and current. Maximum current is o en stated by the manufacturer and maximum speed in no-load conditions 0 can be calculated from the KV parameter multiplied by the applied voltage : With a constant voltage, when current is applied, the motor starts exerting torque on the sha accelerating it until its torque equals the load torque, assuming the mechanical losses are neglected. At low speed, far from the motor constraints, it is assumed that the relation between motor torque and current is constant and expressed with motor torque constant ( ). erefore, the applied current is transformed into the torque based on the motor characteristic, then the torque is transformed into speed based on the propeller torque-speed characteristic, and nally the speed is transformed into thrust using the propeller thrust-speed characteristic. is sequence makes the propulsion chain easy to calculate analytically as a SISO system.

Electronic Speed Controller. Although Electronic Speed
Controllers (ESCs) serve a very important purpose in the real-life multirotor, in the propulsion chain model it has very little importance. In the model, its function is reduced to transferring current from the battery to the motor under constant voltage. However, when designing a multirotor, ESC still needs to be sized according to the maximum current owing to the motor.

Battery.
When it comes to lightweight aerial vehicles, Lithium Polymer (LiPo) batteries currently dominate the market due to their high energy density and high current discharge capabilities [5,12]. ese batteries are composed of several cells connected in series (rarely in parallel). Cell voltage changes according to the state of charge with 4.2 V being at 100%, 3.85 V at 50% and 3.7 V (nominal) at 20%. However, discharging a LiPo cell under 3 V leads to permanent damage to the battery. erefore, it is recommended to only discharge the batteries to about 20%, which grants a Depth of Discharge (DoD) of 80%. e cells can be connected in series or in parallel, denoted by or , respectively, so for example, 4 1 is a 4 cell battery with 14.8 V nominal voltage. Additionally, the batteries are characterized by their capacity in mAh and a C-rating ( ), which speci es the maximum current that can be drawn continuously, for example 35 C × 5.2 Ah = 182 A (the unit being C and not Coulomb). It is evident that maximum discharge current is not dependent on battery capacity.
(1) 0 = KV × . e propulsion system model used here is only applicable in static conditions and at constant speed. Modelling a multirotor in ight is much more complicated due to the presence of aerodynamic e ects such as variable angle of attack, reduction of thrust coe cient with advance ratio, and additional frame drag. However, an approximation of the required performance for full controllability in ight is made using the model only in static conditions of operation. It uses a state of equilibrium achieved at hover (in no-wind conditions), where thrust generated by the propellers is equal to the multirotor's weight. is thrust can be multiplied by a constant thrust-to-weight ratio to achieve a value of static thrust that guarantees speci c performance in the air depending on the application. is approach appears imprecise; however, during the years of use of similar methods in the community of radio controlled aircra modellers, the values of thrust-toweight ratio required for di erent applications have been validated with many test ights. A quick summary of typical values can be found in Table 1, which is based on [13,14]. Additionally, in static conditions there is no in uence of rotor inertia on motor performance, so the propeller and motor selection can be decoupled, further simplifying the process.

Sizing Methodology
By inverting the propulsion system model developed in the previous section, a new model can be obtained allowing to estimate battery voltage based on thrust generated, as shown in Figure 3. is allows for an iterative approach in order to determine the time required to deplete the battery at constant power draw, which e ectively serves as a ight time estimate.
us, two distinct subsystems can be distinguished in the system model: the actuating system and the power system. is manifests itself in the sizing methodology, which is also divided into two parts. Figure 4 shows a simpli ed view of the methodology. Although it is based on the diagram in Figure 3, it also shows the separation between battery sizing and battery simulation ( ight time simulation).

Actuating System.
e actuating system provides the thrust propulsion to the vehicle and consists of the propeller, the motor, an ESC to control the motor and a battery to power the motor. e propeller sizing and selection is performed rst, the motor sizing being dependent on the propeller properties. Finally, speci cations for the ESC and the battery are produced.  and where An example of the mapping triplets for two propellers is shown in Figure 5 along with an illustration of obtaining from . Usually = 2 operating points are calculated: the operating point at hover (1) , and the Wide Open rottle (WOT) operating point (2) . ese signify the lower and upper boundaries of the ight performance, respectively. A third operating point ( = 3) can also be de ned that corresponds to the propeller limit speed designated by the manufacturer; this can be used for checking the feasibility of the other operating points. e thrust requirements, (1) for the hover condition and (2) for the WOT condition, can be calculated from where total is the estimated total weight of the multirotor, rot is the number of rotors and is the thrust-to-weight ratio. Except for the propeller (and motor) set ltering purposes, the methodology uses only the total estimated weight of the multirotor, as it is presumed that the frame, battery size, payload and control modules are preselected from the ones available to the user and suited for the application. As only static conditions are considered (multirotor inertia not considered), the weights of those components are of lower importance as opposed to the estimated weights of propellers, motors and ESCs, which are multiplied by the number of rotors In practice, due to the fact that the propeller characteristics mappings de ned by (8) are o en given in the form of sample points, interpolation must be used for the calculations. is introduces errors. erefore, although in theory = , o en in practice (dependence on removed for notational simplicity) hence an average of those two values is taken To choose the propeller, various selection criteria are available. If > 1, then determining the minimum power solution is a 3.1.1. Propeller Sizing and Selection. e propeller sizing and selection process starts by de ning a propeller database represented as a set of available propellers where the ith propeller p is de ned by the pair where f denotes the ith propeller performance, which will be de ned later, and denotes its physical properties expressed as a 4-tuple where is the ith propeller diameter, is its pitch angle, is its mass, and is a discrete parameter representing the propeller series name. e propeller set P is then ltered to obtain a set of propellers P ⊆ P that satisfy a requirement 4-tuple where min is the minimum diameter, max is the maximum diameter, max is the maximum mass, and S is a set of preferred series names us is helps save time when evaluating the performance data and calculating operating points that is done next. e performance of the ith propeller f is denoted as a triplet of bijective mappings where is the rotor speed, is the thrust, is the torque, and is the propeller power. Let ( ) denote a required thrust. For each p ∈ P , we determine a set of operating points S := : = 1, . . . , .  where is the current, is the mechanical power, is the electrical power, is the e ciency and where denotes the motor properties expressed as a triplet where max is the maximum allowable ith motor current, 0 is its maximum no-load speed and is its mass. Unlike the process for the propeller selection, the performances of the motors must be evaluated rst. e required motor power is set to be = ( ) selected . en for each m ∈ M , we determine motor operating point triplets where (dependence on removed for simplicity) multiobjective problem, and some user interaction is then helpful in making the selection. However, it is o en possible to reduce the problem to the simplest case for = 1, where the lowest power at hover operating point can be computed as follows In this case, the minimization can be quickly carried out through exhaustive search, thanks to the small set size due to the ltering in previous steps.

Motor Sizing and Selection.
In a similar manner as for the propeller, let M be the set of available motors where f is the motor model described by the triplet of mappings (19)  Again the ltering operation in (28) makes it possible to use exhaustive search for the minimization purpose.

ESC and Battery Sizing.
e Electronic Speed Controller is sized mainly in regards to the maximum current it can handle. As it is assumed that the multirotor will never need more thrust than achieved at WOT operating point, the current should also not go over the calculated value. erefore, it can be said that It should be noted that the mapping → ( ) is not bijective in terms of motor characteristics, because at high current values most of the energy is dissipated as heat. However, considering the domain only up to the maximum current speci ed by manufacturer, the function is almost always monotonic. erefore, in practice, over the domain 0; max the inverse of power function −1 can almost always be evaluated.
Knowledge of for all m ∈ M allows for ltering of the motor set in regards to maximum current, speed and mass, thus obtaining M ⊆ M that satis es maximum current requirement on each motor ≤ max and a requirement pair where max = (2) selected is the propeller speed at WOT and max is the maximum motor mass. us Like in the propeller's case, various selection criteria could be used to choose the motor. In the simple example for = 1 it could be the lowest electrical power (29) selected := arg min m ∈M (1) .

Create propeller database set
Filter propeller set using (7) Define propeller requirement Determine propeller operation points using (10)- (13) Calculate thrust requirement using (14) & (15) Select propeller using (19) Selected propeller  (2) selected ; rated torque (2) selected ; rated mech. power (2) selected ; rated el. power (2) selected ; rated e ciency (2) selected ; nominal voltage ESC speci cation Maximum current ESC Battery speci cation Cell number ; minimum C-rating ; capacity by Traub [15]. It features two important phenomena-decrease of capacity with the increase of current and drop in voltage due to discharge. Additionally, the power demand can be varied throughout the simulation; however, in the base version of the methodology this is not used, as the operating points are constant. A block diagram of the calculations for one operating point can be seen in Figure 7.
Modelling of the battery capacity varying with drawn current is done through modi ed Peukert's equation in the form of: where is battery hour rating (1 hour in case of small packs) and is Peukert's constant (1.3 for LiPo) dependent on battery type and temperature.
Measuring battery voltage is one of the main ways of measuring remaining charge in-ight. Typically, Lithium Polymer (LiPo) cells used in drones have 4.2 V when at full charge and drop to 3.7 V when at 20% charge. e voltage drop curve is nonlinear, but for the model it has been linearized and is expressed through where ESC is the rated (maximal) ESC current and (2) selected is the motor current at WOT operating point.
A substantial part of battery speci cation needs to be provided by the user to realise ight time estimation as described in Section 3.2. However, the methodology allows to complete the battery speci cation by sizing the C-rating parameter where is the minimal required battery C-rating and is the battery capacity. e whole actuating system sizing methodology is depicted by the data ow chart shown in Figure 6. It shows the dependence of motor sizing on propeller speci cation and ESC and battery sizing on motor speci cation. e light cyan blocks correspond to the methodology stages, the dark blue blocks show requirements and constraints and the orange ellipses signify points of database access. e output data in green ellipses include speci cation parameters for sizing all of the major components of the propulsion system (namely propeller, motor, ESC, and battery) and the calculated propeller and motor operating points that can be used for calculating additional data, such as estimated ight time. e data corresponding to each of the outputs can be found in Table 2.
In Figure 6, a substantial impact of estimated total drone weight can be also seen-it is used to calculate required thrust that plays a key role in selecting the propeller, and consequently the motor. Due to the discrete nature of propeller and motor parameters, the relationship is highly nonlinear, so it needs to be analysed numerically. However, it is easy to implement the methodology in a loop to plot the characteristics of ight time versus weight, which may be used in a payload sizing application.

Power System.
e power system section of the methodology focuses on ight time estimation by modelling the battery. e model is based on the iterative approach presented    decreasing available battery capacity due to Peukert's e ect, as can be seen in Figure 8. e simulation is stopped when voltage reaches or when capacity reaches 20% of initial capacity (only works when power drawn is constant). e output is simply the simulation time, calculated as the product of the time step value and the number of iterations.

Example Results
e methodology presented has been implemented as a MATLAB script. is allows to easily process large quantities of data from propeller and motor databases and to plot component characteristics on every stage of the selection process.
In this example, performance data published by APC Propellers [16] will be used for the propeller database. It contains static and dynamic performance obtained through analytical methods of all products currently manufactured by the company. Due to the reliance on external computer so ware, airfoil drag (and consequently, torque) may be under-predicted at low speeds. Additionally, wind tunnel measurements of selected propellers [17] show overprediction of thrust coefcient (and consequently, thrust) of around 12% on average across all tested propellers. Detailed results are shown in Table  3 and in Figure 9. erefore, an easily adjustable parameter called Safety Factor ( ) was introduced that increases required power at the WOT operating point to reduce the impact of mentioned inaccuracies and guarantee that the chosen motor will be able to reach the expected speed ere is no need to include Safety Factor in the ESC sizing, as the WOT operating point at which it is sized, in typical operating conditions, is achieved only for a few seconds at a time, not enough to damage the unit. e inclusion of the Safety Factor parameter in the battery sizing is recommended, as LiPo batteries are prone to ageing, which increases their internal resistance. Hence, with time at high currents more and more heat is generated, eventually leading to battery damage. What is more, cheap batteries are known for parameters varying between each unit, further justifying the need for an additional safety measure. erefore, Equation (31) becomes For the motor database, a database bundled with Drive Calculator [2] so ware was used. It is based on measurements done and uploaded by its users, so it is impossible to accurately measure the discrepancies with real products, but they are estimated to be around 5-10% overall. However, a signi cant inaccuracy is introduced with the simpli ed motor model used where 0 is the initial voltage, 1 is the voltage drop coe cient, 0 is the initial battery capacity, is the maximal Depth of Discharge, and is the number of battery cells. Based on Traub [15] the battery model can be de ned with a set of iterative equations with the initial state de ned as e information ow in the model is visualized in Figure 7. As time passes, the voltage decreases, therefore increasing current draw to achieve the same power, and consecutively Error (%) F 9: Relative errors between measured and simulated propeller coe cients. rated at 3.7 V per cell, are used. Additionally, V2.0 uses FOCenabled drivers, which generate sinusoidal signals instead of the usual trapezoidal. However, the manufacturer advertises it as a means to reduce noise instead of improving performance, so it can be assumed that in this case the di erence can be neglected.
e MATLAB script has been run considering two operating points: hover and WOT. e goal was to reduce energy usage at hover, as the platform's main purpose is photography. For the thrust the unit of gram-force (gf), which corresponds to the force acting on 1 gram of mass in a standard gravitational eld, is used due to intuitiveness in this application. Additional sizing parameters are listed in Table 5. e results are below: Results. For a 4-rotor drone with estimated AUM of 1375 g: As can be seen, both the propeller and the motor were successfully selected and the estimated ight time has been calculated. e propeller is of lower pitch than in the reference drone, which might be explained by the unavailability of 9 × 5.5 propellers in APC's range, and 9 × 6 being too power-consuming. Especially interesting is the choice of E-series (electric airplanes) propeller over MR-series (multirotors), to calculate characteristics based on scarce data. e model, applicable both to BLDC and DC motors, considers only two sources of losses: copper losses, calculated using winding resistance and iron losses, calculated using no-load current where Cu are copper losses, is the windings resistance (of all simultaneously working phases), motor is the current delivered to motor windings, iron are iron losses, is the nominal voltage and 0 is the no-load current. As the no-load measurement is usually done through an ESC, the iron losses also incorporate losses from the controller. e model, based on [18], is calculated as follows: where prop -is the power delivered to the propeller, prop is the propeller torque, prop is the propeller speed, motor is the motor electrical power, and motor is the motor e ciency.
To demonstrate the capabilities of the methodology a set of example results is presented for a low-weight drone. e results are validated against a similar commercial product. Based on the ndings, a hypothetical usage of the methodology for sizing of Personal Air Vehicles is demonstrated.

Small Drone.
For the ease of validation, the input parameters of the methodology were set to match those of the DJI Phantom 4 Pro V2.0, as indicated in Table 4. is enables easy comparison of the vehicle's published speci cation [19] with the sizing method's results in terms of ight time and propeller dimensions, as the manufacturer does not provide motor data. It should be noted here that the Phantom 4 uses LiHV (High Voltage LiPo) batteries rated at 3.8 V per cell, however in the calculations the more popular LiPo batteries, stated by the manufacturer is 30 min [19], but it was probably measured in ight at best endurance speed, which uses slightly less power than in hover ( [21]) due to the reduction of the which can be in uenced by numerical errors due to interpolation, speci cally at low speeds required for hovering. Comparison of power characteristics of propellers considered in this example can be seen in Figure 10.
Hacker B20 26L is a surprising choice for the application, as it is an inrunner motor that usually comes with gearing to increase its torque for traction applications. However, in this case it is used in direct drive con guration, which is possible due to the low speed of a large propeller. Its measured KV is 2080 (as opposed to 2020 stated by the manufacturer [20]), which puts the hover operating point almost at the maximum of the e ciency curve, therefore increasing the ight time, as can be seen in Figure 11. e calculated ight time seems to be in line with the achievements of the reference drone. Maximum ight time

Personal Air
Vehicle. e current implementation of the methodology as a MATLAB script does not allow the sizing of heavy platforms, such as PAV, due to the lack of a sufficiently large propeller in database. However, the methodology can be implemented with different databases and even modified to help with the design of components: propeller specification provides enough data for presizing of an electric motor, and thrust requirements along with size and weight constraints can be used as input in propeller design. Additionally, using only scarce data, a flight time estimation can be performed to validate the design of components. is is an especially important feature, as the methodology has been designed with the ability to be used inside another algorithm to further enhance the optimisation process.
at way questions, such as rotor number, propeller, size or maximum payload, can be answered. is is especially important for PAV, where the mass constraint is very tight because of the payload in the form of a passenger. Table 7 outlines example uses of the methodology in scenarios with different data available.
Some of the problems of Personal Air Vehicles, such as high weight of the platform, can be addressed by alternative multirotor designs. Papa [27] discusses a multirotor in which a part of the li ing is done by a balloon. Our methodology is simple and flexible enough to complement the approach in [27]. Papa's method can be used for sizing the balloon while our methodology sizes the multirotor part by subtracting the calculated balloon's li from the estimated platform's weight and using it as an input. Validation of this approach, however, needs to be performed.

Conclusion
e methodology presented in this paper answers the need to have an automated process of selecting multirotor components using a simple input of estimated drone weight. Validation was performed using data from four commercially available multirotors (including DJI Phantom 4 V2.0) and one specialised platform, which shows that the obtained results are in accordance with manufacturer data and independent tests.
e simplicity and open-loop approach are also the limitations of this methodology. e use of static model does not provide enough information to estimate the acceleration, turn speed or performance in wind conditions. However, the inclusion of a dynamic model would require the bandwidth limitations of the actuators to be considered. is would overly increase the complexity of the methodology and would demand much more input data, thus limiting the usability.
Although there are no conceptual constraints preventing the use of the methodology for sizing large passenger multirotors, considerable limitations are introduced by the induced drag. erefore, it can be assumed that the maximum hover time will be close to the 27 min calculated, which seems to be confirmed by independent tests achieving 23-26 min of hover [22,23]. However, as the calculations do not include dynamic effects of flight, the prediction accuracy for the WOT operating point is considerably lower. Furthermore, that point is set arbitrarily based on thrust-to-weight ratio, and is rarely measured in real operation, so no validation could be performed.
e reference drone is a commercially popular product, therefore it can be assumed that its performance is close to optimal for its given weight and application (aerial photography). erefore, achieving results of similar value to the reference may indicate that the chosen configuration has performance close to optimal. Considering the accuracy of results, the assumptions and estimations used and the low computational cost, methodology performance can be considered satisfactory for applications in other research projects and on its own.

Further Validation.
In similar manner to validation through comparison with DJI Phantom 4 v2.0, more tests of different configurations were conducted. e input parameters are summarised in Table 6. 6S batteries were assumed for Fox 4 and PD6-AW2 BASIC platforms, as those are more suited for the heavy li ing application. e weight of IRIS+ is taken with a sample payload. rust-to-weight ratio was adjusted so if more payload was added up to maximum allowable mass, the drone would still maintain controllability with thrust-to-weight ratio of 2. In 3 of the test cases, results shown in Figure 12 seem to be in satisfactory agreement with the manufacturer's specification considering that the methodology does not include the power usage by the flight controller, sensors, RC communication or payload. e significant difference in the case of GTQ Mini needs to be addressed separately. e methodology has returned similar results to those of the methodology presented by Bershadsky et al. [8]. Our methodology has chosen 5 × 4.3 propellers as compared to 5 × 3, 1378 KV motor as compared to 1383 KV and uses 4.54 A in hover (at full battery) as compared to 4.49 A. However, there is a 1.9 min difference in calculated hover times. With the same battery capacity and similar current drawn, the discrepancy might be that in [8] the simulation is stopped when battery reaches 3.6 V, while our implementation is set up to stop earlier at 3.7 V. Another difference is probably in the battery model used, as our methodology simulates the decrease of voltage with discharge, leading to the increase in current drawn from 4.54 A to 5.15 A throughout battery operation, as can be seen in Figure 13. databases used, which rarely provide data on large propellers in the 50-60 inch range and motors able to support them. However, it is assumed, that certain elements of the methodology, such as flight time estimation based on limited data, can be useful in the process of PAV design. Finally, the proposed methodology is also flexible enough to accept data of custom designed components or to be used for sizing of certain alternative multirotor topologies. Unfortunately, one of the most important disadvantages of this methodology is its low, hard to estimate, accuracy. Great care was taken to make the results as close to reality as possible, but due to assumptions made for the sake of simplicity and speed, such as the use of thrust-to-weight ratio instead of calculation of maximum required thrust, the accuracy of calculations is impossible to measure. If needed, it can be enhanced, for example by improving motor model or using databases with only measured data, but it is advised against relying on the results in safety-critical applications.
Data Availability e MATLAB code used to support the findings of this study have been deposited in the GitHub repository (https://github.com/ mbiczyski/Multirotor-Sizing-Methodology). APC propeller performance data used to support this study is available at https:// www.apcprop.com/technical-information/performance-data/. ese datasets are cited at relevant places within the text as reference [12]. Previously reported propeller experimental performance data were used to support this study and are available at http://m-selig.ae.illinois.edu/props/propDB.html. ese prior studies (and datasets) are cited at relevant places within the text as reference [14]. Motor performance data used to support this study is available at http://www.drivecalc.de/. ese datasets are cited at relevant places within the text as reference [3].